Remerciement

Je tiens tout d'abord à remercier M. Fisher et M. Yang d'avoir accepté d'être rapporteurs de ma thèse ainsi que M. Auradou et M. Ruffier pour leur participation à mon jury. Mes plus sincères remerciements vont à Gilgueng, mon encadrant de thèse, qui avec beaucoup de patience et pédagogie m'a accompagné et encouragé tout au long de ce doctorat. Sa curiosité sans faille et sa grande tolérance me rendent son amitié chère.

Ma gratitude va aussi à toutes les personnes avec qui j'ai eu le plaisir de travailler : Laurent pour nos intéressantes discussions, notre participation aux compétitions de robotique et la métallisation de mes microrobots; Dominique pour la fabrication et la grande qualité de mes échantillons; Hugo et Sebastien pour m'avoir chaleureusement accueillis dans l'équipe et sans qui les débuts de ma thèse auraient était bien plus difficiles; Lorenzo pour m'avoir épargné la programmation ardue de "drivers"; finalement je remercie Alisier à qui je souhaite beaucoup de réussite dans sa thèse et pour la suite.

Je tiens également à remercier pour leur aide et discussion : Jean-Christophe Gala et ses conseils en microfabrication et microfaisage, Emmanuel Roy et sa grande connaissance des différents matériaux ainsi que Pierre Belleoud pour son expertise sur la convection naturelle.

Toutes les personnes de l'équipe Nanoflu m'ont aussi permis de m'épanouir scientifiquement et personnellement. Merci à Juan, Adrian, Jonathan, Anton, Nicolas Beyraud. Je suis aussi reconnaissant à tout le personnel du LPN qui permet de maintenir un environnement propice à la curiosité et la recherche dans une ambiance agréable.

Je remercie profondément mes parents, mes deux frères et ma tante d'avoir toujours poussé ma curiosité et fait découvrir avec tolérance le monde dans sa richesse et sa complexité.

Microrobot hélicoïdal sur puce microfluidique pour des applications de mesure de force.

Un résumé en français

Dans les années 1960, les techniques de micro-fabrication développées notamment pour l'industrie de la microélectronique ont été appliquées pour la manipulation de fluides. De ceci émergea des plates-formes dites "microfluidiques" où des canaux à l'échelle du micron sont gravés sur une puce et permettent la réalisation d'expériences de chimie, de physique ou de biologie. L'avantage de cette miniaturisation est de réduire la consommation de produits chimiques, d'automatiser un cycle d'expérience et d'offrir un environnement scellé plus facilement contrôlable et à l'abri d'une éventuelle contamination. La domination de la viscosité et des forces de tension de surface à cette échelle amènent aussi des propriétés intéressantes.

Cependant cette environnement étant par définition fermé, il est très difficile d'y amener des outils reliés à un contrôleur de position pour de la manipulation précise ou d'un capteur mobile devant relié à un fil à l'extérieur par un fil. C'est pourquoi nous proposons d'envoyer un microrobot à l'intérieur de cette puce afin de proposer un outil mobile sans fil. Dans cette thèse, nous avons choisi de nous concentrer sur l'utilisation d'un tel robot pour la mesure d'une force, d'environ 1 à 100 piconewton. Ce choix est motivé par la nécessité du développement d'un protocole de mesure quantitative qu'il impose et qui nous pousse à mieux comprendre la physique du microrobot.

Bien sûr, il existe déjà des outils permettant de mesurer une force dans cette fourchette de valeur. La première technique est l'AFM (Atomic Force Microscopie) qui est très précise, mais ne permet pas de faire des mesures dans un environnement fermé. Les deux autres principales techniques sont les pinces magnétiques et optiques. Par rapport aux pinces magnétiques, un microrobot aurait l'avantage d'être sélectif sur la position où appliquer la mesure. En effet, une pince magnétique applique une force via des micro-billes magnétiques qui sont fixées sur l'objet à étudier par des réactions chimiques, la localisation des billes n'est donc pas garantie. L'encombrement d'un tel dispositif est aussi gênant, car le bout des aimants actionnant les billes doit être placé à environ 1 mm de l'objet à étudier. De plus le champ magnétique et bien plus important, de l'ordre de 1 Tesla contre 10 millitesla pour le microrobot. Par rapport à une pince optique, le principal avantage du microrobot pourrait être sa robustesse. En effet pour fonctionner, une pince optique, requiert que les conditions optiques soit optimales ce qui n'est pas forcement le cas près d'une paroi, dans un micro-canal ou tout simplement dans un milieu absorbant la lumière. Les pinces optiques sont aussi connues pour chauffer le milieu ambiant, ceci pouvant perturber la mesure de force.

Les potentielles applications pour un micro-robot sur puce microfluidique ne concernerait pas la mesure de paramètres précisément identifiés tel que l'élasticité d'une molécule ou sa force d'adhésion à une autre. En effet pour de telles applications un protocole peut facilement être adapté pour répondre aux spécificités des solutions proposées ci-dessus. Un microrobot effectuant une mesure de force trouvera donc sont utilité pour la mesure dans un milieu complexe tel que par exemple la croissance d'un tissu biologique qui ne pourra pas être facilement adapté à un outil de mesure classique. Permettre à un microrobot de mesurer des informations sur son environnent est aussi un atout pour son contrôle, cette mesure permettant d'adapter la façon dont le robot se déplace en fonction de ce qu'il détecte de son environnement. Afin de faire des mesures de force, il est essentiel de quantifier précisément la force développer par le robot. Ainsi cette force pourra être appliquée à un objet de l'environnement pour comprendre la réaction à cette perturbation ou bien pour déplacer un objet afin de quantifier la friction entre cet objet et une surface. Le but de cette thèse est donc d'intégrer un robot sur une puce microfluidique et de le caractériser afin de connaître précisément la force qu'il développe. Des preuves de concept des potentielles applications sont aussi proposées.

Pour répondre à ce but, nous avons choisi de concevoir un robot hélicoïdal se propulsant grâce à sa rotation tel une hélice de bateau. En effet, un tel robot développe une force proportionnelle à sa vitesse de rotation donnée par l'équation suivante :

F = aV + bω, (1)
avec F la force, a le coefficient de frottement visqueux, V la vitesse du robot, b le coefficient de propulsion et ω la vitesse de rotation. En contrôlant ω et en mesurant la vitesse du robot, il est donc possible d'appliquer précisément une force désirée. Afin de faire tourner ce microrobot nous avons utilisé un champ magnétique tournant. En rendant le robot ferromagnétique par un dépôt de métal, la rotation de ce champ provoque celle du microrobot.

Récapitulatif des différents chapitres

Le chapitre 2 présente les choix de conception pour le microrobot et pour le dispositif de contrôle. La figure 1 a) présente une vue du microrobot au microscope électronique après sa fabrication. La figure 1 b) montre la totalité du substrat de fabrication où plusieurs microrobots sont fabriqués plutôt. Nous appelons ce modèle de robot RTS (Roll-To-Swim). Comme nous ne recherchions pas à développer une application précise, mais un capteur de force général, nous avons pu bénéficier de la flexibilité offerte par différentes technologies de prototypage. Cela nous a permis d'explorer rapidement les différents paramètres de chaque solution technique afin de proposer un système complet et effectif dans le temps de cette thèse. Cela nous a aussi permis d'atteindre une grande flexibilité dans la conception grâce à laquelle nous avons pu réagir rapidement aux différents problèmes techniques découverts au cours de cette thèse. Pour la fabrication du RTS, la lithographie 3D basée sur la polymérisation de deux photons est utilisée. Cette machine (Nanoscribe) nous a permis d'explorer différents conception de microrobots. Le RTS peut ensuite être détaché de manière individuel du substrat de fabrication par une pointe de 10 microns de diamètre. Afin de déplacer le RTS avec un champ magnétique, une couche de 200 nm de nickel est déposée par dépôt physique en phase vapeur (PVD). Pour réaliser le champ magnétique déplaçant le RTS, nous utilisons trois paires de bobines de Helmholtz qui permettent de produire un champ homogène à l'endroit où se trouve le RTS afin de ne pas perturber le déplacement du robot avec un gradient magnétique. Pour fabriquer ces bobines et leurs supports, nous avons utilisé une imprimante 3D. Cela nous a permis d'adapter facilement et de reproduire un dispositif expérimental adapté à un microscope plus puissant quand une meilleure résolution optique est devenue nécessaire. Un programme en C++ nous permet de contrôler ce champ magnétique dans n'importe quelle direction. Ce programme permet aussi d'acquérir l'image venant de l'optique du microscope et d'effectuer un algorithme de suivi du robot. Cette suivie automatique nous a servi à faciliter l'acquisition de mesures pour la caractérisation du robot mais aussi à développer un contrôle automatique grâce à une boucle de rétroaction sur la position du RTS. La fabrication des puces microfluidiques est elle aussi réalisée grâce à une technologie de prototypage rapidement adaptable. Les puces sont faites en PDMS, un plastique pouvant se mouler facilement. Les moules sont fabriquées en PMMA avec une microfraiseuse ce qui permet de concevoir des géométries 3D complexes impossibles à réaliser par lithographie. Le choix de ces technologies de prototypage présente quelques inconvénients. D'abord, la magnétisation du RTS est faible car on ne dépose qu'une faible couche de matériaux ferromagnétiques sur le robot. L'état de surface du robot n'est pas optimisé ce qui nous impose de réaliser les expériences dans de l'isopropanol afin d'éviter l'adhésion du robot à la paroi. Les supports en plastique des bobines se déforment avec la chaleur et limitent la puissance maximale du champ magnétique. Finalement, le PDMS est poreux ce qui entraîne des flux parasites. Cependant, ces désavantages sont le prix à payer afin d'avoir des solutions techniques suffisamment flexibles pour s'adapter rapidement aux enjeux inconnus émergeant lors d'une telle conception où les phénomènes physiques sont mal connus et difficiles à prévoir. Cela a été essentiel pour la réalisation du protocole de caractérisation du RTS. En particulier, cela permet l'identification rapide des besoins réels et nous a permis de ne pas perdre de temps dans des optimisations inutiles.

Le chapitre 3 montre comment ce système de contrôle permet d'intégrer le microrobot à l'intérieur d'une puce microfluidique. Ceci est une avancée majeure, car le principal avantage du développement d'un microrobot capable de mesure de force est de pouvoir l'intégrer sur une plateforme où ces mesures sont difficilement réalisables par une sonde reliée à l'extérieur par un fil. De plus, une puce microfluidique permet de contrôler les paramètres expérimentaux comme les gradients de température, la vitesse du fluide et la proximité des surfaces ce qui est indispensable pour caractériser le microrobot. Pour réussir cette intégration, les différents modes de déplacement du microrobot on été classé en trois types déplacements différents : 1-le mode "nager" (swim), où le robot évolue en trois dimensions et n'est en contact avec aucune surface de la puce; 2-le mode "rouler" (roll) où le RTS touche la surface sur toute sa longueur; 3-le mode "toupie" (spintop) où une seule extrémité du robot touche la surface. Le mode "nager" et "rouler" on déjà été présentés dans d'autres travaux, mais le mode "toupie" semble être exclusif à ce travail de thèse. C'est pourquoi ce mode de déplacement est étudié plus amplement dans ce chapitre. Deux types de contact avec la surface ont été mis en évidence pour le mode "toupie", l'un où le contact semble respecter une loi de friction de type Coulomb et un autre où le contact suit une loi de frottement lubrifié. Malheureusement, il ne nous a pas été possible de conclure sur la raison provoquant l'un ou l'autre type de frottements.

Ce chapitre démontre aussi que ces différents modes de déplacement ont des avantages et des inconvénients complémentaires. Le mode "nager" permet au robot d'évoluer en trois dimensions, mais il est alors très sensible à la vitesse de l'écoulement. Lorsqu'il est en mode "rouler", le robot est peu impacté par cette vitesse, par contre il est très sensible aux conditions de surface. Le mode "toupie" est un compromis entre les deux et possède de plus l'avantage que le robot peut être précis. De surcroit, ce mouvement peut être facilement automatisé par une boucle de rétroaction. En combinant ces différents types de déplacements, le RTS peu potentiellement bénéficier de tous ces avantages en étant moins sensible à un inconvénient particulier. Cette amélioration de la mobilité du robot a été la clé permettant l'intégration sélective du RTS dans la puce microfluidique par lui-même. En effet, le trajet du RTS depuis le substrat de fabrication d'où il est détaché jusqu'à l'intérieur de la puce nécessite des changements brutaux d'altitude et donc d'alterner entre plusieurs modes de déplacements. Le mode "nager" est utilisé dans le micro-canal entre la partie ouverte de la puce avec le substrat car les écoulements sont opposés à la direction du robot. Le mode "rouler", lui, est utilisé à l'intérieur de la puce. Un protocole d'intégration ainsi qu'une conception particulière de puce microfluidique sont présentés dans ce chapitre. Ce protocole n'est pas limité au RTS et nous pensons qu'il peut être adapté simplement à d'autres microrobots hélicoïdaux. Nous avons aussi développé une manière de stocker le RTS à l'intérieur de la puce pour une longue durée supportant éventuellement le séchage de celle-ci. La difficulté majeure est de prendre en compte le front de séchage entre la phase liquide et gazeuse, qui a un impact très important à cause de la très petite taille des objets. Une solution a été trouvée. Malheureusement, le RTS est en général partiellement endommagé par ce front, ce qui n'empêche pas son utilisation mais change sa caractérisation.

La majeure contribution du troisième chapitre est de proposer une manière d'intégrer un microrobot de façon sélective (c'est-à-dire un à la fois) et par lui-même à l'intérieur d'une puce microfluidique. Cela s'oppose à une méthode plus conventionnelle consistant à injecter une solution contenant une importante quantité de robots par les connexions fluidiques. La sélectivité de notre méthode est pour nous cruciale, car la caractérisation indépendante de chaque robot est importante pour une application de mesure de force. De plus, cela limite les perturbations pouvant résulter de l'intégration d'autre microrobot se déplaçant tous en même temps.

Le principal enjeu du chapitre 4 est de présenter le dispositif expérimental et son protocole associé afin de garantir que la caractérisation du RTS n'est pas perturbée par des flux parasites. Grâce à l'intégration du RTS à l'intérieur de la puce microfluidique, nous avons pu bénéficier de la qualité de contrôle qu'offre cet environnement pour résoudre ce problème. En effet, l'environnement fermé d'une puce microfluidique limite les flux parasites créés par l'évaporation de l'isopropanol et les petites dimensions limitent les flux liés à la convection thermique. La caractérisation du RTS se fait en mesurant les vitesses ascensionnelles de celui-ci pour différentes fréquences de rotation. De cette façon, le poids et la force d'Archimède sont utilisés comme forces de référence dans l'équation [START_REF] Terry | A Gas Chromatographic Air Analyzer Fabricated[END_REF] et permettent l'identification des paramètres a et b. Nous avons donc d'abord établi une méthode pour mesurer la vitesse ascensionnelle du RTS. Pour cela, nous déplaçons le plan focal du microscope entre deux altitudes de référence et nous analysons la mise au point de l'image a posteriori. Pour ces tests nous avons également réalisé une chambre expérimentale sur la puce microfluidique (drop test chamber). Cette chambre est un cylindre de 1mm de haut et de 400 µm de diamètre. Pour que le microrobot puisse y accéder, un canal microfluidique de section carrée de 80 microns de côté connecte cette chambre à la chambre principale. Comme cette chambre n'est accessible que par un seul chemin, elle n'est pas influencée par les flux parasites pouvant être créés par les différences de pression entre l'entrée et la sortie de la puce microfluidique. De plus, nous avons démontré théoriquement que les petites dimensions de cette chambre garantissent l'absence de flux de convection. Finalement pour supprimer les flux parasites dus aux fuites à travers le PDMS et l'interface entre le PDMS et le verre, cette chambre est entourée par la chambre principale afin de provoquer un courtcircuit sur les potentielles fuites. Pour déterminer l'absence de ces flux parasites avant une série d'expérience, la vitesse de chute du RTS sans rotation est effectuée à différents endroits de la puce et les résultats sont comparés. Afin de prouver que la géométrie de la chambre n'impacte pas la caractérisation du RTS, des tests de caractérisation ont été effectués à différents endroits de la chambre. Finalement, pour trouver les valeurs a et b d'un RTS, il ne reste plus qu'à calculer son poids et son volume. Pour cela nous avons réalisé une simulation du processus de lithographie 3D ainsi que du processus de PVD utilisés lors de la fabrication du robot, ce qui nous a permis de calculer ces valeurs tout en estimant l'erreur maximale faite par cette simulation.

Dans ce chapitre nous avons aussi essayé de mesurer le couple délivré par le RTS. Malheureusement, nous n'avons pas pu réalisé cette mesure en raison du faible champ magnétique nécessaire pour garder le robot vertical durant les tests de chute. Ce champ magnétique l'empêche de tourner sur lui-même durant cette chute, ce qui empêche la caractérisation du couple.

Finalement, le chapitre 4 propose un protocole pour la caractérisation systématique de robots hélicoïdaux ainsi qu'une estimation de l'erreur faite sur cette mesure. Nous en avons conclu que la force délivrée par le RTS dans sa conception actuelle varie entre 10 à 50 piconewton avec une marge d'erreur de 38 %. Plusieurs caractérisations effectuées sur le même RTS ont révélé une importante erreur sur la répétabilité de la caractérisation (representant 73 % de l'erreur total). Pour expliquer cette erreur, notre principale hypothèse est que la magnétisation du RTS change en fonction de son historique, ce qui impacte l'alignement de sa rotation et donc sa propulsion. Nous avons constaté que ces changements de propulsion apparaissent tout particulièrement quand le RTS a eu le temps de sédimenter sur la surface. Aucun changement n'a été observé pendant l'utilisation constante du RTS quand les chocs brutaux avec les surfaces ont été évités. Ceci est une conclusion importante du chapitre 4 et nous considérons que cela illustre la validité de notre approche basée sur des technologies de prototypage, en nous permettant de développer en un temps raisonnable une plateforme de contrôle et un premier dispositif de caractérisation. Par la suite, ce dispositif a été utilisé pour identifier les optimisations nécessaires, ce qui était impossible auparavant. Plus précisément, l'optimisation devrait se porter sur la conception du RTS et du dispositif de contrôle afin que le microrobot soit magnétisé de façon identique avant chaque expérience. Comme nous l'avons mentionné précédemment, nous avons choisi de développer des applications de mesure de force en général afin de ne pas être pénalisés par les contraintes inhérentes au développent d'une application précise. En effet, la considération de telle contraintes parait pour l'instant prématurée et trop spécifique pour bénéficier au développement à long terme des microrobots hélicoïdaux. Cependant, notre but était malgré tout de réduire l'écart entre l'état de l'art et les potentielles applications. Nous avons donc réfléchi aux applications possibles et nous en avons illustré quelques unes par des preuves de concept afin de prouver que la caractérisation du robot présenté dans le chapitre 4 rapproche bien cet état de l'art des applications éventuelles. Nous les présentons dans le chapitre 5. Afin de ne pas être pénalisés par la non-répétabilité de la caractérisation du RTS, nous avons proposé une façon de réaliser une caractérisation rapide juste avant l'utilisation du RTS pour effectuer une mesure. Cette caractérisation ne se substitue pas au protocole de caractérisation complet développé dans le chapitre 4. Celui-ci reste en effet essentiel pour la mesure de la vitesse de chute du RTS sans rotation et pour une mesure précise qui permet d'identifier les différentes sources d'erreur. Grâce à cette caractérisation rapide du RTS, nous avons pu réaliser les preuves de concept suivantes détaillées ci-dessous.

Premièrement, nous proposons d'utiliser la force appliquée par le RTS pour analyser les coefficients de friction dynamique et statique à la surface de la puce microfluidique. Pour cela l'utilisation de billes microscopiques comme interface entre la pointe du microrobot et la surface semble la solution la plus simple, car le contrôle de l'état de surface des billes est une technique bien maîtrisée et leur forme sphérique les rend plus faciles à modéliser. Nous avons donc prouvé que ce type de bille microscopique pouvait être placée de façon stable à la pointe du RTS et nous avons pu évaluer l'impact de la proximité de cette bille sur la force de propulsion du robot. Ceci a été réalisé en comparant la caractérisation du microrobot seul à celle du microbot poussant une bille. Nous en avons conclu que la force du RTS diminue de 6 % lorsqu'une bille de 10 µm est placée à l'avant de celui-ci. En réalisant des tests avec des billes de diamètres différents, on pourrait calculer la variation de la force du RTS sur n'importe quel objet sphérique, notamment une cellule pour des applications biologiques. Une autre application pourrait être de mesurer la vitesse du flux à un endroit précis en faisant la différence entre la vitesse théorique et la vitesse réelle du microrobot. Pour illustrer cette possibilité, nous proposons comme preuve de concept la mesure de deux différents profils de flux dans différents canaux fluidiques. Finalement, nous montrons comment cette mesure du flux peut être utilisée pour améliorer le contrôle du microrobot en adaptant automatiquement son mode de déplacement aux conditions du flux afin de ne pas être emporté par le courant dans la puce microfluidique.

Malgré tout, il restait encore une différence majeure entre le dispositif expérimental utilisé pendant cette thèse et les dispositifs classiques utilisés dans d'autres domaines. En effet la puce microfluidique que nous avons réalisée pour les différents tests et la caractérisation du RTS possèdent des dimensions plus larges qu'une puce microfluidique classique, ceci afin que la proximité des murs de la puce n'ait pas d'impact sur la caractérisation du robot. Cependant comme nous voudrions pouvoir contrôler le RTS dans des puces conventionnelles, il nous fallait d'abord étudier le contrôle de celui-ci dans des canaux d'une grandeur nominale inférieure à 20 fois le diamètre du RTS. Nous avons prouvé que ce contrôle est possible et qu'un phénomène de stabilisation guide le RTS dans de tels canaux. Ce phénomène est dû à la proximité des cloisons du canal sur le la distribution de l'écoulement du fluide qui fait circuler la position du RTS dans le plan de la section du canal. Ceci résulte en une trajectoire proche d'une trajectoire hélicoïdale. Des simulations simples en deux dimensions ont été réalisées pour expliquer ce phénomène. Le coefficient de friction latéral du RTS est une donnée importante de cette simulation et nous utilisons le même protocole que pour la caractérisation du RTS pour le mesurer. Finalement, un algorithme de contrôle a été proposé pour le contrôle d'un microrobot hélicoïdal dans un micro-canal arbitraire avec une direction évoluant en trois dimensions, comme par exemple de la forme d'un vaisseau sanguin. Ce contrôle a prouvé son efficacité théorique sur la trajectoire issue de nos simulations.

La figure 2 récapitule les différents sujets et contributions de chaque chapitre.

Conclusion et Perspective de la thèse

L'effort principal de cette thèse a été de montrer comment un microrobot hélicoïdal à propulsion magnétique pouvait être amené sur une puce microfluidique et caractérisé en vue de la réalisation d'une mesure de force. Mais le choix de la mesure de force n'est pas anodin car il nous a poussé à développer une plateforme de mesure quantitative. En effet même si la caractérisation de microrobots hélicoïdaux a déjà été proposée dans d'autres travaux, elle n'a jamais été associée à une estimation de l'erreur de mesure ou de la répétabilité de la mesure. Cependant les paramètres issue de la caractérisation pzuvent être utiliser comme indicateur pour l'optimisation de la conception du RTS. Cela constitue également une base pour rechercher les mécanismes physiques du microrobot et de son interaction avec l'environnement.

Cette thèse ne propose donc pas seulement les paramètres de la caractérisation de plusieurs RTS, mais offre aussi une plateforme et une méthode pour étudier quantitativement la physique des microrobots. C'est sa contribution majeure au rapprochement de l'état de l'art avec de potentielles applications. En effet sans valeur quantitative, il est très difficile de faire le lien entre une preuve de concept et les applications réelles car les paramètres à optimiser et la manière de les optimiser sont inconnus. Cette plateforme est donc un outil qui permettra de faciliter la recherche fondamentale afin d'acquérir des connaissances sur les mécanismes des microrobots hélicoïdaux. C'est pour l'instant une étape essentielle pour aboutir à des applications concrètes. De plus, notre dispositif expérimental nous permet d'analyser les effets de paramètres physiques tels que la température, la proximité des parois ou la vitesse de l'écoulement. Il est également indispensable de contrôler ces paramètres pour obtenir des mesures répétables. La conclusion du chapitre 4 démontre bien cet avantage puisque le contrôle des paramètres externes était indispensable pour identifier que la non-répétabilité de la mesure venait d'un mécanisme interne au microrobot. Sans cette précision, il aurait était impossible de conclure que les futurs efforts devraient portait sur l'optimisation de la magnétisation du microrobot.

Nous proposons de conclure sur la considération de potentielles applications. Un premier exemple est celui de la stimulation de cellules. Pour réaliser cela, l'intégration du microrobot sur la plateforme microfluidique est indispensable, car elle permet de faire l'interface entre la micro-robotique et la biologie. Pour ce genre d'applications, il faudrait d'abord étudier la compatibilité du microrobot avec des fluides biologiques. Dans ce but la caractérisation quantitative du robot pourra permettre une étude fine de l'impact du fluide via l'évolution de ses propriétés de propulsion. Le second exemple est le développement de manipulateurs robustes à l'intérieur de puces microfluidiques. Pour un tel développement, une information quantitative sur des paramètres environnementaux tels que la vitesse de l'écoulement et la friction sont nécessaires pour adapter en temps réel la stratégie de contrôle. À cela vient s'ajouter le déplacement du microrobot dans de petits micro-canaux. Ici une étude quantitative des forces en jeu pourrait permettre l'optimisation de la forme du robot afin qu'il se déplace plus facilement dans cet environnement. Finalement l'intégration du microrobot dans un environnent in vivo parait une autre application intéressante. Pour cela, il faudra mener des études sur la caractérisation du robot dans ce type de fluide complexe. Un autre axe intéressant serait d'optimiser la forme du robot afin qu'il puisse suivre des vaisseaux sanguins ou lymphatiques avec le moins d'informations possibles sur la position, difficiles à obtenir dans un tel milieu.

Introduction

Microfluidic and lab-on-a-chip

In the 1960s microfabrication technologies which were already widely used for microelectronics, were used to build microchannels for manipulating fluids. The goal was to miniaturize fluidic devices and to deal with small volumes. These fluid microchannels develops new applications for Microelectromechanical System (MEMS) and it enabled the creation of innovative systems. The best known commercialized example is probably the ink-jet cartridges which can deliver a precise droplet of ink with a voltage command input.

In 1979 Stephen Terry et al. [START_REF] Terry | A Gas Chromatographic Air Analyzer Fabricated[END_REF] proposed to apply this technology to miniaturize a full experiment from a large instrument to a pocket-sized device. They designed a gas chromatograph which is an apparatus used to separate different gas compounds. This device marked the beginning of the lab-on-a-chip development. The idea of such tools is to miniaturize the different tasks performed in a laboratory to perform a given protocol on few square centimeters footprint system called a microfluidic chip.

The 1990s and 2000s decades have seen the rise of this technology for research purpose, especially in biology and medical science. For biologists microfluidic chips are convenient because they provide a controllable environment in terms of nutrients, drugs, temperature, flow and dimension. Moreover the microfluidic chip can easily be placed under a microscope allowing a constant image acquisition during the experimental process. For medical science the benefit is to simplify, automatize and accelerate a diagnosis. These tools are still largely under development but they ultimately could contribute to a faster feedback from the diagnosis to medical care by reducing the time and automatize the laboratory analysis steps. Therefore the use of such techniques could increase the quality of medical care while reducing its cost.

The needs for on-chip force sensor

Nevertheless closed environment of a microfluidic chip does not only offer advantages. As it provides a very controllable environment protected from outside contamination, it also leaves no possibility to directly access and control the elements inside the chip. Indeed manipulating and performing measurements inside this device is not straightforward as most tools for such tasks are tethered to a macroscopic part. Naturally most of these functionalities can be embedded in the lab-on-a-chip design. For manipulation there are several examples of biological cells sorting chips (actively [START_REF] Macdonald | Microfluidic sorting in an optical lattice[END_REF] or passively [START_REF] Gossett | Label-free cell separation and sorting in microfluidic systems[END_REF]) and chips detecting the presence of different kinds of molecules.

But some tasks are difficult to be performed by a good design of the microfluidic chip itself. This is particularly the case if we want to perform a task at a precise position located in a random place of the chip. For such needs, mobile untethered microrobots evolving in fluids have been proposed. These microrobots have different sizes from few millimeters to nanometers. Their principal characteristic is to be untethered i.e. evolving freely into the fluid without being attached to any macroscopic frame. They were demonstrated for applications inside microfluidic chips of selective cells and bacteria manipulation [START_REF] Hagiwara | Precise Control of Magnetically Driven Microtools for Enucleation of Oocytes in a Microfluidic Chip[END_REF][START_REF] Petit | Selective trapping and manipulation of microscale objects using mobile microvortices[END_REF], gene transmission [START_REF] Qiu | Magnetic Helical Microswimmers Functionalized with Lipoplexes for Targeted Gene Delivery[END_REF], force sensing [START_REF] Kawahara | On-chip microrobot for investigating the response of aquatic microorganisms to mechanical stimulation[END_REF][START_REF] Jing | Micro-force sensing mobile microrobots[END_REF] In this thesis we propose to answer this need by using microrobots.

and outside microfluidic chips towards helping for extitin-vitro fertilization [START_REF] Medina-Sánchez | Cellular Cargo Delivery: Toward Assisted Fertilization by Sperm-Carrying Micromotors[END_REF]. This thesis proposes to evaluate the sensing potential of magnetically driven microrobots inside a microfluidic chip and in particular for force related sensing as presented in Figure 1.1. For now only two examples show millimetric robots tuned to apply force with a maximum resolution of a millinewton [START_REF] Kawahara | On-chip microrobot for investigating the response of aquatic microorganisms to mechanical stimulation[END_REF] and nanonewton [START_REF] Jing | Micro-force sensing mobile microrobots[END_REF]. We believe that smaller robots could deliver forces in range between the piconewton and the nanonewton. Such force range can answer the needs described in the following subsection.

Needs in biology

In biology the mechanical interaction plays an important role in cell development. For example, in plant cells, surface forces have been shown to govern the cell wall orientation [START_REF] Lintilhac | Stress-induced alignment of division plane in plant tissues grown in vitro[END_REF]. Understanding the stiffness change in plant tissue has also brought attention [START_REF] Routier-Kierzkowska | Cellular Force Microscopy for in Vivo Measurements of Plant Tissue Mechanics[END_REF]. In animal cells, mechanical stimulation influences the development of particular tissues [START_REF] Helmlinger | Solid stress inhibits the growth of multicellular tumor spheroids[END_REF][START_REF] Kim | Cyclic mechanical strain regulates the development of engineered smooth muscle tissue[END_REF] as well as cell inner mechanisms [START_REF] Meyer | Mechanical control of cyclic AMP signalling and gene transcription through integrins[END_REF]. Moreover, force stimulation on cell or tissue is also a concern for medical science as it is demonstrated that the cell stiffness can be related to the metastasis potential of some cancer cells [START_REF] Xu | Cell Stiffness Is a Biomarker of the Metastatic Potential of Ovarian Cancer Cells[END_REF][START_REF] Swaminathan | Mechanical Stiffness grades metastatic potential in patient tumor cells and in cancer cell lines[END_REF] and that mechanical impulses can control metastasis progression. [START_REF] Itabashi | Mechanical impulses can control metaphase progression in a mammalian cell[END_REF] But cells are not the only biological component in needs of mechanical characterization. Proteins such as enzymes or DNA are also extensively studied [START_REF] Strick | Twisting and streching single DNA molecules[END_REF]. These studies focus on the elasticity of the protein or the force needed to break weak molecular interactions. These forces are important to understand the mechanisms involved in protein folding or DeoxyriboNucleic Acid (DNA) strand opening and closing.

At a larger scale a proof of concept presents the influence of mechanical stress on aquatic microorganisms by using millimetric robots for the force stimulation [START_REF] Kawahara | On-chip microrobot for investigating the response of aquatic microorganisms to mechanical stimulation[END_REF]. Of course in some cases the presented biological interrogation can be answered without the help of a microfluidic platform. In designing such experiments one must consider that this technology requires an additional fabrication step which necessitates a microtechnology facility. However the advantages of this platform for research purposes in biology are important and can be stressed again. The high controllable environment guarantees a better reproducibility, the imaging can be performed at the same time as the experiment, the closed environment prevents from contamination and finally dealing with small quantities can be an advantage for example in the use of very rare, expensive or toxic products.

Needs in physics

A force sensor could investigate the surface adhesion, i.e. the amount of force that needs to be applied on an object to make it move or to detach it from a surface. Therefore it is particularly important at small scale as the surface-to-volume ratio gets bigger. Measuring this parameter can reveal changes in the material composition of the surface. Outside microfluidics, the the Atomic Force Microscopy (AFM) in amplitude and phase shift mode is broadly used to measure this value in air [START_REF] Zhong | Fractured polymer/silica fiber surface studied by tapping mode atomic force microscopy[END_REF][START_REF] Martínez | Measuring phase shifts and energy dissipation with amplitude modulation atomic force microscopy[END_REF] and liquid [START_REF] Hansma | Tapping mode atomic force microscopy in liquids[END_REF], but this technology is not compatible with microfluidic chips.

Local flow speed determination is also a need inside microfluidic platforms. Indeed if several technologies already exist to measure the average flow speed [START_REF] Gravesen | Microfluidics-a review[END_REF], only Particles Image Velocity (PIV) allow to measure local flow speed in microfuidic environments [START_REF] Santiago | A particle image velocimetry system for microfluidics[END_REF]. This method consists of injecting in the flow several particles and analyzing their motion to deduce the flow speed at each particle position. But this method can lead to particle contamination as a large amount of them needs to be injected to be sure to have at least one particle in the region of interest. Moreover these particles can settle either on the top or on the bottom of the chip with time if their buoyancy is not neutral and that a cyclic flow is studied.

Needs in robotics

The last need that a robotic force sensor inside a microfluidic chip could address concerns robotics itself. Indeed, every robot and almost every automatic system uses feedback to adapt to the environment and to get a better control. For example, an exploration space probe will use its camera and sensors to adjust its trajectory to target a celestial object. To cite a technically simpler example an elevator uses sensors to detect when it arrives in front of a floor.

For robots at this tiny scale the challenge is to deal with their high surface-to-volume ratio. This means that their weight and inertia are negligible compared to the surface induced forces like the friction, stiction or a too strong flow. Therefore a direct force measurement which is linked to the adhesion force, could help for example to detect hazardous areas and to directly adapt the path planning strategy to go to the desired position. Another example is the flow speed measurement. If this value is larger than the maximum speed of the microrobot there is a risk of losing it in the flow stream. To avoid this, strong flows need to be detected and the motion strategy corrected accordingly. However no microrobot uses for now feedback information to enhance their control.

From our experience, we believe that a rich feedback of the environment is an essential key to enhance robot robustness at this scale. Developing a robust robot and setup able to be developed towards practical applications is also a concern of this thesis work. It is for now the main limitation to apply this technology as an in-vitro tool inside a microfluidic chip. Moreover the same kind of navigation challenges will arise in the perspectives of in-vivo microrobotic applications where rich feedback could be an essential component to avoid losing or be unable to retrieve the robot from a complex organism. Therefore the microfluidic constraint makes it an interesting test platform to get knowledge on how to make viable microrobots for in-vivo missions as surgeries.

Review of existing on-chip force sensing technologies

To answer these force measurement needs, four devices are currently used in most of the cases: they are the AFM, the optical tweezers, the magnetic tweezers and the comb drive actuators. A brief presentation of the basic mechanisms of these devices is presented in the following subsections. The goal is to see for which kind of application a mobile microrobotic force sensor would offer advantages compared to the tools currently used.

Atomic force microscopy

The Atomic Force Microscope (AFM) is mainly an imaging tool. It was proposed as an extension of the scanning tunneling microscope for non-conductive samples [START_REF] Binnig | Atomic force microscope[END_REF]. Figure 1.2 a) shows its working principle. A tip is put onto a characterized cantilever beam. Then by knowing the stiffness of the beam, its deflection can be linked to the force applied by the tip on a surface. The deflection of the tip is measured through the deflection of a laser reflecting on the top part of the cantilever.

The main advantage of this technology is its simple concept. It allows easy surface modification of the tip which makes it used in biology to attach different molecules to it and to stretch them [START_REF] Lee | Direct measurement of the forces between complementary strands of DNA[END_REF][START_REF] Hinterdorfer | Detection and localization of individual antibody-antigen recognition events by atomic force microscopy[END_REF][START_REF] Moy | Intermolecular forces and energies between ligands and receptors[END_REF]. Also when the cantilever is well calibrated, few sample preparation is required. The stiffness of the beam needs to be chosen for the desired force range application. The minimal cantilever possible stiffness limits the minimal force to about 10 piconewtons. However this technology was first designed to be used in vacuum to apply force with atomic resolution. Therefore adaptations are required to adapt to liquid medium which is highly damped [START_REF] Hansma | Tapping mode atomic force microscopy in liquids[END_REF][START_REF] Doktycz | AFM imaging of bacteria in liquid media immobilized on gelatin coated mica surfaces[END_REF] and to biological resolution [START_REF] Routier-Kierzkowska | Cellular Force Microscopy for in Vivo Measurements of Plant Tissue Mechanics[END_REF].

But the main drawback of AFM for the scope of this thesis is the incompatibility of this technology with microfluidic. In fact the beam displacement is performed by piezoelectric stage which is too big to be included in a microfluidic device.

Optical tweezers

The optical tweezers [START_REF] Ashkin | Acceleration and Trapping of Particles by Radiation Pressure[END_REF] trap particles at the diffraction-limited focus of a laser beam. As displayed in Figure 1.2 b), dielectric particles in the proximity of the trap are polarized by the light field, therefore they act like an electrical dipole. Then the electrical field created by the light beam interacts with this dipole and the resulting force traps it on the focal point of the laser. For the trap to work, this force needs to be higher than the scattering force that pushes the particles in the direction of the light beam. This tool was proposed in biology to trap bacteria and viruses [START_REF] Ashkin | Optical trapping and manipulation of single cells using infrared laser beams[END_REF] as well as organelle inside cells [START_REF] De Vries | Micro magnetic tweezers for nanomanipulation inside live cells[END_REF]. The trapped object can vary from 20 nanometers to few micrometers. To perform a force measurement the trap force can be modeled by a simple spring for small displacements. The stiffness of the spring depends of the laser intensity and focalization as well as the particles optical characteristics. Therefore to perform a force measurement this stiffness needs to be calibrated on a similar object.

Optical tweezers have been widely used as force sensors on proteins by chemically attaching a polymer bead to the desired part of the protein. Protein stiffness was also studied. In this case the distance between the trapped object and the trap center needs to be measured. This can be done directly by microscope imaging for big samples or by a diffraction pattern or interferences using a second laser.

Optical tweezers are particularly fit to microfluidic applications as in most cases transparent materials are used. However liquids and materials still need to be tuned to avoid absorbing the laser light and local heating. The drawbacks of this techniques are mainly linked to the heating and photo damage of the trapping object by the light beam. This damage is particularly a problem for biological samples [START_REF] Neuman | Characterization of photodamage to Escherichia coli in optical traps[END_REF]. Moreover the created thermal noise can be a source of physical measurement perturbation. The non-specificity of the trap can also be problematic.

Magnetic tweezers

Magnetic tweezers use the magnetic field gradient to apply a force on one or several magnetic beads. As for optical tweezers, the bead is attached to the object to measure. The main difference compared to the AFM and optical tweezers is that the stiffness of the equivalent spring is much more larger than in optical tweezers and AFM. This means that the input of this system is directly the force on the object through the magnetic field intensity and not its position. This makes the precise positioning of a free bead complicated as its position needs to be tracked in real time and a closed-loop has to be implemented on the control of the magnetic field [START_REF] Lang | An automated two-dimensional optical force clamp for single molecule studies[END_REF]. However this is an advantage for constant force measurement which is difficult to realize with other technologies. the AFM: at the contact of the tip with the surface the beam bends. A laser reflecting on the cantilever surface detects this bending, by determining the cantilever stiffness the bending can be linked to the applied force. b) is the optical tweezers: the radiation pressure of the focalized light beam traps the particle. The difference between the particle position and the center of the trap gives an information about the external force applied on the particle. A linear approximation is used to link this displacement to a force. c) is the magnetic tweezers: the magnetic gradient applies a force on a ferromagnetic or magnetic bead. This magnetic gradient is either created with permanent magnet or electromagnet. d) is the comb drive: when the tip touches the surface, its fixations with the frame act like a spring thus the force is proportional to the displacement. The displacement is measured by the electrical capacitance change in the comb.

CHAPTER 1. INTRODUCTION

As shown in Figure 1.2 c), there are two kinds of magnetic tweezers. The first one uses a permanent magnet [START_REF] Yan | Near-field-magnetic-tweezer manipulation of single DNA molecules[END_REF]. These magnets are mounted on a stage position control and the magnetic gradient is controlled by the position of the magnet. This method does not allow three dimensions (3D) control of the pulling force. However, it allows rotation control of the bead. [START_REF] Strick | Twisting and streching single DNA molecules[END_REF]. The second kind uses electromagnets, the advantages are that the magnetic gradient force is much easier to control. Indeed the electromagnet does not need to be moved and 3D positioning is possible [START_REF] Fisher | Thin-foil magnetic force system for highnumerical-aperture microscopy[END_REF]. But it requires a complicated space configuration.

Compared to the optical tweezers there is no damage and parasite local heating of the manipulated objects. The selectivity on the magnetic material is also an advantage. However the magnetic field gradient decreases rapidly with the distance from the magnet or electromagnet (≈ 1 r 4 ). Therefore the magnetic system needs to be relatively close to the manipulated object. This leads to important constraints on the design, especially for microfluidic integration, as well as heating problems from the current in the electromagnets.

Comb drive actuators

Comb drive actuators use the electrostatic interaction between two sets of interdigitated fingers [START_REF] Willium | Laterally driven polysilicon resonant microstructures[END_REF]. This comb structures is built to increase the interacting surface between the two comb sets. By using the electrostatic interaction, these structures were used for several applications such as: resonators, optical shutters, electromechanical filters, migrogrippers, voltmeters and vibromotors [START_REF] Legtenberg | Comb-drive actuators for large displacements[END_REF]. Figure 1.2 d) explains how these structures are used as a force sensor. By measuring the change of electrical capacity between the two combs the displacement can be measured with a resolution of 10 nanometers [START_REF] Sun | A bulk microfabricated multi-axis capacitive cellular force sensor using transverse comb drives[END_REF]. By attaching one of the comb structure on a flexible beam with a known stiffness, the force on the beam can be measured by the change of electrical capacitance. A tip can be fixed to the beam to apply the force on a specific point.

Compared to the AFM, this technology allows a bigger range of applied forces. It is simpler to use as no optical feedback is necessary. It is also possible to use different combs in two directions to achieve a force measurement in these two directions. However, like in the AFM this device needs to be tethered which clearly prevents it from a use in any microfluidic application. This technology is now commercially available (www.femtotools.com) and allows a force resolution from 100 millinewtons to 5 nanonewtons. When the accessibility becomes constrained by considering the access inside a microfluidic chip, some technologies are not compatible. As we already mentioned, this is the case for the AFM and the comb drive actuator because the sensing part of these two technologies are tethered to a macroscopic frame. Magnetic tweezers offer a large spectrum of force. But even if their integration in microfluidic chips is possible, it is largely restrained by the proximity of the electromagnetic coil tip of the magnet. Moreover the system gains in complexity for each supplementary degree of freedom. Thus as the environment becomes even more confined, integrating multiple magnets or electromagnet tips is difficult and the manipulation becomes more difficult. Optical tweezers do not suffer from these proximity footprint problems and they have the advantage of being highly compatible with microfluidic technologies. The only requirement is that the microfluidic chip needs to be transparent for the trapping laser. As only optical trapping is feasible in small microchannels, it is not possible to measure the deformation of an object with a constant force except by doing a complex closed-loop system.

Comparison

But a comparison between these technologies is more complicated than what can be presented by only considering force range and accessibility. Therefore in Table 1.1, we present the other notable characteristics and specificity of each technology. The main technology to consider here is the optical tweezers as it is the only technology that can easily be implemented in a small microchannel. [START_REF] Enger | Optical tweezers applied to a microfluidic system[END_REF][START_REF] Wang | Robot-assisted automatic cell sorting with combined optical tweezer and microfluidic chip technologies[END_REF] One of the drawbacks of the optical tweezers force sensing technology is that a very homogeneous environment is required on the optical path to obtain a precise force. This homogeneous environment is not a problem for measuring precise values on a chosen protein or on an organism. Indeed it has been proved to be a powerful tool to understand and quantify the mechanics and chemical forces in proteins and cells [START_REF] Neuman | Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy[END_REF]. However the measurement needs to be made in a very controlled and transparent environment to be sure that no perturbation will change the trap stiffness. Therefore these tools are inappropriate to perform measures on complex structures such as biological tissues or through a half-transparent surface.

In other words, optical tweezers are very powerful to measure intrinsic parameters through a complex preparation protocol but lack of robustness to be used directly to measure and characterize an object in situ inside a complex environment. The local heating and light exposure can also be a problem. Local heating can induce a convection flow that can interfere with the measurement and the light exposure can damage the trapped object.

Due to their different advantages and drawbacks, these technologies have been used for different purposes which are displayed in Table 1.2. Optical and magnetic tweezers have been widely used for different protein characterizations in a wet environment. Indeed these two technologies are meant to be used in liquids whereas AFM needs to be adapted for this particular application. However for surface mapping or complex structures the AFM is more adapted. Indeed it is impossible to directly apply forces on precise surfaces either with magnetic tweezers or optical tweezers. For magnetic tweezers only a ferromagnetic bead can convert the magnetic field into a force. As this one is hard to place and is in most cases chemically attached to the object to measure, repeatable measurements is too difficult. For optical tweezers the proximity of the surface can disrupt the trapping force if the surface is not fully transparent and with the same

Open environment Microfluidic environment

Protein analysis AFM [START_REF] Lee | Direct measurement of the forces between complementary strands of DNA[END_REF]/Magnetic tweezers [START_REF] Lang | An automated two-dimensional optical force clamp for single molecule studies[END_REF] Optical tweezers [START_REF] Yan | Near-field-magnetic-tweezer manipulation of single DNA molecules[END_REF] magnetic tweezers [START_REF] Strick | Twisting and streching single DNA molecules[END_REF] optical tweezers [START_REF] Enger | Optical tweezers applied to a microfluidic system[END_REF]

Micro-organism propulsion characterization

Optical tweezers [START_REF] Ashkin | Optical trapping and manipulation of single cells using infrared laser beams[END_REF] Optical tweezers [START_REF] Chattopadhyay | Swimming efficiency of bacterium Escherichia coli[END_REF] Micro Electrical Mechanical System (MEMS) caracterisation AFM [START_REF] Binnig | Atomic force microscope[END_REF] / Comb drive [START_REF] Willium | Laterally driven polysilicon resonant microstructures[END_REF] Helical microrobot

Non biological surface analysis AFM [START_REF] Zhong | Fractured polymer/silica fiber surface studied by tapping mode atomic force microscopy[END_REF] Helical microrobot

Biological surface analysis AFM [START_REF] Routier-Kierzkowska | Cellular Force Microscopy for in Vivo Measurements of Plant Tissue Mechanics[END_REF][START_REF] Hansma | Tapping mode atomic force microscopy in liquids[END_REF] Helical microrobot

In conclusion, we can highlight the needs of on-chip force sensing that are not covered by the current technologies. Firstly, only the optical tweezers is usable for applications inside microchannels under 100µm. As explained above the possible measurement in such channel is limited to homogeneous and transparent condition which requires a sample preparation and limits the field of possible measurements. Secondly, the needs concern the surface mapping and stiffness mapping that is provided by the AFM only in open conditions. Therefore we believe that a helical microrobot could be used to provide these two different needs.

Magnetic actuated helical microrobot for force sensing

To explain why we choose to use a magnetic actuated helical microrobot as force sensor in order to answer the needs presented above, we first need to consider the microrobot design and propulsion mechanism. For building a robot at the micro or the nano scale, a top down approach by miniaturizing existing components is impossible. In fact the best example of such an approach in robotic remains at the millimetric scale [START_REF] Russell | Fly on the wall[END_REF]. Indeed Central Processing Unit (CPU), motors, actuators, joints and sensors cannot be miniaturized and assembled below this scale. Therefore a bottom up approach is used with a simple design and external controls.

The propulsion of such micro and nano robots was the first to be historically investigated therefore these different propulsion manners have been widely studied. The investigated solutions are mostly based on fuel propellant [START_REF] Sánchez | Nanorobots: The ultimate wireless self-propelled sensing and actuating devices[END_REF] [57], electric and electromagnetic fields.

Electric field solutions propose to produce an electro-osmotic flow on the robot surface to make it move [START_REF] Hwang | Electro-osmotic propulsion of helical nanobelt swimmers[END_REF]. But to control the direction of this field in every direction is complicated as the current goes from one electrode to another. Moreover the electric current can damage the environment. Therefore we did not choose this method but we focused on a solution based on magnetic field propulsion.

The most conventional magnetic field solution is to move ferromagnetic robots [START_REF] Ivan | NIST and IEEE challenge for MagPieR: The fastest mobile microrobots in the world[END_REF][START_REF] Yesin | Modeling and Control of Untethered Biomicrorobots in a Fluidic Environment Using Electromagnetic Fields[END_REF][START_REF] Choi | Two-dimensional actuation of a microrobot with a stationary two-pair coil system[END_REF] or robots with a permanent magnet part [START_REF] Hagiwara | Precise Control of Magnetically Driven Microtools for Enucleation of Oocytes in a Microfluidic Chip[END_REF] by using a magnetic gradient such as the one created by a magnet. This prevents from any damage on the environment. Moreover the interest of magnetic field interest compared to electric field is to avoid the contamination of the liquid from electro-chemical reactions. Compared to fuel propellant it can be used for a theoretically infinite time as it cannot run out of propeller. In a way to propel a microrobot with magnetic gradient can be considered as a scaled up version of magnetic tweezers with a selective bead called "microrobot" and with dimension typically between 1mm and 100µm. The main similarity is that the system is controlled by the intensity of the magnetic field gradient and so by the force applied to the robot and not by its position. Therefore to achieve a position control, real time feedback information on the position is needed [START_REF] Salmon | Swimming property characterizations of Magnetic Polarizable microrobots[END_REF][START_REF] Kummer | Octomag: An electromagnetic system for 5-DOF wireless micromanipulation[END_REF]. But one major difference is that these robots are mainly used in 2D where the friction with the surface is important and has complex forms. Therefore it has become hard to link the magnetic intensity and the force applied by the robot in a quantitative and reproducible way.

To overcome this, a bendable beam has been embedded in robots at the millimetric scale [START_REF] Kawahara | On-chip microrobot for investigating the response of aquatic microorganisms to mechanical stimulation[END_REF] for force resolution of the millinewton and on robots at sub-millimetric scale (≈ 800µm) [START_REF] Jing | Micro-force sensing mobile microrobots[END_REF] for force resolution around 100 nanonewtons. But these designs are difficult to miniaturize below this dimension. Indeed the beam becomes stiffer as its dimensions are scaled down. Therefore, to maintain this stiffness constant, an even finest beam is needed which becomes impossible due to fabrication technology limitations. Thus to make a force sensor and a microrobot below (≈ 800µm) we need to find another solution. For further miniaturization, an alternative design that could link in a reproducible way an input parameter to the applied force is needed. The solution we chose here is to use an external rotating and homogeneous magnetic field to produce a torque on an helical shape structure [START_REF] Abbott | How Should Microrobots Swim?[END_REF]. In Table 1.3, we show where this microrobot technology is situated compared to other existing microrobots. The chosen technology is highlighted in red. By designing a corkscrew helical tail, the rotation torque is transformed into a linear propulsion force as shown in Figure 1.4 exactly like in the flagella of bacteria or of spermatozoa. This corkscrew shape is essential at this scale because reciprocal motion is impossible in a Newtonian fluid [START_REF] Hess | Clinically meaningful blood pressure reductions with low intensity isometric handgrip exercise. A randomized trial[END_REF] and very slow in non-Newtonian fluid [START_REF] Qiu | Swimming by reciprocal motion at low Reynolds number[END_REF]. Millimeters scale robots were first used to prove the possibility of a rotating helix based motion [START_REF] Honda | Micro swimming mechanisms propelled by external magnetic fields[END_REF]. Later the 3D navigation was demonstrated by overcoming the gravity effect with the generated thrust [START_REF] Mahoney | Velocity Control with Gravity Compensation for Magnetic Helical Microswimmers[END_REF]. Closed-loop automatic control base on visual feedback was also studied at the millimetric scale [START_REF] Xu | Propulsion Characteristics and Visual Servo Control of Scaled-up Helical Microswimmers[END_REF]. The miniaturization has been explored and 3D helical microrobots have been fabricated and controlled in their motions with high precision [51] [50]. Further miniaturization was achieved to demonstrate their actuation in complex viscoelastic media [START_REF] Schamel | Nanopropellers and their actuation in complex viscoelastic media[END_REF].

Therefore helical ferromagnetic robots driven by the rotation of an homogeneous magnetic field are good candidates for force sensing applications. Here is a summary of the advantages that led to this choice.

• Low Reynolds condition guarantees a linear relation between the rotation speed of the helical part and the applied force. This allows a small design (≈ 50µm) for the microrobot as there is no need to embed a low stiffness beam to know the applied force. Moreover as the force is controlled by the rotating speed of the magnetic field, no precise information on the local intensity of the field is required.

• A relatively low magnetic field is used to drive this robot (around 10 mT). This is a good point compared to magnetic gradient propelled robots or magnetic tweezers because the electromagnet can be placed far from the chip. Thus it leaves a lot of freedom and versatility on the design of the microfluidic chip and there is less perturbations from the heating of the coils.

• The direction of the field is simpler to control in 3D than the gradient. It can be done with an automatic control which does not require position and speed feedback.

• This design is easy to scale up or down as examples go from the millimetric to nanometric scale.

Although helical microrobots are good candidates for on-chip force sensor, they are not yet examples of such demonstration. There are two main reasons for this. First their individual CHAPTER 1. INTRODUCTION integration on microfluidic chips is difficult and have not been shown yet. Secondly, they need to be characterized individually inside the chip to take into account any particular deformation that can arise during either the fabrication, the detachment from the fabrication substrate or the rough integration inside the microfluidic chip. Therefore solutions to these issues defines the goals of this thesis.

Goals and challenges of the thesis

Thesis goals definition

The goals aimed by this thesis are summed up in Figure 1.5. We propose the development of a mobile untethered microrobot with a force sensors capability. This robot should be able to be integrated and calibrated inside a microfluidic chip. Moreover, it should be able to access and perform force sensing on any surface as well as to move freely in 3D inside the chip.

It should be noted that we do not aim to solve directly biological needs. Indeed the experiments were performed in isopropyl alcohol to limit adhesion problems of the robot with the surface. Improving the design of the microrobot to make it compatible with biological media will be one important perspectives of this work. This bio-compatibility adaptation could largely benefit from the microrobot force characterization to measure quantitatively how the microrobots react to a particular medium.

Also for the scope of this thesis we focus on the force sensing ability and not stiffness measurement. Indeed to measure stiffness the displacement of the robot would need to be measured with precision around 10 nanometers which is too small compared to our resolution. This could be possible to reach such a resolution by using different optical techniques used for example in optical and magnetic tweezers.

Challenges

Before performing any sensing inside a microfluidic chip, these helical microrobots need to be able to be integrated inside one. Even if on-chip microfluidic integration was already demonstrated with milli- [START_REF] Kawahara | On-chip microrobot for investigating the response of aquatic microorganisms to mechanical stimulation[END_REF], micro- [START_REF] Hwang | Mobile microrobotic manipulator in microfluidics[END_REF][START_REF] Salmon | Swimming property characterizations of Magnetic Polarizable microrobots[END_REF], and nanometric robots [START_REF] Hayakawa | Fabrication of an on-chip nanorobot integrating functional nanomaterials for single-cell punctures[END_REF], it was never demonstrated with helical microrobots using a rotating magnetic field.

For robots with at least two dimensions above around 300µm, manual integration during the chip fabrication process is possible. Another solution at this scale is the self-detachment of the robot inside the chip. This means that the robot uses its own propulsion force to detach 1.5. GOALS AND CHALLENGES OF THE THESIS 29 from the substrate inside the fluidic chip [START_REF] Kawahara | On-chip microrobot for investigating the response of aquatic microorganisms to mechanical stimulation[END_REF]. This method works well for robots with millimetric dimensions but is more difficult for smaller robots with a higher surface-to-volume ratio. Indeed in the case of a magnetic propulsion, the maximum propulsive force of the robot compared to the force needed to detach it from the fabrication substrate decreases with the robot size.

Therefore self-detachment is not an option for a magnetic robot at our working scale and was not proved yet to the best of our knowledge. Current methods use non-selective integration, mostly by using the fluid inlet of the microfluid chip to inject a lot of microrobots [START_REF] Ding | Microfluidic-based droplet and cell manipulations using artificial bacterial flagella[END_REF]. But in this thesis, we want to be capable of selective integration. Indeed we need to choose and characterize individually each helical microrobot that we could use for force sensing purposes. Therefore the first challenge of this thesis was to develop the selective integration of a helical robot inside a microfluidic chip.

Selective integration (i.e. one by one) at this scale was never performed before this thesis because helical microrobots suffer from a lack of robustness and mobility due to their high surfaceto-volume ratio. Indeed they have usually a limited robustness as they can easily get stuck on the surface if they touch it. Their mobility is limited because they cannot go to a precise area if the path to access it presents a moderately strong flow. One way of overcoming these problems is to make the robot capable of interacting with the surface. It has been proved that the friction gradient caused by a surface is enough to propel a microscale object close to it with a rotating magnetic field [START_REF] Tierno | Controlled swimming in confined fluids of magnetically actuated colloidal rotors[END_REF]. This field makes the particle tumble and therefore move. This motion has been studied in micro and nanoparticles [START_REF] Courcier | Tumbling motion yielding fast displacements of synthetic antiferromagnetic nanoparticles for biological applications[END_REF][START_REF] Morimoto | Tumbling motion of magnetic particles on a magnetic substrate induced by a rotational magnetic field[END_REF] and controlled for the locomotion of nanowires where it is shown to be robust to surfaces irregularities and capable of cargo transport [START_REF] Zhang | Controlled propulsion and cargo transport of rotating nickel nanowires near a patterned solid surface[END_REF]. The friction with a surface can be used directly for propulsion by making the robot roll on it. As tumbling motion, rolling uses the proximity of the surface to move. The difference is that the rotation is made around the symmetric axis of the robot. However a major drawback of tumbling and rolling is to restrain the mobility of the robot to a two dimensional surface where it could be blocked by utterly impassable obstacles.

To overcome this difficulty and solve the first challenge of selective integration, we developed a microrobot capable to use a swimming motion in 3D as well as different surface motions. Indeed this choice between different motions allows the robot to benefit from the advantages of the different motions while being less vulnerable to their specific drawbacks. Thus the robustness and mobility of the helical microrobots is greatly improved and the selective integration inside a microfluidic chip becomes possible. Its mobility allows to travel up to several centimeters in 3D as well as entering microchannels of around 10µm diameters. This microrobot was named Roll-To-Swimm (RTS) as a reference to its multiple motions capability.

The second challenge was to develop a protocol to characterize the robot. Indeed, as it is explained in Figure 1.4 the rotating frequency can be linked to the force applied by the robot. But for a precise measurement, each RTS needs to be characterized as differences between them can arise from fabrication and individual detachment from the subtract. It is also important to verify in which frequency range the relation between the rotation and the force is linear and if the chosen design offers a repeatable behavior in time. To perform this characterization, the classical approach is to perform dropping tests and to deduce the force developed by the corkscrew from the weight and buoyancy force. To get a precise value with a good error approximation, a very well-controlled environment is required. Indeed parameters such as temperature and parasite flows from evaporation in porous microfluidic chips or convection need to be controlled. On our setup, this control of the parameters was only made possible thanks to the environment of the microfluidic platform.

Precise positioning and automatic control is also one of the requirements to perform force sensing. Especially, one major contribution of a sensing microrobot could be for surface friction measurement. In this case automation is essential. To answer this need, we investigated a newly reported surface motion for helical swimmer that we have called "spintop". This motion allows a precise positioning with closed-loop control. For now this positioning is limited by our optic resolution to a resolution around 2µm. This motion allows to access any surface without depending on its orientation, as well as a tunable force interaction with the surface.

The last goal of this thesis is to show that the on-chip characterization of helical microrobots brings the state of the art closer to potential applications of microrobot on this platform. For this we show that this quantitative force measurement allows us to investigate rigorously the CHAPTER 1. INTRODUCTION design optimization of the RTS, its interaction with other objects towards force sensing and its manoeuvrability in a constrained environment such as a microchannel. Moreover, we show that the sensing on microrobots is not only for potential external measurements but also provides a feedback for a better control and robustness. To illustrate this we develop an instant evaluation of the flow speed that is used to automatically adapt the RTS control to the safest path in the microfluidic chip.

Presentation of the chapters

Each following chapter presents a specific challenge that was solved to perform on-chip force sensing with a helical microrobot. The detailed solutions as well as the results are discussed.

Chapter 2 explains the fabrication of the robot and its control. Firstly, the details of the microfabrication of the helical microrobot are explained as well as the microfluidic chip fabrication. Secondly, the software and hardware design that provide a homogeneous magnetic rotating field are described. Finally, the optical feedback, tracking and closed-loop control mechanisms are presented.

Chapter 3 presents the selective microfluidic chip integration challenge of the helical robot. Three different motions are used on a single robot to improve its robustness and mobility. Firstly, these motions are explained and a model of the newly reported motion called "spintop" is presented. The potential of combining these motions for cargo transport and accessibility on any surface is also reported. Secondly, the microfluidic chip integration strategy is explained and demonstrated as well as the capacity to store the helical robot inside the microfluidic chip for a long term storage and use.

Chapter 4 presents the characterization of the microrobot. Firstly, a theoretical explanation on the propulsion model of microhelical objects is provided. Secondly, the experimental setup and protocol to identify the model parameters on a microfluidic chip for a single robot are explained. An evaluation of the measurement error is performed and its different sources are quantified to present the most relevant optimization choices.

In Chapter 5, some steps towards potential applications made possible thanks to the microrobot force characterization are considered. The microbeads manipulation and their impact on the microrobot force is firstly investigated. This investigation is essential before we can consider applying force on any spherical object such as biological cells. Microbeads could also serve as an interface between the microrobots and the surface for friction measurement. Indeed they have the advantage to present a well known geometry with easily tunable surface conditions. Then we present flow measurements at a precise location and how it can be sent as feedback to the microrobots for a better control. Finally we present an integration and the control of the microrobot in a microchannel with a section below 100µm.

The last chapter presents the conclusion of this thesis. After a review of the different contributions of this work, we present how the developed setup and protocols could contribute to helical microrobot development towards applications. Indeed by enabling quantitative measurements, we bring a more concrete way to develop and optimize microrobot for potential specific applications.

Chapter 2

System

As mentioned in the introduction, robots at the microscopic scale are too small to be embedded with all the necessary actuators and sensors required to be autonomous. Therefore to solve this problem, the following functions are externalized:

• Propulsion, by using a magnetic or electric field generated and controlled by a macroscopic external setup.

• Localization, by using a microscope and a camera.

• Processing (for example, closed-loop position control), by using a standard computer.

One notable exception to this externalization concerns the chemically propelled robots [START_REF] Wang | Cargo-towing synthetic nanomachines: towards active transport in microchip devices[END_REF]. The chemical energy for generating the propulsive force of these robots is directly stored on the robot. However an external magnetic field is needed for steering [START_REF] Sanchez | Microbots swimming in the flowing streams of microfluidic channels[END_REF]. This chapter presents both the fabrication of the RTS and the associated external setup providing the propulsion, localization and processing required for the helical microrobot.

Torque Magnetic field

Induced magnetisation

Rotation of the magnetic field In the introduction we mentioned why we choose to actuate the RTS with a homogeneous rotating magnetic field (see Chapter 1.4). The main advantages are: 3D control, easy access of the robot to the environment and the promising ability for quantitative force measurement. Figure 2.1, displays how the external homogeneous magnetic field propels the RTS. The external magnetic field induces the magnetization of the ferromagnetic microrobot. Therefore a torque is created between the magnetization direction and the direction of the external magnetic field. This phenomenon is similar to a compass aligning itself with the earth magnetic field. Then by making this field rotate, a constant torque is created and the RTS rotates along its axis. This rotation is used to provide all the different kinds of motions to the RTS.

RTS rotation

This chapter firstly presents how we fabricate a helical microrobot that can be actuated by a homogeneous magnetic field along with a microfluidic chip compatible with this microrobot. Secondly, it focuses on how we control this magnetic field in order to move the microrobot. and surfaces. These questions will be handled in Chapter 3. The final section explains why two different setups have been made and their principal differences.

As in any system design, there are several possible technical choices. In this chapter we also explain the different possible solutions for each technical and fabrication problem and the reason why we choose a particular one in this work. These reasons are often motivated by our great need for versatility and quick prototyping. Indeed the system contribution of this thesis does not aim at proposing an optimized solution but aims at being fast to adapt to any new parameters investigation. This system is therefore designed to reveal and explore the different feasible manipulations and sensing applications in microfluidic platforms.

For these concerns, we chose a rapid-prototyping approach for the RTS design, microfluidics and the external setup. This allows to be widely adaptable to the different needs during the tests for new feasible applications. These rapid prototyping technologies will be described in the following sections. They include 3D laser lithography with two-photon polymerization technology for the RTS, micro-milling machine for microfluidics, and 3D printing for setup fabrications. These prototyping methods allow quick experimental feedback which is here preferred to the analysis through numerical models of the helical robots. Indeed, such models are for now limited by the nonlinear physics such as stiction and the lack of background knowledge preventing from making a pertinent hypotheses choice.

Thanks to this high versatility many helical microrobot tests were performed and we started to be convinced that their potential for force sensing were worth investigation. Therefore we decided to optimize our setup design in order to allow a fine characterization of the RTS which is a requirement to demonstrate quantitative measurement applications. For this, a second setup with temperature control and better optics was conceived. The on-chip selective integration of the RTS, developed in Chapter 3, is another requirement for this fine characterization as it allows us to provide a well-controlled environment. The 3D versatility of micro-milling technology was used to optimize the environment conditions for this characterization. Moreover it was also used to investigate challenging or physically interesting environments as small channels of different sizes, or brutal flow variation. They are discussed in Chapter 5. Finally inclined walls inside the microfluidic chip were used to integrate a side view mirror inside the chip for characterization purposes. This is presented in Chapter 4.

RTS and microfluidic chip fabrication

RTS fabrication

Helical structure fabrication ≈ 100nm + -++

The helical structure of the RTS is the key feature for its mobility and force sensing. Indeed the helix acts like a boat propeller and transforms its axial rotation into a propulsive force. Table 2.1 shows the different existing technologies to build such helix. At millimetric scale, the helix structure and magnetic components for magnetic actuation are made and assembled manually [START_REF] Honda | Micro swimming mechanisms propelled by external magnetic fields[END_REF] or by 3D printing [START_REF] Xu | Modeling and swimming property characterizations of scaled-up helical microswimmers[END_REF].

But at the micrometric scale, these conventional processes are no longer possible. Therefore self-scrolling, template electro synthesis and Physical Vapor Deposition (PVD) technics, use physical or chemical phenomena to build a 3D helical geometry.

For self-scrolling, the stress difference in different materials is used [START_REF] Zhang | Artificial bacterial flagella: Fabrication and magnetic control[END_REF] on a ribbonlike structure. This makes the surface bend in a helical form. Template electro synthesis use electrochemical deposition on a very well-controlled environment into nanoscopic pores to grow a helical structure [START_REF] Li | Template electrosynthesis of tailored-made helical nanoswimmers[END_REF]. Finally, e-beam vapor deposition uses a combination of nanoscale patterning and shadowing effect to build an array of 3D helices [START_REF] Mark | Hybrid nanocolloids with programmed three-dimensional shape and material composition[END_REF]. These methods, where the helical structure is made directly by a physical phenomenon, are interesting because they generally allow massive production of microscale helices. Indeed as they are all made in parallel, the same process can be used to build one helix or a large array with thousands or millions helices.

However there are important constraints on the design method because external physical phenomena such as differences in material constraint for self-scrolling or shadowing effect for PVD are used to build the helix shape. Indeed usually only one or two fabrication parameters can be modified. Thus a total freedom in the design shape is impossible.

As the scope of this thesis is to investigate and propose new protocols for force sensing applications, we want to be as independent as possible from fabrication constraints to freely change and optimize our design. This allows us to focus more on the physical phenomena and CHAPTER 2. SYSTEM less on the fabrication process. We also want an important freedom on the design and to be able to independently investigate the influence of each parameter. Indeed it seems more interesting for the moment to work on prototypes in order to identify and answer the different challenges for microrobot applications instead of spending time in fine optimization of the system design. When these problems will be clearly identified more massive and constrained ways of producing helical robots should be investigated.

These reasons led us to choose the 3D lithography process using two-photon polymerization [START_REF] Erskine | Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication[END_REF]. This technology uses the interaction of two photons to cure a resist in a sub-micrometric volume element called voxel. By making the laser move on the resist any shape can be realized. We currently use the commercially available system called "nanoscribe" (model:photonic processional). The resist is the IPG 780.

Ferromagnetic layer deposition

One drawback of using 3D lithography is that the polymer resist does not have magnetic property. Therefore it is impossible to make the robot move with a magnetic field. To make it magnetically responsive one solution is to mix the polymer resist with magnetic nanoparticles. It has already been shown to be viable in helical microrobot design and applications [START_REF] Suter | Superparamagnetic microrobots: Fabrication by two-photon polymerization and biocompatibility[END_REF]. However this solution requires a careful tuning of both 3D lithography apparatus and the proportion of magnetic nanoparticles and polymer needs to be adjusted, which reduces the precision of the voxel size. Another way to make the helix magnetic is to use e-beam Physical Vapor Deposition (PVD) of ferromagnetic materials [START_REF] Tottori | Magnetic helical micromachines: Fabrication, controlled swimming, and cargo transport[END_REF]. This method was chosen in this thesis for its relative simplicity. As shown in Figure 2.3, the substrate is placed on a rotating platform that can be tilted. This permits to reduce the shadowing effect and to cover the RTS more uniformly. The PVD machine (Plassys MEB550SL) first deposes a 20nm chrome layer both at 0 • and 75 • inclination for adhesion. Then it deposes a 100nm nickel layer both at 0 • and 75 • inclinations.

However it remains impossible to cover the whole RTS as some parts are in contact with the substrate. This is an important drawback as this polymer part is more hydrophobic than the nickel and will lead to the trapping of bubbles at this location. We believe this explains the high probability to stick on the surface when the RTS evolves in water conditions where a lot of microbubbles are present on this surface. As the goal of this thesis is not to optimize fabrication technologies but to explore the physics of microrobots, we use isopropyl alcohol as a liquid medium for our robot. Indeed, gases are more easily diluted in this alcohol and the probability of bubbles appearing on the surface is almost reduced to zero, which suppresses stiction problems.

As biological media are based on water, solving the adhesion problem in this medium will be one important perspective of this thesis. Here getting the ferromagnetic property by mixing ferromagnetic nanoparticles with the resist could be an interesting solution to offer a more homogeneous surface. However it is still unclear if this mixture can offer good enough anti-stiction effect to allow one given robot to be robust enough to be used for several hours in an unconstructed environment (which is a robotic term for an environment with external perturbations, not designed especially for the robot). Therefore investigation needs to be performed. One other solution could be to use 3D lithography to make a negative mold of the robot and perform an electric growth. This solution has been proved on gold helix [START_REF] Gansel | Gold Helix Photonic Metamaterial as Broadband Circular Polarizer[END_REF] and needs to be developed with ferromagnetic materials like nickel. This approach has the advantage to build a homogeneous metallic robot which should suffer less from stiction related to bubbles and increase the helical robot magnetization.

Coming back to other fabrication techniques presented in Table 2.1 could also be interesting when biological applications will be aimed and when the physics of the helical microrobot will be better understood. At this point the large freedom of the design of the 3D lithography would not be required anymore. Indeed, despite the disadvantages presented above, 3D lithography is perfect for prototyping. Even if this limits the choice of the fabrication material and mass production, this allow us to investigate easily a large choice of RTS shapes and scales. This is therefore the ideal technology for our work as the RTS optimal design is not yet stabilized and it needs to be rapidly modified to investigate potential applications or to understand a physical phenomenon. Therefore we believe it is for now the best solution and that other fabrication methods should be considered later for precise applications. In all the fabrication methods presented above, helical microrobots are attached to the fabrication substrate at the end of the fabrication. The most common way to remove them is to use a global method that removes all the helical robots from the substrate at the same time. This can be done using mechanical stimulation with sonification [START_REF] Mark | Hybrid nanocolloids with programmed three-dimensional shape and material composition[END_REF] or chemically [START_REF] Li | Template electrosynthesis of tailored-made helical nanoswimmers[END_REF] by etching a sacrificial layer between the helical robot and the substrate. These methods have the advantage of minimizing the damage to the helices during the detachment.

Detaching the RTS from the substrate

However with these global methods it is impossible to detach only a single helix at a time. This is firstly a practical inconvenience as a new sample needs to be designed each time a new CHAPTER 2. SYSTEM experiment is performed. This increases significantly the time of research allocated to the sample fabrication and it becomes more difficult to obtain repetitive measurements as the difference between two fabrication substrates is difficult to control. Secondly, we believe that selective manipulation of such microrobots is an important technology to develop in order to propose applications. Indeed to use a global method for the release of the microrobots, one needs to inject a large quantity of helical robots in order to use only one. This results in the pollution of the environment, either in a passive way by the helical robots presences, or in a dynamical way as all the detached robots will move at the same time even if only one is to be controlled. This robot pollution due to massive detachment can also lead to problems for the fine characterization of RTS. Indeed the RTS to characterize can be stuck to another one or perturbed by its flow. Moreover it is making the investigation between two different RTS designs more difficult. Indeed the difference must be clearly visible by the optics feedback to select the RTS to characterize. This limits the investigation to important geometry changes and does not concern for example surface coating or inner structures.

Therefore we chose to detach individually each RTS from the substrate [START_REF] Zhang | Artificial bacterial flagella: Fabrication and magnetic control[END_REF]. For this we used a tungsten tip. Its shaft diameter is 10µm and the point has a round radius below 0.1µm. This tip is fixed and the stage controller moves the entire microfluidic chip which contains the fabrication substrate in a chamber open at the top. The precision of this stage controller is 0.1µm. The tip direction has an angle of 20 • to 40 • with the fabrication substrate to touch it in a single point. Figure 2.4 shows experimental views of the detachment process of a single RTS from the fabrication substrate. After the detachment the tungsten tip is removed so that the detachment area can be closed by laying a glass substrate on it. This sealing is only maintained by the glass adhesion with the PDMS and can present some leaks. However it reduces the evaporation of isopropyl alcohol enough to allow us to move the RTS inside a permanently closed chamber of the microfluidic chip. At this point the detached RTS is able to rotate freely with the rotating magnetic field. More details on the integration of the RST inside the microfluidic chip are presented in Chapter 3.3 Even if this method has the inconvenience of damaging a bit the RTS during the detachment, we are able to reuse the fabrication substrate as long as there are RTS on it. Since the remaining attached RTS support to be dried, the use of a single sample for approximately 30 RTS detachments is possible and was often done during this thesis.

3D microfluidics with screw valve

As we develop on in Chapter 3.1.2, a part of this thesis has been focused on discovering new motions of the RTS to increase its mobility and perform a selective integration inside a microfluidic chip. However this method cannot be applied to any existing chip and some design requirements are needed on the chip for the RTS to be integrated inside. Moreover we want to investigate especially the 3D mobility and navigation of the RTS. For these two studies, it was essential to choose a microfluidic chip technology that allows the design of complex 3D shapes such as different channel altitudes or walls with inclination angles.

Microfluidic chip materials: PDMS bond to glass

Historically, the first microfluidic design was made on a silicone crystal substrate [START_REF] Terry | A Gas Chromatographic Air Analyzer Fabricated[END_REF]. This was the most natural material to use as microfabrication technology was widely developed with this material thanks to the development of microelectronic in the second half of the 20 th century. However when microfluidics started to be used for biology, a need of in situ imaging emerged. Therefore light transparent materials were investigated.

Glass is the most straightforward transparent material one can think of as it has a great chemical stability and has been used for centuries in chemical and biological science. However one main drawback is that the machining of this material is not as simple as for silicon crystal. One solution is to deposit a metallic protective mask with the negative design of the channel. Then a wet etching can be realized by acid. Hydrofluoric acid is the most commonly used. Reactive-ion etching can also etch the glass left unprotected by the metallic mask. Other solutions include selective etching by laser, either directly [START_REF] Sugioka | Three-dimensional micromachining of glass using femtosecond laser for lab-on-a-chip device manufacture[END_REF], or inside an etching bath [START_REF] Cheng | Crack-free directwriting on glass using a low-power UV laser in the manufacture of a microfluidic chip[END_REF]. For this etching, the laser position is monitored by a stage control or mirror control in order to build the channel design.

Secondly, the bonding of the etch glass with a cover glass is difficult. It can be done at high temperature (around 300 • C) or with a resist that cures into glass. But above all, glass is hardly compatible with 3D design. To manage different channel altitudes, different etching steps are required by covering with a protective layer for each step the area to not etch. This requires as many fabrication steps as different altitudes in the design. A precise alignment between lithography deposition of the protective layer is also needed. Moreover it is impossible to perform inclined shape. With direct laser etching, 3D structures are possible by etching selectively small volume elements [START_REF] Sugioka | Three-dimensional micromachining of glass using femtosecond laser for lab-on-a-chip device manufacture[END_REF]. However, this method is not straightforward to use and requires the fabrication of a complex system which is an excessive investment for the scope of our research.

So even if glass is a very interesting material for microfluidic chips it presents several fabrication challenges that make quick prototyping hard and mass production difficult. Moreover, 3D fabrication is difficult and limited. Otherwise transparent polymers can be used. Indeed their cross-link ability to solidify and plastic deformation make their use easy for microfluidic chic fabrication with a primary mold. Thanks to a mold it is easy to replicate a design, which saves time. Moreover the processes to fabricate a mold are not so restrained than the one to fabricate directly the material and new designs are simple to investigate. 3D design is also possible thanks to milling and is presented in the next subsection.

This design liberty is the main reason that led us to choose transparent polymers for this thesis. Indeed our research is still at a prospective step and the ability to investigate different designs quickly was more interesting than the chemical stability offered by the glass. Therefore we chose to use Polydimethylsiloxane (PDMS) which is a very commonly used polymer for microfluidic chips. Indeed its use is simple and requires no expensive equipment. It can be purchased uncured and cured directly on the mold by using a curing agent at relatively low temperature (70 • C). This allows important aspect ratio. The PDMS is then sealed to a glass slide using an oxygen plasma that oxidizes both the PDMS and the glass surface [START_REF] Duffy | Rapid prototyping of microfluidic systems in poly(dimethylsiloxane)[END_REF].

On top of the reasons explained above the choice of PDMS material is motivated by the following reasons:

• We can easily design valves by applying pressure on the chip to deform and close a microchannel. The large elastic deformable range of PDMS allows this [START_REF] Unger | Monolithic Microfabricated Valves and Pumps by Multilayer Soft Lithography[END_REF]. In order to integrate the RTS inside the microfluidic chip, it is essential for us to have a valve.

• The gas bubbles remaining in dead end channels are absorbed by the PDMS. In order to perform the characterization tests presented in Chapter 4.2.2, dead end channels are needed. Gas bubbles often remain in this kind of channel after liquid injection. As PDMS is porous to gases, these bubbles can be suppressed by increasing the pressure in the chip. In our case the pressure was increased to 0.5 bar above ambient pressure during approximately ten minutes to remove these bubbles.

But using PDMS presents some drawbacks as well. They are mainly linked to the porosity of the PDMS. It leads to an important parasite flow due to PDMS absorption. This flow is particularly problematic for the precise characterization of the robot and is discussed more in detail in Section 4.3. This porosity also leads to bubble formation in the chip after several hours if no flow is maintained in the chip.

Despite these disadvantages the PDMS is still the most interesting material for us. Indeed combined with the mold fabrication by micromilling, it allows fast, 3D and multi-scale design which is particularly suited for our prototyping needs.

Mold fabrication by micromilling machine

Using a mold allows a simple production of the same microfluidic chip as one mold can be used several times for many identical chips. Another advantage is that the mold can be made of any material which offers a large choice for the fabrication method. Let us first look at the different specifications on the mold design. They are represented by the drawing in For the design in Figure 2.5 c), the square section channels with dimensions ranging from 8µm to 100µm are connected to a bigger chamber. Also a fillet at the junction between the small and the large channels was necessary for experimental reasons. Indeed, without these fillets the top end of the channels were largely deformed during the bonding process between the PDMS and the glass, which resulted in the collapse of the microchannel entrances.

The round channel presented in Figure 2.5 d) is used as a fluid valve. By applying pressure with a screw on the top of the chip, the PDMS is deformed and closes the channel. The round shape facilitates a leak-free closing. Indeed we observed leaks on the square channels whereas the round channels were free from any leak even with a chip pressure of one bar over the ambient pressure. The width of these channels is 1mm for a maximum 50µm height.

From these illustrations we deduce the following requirements for the mold fabrication method:

• It needs to allow complex 3D design. Indeed different heights are required for the different channels, the experimental chamber and the valve as well as different shapes such as a microfluidic chip ceiling with an angle.

• The maximum height should be 1mm. This is a requirement to perform the drop test with good precision. Moreover this large height allows us to easily integrate different experimental samples inside the chip during the fabrication to interact with the RTS.

• It needs to have multi-scale precision. The chosen method must allow high precision on small patterns (≈ 1µm) as well as fabrication of relatively big structures (≈ 1mm).

To realize mold designs for microfluidics, the most classical approach is to use lithography. It has the advantage to be a well-known process and it offers a resolution below the micrometer. However, even by using specific resists, its maximum height is limited to 300µm [START_REF] Campo | SU-8: a photoresist for high-aspect-ratio and 3D submicron lithography[END_REF] with a single spin coating. Moreover as the mold is made through the exposure of the resist to light through a 2D mask, the designed shapes are mainly limited to an extrusion of a 2D pattern. There are techniques to achieve more complex 3D shapes, for example different channel heights in lithography [START_REF] Campo | SU-8: a photoresist for high-aspect-ratio and 3D submicron lithography[END_REF] by multiple masks, mask inclination or specific developments. But each of these techniques requires a specific calibration and they are hardly compatible between each other. As lithography requires to give up on some of our specifications, such as different channel heights or slope designs, we decided to use another fabrication technique for the mold. For the same reason we chose PDMS as a material, we wanted to be able to test a new mold prototype quickly. Therefore we chose to use a micromilling machine. This machine can use mills from 50µm to 1mm and is controlled in position with a 0.5µm precision. To increase the longevity of the mill tip the mold is in Poly(methyl methacrylate) (PMMA) which is easier to mill than metal. The milling technique has the advantage to fully answer our specification list:

Z control

• 3D design is possible with some limitations due to the constraint of the mill footprint. It allows the design shown in Figure 2.5 a) b) and c).

• The maximum height of the chamber is important and is only limited by the mill size. For a perpendicular wall, our mill is limited to 1.5mm, due to the shape of the mill. However if the wall is inclined and follows the mill footprint, a depth of several centimeters is possible.

• Multi-scale design is possible by changing the mill size. When the mill is changed, the height sensor is used to calibrate the height of the different mills and guarantees the continuity in the machining process.

However the roughness of the milled surface is the main drawback of this technology. Indeed it leads to two major difficulties. Firstly, the rough surface degrades the optical transparency and thus creates difficulties to image the robot with good enough resolution. Secondly, bonding problems appear between the glass and the PDMS with roughness as the contact surface between the two materials decreases. To solve this problem the most straightforward approach is to optimize the milling process. In fact the roughness can be decreased with the following methods: small mill radius size, high rotation speed, low feed speed on the material, low height of the cut part, low ratio between the material feed to the mill and its radius as well as good lubricant condition. Except for lubrication such optimization increases the mill time of the chip. Therefore CHAPTER 2. SYSTEM we inspired ourselves from classical machining. We separated the milling process in different phases in order to find the best compromise between the time and the roughness as follows:

• Rough machining: removing material using a 500µm mill with 100µm vertical steps and 250µm horizontal steps. A 10µm thickness is left on the material compared to the final shape. The cut speed is 0.7mm • s -1 .

• Final machining: removing the final 10µm material using a 500µm mill with 125µm horizontal steps. The cut speed is 0.7mm • s -1 .

In some cases where high precision is incompatible with the 500µm mill footprint and where lower surface roughness is needed, a smaller mill can be used for the finishing operation. Changing the mill tip can be made thanks to the height sensor shown in Figure 2.6. This allows to recalibrate the height after changing the mill tip. The process is the following:

• Rough machining: removing material using 500µm mill with 100µm vertical steps and 50µm horizontal steps. A 10µm thickness is left on the material compared to the final shape. The cut speed is 0.5mm • s -1

• Final machining: removing the final 10µm material using a 200µm mill with 25µm horizontal steps. The cut speed is 0.5mm • s -1 . With this process the time to mill a 5cm × 2cm chip varies from 4 to 10 hours depending on the design and of the precision. To increase even more the surface quality the milling is performed in a cutting oil bath. The chip is cleaned afterwards by repeating alternatively rinsing in soap water on a sonic bath and isopropyl alcohol cleaning. Appendix A presents the user manual of the micromilling machine for mold production developed by the thesis author for communication purposes internal to the laboratory.

Despite the improvements to significantly reduce the roughness of the chip, it is not sufficient to allow the bonding of the PDMS on the glass with the classical protocol described before. Indeed too little surface contacts are established between the glass and the PDMS which does not provide a seal without leak. One solution could be to increase the pressure force during the ceiling of the chip to deform the PDMS and increase the surface contact with the glass. However the valve of our chip is designed to be closed with surface pressure. Hence this results in closing definitely this valve if too high pressure is applied during the bonding process. Therefore to solve this problem we adapted the PDMS fabrication protocol. Instead of curing the PDMS completely we now only wait the minimum possible time until the detachment of the PDMS from the mold is possible. This corresponds to a baking at 70 • C for 50 minutes in an oven with a curing agent proportion of 1 10 . This process results in more deformable PDMS that offers more contact with the glass during the bonding with some pressure. Then the chip is put in a 70 • C oven for at least 12 hours for the PDMS to finish curing. This increases even more the adhesion between the glass substrate and the PDMS.

High optical resolution, needed for example for tracking and RTS characterization, can be achieved by avoiding milling some parts of the mold to keep the original transparency of the PMMA substrate. In practice the top part of the mold is not milled in the process. Therefore the higher channel of the chip has an optimal optic quality.

Figure 2.7 sums up the different steps to fabricate a microfluidic chip with a new design. First we use Solidworks, a Computer Assist Design (CAD) software, to design the chip in 3D. Then this model is exported to another software (VisualCAM from Mecsoft) to generate the milling part. Here we can tune the different mill steps in order to get a satisfactory ratio between the precision and the machining time. After milling, PDMS is poured on the mold, and then placed in a vacuum chamber for 15 minutes before the reticulation in the oven to remove the bubbles inside the PDMS.

Figure 2.8 shows optical microscope pictures of the PDMS chip. In Figure 2.8 a) the top surface of the big chamber and the drop test chamber is molded on the original surface of the PMMA substrate which guarantees good optical properties. Indeed good image quality is essential to characterize the RTS. Figures 2.8 b) and c) show the microfluidic chip before and after bonding the PDMS to the glass. We can see that after bonding only few isolated areas remain unbonded without any effect on the sealing quality. Figure 2.8 d) shows the roughness precision of the milling machine. For a flat surface, the evolution of the surface is less than one micrometer. However when arriving on the side of a channel, the mill can only perform one cut along this channel. Therefore as the mill tip is not a straight cylinder because of fabrication defects and damages after several uses, making a channel with a perfect step profile is impossible. Fortunately Figure 2.8 c) shows that the pressure applied during the bonding is sufficient to deform these irregularities and bond them to the glass.

The reticulation and bonding of the chip is made as explained above to ensure good adherence. Just before the bonding, fluidic inlet and outlet are pierced with a cutting tool. Due to the footprint of the chip inside the magnetic setup, we make these connections on the side. As the chip is relatively thin (approximately 3 to 4mm) this guarantees a better holding of the fluid connection and thus prevents leaks at this location. Finally, a device to control the fluid valve state needs to be mounted on the chip. This device needs to apply some pressure on the round microchannel to close it. For this we use the part presented in Figure 2.9. This part is mounted on the glass substrate and can slide laterally to clean the optical pathway when the RTS goes through the open valve. Then it can be slid back and a 2mm diameter screw compresses the PDMS at the channel location. This part is made with a 3D printer so we can easily produce several of them for different chips or adapt the design to a special need.

Even if this design is rudimentary compared to a pressure controlled valves or an electric controlled valve it has the advantage to be bistable. This means that once it is in one position, it remains naturally in this position if no external command is applied. Therefore the channel can remain closed when the chip is disconnected and stored for a long period. Moreover this design does not perturb the magnetic field.

Microfluidic setup integration

Of course the microfluidic chip needs to be integrated with the rest of the setup and to interact with the other components. To guarantee the homogeneity of the magnetic field and optic view centered on the RTS, the chip is mounted on a stage controller (sutter instrument -MP285). This stage controller controls the three spaces direction with a 0.1µm resolution. It can be controlled manually or by a computer.

Finally the microfluidic chip has to be connected with a fluid inlet and outlet. Figure 2.10 shows the fluidic circuit which connects the microfluidic chip. A pressure controller pressurizes a hermetic bottle filled with isopropyl alcohol (IPA). A tube connects the IPA of this bottle to the inlet of the chip. As the outlet of the chip is connected to the ambient pressure, a flow is therefore created if P i > P Atm . The speed of the flow is proportional to this pressure difference.

In practice the pressure controller can create a maximum pressure of 1 bar with 1 millibar resolution. This pressure is set manually. The output valve can be closed to raise the pressure inside the chip. In this case, as there is no outgoing flow, the pressure displayed on the pressure controller is equal to the pressure inside the chip. This rise of pressure is used to remove gas bubbles in dead end channels. This ability to control the pressure is the main reason that led us to choose pressure driven flow instead of a syringe pump that directly controls the flow. When characterization or manipulation of the robot is performed inside the chip, the outlet valve is usually closed to prevent any residual flow.

Control Path

The rotation of the helical microrobot is provided by an external rotating homogeneous magnetic field. This section explains how we produce and control this magnetic field. Then we describe how the optical feedback of the RTS works as well as the tracking of its position. Finally, we present the automatic tracking used for the closed-loop control and its utility. More details about specific closed-loop controlled depending on the motions can be found in Chapter 3.2.2.

Ampli

Delivers current to the coils.

3D helmholtz coils

Transforms the current in an homogenous and constant rotating magnetic field in any direction of space.

Screen

Displays camera image and tracking result to user In manual control, a computer software reads, in real time, the command of the user through the keyboard. From this command, it produces an associated signal to generate a rotating magnetic field. This signal is then amplified and sent to three pairs of electromagnets. Note that this assumes that the coils behave linearly, which means that the magnetic field direction and amplitude can be reconstructed by adding the magnetic field generated by each coil pair. Moreover these electromagnets are designed to guarantee the Helmholtz conditions. Therefore the magnetic field is approximately homogeneous (i.e. with no gradient) at the center of setup, where the RTS is placed inside the microfluidic chip.

DAC card 1 kHz 3 Tension values 3 current intensities

A camera mounted on a microscope sends back the image of the robot to the software which displays it on the screen for the user. The software can also track the robot position on the screen and store it. This is especially used for automated speed acquisition during the RTS characterization. This tracking information can also be used to perform closed-loop position control and generate a command that replaces the user.

Magnetic field generation

Electromagnetic coils

There are several ways to generate magnetic fields to propel helical microrobots. The first and most simple one is to use a permanent magnet and to make the microrobot rotate [START_REF] Honda | Micro swimming mechanisms propelled by external magnetic fields[END_REF][START_REF] Xu | Modeling and swimming property characterizations of scaled-up helical microswimmers[END_REF]. This method is simple, has a small footprint and can generate an important magnetic field. However the permanent magnet solution becomes more complex when steering of the robot is required. It can be performed by adjusting the radial and axial position of the rotating magnet around the robot [START_REF] Fountain | Wireless control of magnetic helical microrobots using a rotating-permanent-magnet manipulator[END_REF]. But in practice some directions can be difficult or impossible to reach. Indeed the rotating magnet should access each point of a closed surface around the robot in order to control every direction. On top of that, the magnetic gradient generated by a single magnet can create a perturbing force. To reduce this perturbation two magnets can be used [START_REF] Alshafeei | Magnetic-Based Motion Control of a Helical Robot using Two Synchronized Rotating Dipole Fields[END_REF] to cancel the gradient at the microrobot location. But this brings even more footprint problems.

The second method is to propel the helical microrobot with electromagnetic coils [START_REF] Tottori | Magnetic helical micromachines: Fabrication, controlled swimming, and cargo transport[END_REF]. The minimal magnetic setup footprint cost to make a helical robot move is quite high compared to a permanent magnet. Indeed a minimum of two electromagnets is needed for 2D actuating and three are needed for 3D. If no magnetic gradient is required a total of three pairs of opposite electromagnets centered around the microrobot are needed.

However once these coils are in place every rotating direction is reachable with the same level of difficulty as the command is just linearly decomposed on the three electromagnets. Moreover it can guarantee an homogeneous magnetic field. And the electric cut-off of the electromagnet is higher than the one of the rotating permanent magnet by roughly one order of magnitude. As we wanted a system able to explore every configuration in 3D without constraint, we chose to produce the magnetic field with electromagnets. We made two of these setups to fit two different optics. Figure 2.12 shows the CAD design of the first electromagnetic setup (referred as setup 1). The design is similar for the two setups except for their dimensions and support. Both characteristics are displayed in Table 2.2. The size and therefore the maximum magnetic power intensity is the main difference between these two setups.

For the three directions the setup dimensions respect the Helmholtz conditions. This condition guarantees that two similar coils assimilable to single wires, separated from a distance equal to their radius and fed with current in the same direction will provide an approximately homogeneous magnetic field in their common center. In practice as our coils cannot be modeled as a single wire we perform numerical simulations to asset this homogeneity. According to these simulations, the intensity difference on a 2mm 3 square center in the middle is less than 0.1 %. This difference is small enough and no drift due to magnetic gradient is observable on the RTS. The support of the coils are made in Acrylonitrile Butadiene Styrene (ABS) with a 3D printer. The calculus sheet used to find good parameters for this magnetic coils setup is presented in Appendix B.

As it can be seen from the coils picture in Figure 2.12, the microfluidic chip can be integrated from the side to the center of the electromagnet. The vertical axis is used for imaging the RTS.

The coil pairs are each fed in current by a linear amplifier (Maxon motor 4QDC). This linear amplifier controls the current sent into the coils. They are directly controlled by the three commands coming from the computer in order to create the desired homogeneous rotating magnetic field commanded by the user.

Calibration

Even if the pairs of coils are designed to provide the same field output with one command a tuning needs to be made. Indeed the manual design of the coils can lead to some errors. Therefore we measure the difference of magnetic field intensity on each coils pair for the same static command with a Gaussmeter (Hirst GM04). Then the command part can be corrected in the software command. For the setup 1, a frequency calibration is also performed. For more details, we refer to Section 2.3.1. The protocols associated with these characterizations are displayed in Appendix C.

Generating the Rotating Magnetic Field

On our setup, the three pairs of electromagnets allow us to control the components of the magnetic field in the three directions. To make the RTS rotate, we need to make the direction of the magnetic field rotate in a plane perpendicular to the wanted RTS direction. For doing this we need to decompose this rotation signal in the basis defined by our three pairs of coils. This will give us the command needed for each coils to create the rotating field in this given plane.

For this frame change, we use the same parameters as the ones we use to define the orientation of the robot (see Chapter 3.1.1). Indeed normally the direction of the RTS follows the axis of rotation of the magnetic field. As is it displayed in Figure 2.13 the yaw and pitch angles are The frame "coils" is associated with the three different electromagnet pairs. The angles θ and ψ represent the difference between these two frames.

used to represent the RTS orientation in space. We call this frame the "RTS frame" as we assume here that the RTS is immediately aligned perpendicularly with the field direction. By using these angles we can deduce the components of a rotating plane in the frame defined by our electromagnets directions.

For this let us assume that we want a rotating magnetic field defined by the RTS direction to make it rotate around this direction. Therefore in the RTS frame we obtain:

B = B   0 cos(2πωt) sin(2πωt)   RTS , (2.1)
where ω is the rotation frequency of the field, t the time and the B the field power. By representing the RTS orientation by θ for the yaw angle and ψ for the pitch, this field is expressed in the frame associated with the setup coils by:

B = B   sin(2πωt) sin(ψ) cos(θ) -cos(2πωt) sin(θ) sin(2πωt) sin(ψ) sin(θ) -cos(2πωt) cos(θ) sin(2πωt) cos(ψ)   coils . (2.2)
Therefore by sending these three commands to our coils we can reconstruct a rotating magnetic field making the RTS rotate in the direction defined by θ and ψ.

Control software

The control software needs to answer several specifications:

• The user should be able to fully control the magnetic field orientation and frequency in real time. Reading the frequency and updating the command needs to be fast enough so that no delay is perceived by the user.

• The command output frequency needs to be high enough to allow the construction of a 200Hz sinusoidal signal.

• Tracking in real time needs to be possible and fast enough, so that no delay is perceived by the user. For the user command inputs we chose to simply use the computer keyboard instead of a more intuitive controller like a joystick. The motivation comes from the great flexibility and choice of controls offered by keyboards. Indeed we find that the ability to quickly add a key in order to control a new unstudied parameter is very important for prospective experiments. Moreover it also allows to simplify the hardware requirements and thus facilitates the duplication of a full experimental setup. Thank to this the software is running in three different experimental setups at the current time.

Main loop

Figure 2.14 shows the organization of the program. To ensure the needed high frequency output as well as performing time-consuming tasks, we chose to work with two threads. The main one has a frequency around 10Hz and is used for: reading keyboard inputs, calculating the new command parameters, displaying the image and tracking the RTS. Each main program loop turn the updated command parameters which define the direction and frequency of the rotating plane, are sent to the second thread in an asynchronous way. This second thread generates the time dependency in order to generate the signal. At each turn, it calculates the new static command to send to the electromagnetic coils to create the rotating magnetic field. According to the Shannon criterion it is useless to command a rotating frequency above 500Hz. In practice the cut-off of the current amplification coupled with the electromagnet does not allow frequencies above 250Hz. To output the direct analog signal from the computer we use a commercially available S626 direct analog converter card from the company sensoray. To easily benefit from third party libraries and to allow high performance we chose to write this software in C++. A user manual of this software written for communication inside the laboratory in presented in Appendix D.

Feedback path

Optical microscopes

Even if optical imaging is the most simple way to get feedback from a microrobot it is generally not fit for medical applications. Exceptions exist for very particular cases like in eye surgery [START_REF] Yesin | Guidance of magnetic intraocular microrobots by active defocused tracking[END_REF] where the inside of the eye is a transparent medium. Therefore other ways have been discussed to get feedback in-vivo from microrobots. This concerns Magnetic Resonance Imaging (MRI), X-ray scan, and magnetic detection. However these techniques are often limited in resolution: around 1mm for MRI [START_REF] Schick | Whole-body MRI at high field: Technical limits and clinical potential[END_REF], and 0.2mm for X-ray [START_REF] Duryea | Semiautomated three-dimensional segmentation software to quantify carpal bone volume changes on wrist CT scans for arthritis assessment[END_REF]. MRI can also suffer from a low signal-tonoise ratio in detecting magnetic components. Compared to these methods, ultrasound detection has the advantage of being less expensive and safe for the patient while being an already mature technology. The frame rate is interesting as it can reach 100Hz [START_REF] Yen | High-frequency high frame rate ultrasound imaging system for small animal imaging with linear arrays[END_REF]. However the signal-to-noise ratio is also quite low and the maximum resolution is limited to 0.5mm [START_REF] Vilkomerson | A system for ultrasonic beacon-guidance of catheters and other minimally-invasive medical devices[END_REF].

Therefore as our study is in transparent media and we want high resolution to understand the physical mechanisms, the optical imaging gives the best possible feedback. Indeed these other technologies will become really interesting when medical applications with helical microrobots will become more mature. Prior to this, a good understanding of the robot physics and control is needed and optical imaging is undoubtedly the best fit for this need as it allows sub-micrometer resolution at high a frame rate.

As mentioned in Section 2.2.1 two magnetic setups were conceived. The ratio between the field power and the optics quality is the main reason for this choice. For the setup 1, the optics is an assembly of optical parts from the company navitar (1-6010,1-6030,1-60123A). The main advantage is to allow a high working distance of 95mm allowing more space for the coils. A tunable zoom can change the magnification of this device from 15 to 60 times which is useful as we can use large zooms to a have good measurement precision and small zooms to navigate the RTS on long distances. With the highest zoom, the precision of the image is around 2 micrometers.

For the setup 2, the optics consists of an inverted microscope (Zeiss axiovert 200), the objective allows a magnification of 20 times with a working distance of 2.6mm. The maximum resolution is better than the setup 1 and is around a 250 nm.

Realtime video tracking and closed-loop control

Realtime video tracking is essential to allow closed-loop automation of the RTS control. It is also a key feature to enable reproducible sensing measurements as well as to develop assisted control of the robot that relies less on the user skills. More practically, tracking is also an essential tool to record automatically a series of measurements and directly compute the RTS speed. This feature was a major requirement in order to repeat motion characterizations on several directions and on several robots to assure statistically credible data.

To acquire the video a camera (Allied-Pike F-032B) is mounted on the optic. This camera is connected to the computer running the control software. On this software, we use the third party library called Visp developed by INRIA (http://visp.inria.fr/). This library allows to acquire the video and to track the RTS. For this we use the function VpDot that tracks the connected pixel with close grey levels in a series of frames. The result of the tracking gives us the mean position of the microrobot as well as its orientation (yaw angle) if it is not standing vertically.

These data are then stored in a folder for offline post-analysis along with all the command parameters. They can also be sent to the closed-loop function of the program. In this function the pitch angle is assumed to be identical to the one set in the command part. Depending on the motions the closed-loop control works differently. We refer to Chapter 3.2.2 and Chapter 5.3 for more details on closed-loop on surface and the 3D motion respectively. As previously mentioned two setups were realized for this thesis. Our first experiences have been performed on a first setup (setup 1) but the need of a higher image quality led us to develop a second setup (setup 2). However the second setup uses an inverted microscope with a much higher footprint than the first setup and therefore has a less powerful magnetic field and a smaller working region that prevents to perform the detachment and the integration protocol of the RTS inside the chip on this setup. The second setup is principally made for fine characterization of the RTS and particular efforts were brought to temperature control. Therefore, the selective integration of the RTS inside the microfluidic chip is done with the first CHAPTER 2. SYSTEM setup. Then the microfluidic chip is moved on the second setup to perform the characterization of the RTS. A schematic side view of these two setups is drawn in Figure 2.16.

Differences between the two setups

Table 2.3 -Differences between the two setups

Robot detachment

The setup 1 is particularly adapted for the selective integration of the RTS inside the microfluidic chip. Firstly, as it can be seen in Figure 2.17, it is possible to move the electromagnetic coils and the optic separately. Therefore we can easily remove the coils to access the chip with a micromanipulator tip in order to detach the RTS from its substrate as shown in Figure 2.4. While doing this, imaging of the microfluidic chip with the optics is necessary to see the position of the robot and the tip. It could be possible to design a bigger coils to allow the access of the manipulator from the side without moving the electromagnet. However we believe from our experience that removing the coils makes the approach of the micromanipulator tip much simpler and safer for this delicate equipment.

To allow the integration of the RTS, an important feature is the possibility to switch between front light and back light. As the robot is not transparent, back light imaging procures a better image quality and is essential for the calibration and tracking of the RTS. This light is provided by a LED system on the magnetic setup supporting base and the light intensity is controlled by an Arduino board. However the fabrication substrate of the RTS is opaque and makes back light impossible to use during its detachment and moving on the fabrication substrate because the back light is blocked by the metal deposited by PVD on the fabrication substrate. Therefore in this case we need a front light. This light is generated by a MI-150 light generator from the company Edmund optics. Then a optical fibber guides it to the optics tube. In the optics tube a mirror sends this light into the imaging plane. As shown in Table 2.2 the setup 1 is designed to provide the same power in each direction. This setup is especially used to study motions where the pitch angle has an important influence. As this angle is not measured in the image but directly set by the command, a precise tuning of the coils is important.

Precise pitch control

First the magnetic power in each pair of coils is measured with a static input command with the help of a Gauss meter. At this step, small imperfections in the coils or in the amplifier can be adjusted for the coils to deliver the same magnetic field with the same static command. Then we need to guarantee that at a given frequency each coil will deliver the same power for the same sinusoidal command. For this we use an ampere metric clamp measuring the evolution of the current in the coils and therefore the amplitude of the magnetic field. Figure 2.18 a) displays this measurement. With this measurement, a correction depending on the frequency is generated by the software. The protocols associated with this tuning are displayed in Appendix C.

For this correction, two choices are possible. Firstly, we can choose to apply an amplitude correction to make the field output constant in a frequency range. This could be interesting if we wanted to measure the cut-off phenomenon of the robot which is the frequency from which the rotation of the RTS cannot follow the rotation of the field. This phenomenon happens when the frequency is raised until the magnetic torque produced by the magnetic field is not sufficient to counterbalance the drag of the fluid. Secondly, we can choose to apply a correction that allows the maximum possible magnetic intensity.

As the cut-off frequency is not studied in this work, we chose to apply the correction that gives the maximum power for a given frequency in order to enhance the RTS stability. Indeed when the power decreases the RTS is more inclined to start wobbling and changing its magnetization direction with a brutal orientation change. Figure 2.18 b) displays the result of this correction.

Setup 2: high resolution and temperature control

As it was explained in Section 2.2.3 the main reason for the creation of the second setup was to increase the image quality. Having a good resolution is essential for determining the propulsion parameters of the RTS as explained in Chapter 4. A better resolution is also important to observe physical phenomena and propose hypotheses relative to the microrobot physics. This is a fundamental step to the design of new experiments. For example, the high image resolution reveals that gas bubbles have the tendency to stick to our RTS. The optical resolution was essential to understand that high stiction problems of the robot on the surface were due to these bubbles. This conclusion would have been much harder with the use of the first setup only. The characterization of the RTS is determined with the help of the setup 2 and it requires a precise control of the fluid viscosity. The viscosity is strongly dependent on the temperature. Therefore to limit the viscosity variation below 1%, the temperature has to be controlled with a precision of 0.2 • C [START_REF] Sovilj | Kinematic Viscosities of Binary and Ternary Liquid Mixtures Involving Chloroform, 2-Propanol, and 2-Butanol at Several Temperatures[END_REF]. To avoid convection flow it is also essential to limit temperature gradient. The major problem to control this temperature is that the electromagnets are heating due to their current resistance. Indeed, their temperature can reach up to around 80 • C.

To guarantee a constant temperature inside the chip we use two different cooling systems. As it can be seen in Figure 2.19 a fan is set on the side of the coils. The purpose of this fan is to help the coils to cool as well as to bring fresh air in the surroundings of the chip cover. However as we want the temperature to be totally independent of the coils temperatures a second cooling system is designed. Its goal is to isolate the air heated by the coils from the air surrounding the chip. For this ambient temperature air blows from the compressed air network of the laboratory around the microfluidic chip. A wind channel around the chip guides this air from one side of the chip to the other and covers all its length.

To measure the temperature inside the chip the inlet temperature of the second cooling system is measured with a thermocouple. To guarantee that this temperature is equal to to the temperature inside the microfluidic chip we performed measurement with a microfluidic chip with no liquid and equipped with a thermocouple inside the microfluidic chamber. Figure 2.20 shows the result of this experiment and guarantees that the two temperatures are equal up to a 0.2 • C maximum error. When the system is turned on (t = 0 minute) we can see a temperature decrease due to the difference between the air at ambient temperature and the cooling air coming from the pressurized air network. After two minutes there is no significant difference between the temperature measurement of the outlet and the one inside the chip as the difference reaches the precision of the thermocouples of 0.1 • C. We can also notice that there is no temperature evolution. In practice for characterization experiments, we wait for a minimum of four minutes from the start of the cooling system to be sure that the equilibrium is reached.

As there is no front-light system and limited free space, the detachment of the RTS from its fabrication substrate is impossible on the setup 2. Therefore the RTS is detached and in- tegrated in the chip on the setup 1. Then the chip can be mounted on the setup 2 for further characterization of the RTS.

Conclusion

The goal of this thesis is to develop an on-chip untethered force sensor. This chapter has presented the different system requirements that will allow us to assess the potentiality of helical microrobots driven by a homogeneous magnetic field for this task.

First we present how 3D lithography is used to realize the 3D shape of the helical microrobot and how the PVD process deposes a nickel layer on the robot to make it ferromagnetic. We also present how a micro-milling machine is used to make a PMMA mold for the microfluidic chip and how we use this mold to fabricate microfluidic by pouring PDMS inside. These microfluidic chips are closed by bonding them on a glass.

Then we explain how we use threes pairs of electromagnets to generate a homogeneous magnetic field. We presented the equation for the command of each of the coils pair leading to the creation of a rotating magnetic field. This command can be adapted to any of the rotating field direction and therefore to any RTS direction. To generate this rotating magnetic field as well as to track the robot position and allow the user to command the robots we wrote a C++ program. The image of the robot is sent in real time to this software by a camera connected to an optic. Two different setups with different pairs of coils and optics were presented. The first setup focuses on the robot detachment, the integration on the chip and the surface motion analysis and the second setup focuses on the precise robot characterization presented in Chapter 4. This second setup is controlled in temperature to limit convection and to fix the density and viscosity value of the fluid.

The common point between all these technical solutions is the great versatility of design. Of course we pay the price of this versatility on the performance of our system. The non-homogeneity of the robot surface forces us to work in isopropyl alcohol. The high chip surface roughness makes channels sticky. The plastic parts of the setups do not resist well to high temperature and their low Young modulus forces us to build large structures. However in this work we chose the rapid prototyping because we are still at an early stage of development. Therefore the current need is to study the physics and control strategies of these helical microrobots which need a fabrication method easily adaptable to new challenges and to investigate potential experiments or applications.

Concretely, thanks to this prototyping technologies, we have used around 10 different designs of helical microrobots (by varying the head, the pitch, size and direction of the helix) and 18 different designs of microfludic chips. Three different control setups were built, the first one is not presented here because it was only used for prospective experiments at the beginning of this thesis. We believe that such different tests were only possible in the period of this thesis thanks to these technological choices.

Chapter 3

Robot Motions and Microfluidic Chip Integration

To develop a force sensing tool inside a microfluidic chip, the first requirement is to integrate this tool (here the RTS) inside the chip. Using such platform also simplifies the development of the RTS because if offers good experimental conditions. For example it reduces parasite flows and allows to control physical parameters (temperature, wall proximity, etc). This control of the environment is essential to perform quantitative measurements on the RTS in order to tune the force sensor as we present in Chapter 4.

Force Microfluidic chip

Characterization and physical measurement

On-chip force sensor applications Long time storage In Section 1.5.2, we developed on several existing methods to integrate a microrobot inside a microfluidic chip. We explained that the RTS is too small to be integrated by hand during the chip fabrication and contained inside the chip during liquid filling. We also presented its lack of power to detach itself from the fabrication surface. Therefore we decided to develop a new solution where the microrobot uses its own mobility to integrate itself inside the microfluidic chip. We also chose this solution because it offers a selective way, i.e. a way to embed one robot at a time inside the chip. For this solution to work, the microfluidic chip needs to offer an open chamber where the fabrication substrate of RTS can be manually put and where a tethered probe can selectively detach one RTS. Moreover the RTS needs to be robust and have enough accessibility to move by itself from this open chamber to the inside of the microfluidic chip.

To address this requirement, we decided to use multiple ways of moving the RTS. Indeed by moving the orientation of the rotating magnetic field and depending on the surrounding conditions, the RTS does not move by using the same mechanism. In fact, three types of motions 56 CHAPTER 3. ROBOT MOTIONS AND MICROFLUIDIC CHIP INTEGRATION are possible: two of them propel the RTS by using its interaction with the surface and the third one propels it in 3D inside the fluid. Having both 3D and surface motions as well as being able to switch easily between them increases the mobility of the RTS inside the microfluidic chip. Indeed some parts of the chip can be accessible with only one type of motion. Therefore if the microrobot cannot perform this motion, for example because of its design or of the experimental setup, it will not be able to reach such parts of the chip. This is illustrated in Figure 3.2 a) where the only available motion is a surface motion and therefore the robot is blocked by an impassable obstacle. Hence some places become reachable only by using a combination of these motions. The multi-modularity in terms of motion also improves the robustness of the RTS. For example, in Figure 3.2 b), if the microrobot can only swim, it can be carried away when facing a relatively important flow or stuck when it touches the surface. With a microrobot also offering surface motion, switching to another motion remains a possible alternative if the environmental conditions restrain the use of the current motion. Therefore the RTS will suffer less from the drawbacks of a particular motion and the robustness will be higher. This chapter focuses first on the different motions of the RTS. After a short introduction on each of the three moving ways, we compare them to see their individual strengths and weaknesses and explain their complementarity. This study is essential to understand the gain in accessibility and robustness offered by the multiple motions ability. This ability does not only allow the self-integration of the RTS inside a microfluidic chip, it also allows special moves, for example surface motion against gravity and cargo transport of micro-particles, which we will also present in this chapter.

As the spintop motion was not presented in other works, the second part of this chapter presents in more detail its specificity. Firstly, we present a model that helps to understand its underlying physics. Secondly we demonstrate that this motion is well suited for a closed-loop control.

The third part of this chapter develops the integration of the RTS inside the microfluidic chip. On top of being one of the goals aimed by this thesis, this is also used to demonstrate the robustness of the RTS. As mentioned earlier, the microfluidic chip design needs to be adapted to allow this integration process. We first present these adaptations. Then the protocol and results of one integration process are shown as well as the ability of the RTS to exit the microfluidic chip. This work has been the subject of a publication [START_REF] Barbot | On-chip Microfluidic Multimodal Swimmer toward 3D Navigation[END_REF].

Finally, the possibility of RTS long-term storage inside the chip is analyzed. The different problems posed by this storage are presented and a solution to store the robot on a dried chip is proposed. The impact of this storage on the robot is finally investigated experimentally. This storage method has been presented at the Micro and Nano Engineering conference (MNE) in 2015 [START_REF] Barbot | On-chip glass microfluidic trap and storage of helical magnetic microrobot[END_REF].

Characterization of the different robot motions RTS actuation principle

For all motions of the RTS, the propelling force comes from the rotation of the microrobot. This rotation is in the direction of the helical axis of the RTS. In Chapter 2 we presented the magnetic setup and showed how a homogeneous rotating magnetic field is produced in the RTS environment. This rotating magnetic field makes the RTS rotate because its surface is coated with a nickel layer using PVD process.

Let us consider the magnetic field B. Under this field, the nickel layer of the RTS is magnetized and can be considered as a magnetic dipole with a corresponding magnetization µ r . This dipole will interact with the external magnetic field by creating a moment τ and a force F on the RTS which are given by the following formulas:

τ = µ r × B (3.1) F = ∇(µ r • B), (3.2)
where τ and F are respectively the torque and the force applied to the microrobot by the magnetic field.

As the magnetic field setup is designed to provide an homogeneous magnetic field, we can consider that the magnetic field amplitude does not vary with space as well as the RTS magnetization created by this magnetic field. Therefore the direct magnetic force on the RTS given by the equation 3.2, can be considered to be zero.

The torque is given by the equation 3.1. It explains why the RTS direction can be controlled via the magnetic field direction and why the RTS rotates with the magnetic field. To demonstrate this, we need to make the hypothesis that the RTS magnetizes in a perpendicular direction to its axis. This hypothesis on the RTS magnetization direction is validated experimentally only if the frequency is above a certain limit. We will discuss later the case where this hypothesis is not verified in practice. µ r is the magnetization, B the magnetic field and β is the angle between the rotation axis of the robot and the rotation angle of magnetic field. α is the angle between µ r and the projection on r ⊥1 .

To understand the total resulting torques we decompose B and µ r on the frame defined by the following three axes:

• r : the RTS longitudinal axis.

• r ⊥1 : the axis perpendicular to the RTS longitudinal axis included in the plane defined by the RTS longitudinal axis and the magnetic field direction.

• r ⊥2 = r × r ⊥1 .

This decomposition is valid at a given time and so for a given position of the magnetic field vector. So the axes r ⊥1 and r ⊥2 rotate synchronously with the rotation of the magnetic field.

The decomposition is therefore the following:

• B (the external magnetic field) decomposed into B on the r axis, and on B ⊥ on the r ⊥1 axis.

• µ r (the RTS magnetization) decomposed into µ ra on the r axis, and into µ rm on the r ⊥2 axis.

Thus the equation 3.1 becomes:

τ = (µ ra + µ rm ) × (B + B ⊥ ). (3.3)
Distributing the cross product leads to consider four vector products:

µ ra × B ⊥ = 0
Null because these vectors are aligned.

(3.4)

µ ra × B = µ r B cos(α) sin(β)
Aligns the RTS with the field.

(3.5)

µ rm × B ⊥ = µ r B sin(α) cos(β)
Creates the rotation of the RTS.

(3.6)

µ rm × B = µ r B sin(α) sin(β)
Tends to misalign the RTS along its normal axis. (

The angle α corresponds to the phase shift between the rotating field and the rotation of the RTS. Equation 3.6 shows that if this phase shift increases the torque also increases. However if the torque needed to sustain the rotation is higher than the maximum value obtain for α = π 2 then the rotation cannot be sustained. This phenomenon is called the cut-off, it is similar to the cut-off torque in any electrical motor. Equation 3.5 shows that a stable rotation is created around the value β = 0. This stability corresponds to the value for which the RTS is aligned with the rotation axis of the field. Therefore by controlling this direction with the setup presented in Chapter 2.2 we can control the orientation of the RTS.

However the equation 3.7 reveals that a misalignment torque is present. Eventually this torque can overcome the alignment torque and unsettle the RTS. This misalignment torque is increasing with α. Therefore the closer to π 2 the phase shift between the magnetic field and the magnetization will be, the less stable the RTS will be. Experimentally this is particularly noticeable when the fluid torque on the RTS is important compared to the magnetic torque. This happens either at low power or high frequency. In this case a brutal change of the RTS direction is impossible without destabilizing the RTS. Instability can also be triggered by surface perturbations.

But the magnetization is not the only parameter that plays a role in the stability of the RTS rotation. Indeed the force applied by the surrounding fluid on the RTS needs to be considered. On any helical shape in a viscous fluid, the average force on one rotation along the helical axis only has a component on this axis, which is called the thrust. However at a particular instant the distribution of the force creates a torque along the normal axis of the helix. This is called the wobbling regime and it has been theorized for microhelical swimmers with a magnetic head [START_REF] Man | The wobbling-to-swimming transition of rotated helices[END_REF]. But it can be even more important on ferromagnetic microrobots as the wobbling tends to change the magnetization on a longitudinal axis. In this case the pure longitudinal magnetization hypothesis is not verified and the control of the RTS is nearly impossible. This phenomenon is present at low frequency and tends to disappear when the frequency increases. In practice it forbids us to use low frequencies to actuate the RTS. It is therefore impossible to move it at small speed, which makes a precise control of the RTS difficult. We will see in the following how the spintop motion can be a solution to reach low speed with a surface motion.

Presentation of the different motions

Swimming motion

At the RTS scale, a low Reynolds regime of the flow is guaranteed. Indeed all the experiments were carried out using isopropyl alcohol at 21 • C. The maximum speed for the robots stays below 300µm • s -1 . It corresponds to a Reynolds number inferior to 2 • 10 -2 . This means that the inertia of the flow is negligible compared to motion due to viscosity. Therefore the Navier-Stokes equation that models fluid mechanics can be simplified into the following Stokes equation:

ν∇ 2 u -∇P + f = 0, (3.8)
where ν is the dynamic viscosity, u is the speed of the flow, P the pressure and f the external volume force. Here the compressibility of the fluid is neglected. This equation has the particularity of being linear and time-independent. This implies the time reversibility of the equation. In practice it means that a body immersed in this fluid and performing a cyclic movement will not be able to generate any thrust. This is named the scallop theorem [START_REF] Hess | Clinically meaningful blood pressure reductions with low intensity isometric handgrip exercise. A randomized trial[END_REF] as a scallop can only move in high Reynolds number conditions. Indeed a scallop uses the non-linearity of the flow to create a propulsive force by opening slowly its two shells and closing them quickly. This opening and closing results in different flow structures and the sum of their force on the scallop is non-zero which creates a propulsive force. However in a low Reynolds environment, the flow structure is linear and the action of the opening shell is exactly counterbalanced by the closing, regardless of the speed. So to avoid suffering from this effect, a common way of moving for micro-organisms is to use a rotating flagellum that works in a similar way than the helix propeller of a boat. Helical microrobots were inspired by this and use the rotation provided by the magnetic field to generate thrust.

Millimeter scale robots were first used to prove the possibility of this motion [START_REF] Honda | Micro swimming mechanisms propelled by external magnetic fields[END_REF]. Later the 3D navigation was demonstrated by overcoming the gravity effect with the generated thrust [START_REF] Mahoney | Velocity Control with Gravity Compensation for Magnetic Helical Microswimmers[END_REF]. The closed-loop control with visual feedback was also studied at this scale [START_REF] Xu | Propulsion Characteristics and Visual Servo Control of Scaled-up Helical Microswimmers[END_REF]. The miniaturization has been explored and 3D helical microrobots have been fabricated and controlled in their motion with high precision [START_REF] Tottori | Magnetic helical micromachines: Fabrication, controlled swimming, and cargo transport[END_REF][START_REF] Hwang | Electro-osmotic propulsion of helical nanobelt swimmers[END_REF]. Further miniaturization was achieved to demonstrate their actuation in complex viscoelastic media [START_REF] Schamel | Nanopropellers and their actuation in complex viscoelastic media[END_REF]. As such robots can evolve in 3D, we will refer during this thesis to this motion which evolve surrounding by fluid, as the "swim" motion.

Nevertheless let us mention that a reciprocal motion at low Reynolds number was proved recently in a non-Newtonian fluid [START_REF] Qiu | Swimming by reciprocal motion at low Reynolds number[END_REF] thanks to a flow speed dependency involved in the viscosity coefficient which brings non-linearity. However this mode of motion is for now relatively slow and will not of interest in this work.

Rolling motion

Another way to move is to make the RTS capable of interacting with the surface. Pietro Tierno et al. have proved that the friction gradient caused by a surface is sufficient to propel a microscale object close to it [START_REF] Tierno | Controlled swimming in confined fluids of magnetically actuated colloidal rotors[END_REF] with a rotating magnetic field. This field makes the particle tumble and therefore move. This motion has been studied for micro-and nanoparticles [START_REF] Courcier | Tumbling motion yielding fast displacements of synthetic antiferromagnetic nanoparticles for biological applications[END_REF][START_REF] Morimoto | Tumbling motion of magnetic particles on a magnetic substrate induced by a rotational magnetic field[END_REF] and controlled for the nanowires locomotion where it is shown to be robust to surface irregularities and capable of cargo transport [START_REF] Zhang | Controlled propulsion and cargo transport of rotating nickel nanowires near a patterned solid surface[END_REF]. The friction with a surface can directly be used for propulsion by making the robot roll on it. As tumbling motion, rolling uses the proximity of the surface to move. The difference is that the rotation is made around the longitudinal axis of the robot and not around its normal axis. This motion has been demonstrated with a square section robot [START_REF] Tung | Noncontact manipulation using a transversely magnetized rolling robot[END_REF], by showing its ability to trap particles with a fluid vortex created above the robot.

Spintop motion

This motion is similar to rolling but only one extremity of the RTS is touching the surface instead of all its length. In the spintop motion the speed is affected both by the frequency of the magnetic field and the pitch angle. If the pitch angle is π 2 , which means the robot is rotating perpendicularly to a horizontal surface, the speed is zero. If the pitch angle decreases, a rotating component parallel to the surface appears and propels the RTS. This way of moving has been 60 CHAPTER 3. ROBOT MOTIONS AND MICROFLUIDIC CHIP INTEGRATION described on rotating spheres [START_REF] Ye | Micro-manipulation using rotational fluid flows induced by remote magnetic micro-manipulators[END_REF]. The difference here is that the helical tail of the robot either pushes or pulls the RTS on the surface, depending on the rotation direction. This influences the friction between the surface and the RTS and therefore impacts the motion. In Section 3.2, we propose an empirical model to describe this phenomenon. For each motion, Figure 3.4 explains the force equilibrium, speed characterization and its main advantages. For the three motions, the magnetization is considered on the normal axis of the RTS, therefore the rotation is around its main axis. The inertia of the RTS and the flow are small, so the acceleration time between two different directions or movements is negligible. This is why we only consider cases where the sum of the forces applied on the RTS are zero i.e. where the acceleration is null. For each characterization the average speed on the four sides of a 200µm square trajectory was calculated from the measurements on each side. This reduces the perturbation induced by slightly tilted surfaces or parasite flows, because an effect in one direction balances the effect in the opposite direction. The error bars represent the standard deviation between the measurements on each side of the square trajectory. The points on the curves represent the mean values of the average speeds on each of these sides.

Characterization and comparison of the motions

While rolling, the RTS is in contact with the surface on all its length as illustrated in Figure 3.4 a). The RTS rotation creates a friction force with the surface that propels it. But depending on the surface friction, the robot can slide on the surface. Indeed, it advances less than its section perimeter per each rotation. Figure 3.4 d) shows the speed evolution versus the frequency of the magnetic field. Between 20Hz and 140Hz the surface friction increases proportionally with the magnetic field rotation. So the speed evolves in a linear way. Below 20Hz the robot rotation starts to change due to the wobbling effect which leads to an increase of the speed at low frequency. Therefore a precise control of the robot is difficult at slow speed. Through a manual control, a control precision of about 20µm is achievable. Above 140Hz the viscous drag is higher than the magnetic torque. This leads to a cut-off behavior. In rolling motion, the RTS stays close to the surface. This has the advantage of being less influenced by the flow compared to the other motions. Figure 3.4 g) shows that rolling motion can move the RTS in an upstream flow. This is the main advantage of the rolling motion.

In spintop, the length of RTS is not parallel to the surface any more. The RTS touches the surface with the extremity of one head while spinning around its axis. If the RTS is perpendicular to the surface, it is not moving. However, if the pitch angle is smaller than π 2 radians, the RTS starts to make a translational motion as shown in Figure 3.4 b). The Figure 3.4 e) displays the evolution of the speed with the pitch angle. The local surface interaction which varies for every experiment leads to an important standard deviation. Between π 2 and 0.75π 2 the speed decreases linearly to zero. This is achieved at a constant frequency (40Hz ) where there is no wobbling. Therefore in spintop motion the speed control can be made only with the pitch angle. This is a key advantage compared to the rolling motion because it makes the RTS manoeuvrable at low speed while maintaining a high frequency to avoid wobbling. Thanks to this, it is easier to implement a closed-loop control (Figure 3.4 h). It is carried out with a simple PID controller (Proportional Integral Derivative controller) that controls the speed through the pitch angle. With the closed-loop control of the spintop motion, the static accuracy is below 2µm. More details on this closed-loop is presented in Section 3.2.2.

In the swimming motion, the RTS is not in contact with any surface. The rotation of the robot provides a corkscrew force from the helical part. This propelling force both compensates the gravity and propels the robot as explained in Figure 3.4 c). Just as rolling, wobbling happens at low frequency. As the surface contact tends to suppress small wobbling, the frequency must be above 40Hz to avoid this phenomenon in swimming mode, as shown in Figure 3.4 f) by the increase of the standard deviation of the measurements, which reveals wobbling below this frequency. The speed increases linearly with the magnetic field rotation frequency until 120Hz. A cut-off behavior appears above this frequency. The great advantage of this mode is that it allows 3D control. On top of that, the RTS can reach any surface in the microfluidic chip.

To recapitulate, each of the three motions improves the RTS capability. Swimming allows to reach any place in 3D and allows to move independently from the surface condition. Rolling motion allows to move against flow speed which is essential to move forward into an upstream flow and to be more robust to potential parasite flows. Finally spintop allows a great precision and an automatic control as well as a single contact point with the surface. The transition from one motion to another is easy. The person controlling the RTS just has to change the direction of the external magnetic field. In this work, these complementary advantages were essential for a successful selective integration of the robot inside the microfluidic chip. The supplementary information video 2 of the paper presenting the integration of the RTS [START_REF] Barbot | On-chip Microfluidic Multimodal Swimmer toward 3D Navigation[END_REF] shows the switch between these different motions.

Achieving special tasks by combining motions

On top of the microfluidic chip integration, the multiple motions of the RTS allow other on-chip applications. Figure 3.4 shows three different examples of RTS maneuvers requiring multiple motions.

In Figure 3.5, part a) shows a combination of swimming and spintop motions. First, the RTS can reach any surface by using 3D swimming. Then the RTS can displace itself using spintop motion on this surface even if the gravity force tends to detach it from it. In fact, the upward propelling force applied by the corkscrew tail counterbalances the gravity and provides enough friction for the spintop motion to work properly on the chip ceiling. Figure 3.5 b) shows that a closed-loop control similar to the one carried out on the bottom surface can be performed on the top surface of the chip. The performance of the closed-loop control on this path is similar even if the ceiling of the chip is in PDMS and not in glass. The supplementary information video 4 of the paper presenting the integration of the RTS [START_REF] Barbot | On-chip Microfluidic Multimodal Swimmer toward 3D Navigation[END_REF] shows a record of these motion combinations.

Finally, Figure 3.5 c) explains how the RTS combines spintop and swimming motions for cargo transport. This micromanipulation includes trapping, moving and releasing the particle inside the closed microfluidic channel. Figure 3.5 c) shows a schematic of these different steps. Spintop motion creates a flow vortex around the RTS. This vortex can trap adjacent particles up to 30µm. Then when the RTS moves, the particles remain trapped and follow the robot by orbiting on a streamline around it. To release the particle, the RTS switches to swimming. It moves up and the particles stay on the floor of the chip at a desired location due to the gravity force. The precision of this deposition is of around 10µm. The supplementary information video 6 of the paper presenting the integration of the RTS [START_REF] Barbot | On-chip Microfluidic Multimodal Swimmer toward 3D Navigation[END_REF] shows a record of these particles manipulation.

The spintop motion Model

As previously mentioned, the "spintop" motion was not reported in the literature for helical microrobots. The closest similar motion on rotating magnetic microspheres has been reported by Ye et. al [START_REF] Ye | Micro-manipulation using rotational fluid flows induced by remote magnetic micro-manipulators[END_REF]. They move magnetic microspheres by rolling them on the surface using a rotating magnetic field. In this case the rotating axis of the sphere is parallel to the surface and it corresponds to a pitch angle of 0 radian in our frame. They also report the possibility to spin the sphere around its location with a rotation axis perpendicular to the surface. It corresponds

THE SPINTOP MOTION

63

to a pitch angle of π 2 radians. They write that in practice, a pitch angle slightly smaller than π 2 creates a rolling component sufficient to move the sphere on the surface. Unfortunately no characterization curve presenting the speed versus the tilt angle was presented as it was not the main goal of this paper. The principle of the spintop motion for helical microrobots is similar to the displacement of these spheres. The two main differences are the following:

1. The corkscrew in the RTS design links linearly the frequency of rotation and the force applied by the RTS on the surface.

2. The RTS shape has no symmetry axis. Therefore the geometry of the problem evolves with the pitch angle whereas it stays the same for a sphere whose geometry remains unchanged by any rotation.

This second point is a drawback as it makes a theoretical modeling approach much more complex.

However the first point allows to vary the contact force between the surface and the robot, which is interesting and really makes the friction behavior of this motion particular. Indeed normally this force is equal to the difference between the weight and the buoyancy of the object. But in the case of the RTS, the helical shape leads to the creation of a propelling force, which can be controlled by the rotation frequency. For example, a "negative" force can be applied to sustain this motion on the top part of the chip against the gravity as shown in Figure 3.5 a) and b). Moreover this tunable force ability could be of great potential for measuring the surface adherence in closed environment via the measure of the RTS speed. But this potential cannot be used without prior knowledge on the physics of the spintop motion. Therefore we need to develop a model to help us to understand the underlying mechanism of the spintop motion. For this it is primordial to understand the interactions between the RTS, the liquid and the surface. However due to the multiple parameters involved and the relative ignorance of both the contact between the RTS and the surface nature, a purely theoretical approach does not seem appropriate. Indeed the risk of starting from a wrong hypothesis is too important.

Hence we preferred to design simple experiments that would allow us to determine which empirical friction model is better to describe the interaction between the RTS and the surface. We decided to record the evolution of RTS speed with the variation of the rotating speed and therefore of the pushing force on the surface. Let us now recall that thanks to the low Reynolds number flow, the fluid distribution evolves linearly with the change of boundary conditions. Therefore the pushing force made by the helical tail of the robot is proportional to the rotation frequency. These experiments have been reproduced on different substrate materials to see the influence of different surface friction parameters.

Figure 3.6 a) shows the evolution of the RTS speed with the frequency where the force provided by the helical part is pushing the RTS into the substrate. To draw this curve, we integrate several substrates coated with different materials into the main chamber of the chip during the fabrication on a microfluidic chip. The metallic substrates are in glass with a 100µm thickness and the coating is made with a PVD process with a thickness of 10nm. To integrate these substrates into the chip we first bond on the glass cover, a thin sheet of PDMS (≈ 100µm) with a total surface around 25mm 2 . Then we cut the different substrates in 2mm 2 square parts and bond them to the PDMS sheet. Finally, the microfluidic chip is bonded to the glass and the main chamber is placed to contain the PDMS sheet and the different substrates. As this main chamber thickness is 1mm different substrates are still accessible to the RTS by swimming.

For the experiment, the RTS is integrated into the microfluidic chip by the steps that will be presented in Section 3.3. Then the inlet and outlet of the chip are closed to limit parasite flows and the RTS uses swimming motion to reach the different substrates and perform spintop motion. Unfortunately during the experiment a small parasite flow around 5µm was still present.

To analyze these data we consider that the friction point between the RTS and the surface is providing all the propelling force that counterbalances the fluid drag exerted by the fluid. This fluid drag is considered as proportional to the speed thanks to the low Reynolds number approximation.

From the curves in Figure 3.6,we see that two different linear tendencies seem to emerge. They are referred as (1) and ( 2) and their linear approximations are drawn. For the gold surface, two similar experiments were performed but different results were obtained. One follows the tendency (2) and the other follows the tendency (1) until 70Hz where it brutally changes for the tendency [START_REF] Macdonald | Microfluidic sorting in an optical lattice[END_REF]. The reasons of the RTS to be in one of the two regimes is still an open question. To answer it, more control on the environment should be obtained. Indeed for this experiment, glass substrates coated with different materials are manually cut into small pieces. Then they are integrated in a large microfluidic chamber of lateral dimensions 5 and 7mm and a height of 850µm. The first problem for a good reproducibility of these experiments is the manual cutting of the material pieces. This generates dust that bonds to the substrate and deteriorates its homogeneity. The large microfluidic chamber is also causing parasite flows that could impact the measurement. Indeed from Figure 3.6 b) we can see that the curves corresponding to the swimming region have different speeds for the same frequency. As in this case the RTS is surrounded by liquid and free from substrate influence, the most probable explanation for these differences is the presence of a random parasite flow that impacts the swimming speed.

To answer these questions and investigate the reasons for the RTS to be in state (1) or (2), one needs to focus on the fabrication of the substrate by protecting the material during the cutting phase. For example, it could be possible to perform a resist deposition removable by a solvent bath after the cutting of the different substrates. The determination of the influence of the flow speed is also primordial. For this, the chip fabrication has to be realized avoiding parasite flows. One solution could be to change the material of the chip or the liquid medium as isopropyl alcohol is greatly absorbed by the PDMS and creates parasites flow.

However even if it is not possible for now to understand the reasons of the RTS to switch between these two tendencies and how much this depends on the surface composition, we can still make some interesting assumptions on the underlying physics. The main difference between these two linear tendencies is that when the frequency is null, (1) seems to extrapolate to a null value and (2) to a value around 5µm • s -1 . This difference can be explained by different friction models. The tendency (1) seems to be well explained by a lubricated model where liquid remains between the RTS and the surface. In this case, the friction on one object is obtained only by the fluid action on this object. The friction force is then given for a low Reynolds flow by the following equation:

dF = ν • ∂u ∂n , (3.9)
where dF is the force element at a given point, ν the viscosity, u the speed of the fluid and n the normal axis to the surface on the point.

As we are in a low Reynolds flow, the flow speed at the boundary must match the speed of the objects. In this case, if the rotating speed of the RTS is null, the flow speed will also be null at every point and so will be any of its space derivatives. The low Reynolds number approximation also guarantees linearity which means that the rotation speed of the RTS is linearly linked to the flow speed and thus to the RTS speed. Hence the linearity and the null value at 0Hz seem well explained by this lubricated model. The presence of a liquid layer between the RTS and the surface seems therefore a convincing hypothesis for the tendency [START_REF] Terry | A Gas Chromatographic Air Analyzer Fabricated[END_REF].

The tendency (2) seems to fit a Coulomb kinematic friction scheme. This well-established empirical model proposes an interpretation for the increase in surface contact due to the normal force between two objects. It is given by the following equation:

F = K • F N , (3.10)
where F is the friction force, K the cinematic friction coefficient between the two materials and F N the force normal to the contact between the two objects. This model explains also the linearity of the curves [START_REF] Macdonald | Microfluidic sorting in an optical lattice[END_REF]. Indeed the RTS rotation frequency is linearly linked to the normal force thanks to the helical shape that maintains a pushing force on the substrate. But the main justification of this model is that it explains the positive value of the linear approximation of the curve at zero frequency. Indeed the force between the RTS and the surface is the sum of the corkscrew force and the weight of the RTS. Therefore by extrapolating this model to 0Hz, some speed should remain, corresponding to the friction force only due to the weight of the RTS. Thus we can conclude that the friction is in part governed by Coulomb model. In fact in the case (2) we cannot suppress the influence of the propulsion coming from the viscosity which explains the tendency (1). Indeed there is no reason for this viscous force to completely disappear. Therefore the lateral force resulting in the speed of the tendency ( 2) is probably a mix of the viscous drag and solid friction modeled by the Coulomb law. This mix could explain the relative flat evolution of the speed in the spintop region of Figure 3.6 b). Indeed on this curve the rotation direction is creating a force that is pulling the robot off the substrate. Therefore as the frequency increases, the force described by the Coulomb model decreases while the one linked to the lubricated model increases. The total speed remains more or less the same in the spintop region. Unfortunately these results suffer from wobbling of the RTS due to low frequency actuation and parasite flows, which explains the difference in taking-off frequency (transition between spintop and swimming).

The switch between these two regimes during one of the gold surface experiments as well as the gradual change from one regime to another in the gold experiment in Figure 3.6 a) gives credit to these contact model hypotheses. Indeed in both cases the transition happens from the lubricated model to the physical contact model with the increase of frequency, i.e. with the increase in the force that pushes the RTS on the substrate. It seems logical that increasing this force tends to suppress the liquid layer between the two objects.

As previously mentioned, setup improvements are needed for better experimental conditions, in order to develop more on this hypothesis. Understanding the surface interaction between the surface and the RTS is a requirement to perform surface sensing and analysis with helical microrobots. As for force sensing, we believe this application could answer several needs especially in microfluidic environments where tethered probes are not usable.

Closed-loop control

An automatic control of the RTS is possible using a closed-loop control. This offers many advantages. In this thesis it was used to repeat measurements several times in a reproducible way. It is also a way to increase and quantify the ability of the RTS to follow a trajectory or to reach a given position. Without this closed-loop, the control only depends on the user skills. Therefore, developing an automated closed-loop control facilitates its use and control by untrained users. Moreover closed-loop is a first step to provide a more intelligent control of the RTS by forbidding moves that could damage the microrobot. Thus it increases its robustness. A proof of concept for this intelligent control relying on the closed-loop is presented in Chapter 5.3. As shown in Figure 3.4 e) the advantage of spintop is to provide a parameter that can make the speed decrease until zero in an approximately linear fashion thus allowing a simple control through a Proportional Integrative and Derivative gain (PID). This parameter is the pitch angle and the speed reaches zero when it tends to π 2 . Moreover this motion allows an holonomic surface displacement which means that the control can be performed independently on the x and y axes. Therefore the spintop motion is a perfect candidate for automatic control.

Figure 3.7 presents how this control is performed. First the tracking algorithm detects the position of the RTS. Then this position is compared to the desired one at a given time and two errors are computed on the x and y axes respectively. These errors are then sent to two different PID controllers that give a command value C x and C y on the x and y axes respectively. From this a vector C is constructed such that: C = C x x + C y y. This vector C has the direction to aim at with the RTS. Its amplitude is proportional to the command speed. Therefore the pitch angle, which controls the RTS speed, is computed by θ = π 2 -C . The yaw angle which controls the direction of the RTS is set such that the direction of the RTS is the same as the direction of C.

This closed-loop system is tested on a square trajectory. As we work in the camera frame, the coefficients of the PID need to be adjusted when we change the microscope magnification. This also allows us to adapt to different spintop frequency speeds and RTS designs. Figure 3.8 a) and b) shows the path of the RTS as well as the position command. Figure 3.8 d) displays the error between the command point and the position of the RTS. When the command position stops to move this error decreases below 2µm. This limitation is mainly due to optics resolution as these tests were performed in the setup 1.

These results prove the concept of the spintop control and automation simplicity. This feature could be an important advantage of this motion in the development of force related investigation such as surface adherence mapping or roughness detection.

Microfluidic chip integration

As mentioned in the introduction, self-integration of the robot inside a microfluidic chip could answer the need for untethered force sensors in such closed environment. Furthermore this integration can also answer several needs: For this measurement the rotating frequency is set to 60Hz. This experiment was conducted using setup 1 .

• Moving the RTS in a controlled environment. This environment can be designed to suit characterization purposes. This is an essential step to characterize each robot precisely for performing force sensing. Furthermore it could be extended to other measurements or experiments by changing the design of the microfluidic chip.

• Bringing the RTS closer to biological applications. Indeed microfluidic platforms are already well developed to perform biological experiments. These platforms could serve as interfaces between microrobot and biological experiments.

• Simulating a mission in a more unstructured environment. The microfluidic integration challenges could be a first step towards in-vivo integration.

For this integration, the microfluidic chip needs to be adapted to receive the RTS fabrication substrate. Then the multiple motions of the RTS provides enough accessibility robustness to perform this integration.

Microfluidic chip design

The particularity of this microfluidic chip is to have an open chamber. It allows to place and remove the RTS fabrication substrate. This open chamber is connected to the rest of the chip via a microchannel. By compressing this channel with a screw it can be closed and the microfluidic chip is then isolated from the open chamber. More details on this valve are available in Chapter 2.1.2. Figure 3.9 displays a picture of a microfluidic chip. The different components are the following:

• An open chamber. It allows the introduction of the RTS fabrication substrate as well as the tip to remove a single RTS. This square chamber is large enough to allow the manipulation with human hand precision. Its surface is 1cm 2 . When the fabrication substrate is put on this chamber, a thin Gel-Pak layer is placed between the substrate and the chip. The first function of this layer is to prevent from the fabrication substrate to slide when the robot is detached by the tungsten tip. The second function is to facilitate the removal of this substrate by manually handed tweezers manipulation.

• A microchannel. It connects the open chamber to a closed chamber. The section of this channel is a circular arc with a maximum height of 100µm and a width of 1mm. The total length is 11mm. The shape is designed to allow the channel to be closed by applying pressure on the top of the chip. Thus the closed part of the chip can be isolated from the outside. A 2mm diameter plastic screw is fixed just above the chip and can apply a force resulting in a pressure closing the microchannel.

• A closed experimental chamber. In Figure 3.9, its dimensions are 7mm over 5mm with a height of 850µm. However different designs are possible and several of them were used in this work. In any case this chamber is also connected to a fluidic input and output. These connections allow to fill the chamber with liquid and can be used to set a flow in the chamber, in the case of dynamics measurements or the injection of microparticles. They can also be used to increase the pressure inside the chamber.

• A microchannel pocket. It is connected to the closed chamber and is used to store the RTS during the flushing period. This microchannel is 50µm high for a width of 0.5mm. It is displayed on the left in Figure 3.9.

Integration protocol

For the integration process, we place a substrate in the open chamber of the chip with a field of several RTS on top of a thin adhesive Gel-Pak layer. This substrate can be removed after the integration and used again to supply robots in different microfluidic chips. Figure 3.10 illustrates the five major steps of the integration of robots inside the microfluidic chip. The supplementary information video 1 of the paper [START_REF] Barbot | On-chip Microfluidic Multimodal Swimmer toward 3D Navigation[END_REF] presenting the integration of the RTS shows a full record of the integration procedure. We prepare the chip by deposing the fabrication substrate containing the microrobots on the open chamber. For this, we place the adhesive Gel-Pak block with a thickness of around 1.5mm in this chamber. The fabrication substrate is placed on this block. This block gives the temporary adherence needed between the glass and the substrate. It also helps to handle the fabrication substrate. Then the inlet of the microfluidic chip is opened and which results in the filling of the closed chamber with liquid. During this filling the outlet is open to evacuate the air and the valve between the open and closed chamber is closed. Finally, the outlet is closed and the valve is open which results in the filling of the open chamber with liquid. The inlet is stopped when the open chamber is totally filled.

The first step of the integration is to detach a single RTS from the fabrication substrate, displayed in green in Figure 3.10. The microrobots are fixed to a glass substrate during the fabrication process. A tungsten probe tip performs the detachment. It is piezo-actuated on three axes by the user control. Then we remove the tip and put a thin cover glass over the open chamber to limit the residual flow created by the evaporation and avoid the contamination from air. Finally, the RTS uses the rolling motion to move to the edge of the substrate.

In a second step the RTS takes off from the fabrication substrate and swims. Then it dives down around 1.5mm to reach the bottom glass surface of the microfluidic chip. This distance corresponds to the thickness of the RTS fabrication substrate and the Gel-Pak block. The takingoff process is more difficult on nickel because of the high adherence force on the magnetic nickel surface. The conical design of the head is intended to ease this process. When the RTS lands on the bottom of the chip, it can use either rolling or spintop to move to the entrance of the microchannel.

In a third step, the RTS uses the rolling motion to move through the microchannel. The robustness to the flow of the rolling motion is needed here as some opposing flow can remain between the two chambers. Indeed, the top of the open chamber only lies on the chip without permanent bonding. This can cause small evaporation which leads to the concentration of the residual flow in the microchannel.

The fourth step consists of closing the microchannel. This is performed when the RTS reaches the characterization chamber. In that aim, a compressive pressure is applied with a screw pushing down the deformable PDMS top layer of the chip. After this step, the liquid is drained from the open chamber. The fabrication substrate is removed and stored for a later use. During this step the RTS is stored in the microchannel pocket to avoid being displaced by the flow resulting in the valve closing.

The final step illustrates that the spintop motion is used for precise motion inside the chip with a single contact point to the surface. The position control is then limited by the resolution of our optic. To perform this integration process, the multimodal motions and the control ability of the RTS are essential. Both 3D maneuverability with swimming and surface motions are required.

Roll/Swim: Long distance return travel inside microfludic chip 3.11 shows an extension of the microfluidic chip integration. In this figure, we explain that the reversed integration steps are possible to exit the RTS from the microfluidic chip and make it come back to the fabrication substrate. The operation follows the same steps as the integration but in reverse order. However one important difference is that the RTS is not diving from the fabrication substrate to the chip. Instead, it has to move up the 1.5mm from the chip to the fabrication substrate. Figure 3.9 shows that at the end the RTS comes back only 10µm away from the place it was detached. This ability could be interesting by combining it with trapping to either extract selectively an element of a microfluidic chip or to integrate it from an open chamber to the inside of the chip. The supplementary information video 5 of the paper [START_REF] Barbot | On-chip Microfluidic Multimodal Swimmer toward 3D Navigation[END_REF] presenting the integration of the RTS shows a record of this return travel.

Microrobot storage inside microfluidic chip

As mentioned in the introduction of this chapter, the microfluidic platform offers a controllable environment. This is particularly interesting to reduce the parasite flows or to design special shapes to characterize the RTS and investigate the related physics. But it also offers the opportunity to design a way to store the RTS for a long term, up to days or months. As Figure 3.12 displays it, if nothing in particular is designed to store the RTS several problems emerge. Gases interfaces and different flows are one of the main problems. Indeed the PDMS is porous to various liquids including isopropyl alcohol and water. Therefore gas bubbles start forming after one or two hours of use if the input and output of the chip are closed.

During storage, gas bubbles can also form inside the chip. They come from the leaks and liquid evaporation through the PDMS. To prevent this, the chip can be immersed in the same liquid as the one used for filling the chip. This method has the advantage of being simple to realize. Therefore we often used it to store the RTS for several days. However it is not compatible with transport. Indeed vibrations or tilting can move the RTS resulting in its loss or adhesion on a PDMS wall of the chip. We noticed this problem when we wanted to transport the RTS outside our laboratory. Indeed for a collaboration purpose, we wanted to be able to send a ready-to-use helical robot through mail. Moreover the long time storage in isopropyl alcohol degrades the quality of the fluidic connection and leads to leaking problems at the connections.

Therefore we chose to design a trap that can contain the RTS in a given location but which is also robust to the drying of the microfluidic chip. Moreover developing such a trap is interesting towards the integration of multiple microrobots on one chip in order to store and release them selectively (one by one). In this way they could be used independently one at a time by opening the corresponding trap of the desired microrobot. This is particularly interesting in a real case scenario where microrobots could be used to measure or manipulate objects. In this case if a microrobot is lost or destroyed another one can be sent without having to stop an ongoing experiment.

Fabrication and design of the trap

Several materials and techniques were tested for the trap design. Only the final one was successful. However they are all reported here because they reveal interesting problems linked to the microrobot storage inside a microfluidic chip and through the drying of the chip.

Actuation of the trap

In order to store the robot into the trap the following procedure is applied:

1. The trap is in open position.

2. The robot moves in the trap.

The trap is closed.

The reverse operations are applied to exit the robot from the trap. Therefore independently from the trap design, a mechanism is needed to open and close the trap. Figure 3.13 a) presents a microfluidic chip equipped with a RTS trap actuation system. Figure 3.13 b) presents the two methods we used to make this actuation. The first method consists of using a device similar to the part closing the microfluidic valve presented in Figure 2.9 in order to apply a constant force on the PDMS. Two screws push a glass part to produce this force. This glass part is compressing the chamber with the trap and closes it. This force also compresses two side chambers that are filled with air at ambient pressure. To open the trap, we increase the air pressure in the side chambers. As a result the force applied by the top glass in the trap chamber reduces and the trap opens. The pressure needed to open the trap depends on the chip because of the small differences in the trap height. This pressure can go up to 1 bar. As the trap is made of glass, it is fixed to the top of the PDMS chip by the same plasma technique used to bond the bottom glass to the PDMS part.

This method has the advantage of maintaining a constant pressure in the liquid circuit. Moreover as the actuation is controlled by the pressure in the side chamber, it could be possible to design this process in parallel in order to have multiple traps. These traps could be controlled individually by a pneumatic circuit able to selectively contain and release several microrobots. To do so, further investigations on traps and pneumatic control system designs should be investigated. However, the first method (see Figure 3.13) requires to add an inlet to the chip for the pneumatic control as well as a careful tuning of the applied force by the screws. For these reasons and because selective trapping and constant pressure of the chip is not required currently for our experiments, we decided to simplify this process. In the second method, the chamber containing the trap is smaller than the trap height. Therefore some pressure is required to close the PDMS chamber during the fabrication of the chip and it is deformed permanently by the trap.

This PDMS deformation results in an opposing force that compresses the trap and maintains it in closed position. To open it, the pressure of the fluid inside the chip is increased by closing the fluid output and increasing the fluid input pressure. This pressure is increased until it counterbalances and exceeds the force applied by the PDMS deformation. As a result the PDMS is deformed even more until the trap opens. As in the first method, the pressure to open the trap varies with the fabrication imperfections. However, the maximum pressure to open the trap registered during the experiments was always below 0.5 bar. The PDMS chamber height before deformation is 250µm, the trap height is 300µm.

For these two methods the stable position of the trap is the closed one. This is essential for the storage of the microfluidic chip as fluidic connections can be removed. In the following we will present how the trap is built.

PDMS trap: stuck when drying.

In our first trial the trap was directly made of PDMS. Therefore the trap was directly made with the chip mold design and this trap was only compatible with the second method. A circular chamber with a diameter of 50µm and 100µm height was designed. It was possible to enter and exit this trap with the RTS. However during the drying of the chip the RTS was pushed against the PDMS and permanently stuck to it.

SU8 trap: damage RTS.

To prevent from this adhesion to the PDMS surface during drying we designed the trap in glass. The trapping pattern was done with SU-8 resist and lithography. A circular chamber with a diameter of 200µm and 50µm height was designed. As for the PDMS solution, there was no problem to enter and exit the RTS. But the same problem arose during the drying of the chip. Even if the drying is slower in the SU-8 trap than in the PDMS trap, the drying front still pushed the RTS to the border of the trap and stuck it permanently. Our main hypothesis to explain this phenomenon is illustrated in Figure 3.14. The problem could come from a gap between the SU-8 part of the trap and the glass bottom. This gap is due to capillarity forces of the liquid. During the drying, the liquid gas interface pushes the RTS into this gap. Then the drying continues until no liquid remains between the trap and the bottom of the chip. Therefore the capillarity force decreases to reach zero when no more liquid remains. This results in the compression of the RTS between these two surfaces as it is shown in Figure 3.14 d).

RTS

Working solution: glass trap with two different heights

To get a successful drying we decided to find a way of containing the RTS in the middle of the trap during the drying. As it was too hard to find a way to maintain the robot in one place during the passage of the drying front, we decided to use this drying front to center the RTS in the middle of the trap. For this, the trap was designed such that the drying front propagates first all around the center of the trap and isolates a small droplet of liquid in the center containing the RTS. To do so, the trap height is smaller in the middle than on the sides, thus controlling liquid surface tension forces.

Figure 3.15 a) and b) shows how the trap is made and integrated inside the microfluidic chip. As two different levels of etching in the glass substrate are required, we choose to use a milling machine. More precisely, we use the same milling machine as the one used for the PDMS mold. However, the milling parameters are not the same as glass is much more fragile than PDMS. First a rough machining uses a 100µm diameter mill to remove material with 10µm vertical steps and 50µm horizontal steps. A distance of 3µm is left on the material compared to the final shape. The cut speed is 0.016mm • s -1 . The same parameters are used for the finishing machining, in order to remove the remaining 3µm. All the processes are performed in a water bath for cooling and lubrication.

As shown in Figure 3.15 c), this geometry allows the drying to happen first from the exterior of the trap thanks to the higher ceiling in the middle. Indeed due to surface tension, the middle of the trap will dry after the surrounding region. Often during experiments and it is the case in the picture of Figure 3.15, an air bubble remains in the trap and surrounds all the center like during the drying. Figure 3.15 shows that this air bubble is not a problem. Indeed when we open the trap, the gain of space makes the topology of the bubble change from a torus shape to a spherical shape. Therefore the RTS can join the middle of the trap. Finally, Figure 3.15 d) shows that while drying, the RTS is maintained in the center of the trap.

Evolution of the RTS after trapping

To characterize the evolution of the RTS we make a quick characterization. For this we measure the horizontal speed of the RTS in swimming motion at different frequencies. The pitch angle command is set to zero by the magnetic field. The vertical speed of the RTS subject to gravity is not measured and its effect is neglected. Four measurements are made in the opposite direction to average the effects of a constant parasite flow which are common in the PDMS chip because of thermal convective loops or absorption. However these four measurements are not made exactly at the same location as the RTS is falling and therefore the parasite flow can evolve. For each new frequency the RTS is put back at a given position. This characterization method is not as precise as the one developed in Chapter 4 and it does not pretend to give quantitative results on the RTS. However it is enough to see a drastic change in the RTS behavior which reveals a deformation or a loss in the ferromagnetic layer. To evaluate if the trapping procedure had an effect on the RTS, we performed this characterization between the two following trapping processes.

1. The trap is opened and the RTS moves under the trap. The trap is closed. The trap is opened and the RTS moves and exits the trap. The results of these characterizations are displayed in Figure 3.16 a).

2. The trap is opened and the RTS moves under the trap. The trap is closed and the chip is dried. After one day the trap is refilled with liquid. Finally the trap is opened and the RTS moves and exits the trap. The results of these characterizations are displayed in Figure 3.16 b). From Figure 3.16 we can deduce that closing the trap does not damage the RTS as its speed characterization curve stays the same. However the drying procedure affects the characterization. Indeed after each drying step the cut-off of the RTS is lower which means that the ratio between the disposable torque and the drag effect on the rotation has decreased. Our hypothesis to explain this phenomenon is that the RTS gets slightly bent during the drying step. This could come from the gas liquid interface, either when it pushes the RTS to the center of the trap during the drying or just before the total drying, when the RTS has to pass through this interface, from the liquid to the gas medium.

To overcome these problems two solutions corresponding to these two hypotheses could be investigated. First we could design a trap where the central part with the lower height is not flat but presents a clear extremum. In this way we could be sure that this precise point will be the last one where the liquid bubble will remain just before drying totally. Therefore by placing the RTS at this precise location, its displacement by the gas liquid interfaces could be avoided and its damages reduced.

The second hypothesis is more delicate to assess. But by designing precisely the height profile of the central trap part, we could vary the shape of the liquid bubble when the RTS has to pass through the interfaces. Therefore instead of having a circular shape as it can be seen in Figure 3.15 e), we could have a more ellipsoidal shape in the same direction as the RTS. This could help to distribute homogeneously the effort from the surface tension during the drying and therefore reduce the RTS damages.

Nevertheless even if the RTS is affected by the drying it can still propel and be used. After the drying no particular attention on the microfluidic chip is needed and it can be stored or sent by mail. This trapping procedure with drying was used during this thesis for storing a RTS for a live demonstration in the international ICRA conference in 2015. It was also robust enough to be mailed from France to Japan for a collaboration.

Conclusion

This chapter focused on the different requirements needed to perform the integration of a helical rotating microrobot inside a microfluidic chip. These requirements as well as the perspectives of this integration are summed up in Figure 3.17.

To perform this integration it is firstly required to enhance the robustness and accessibility of the helical microrobot. For this we developed three different motions for our helical robot named RTS (Roll-To-Swim). After providing some details on how we use the rotating magnetic field to control the RTS, the different motions were presented. As swimming and rolling were already reported in the literature, we have briefly described their mechanisms and we reported the speed curve of these motions versus the rotating frequency of our microrobot. However spintop is, to our knowledge, a new motion for helical rotating microrobots. Therefore some experimental analysis has been performed to investigate the nature of the propulsive friction in this motion. Two different regimes were discovered. The prevailing hypothesis to explain these different regimes is that one is obtained when a liquid layer remains between the RTS and the surface and the other one is obtained when the two objects are in physical contact.The reasons for the RTS to switch between these two regimes should require further investigations. By combining successively the different motions we have shown that the RTS was able to integrate the microfluidic chip. Moreover this gain in robustness and accessibility allows it to exit the chip, to perform surface motion against gravity and to transport a particle and release it at a desired location. We really believe that multiple motions is an important feature to tend to more independent microrobots that can be adaptable enough to evolve in unknown environments. This integration is a key step in this thesis. Indeed, first, a microrobot developed to perform force sensing inside a microfluidic chip should have a way to be placed inside this chip. But the microfluidic chip also allows us to guarantee good conditions for a selective tuning of each microrobot for force sensing. This is what we will develop in the next chapter.

Storing the robot inside the chip is also important as it allows to separate in time the process of integration from its uses. The separation of these two steps allow the production of on-chip microrobots that are more easily used by a third part as the integration is made during the fabrication of the chip. Producing a relatively easy interface and controlling the full microrobot on-chip system is important for developing either academic or industrial collaborations with other domains. More concretely a system consisting of a microfluidic chip with several trapped robots for different uses that could be selectively released, could be in itself an interesting manipulation or characteristic platform.

Several promising perspectives for in-vivo microrobots applications have been described in the literature. It could mainly serve for less invasive surgery or selective drug delivery. But the performance of such missions where the microrobot is injected into an organism and retrieved at the end of the process is still an unsolved challenge. The integration and exit of a microrobot inside a microfluidic chip could be a first step to identify and answer the problems caused by such a procedure. Moreover the engineering resolution available for microfluidic designs is perfectly fitted to mimic small geometries encountered in the ramification of blood or lymph networks in multicellular organisms. This could enable investigation towards in-vivo integration of helical microrobots.

Chapter 4

Robot Characterization for Force Measurement Introduction

This chapter deals with the possibility of performing measurements with a helical microrobot. Therefore, as a first step, we can wonder what are the interests of using robots for performing measurements. As the definition of "robot" has blurry boundaries, we propose to examine concrete examples to answer this question. For this purpose, we will consider two existing robots at the macroscopic scale conceived to perform measurements. This will allow us to show the interest of embedding sensors on robots.

The first example is the space probes used to explore our solar system. In this case the use of robots makes possible to provide communications through long distances. Moreover, such robots can survive the harsh space conditions which are incompatible with human life. The sensing ability of the space probes is also important for their trajectories, in particular to correct their journeys to follow a desired orbit or to aim a specific celestial object.

The second example concerns medical science. Endoscopy capsules have been used to perform images of the digestive system [START_REF] Iddan | Wireless capsule endoscopy[END_REF]. The main advantage compared to tethered endoscopy is that no surgical act is needed. Therefore the operation is less invasive. These capsules communicate in real time through radio waves to transmit images of the digestive tube. But they still suffer from a lack of mobility as they are moved passively by the digestive system and cannot be controlled. However, ongoing research focuses on solving this mobility problem by controlling the localization of the capsule. This could allow the control of the image acquisition.

From these two examples, we note that embedding sensors into a robot generally aims at two different objectives:

1. To benefit from the mobility of the robot in an environment unreachable by conventional means.

2. To use the robot as a relay allowing untethered feedback of the measured information.

Therefore to develop a useful and reliable microsensor, our robot should be able to accomplish these two objectives.

The previous chapter has demonstrated the high robustness and mobility potential of helical rotating microrobots. This is an essential step to validate the first of the two objectives we just presented. Indeed the ability to reach the inside of a microfluidic chip brings the helical robots in a environment reachable with difficulty by classical tools.

Moreover the RTS has a small footprint and a 3D mobility that makes him access easily all the inside of a microfluidic chip. Therefore it illustrates that sensing with a microrobot is promising for high versatility resulting in only few samples preparation and in a possible transfer to in-vivo measurements.

The second objective (using the robot as an untethered relay for the measure information) requires a way to communicate between the user and the robot. In macrorobotics and particularly 80 CHAPTER 4. ROBOT CHARACTERIZATION FOR FORCE MEASUREMENT for the two examples above, radio waves are used to command the robot to perform measurements as well as to transmit these measurements to the user. In the case of the RTS this communication is much more limited but is still possible. The user can command the position and orientation of the RTS thanks to the magnetic field. Then optical feedback through microscope imaging can be used to bring back the information through the analysis of the RTS reaction to the environment. Therefore when we started to investigate the potential of helical microrobots as force sensors, our first concern was to assess if it was possible to obtain information on the RTS environment through the optical feedback and therefore through the analysis of the RTS motion. The goal was to discover the different ways that the RTS could use to perform various measurements. The experiments of our first attempts to perform sensing with a RTS are briefly presented in the following subsection. After globally detecting the obstacle presence, we investigated a way of characterizing the obstacle nature. For this, the spintop motion was a good candidate. Indeed, in this motion there is only one contact point between the RTS and the surface which is located at the extremity of the robot. This allows to precisely aim a region of interest on the surface. Here, closed-loop control gives the best position precision and is used to perform the measurements. Figure 4.2 a) illustrates the principle of this obstacle characterization. It uses the fact that the RTS gets trapped by the obstacle. To get free from the obstacle, the RTS needs to lower its pitch angle. Indeed, as shown in Chapter 3.1.1, when the pitch angle decreases the speed of the RTS and therefore the propulsive force increases. Moreover this trapping is not observed in rolling motion. Therefore as the RTS evolves from vertical spintop to rolling, the force of the trap created by the object has to decrease to reach zero in the rolling motion.

Preliminary experiments

In this experiment we assessed the relation between this trapping force intensity and the obstacle height. To determine this trapping force intensity, we first need to place the RTS vertically on the obstacle, then we can slowly reduce the pitch angle until the RTS escapes from the obstacle. The higher the obstacle is, the more we need to decrease the pitch angle. Figure 4.2 b) c) shows the results of these experiments by performing spintop either in one rotating direction that pushes the RTS on the obstacle or in the other direction that pulls it away from the obstacle. These results demonstrate the correlation between the escaping pitch angle and the obstacle height. However due to the experimental noise and the uncertainty on the interaction between the RTS and the surface creating the trapping, it was impossible to quantify this correlation. Finally, we realized a quick experiment to show that surface inclination could be detectable using spintop motion. Indeed in this motion the speed is controlled by the angle between the RTS axis and the surface. On a flat surface this angle corresponds to the pitch angle of the RTS. But on a tilted surface it corresponds to the difference between the pitch angle and the surface angle. Therefore even if the RTS rotates vertically, the RTS moves along the surface. Figure 4.3 a) illustrates our experiment. The goal was to measure the surface angle β by measuring the speed of the RTS rotating along a vertical axis. Figure 4.3 b) shows the result of this experiment performed on different tilted surfaces integrated inside a microfluidic chip. We clearly see that the surface angle β is linearly linked to the robot speed. A potential perspective of this result is to develop a surface profile reconstruction by integrating the β measurement on the RTS path.

From these three experiments, it is possible to draw several instructive conclusions. Firstly, these experiments all investigate and propose ways to retrieve information from optical measurements. As presented earlier, this is essential for enabling untethered measurements. For the obstacle characterization, this is made through the RTS yaw angle that indicates the presence of an obstacle. For the obstacle characterization as well as surface detection, the speed of the RTS is used to detect a trapping of the robot or to give information on the angle between the robot and the surface. Secondly, these experiments demonstrate the large potential of a helical microrobot for sensing purposes inside microfluidic chips. Indeed thanks to their high maneuverability and different motions, they have different manners to interact with an object or with the surrounding liquid.

Thirdly, these experiments and especially the obstacle characterization, reveal our lack of knowledge on the RTS physics and interaction with the surface. Indeed it was impossible to conclude quantitatively for these results or to propose further relevant experiments. This physical understanding is decisive to identify necessary research development towards helical microrobot sensing applications.

Therefore in order to develop helical microrobot sensors, it is necessary to make a step backwards and study the fundamental physics phenomena behind these three sensing experiments. It is also important to develop quantitative measurements with error estimations. We could

Force sensing choice

This reason led us to identify the common underlying physics of these three experiments. It turned out that the common phenomenon is the complex interaction between the RTS, the surface and the liquid, each one having an influence on the two others. Furthermore, in all these experiments we wanted to get information on the surface and to understand how it influences the motion of the RTS. In a first step, we tried to model the interaction between the RTS and the fluid, i.e. without any surface interaction. Then this knowledge could serve as a reference case to understand the changes implied by interactions with the surface. Therefore we decide to study first the case where the RTS is only surrounded by liquid. At the end of this thesis, we illustrate this approach by performing an experiment using the RTS characterization surrounded only by fluid as a reference to study the impact of a microbead on the RTS dynamics. This experiment is presented in Chapter 5.2.

Therefore force sensing could go further than the needs presented on the introduction. It could be a basis for sensing other parameters with helical microrobots. This is why force sensing should be investigated and developed first. For example, getting a quantitative value on the force depending on the RTS state (position, orientation, rotation frequency, etc.) could allow to measure physical characteristics of the fluid such as the density or viscosity. We could also measure the flow speed precisely at a given position, which is done in a proof of concept in Chapter 5.3.4. Then it could be possible to make further investigations on the spintop motion. Indeed, it is essential in order to use this motion to extract knowledge on the surface and get back the information of the measurement through the optic as proposed for example in Figure 4.2. Knowing a quantitative value of the force between the RTS and the fluid could also serve to tune numerical simulations or to compare our results with other existing cases. Fortunately, we know how to characterize the force between the fluid and the RTS. Indeed the low Reynolds condition of the fluid guarantees a linear relation between this force and the RTS speed and rotation frequency. These values can be linked to each other through a matrix called the propulsion matrix [START_REF] Hess | Clinically meaningful blood pressure reductions with low intensity isometric handgrip exercise. A randomized trial[END_REF]. The estimation of these matrix coefficients for helical microrobots has been already performed on scaled-up helical models [START_REF] Xu | Propulsion Characteristics and Visual Servo Control of Scaled-up Helical Microswimmers[END_REF] and at microsize [START_REF] Zhang | Characterizing the swimming properties of artificial bacterial flagella[END_REF]. For force sensing, we only need to identify two parameter of this matrix. This is realized with a characterization experiment. These experiments rely on the second Newton's law which states that for a constant movement the sum of the forces are null. Therefore we can use the weight and buoyancy exerted on the RTS as a reference force to quantify the influence of the fluid on the RTS. Then by knowing the fluid force on the RTS, it is possible to deduce the force of the RTS acting on a given object. Figure 4.4 illustrates this protocol. Determining this force for any RTS and evaluating the error of this characterization is the main objective of this chapter.

Even if the measurement of the propulsion matrix was already proposed for microsize helical robots [START_REF] Zhang | Characterizing the swimming properties of artificial bacterial flagella[END_REF], the protocol associated with this measurement did not allow the clear determination of the measurement error. The quantification of this error is essential for sensing applications CHAPTER 4. ROBOT CHARACTERIZATION FOR FORCE MEASUREMENT as a measurement without a precision guarantee is difficult to use afterwards. Moreover it is essential to determine quantitatively the origin of each error component in order to make setup improvements towards a better characterization precision.

RTS characterization challenges

In any physics experiment it is necessary to control the physical parameters in order to get quantitative and repeatable measurements. For the RTS characterization the main parameters to control are the parasite flows, the impact of the microfluidic chip wall proximity and the temperature. To propose a meaningful characterization of the RTS, the main challenge is to guarantee a good control of the parameters influencing the RTS characterization. This is essential to get a precise value of the RTS force and to be able to study the RTS physics through these measurements. Indeed if an unexpected phenomenon arises or if the measure is not repeatable, we need to be able to guarantee that this is not due to the environment but to the RTS inner physics. Therefore such control of the environment is necessary to investigate helical microrobot models and to propose better motion strategies and measurement methods.

If we use a standard fluid container as a Petri dish to conduct the experiments, there will be an open surface (i.e. an air liquid interface). So it will be difficult to guarantee the absence of parasite flows as well as a temperature gradient. Indeed the liquid tends to evaporate on the open surface which results in a flow. Moreover we cannot blow air to guarantee a constant and homogeneous temperature because the open surface will be agitated resulting in a fluid perturbation. Therefore temperature gradients are likely to arise from the nearby electric coils, through air convection. Even if this temperature gradients have a relatively low impact on the fluid viscosity and density, they will create a convection flow that will interfere with the characterization.

Fortunately, thanks to the contributions of Chapter 3, it is possible to move the RTS in a microfluidic chip which simplifies the control of the environment parameters. Indeed, as such a chip is closed, there is no liquid evaporation and the temperature gradient can be limited by blowing air at constant temperature around the chip without perturbing the liquid (as we explained in Chapter 2.3.2). Moreover the small dimension of the chip gives more importance to the viscosity of the fluid compared to its inertia which ensures a thermal diffusion regime and no thermal convection.

Hence the microfluidic chip platform seems to be a good environment to develop the RTS characterization, especially since it is free from external influences. However such development is not straightforward and the following challenges need to be addressed:

• Guarantee that there is no remaining flow due to thermal convection.

• Guarantee that there is no parasite flow from the PDMS absorption or from leaks through the bonding interface with glass.

• Guarantee that the microfluidic experimental area has no impact on the RTS characterization.

• Guarantee that only the rotating frequency of the magnetic field has an influence on the characterization and not on its amplitude (at least below the cut-off phenomenon). This is important because our setup does not guarantee a constant amplitude for different frequencies. (see Chapter 2.3.1).

Chapter overview

To start with, we present the theoretical background of the propulsion matrix model on which the characterization is based. The assumptions of this model are presented and their validity are discussed. We also present the measurement method associated with this characterization. We show how the volume and the mass of the RTS are evaluated and how the experimental video is analyzed to measure the ascending and descending vertical speed of the RTS. Then we compute the impact of the error of the estimated parameters on the final force characterization.

The next section shows how the challenges linked to the environment control are assessed. We present the technical solutions chosen to solve these problems. Concretely we present the design of an experimental chamber inside the microfluidic chip which guarantees the absence of parasite flow under certain conditions. We also prove that its geometry has no impact on the RTS characterization. Finally we demonstrate that this characterization is not impacted by the amplitude of the magnetic field.

Section 4.4 displays the measurement protocol and the results of the RTS characterizations. First the repeatability of the measurement is assessed on one RTS. Then the characterization is performed with two RTS having different helix pitch parameters.

To finish, a final section investigates quantitatively the different sources of error in order to propose possible improvements.

Theoretical background and measurement methods

This section introduces the theoretical background on the propulsion matrix which is essential to understand how the characterization of the RTS is performed. We introduce the coefficients measured during the characterization and their relation to the force produced by the RTS. Then we present the different experimental methods used for the characterization. More precisely, we determine the weight, the volume and the vertical speed measurement protocol of the RTS.

Theory of the propulsion matrix

In order to model the microrobot physics, we first need to make some assumptions. To justify these hypotheses, we consider a model case with the maximum encountered speed for the RTS. Therefore, we consider a RTS with a diameter of 7µm and a length of 50µm, rotating at 200Hz and having a maximum speed of 200µm • s -1 in isopropyl alcohol. In experimental conditions we are always below all these values. By considering this worst case scenario, we can deduce the following hypotheses:

• The fluid is incompressible. Usually this assumption is justified in a fluid when the Mach number is below 0.2. This number is equal the maximum speed of the fluid divided by the sound speed in this medium. By considering the maximum fluid speed at the boundary of the RTS, the Mach number is less than 10 -6 .

• The fluid inertia is negligible. In general, a fluid is governed by its inertia and viscosity. The Reynolds number is the ratio between the inertia and the viscosity terms: R = LV ρ ν , where L is the typical length of the object, V the typical speed, ρ the fluid density and ν the fluid dynamic viscosity. In our theoretical case presented above, R = 2 • 10 -2 which is largely below 1 and therefore justifies neglecting the inertia of the fluid for all the experimental cases.

• The RTS inertia is negligible. By using a rough estimation of the RTS mass and drag coefficient, a RTS in the speed configuration presented above will take approximately 20µs and travels 1nm to stop if the propulsive force is suddenly stopped. As the minimal time interval considered for our experiment is above 1 ms and the minimum distance above 0.1µm, we neglect the RTS inertia and consider that the RTS speed is not time-dependent at constant frequency. Thus we consider that a change in the RTS speed happens immediately.

• The RTS rotates purely on its longitudinal axis. This hypothesis is not verified at low frequency as the RTS starts to wobble. Therefore in all the experiments of this chapter we respect a minimum frequency condition of 50Hz.

By neglecting the inertia of the fluid, the governing fluid equation becomes the Stokes equation:

µ∇ 2 u -∇P + f = 0, (4.1)
where u is the fluid speed, P the pressure and f the external force. As there is no time derivative and only linear terms in the flow equation, the torque and the force applied by the fluid on the RTS is linearly related to the speed v and the rotation frequency ω. We can therefore write the two following equations:

F = av + bω, N = cv + dω. (4.2)
The 2 × 2 matrix a b c d , that relates v and ω to F and N is known as the propulsion matrix (or resistance matrix). This matrix has the particular properties listed below:

• It is easily adaptable from one fluid to another, as the fluid dynamic viscosity is a common factor of each matrix terms. Indeed, only the viscous drag creates the force and torque from the fluid acting on the RTS. On an elementary surface this viscous drag is defined by dF = ν ∂u ∂n , with n the normal to the surface and ν the fluid viscosity. By integrating the elementary drags on the RTS surface we can obtain the force and torque. As these operations are linear, we conclude that F and N linearly depend on ν. This means that the coefficients a , b , c , d are such that

ν a b c d = a b c d .
These coefficients a , b , c , d only depend on the geometry of the RTS, and not on the viscosity. To easily compare our values with other works on helical microrobots, we will use these coefficients for our characterization.

• The combination of different propulsion matrices is linear: if two objects are connected by an infinitely small and long part, the resulting propulsion matrix is equal the sum of the two propulsion matrices. This property requires to neglect the interaction of one object on the flow distribution of the other. Therefore the connecting parts must be infinitely far apart, and infinitely small to have a null propulsion matrix. As this is impossible in practice, we check this assumption experimentally between a RTS and a microbead in Chapter 5.2.

• The matrix is symmetric. This means that b = c. For the technical details linked to this demonstration we refer to the paper from E. Purcell [START_REF] Purcell | The efficiency of propulsion by a rotating flagellum[END_REF].

As we neglect the RTS inertia, the force and torque from the fluid directly counterbalance those provided by the magnetic field to the RTS and presented in Figure 4.5.Therefore to characterize the force that the RTS can apply we need to identify the parameters a and b of the propulsion matrix.

Propulsion matrix coefficient identification

Drop test principle

The goal of the propulsion matrix coefficients measurement is to identify the force applied by the RTS at a given speed and frequency. For this, we need to identify the coefficients in the equation given by the first line of the propulsion matrix given in equation 4.2.and recalled below:

F = ν(a v + b ω), (4.3)
with F the force of the fluid acting on the RTS, ν the fluid viscosity, v the RTS speed and ω the rotating frequency. Here, the term in a v corresponds to the fluid drag applied on the RTS in the opposite direction to its speed. The term b ω represents the propulsive drag force from the rotation of the helical tail providing the propulsion. To identify a and b we need to apply known forces on the RTS in order to create a solvable equation system. The simplest forces to use here are the weight and the buoyancy of the RTS. The value of these forces can be estimated by simulating the RTS fabrication, which will be done in the next subsection. As the weight and the buoyancy are aligned with the gravity, we need to perform speed tests vertically to align these forces with the propulsion and drag force of the RTS. Therefore to characterize the RTS, we work on two kinds of speed measurements. First we measure the ascending speed when the RTS goes up in the direction opposite to gravity. Second we measure the descending speed when the RTS goes down in the direction of gravity. In both cases we write the second Newton's law for the RTS. As the inertia of the RTS can be neglected, we can consider that its acceleration is negligible and therefore that the sum of all external forces is null. These forces include the total fluid drag (F ), the weight and the buoyancy forces. They are displayed in Figure 4.6 a) in an ascending speed measurement. We obtain the following equation:

F + g(M + V ρ f ) = 0, (4.4)
with g the local gravity acceleration, M the mass of the RTS, V its volume and ρ f the fluid density. By combining this equation with equation 4.3 we obtain:

g(M + V ρ f ) = -ν(a v + b ω). (4.5)
As the equation 4.5 has two unknowns a and b , we theoretically need to perform only two measurements with two different rotating frequencies and speeds as shown in Figure 4.6 b). But in order to get a better approximation and to be able to estimate the error on the coefficients a and b , we perform several ascending speed measurements with different frequencies. The correlation between the frequency and the speed is then linearly fitted. However we observed experimentally that using this linear regression to determine the speed corresponding to a rotating frequency of 0Hz (v 0 ) brings an error of order 1µm • s -1 . This is mainly due to the fact that at low frequency (in practice under 50Hz ) the RTS starts to wobble. This results in a non-linear evolution of the speed with the frequency which forbids us to make measurements close to 0Hz. But the value of v 0 is critical to determine the force. Moreover, this speed is relatively small (around 6µm • s -1 for our family of RTS), because it is only due to the weight and buoyancy of the RTS and not to its propulsion. So an error of 1µm • s -1 is proportionally more important on v 0 than on the vertical speed measurement at frequencies above 50Hz.

To gain precision on v 0 , we decided to make drop tests directly at 0Hz. In these tests there is no rotating magnetic field to stabilize the RTS direction as shown in Chapter 3.1.1. Therefore we force the RTS to remain vertical by providing a constant low homogeneous magnetic field. Indeed if we do not provide any field the RTS starts to misalign with the vertical axis during the fall. This field intensity needs to be small in order to not re-magnetize the RTS in another direction. In practice this value is tuned manually during the experiments as the magnetization property of the RTS varies with time. We can therefore find the correct field intensity that forces the RTS to stay aligned with the vertical axis. Then, this drop test at 0Hz is repeated five times to evaluate the value of v 0 as well as its error by analyzing the standard deviation of the five different measured speeds. By taking ω = 0Hz in the equation 4.3, the coefficient a can be computed as

a = g(M + V ρ f ) νv 0 . (4.6)
Then by substituting a in the equation 4.5, we find the value of b .

b = a (v 0 -v) ω , (4.7)
with v the speed of the RTS at the rotating frequency ω. However in our experiments we performed several ascending speed measurements of the RTS at different rotating frequencies. They are used to evaluate the error of our measurements and more details on this error are presented in Section 4.2.4. We perform a linear interpolation of this set of data. This interpolation gives a linear relation between the RTS rotating frequency and its speed. By setting m the slope coefficient of this linear relation, equation 4.7 becomes:

b = -a m, (4.8)
with m this slope coefficient. Its unit is µ • s -1 Hz -1 . It is a constant for each RTS inside a particular fluid.

Image analysis

As we just presented, the speed measurement for the RTS characterization needs to be performed in the gravity direction. Therefore, to measure such speed, we need a way of measuring the altitude of the RTS. In practice, it requires either a side view of the experimental area or a focus tracking. Side view can be interesting as the image processing to get the RTS speed is straightforward. However it requires either a supplementary camera to provide a side view of the RTS, or to rotate the setup from 90 • during the experiment. These two solutions are both feasible but they raise technical challenges. Adding another camera with a quality comparable to the current microscope requires the design of a totally new setup. Rotating the microscope during the experiment is a too delicate operation considering the fragility and weight of such a precise instrument. Therefore we chose to develop a height tracking by using the focus of the microscope. For this, the essential object to develop is a focus indicator which is at its maximum when the image of the RTS is in the focal plane. With a focus indicator we can measure an ascending speed by detecting when the RTS is in the focal plane. Then we can move up this plane from a known distance and measure the time for the RTS to reach the focus at this new altitude. The schematic in Figure 4.7 c) explains this principle.

To compute such focus indicator, each frame of the experimental video record is assimilated to a 2D array, with values corresponding to the grey intensity of each pixel. Then we perform a 2D Fourier transformation of this array. On this transformation result we sum all the intensities corresponding to high frequencies. In practice we consider only the frequencies above 5 pixel -1 . Indeed high frequencies will be present on the frame only if the image is not blurred and will therefore give information on the focus. As shown in Figure 4.7 a) and b), this sum turns out to be satisfactory enough to detect the passage of the RTS through the optical plane. However as the RTS is longer than the depth of field of the focal plane, it is difficult to differentiate between the different parts of the RTS in the focal plane. This corresponds to the numbers 1-2-3 in Figure We propose to solve this problem by using the information contained in the rising and falling part of the focus indicator curve. To perform this, the curve is smoothed by removing the frequencies higher than 2Hz. The result of this operation is displayed in red dotted lines in Figure 4.7 b) and d). Then, the crossing between the RTS and the focal plane is determined by the maximum of this curve. The disadvantage of this technique is that we do not know to which position of the RTS this maximum corresponds. However this position is the same each time the RTS crosses a focal point. It is then enough to measure the time that the RTS takes to make a given distance. In other words, we do not know exactly the absolute position of the starting and finishing plane but we do know the distance between the two.

For this thesis a significant amount of data from drop test experiments were analyzed. This was particularly essential to tune the experimental conditions and reduce all the sources of error. To reduce the time of the experiments, we partially automatized the different steps from the drop test experiment to the ascending and descending speed curves. Figure 4.8 shows all the successive steps to get this curve from experimental data. These steps are automatized with a script. This script uses the avconv library for the video cropping and frame generation. It also uses Python codes for computing the Fourier transformation of each frame as well as for smoothing the curve to detect automatically the maxima of the focus indicator. Finally, the software LibreOffice is used to display the ascending and descending speed. This automatic data analysis is also more reliable and repeatable than a human analysis of the curve which can lead to mistakes or be influenced by an experimental bias.

For the characterization, three steps remain manual for the moment. The first one is the experiment itself. In fact the RTS is commanded manually to go up and down at the chosen frequencies. The second one is the choice of the threshold on the focus indicator to detect the maxima which give the times where the RTS crosses the focal plane. This threshold value is essential to avoid false detection of local maxima due to noise when the RTS is out of the focus. To solve complicated cases, the user can set different threshold values for different moments of the analysis. The last manual step is the storage of the tested frequencies, which is done manually.

For potential applications of helical microrobots as force sensors, these three steps could possibly be automatized without major difficulty. Then it would be possible to characterize the RTS in a completely automatic manner.

The protocol to analyze the ascending and descending speeds from the experimental video and the associated Python codes are available in Appendix E.

Measurement error determination

The determination a priori of the error made in these vertical speed measurements is challenging. In particular, there is a significant risk to overestimate this value. Therefore we propose to measure it a posteriori during the experiment. Concretely it means that this error will be determined by the linear quality regression factor and the standard deviation of our measurements.

According to the linear propulsion matrix model of the RTS, if we measure the ascending speed evolution with the frequency, we should obtain a line. Therefore, theoretically only two measurements are required. But to evaluate the error, we make several measurements and find this line by a linear fitting. By evaluating the quality of this linear fitting we can obtain an estimation of this error. Thus this error contains the external perturbations such as parasite flows or vibration of our imaging system.

Strictly speaking, it also contains the modeling error made by assuming a linear relation between speed and frequency. For example, if the RTS starts to wobble at some frequency, the linear regression between the speed and frequency will present a larger error even if the measurement conditions and instrumentation are perfect. We consider this modeling error to be small. Hence, we do not optimize the model for the time being. However, if further experiments reveal weaknesses in the propulsion matrix model, supplementary experiments should be performed to separate the error coming from the optics and the error coming from the model.

To present the calculus of this error, let us consider the linear fitting equation obtained from experimental measurements of the ascending speed evolution with the frequency:

v(ω) = mω + v0 , (4.9)
with m the interpolated slope coefficient, v0 the interpolated speed at 0Hz, v the theoretical RTS speed deduced from the fitting and ω the rotating frequency. The error will actually depend on a chosen confidence interval. Indeed if we assume that the measurement error is distributed as a Gaussian, then for a finite amount of measurement points, a small probability to get wrong results that still fit on a line with our error tolerance cannot be avoided. The choice of this confidence interval is a classical step in statistical analysis [START_REF] Morrison | Obtaining Uncertainty Measures on Slope and Intercept of a Least Squares Fit with Excel's LINEST[END_REF]. We choose a confidence interval of 90%. Therefore, the error on m and on v 0 obtained directly by experiments at 0Hz are the following:

ε m = S m t(n -2) (4.10) ε v 0 = S v0 t(n 0 -2), (4.11)
with t the Student t-distribution for a confidence interval of 90 %, S m and S v0 the standard deviations on m and v0 respectively, n the number of experiment points used in the linear regression and n 0 the number of experiments performed at 0Hz.

For m, the standard deviation is calculated from linear regression of the experimental ascending speed values. It is given by the following formula:

S m = 1 n -2 n i=1 (v i -v(ω)) 2 n i=1 (ω i -ω) 2 , ( 4.12)
with v i and ω i the speed and frequency associated to the i-th experiment, and ω the frequency average value of measurements. For v 0 the standard deviation is classically extracted from several measurements at 0Hz : with v 0i the speed associated to the i-th experiment, and v0 the average value of the speed measurements at 0Hz. On top of that, we need to add the error of the stage controller. In the best case this error is random and follows a Gaussian distribution. In this case it will directly impact randomly each measure and will be therefore already taken into account in the error presented above. However in the worst case, this error will be a constant shift, and will impact each measurement in the same way. To consider this eventuality we will systematically add this error to our error estimation. For our experiments, we used a mp-285 position controller, for which the error is

S v0 = 1 n 0 n0 i=1 (v 0i -v0 ), ( 4
ε z = 0.1µm.
Hence, for a given speed measurement we will have

V + ε V = (z 1 + ε z ) -(z 2 + ε z ) t 1 -t 2 = V + 2ε z t 1 -t 2 , (4.14)
with ε z the stage error, z 1 , z 2 the altitude of the two focal planes, and t 1 , t 2 the times when the RTS crosses the focal planes. This expression can be simplified into

ε V = 2V ε z z 1 -z 2 . (4.15)
Therefore the total errors on v 0 and m become

ε m = S m t(n -2) + 2mε z z 1 -z 2 , (4.16
)

ε v 0 = S v0 t(n 0 -2) + 2v 0 ε z z 1 -z 2 . (4.17)

Microfluidic focus correction

As the microscope optics is fixed, we measure the altitude of the focal plane by the position of the platform holding the microfluidic chip. However the isopropyl alcohol (IPA) inside the microfluidic chip does not have the same refractive index that the air outside the microfluidic chip. Therefore a correction on the focal plane distance is necessary. Indeed as shown in Figure 4.9, for a given distance between the objective lens and the microfluidic chip, the optical plane is not the same for different refractive indexes inside the chip. To prove this, let us use the notation introduced in Figure 4.9. First we consider the case where the microfluidic chip is filled with air. In this case, the glass layer displaces the focal point. However if we move the microscope from a distance d the focal point moves from the same distance d. Indeed the angle between the light path and the optical axis is the same (θ a ) as the refractive index of the air (n a ) is the same inside and outside the chip. Therefore the focal distance stays constant if the glass support of the microfluidic chip is displaced. So, as the distance between the focal plane in air and the glass wall can be directly measured by the platform positioning, we name it d a . We now use this distance as a reference to study the case where the chip is filled with IPA.

Screen plane

To quantify the difference of path length between the optics and the microfluidic chip when the chip is filled with IPA, we have to study the quantity d a d i . Here d i represents the distance between the focal plane and the glass wall. The refracting index of IPA is noted n i . By applying the Snell-Descartes law at the glass interface inside the microfluidic chip for the air and the IPA we obtain:

n i sin(θ i ) = n g sin(θ g ), n a sin(θ a ) = n g sin(θ g ), (4.18)
which gives the following equality:

sin(θ i ) sin(θ a ) = n a n i . (4.19)
Geometrical considerations give us the following relation:

tan(θ i ) tan(θ a ) = d i d a . (4.20)
Therefore by combining equation 4.19 and 4.20 we obtain:

d i d a = n a n i cos(θ a ) cos(θ i ) . (4.21)
As is generally the case in optics, we are working with small values of angles θ a and θ i . We therefore use the Gauss approximation which leads to cos(θ a ) (θ i ) = 1. The equation 4.21 then gives:

d a = d i n i n a . ( 4

.22)

This means that when the optical system is moved from a distance d from the microfluidic chip, the focal plane in the IPA chamber is moved by a distance d n i n a . In our setup, using the value of the IPA refractive index [START_REF] Chu | Densities and Refractive Indices of Alcohol-Water Solutions of n-Propyl, Isopropyl, and Methyl Alcohols[END_REF], we obtain that when the objective of the microscope is moved from 100µm the focal plane inside the chip is moved from 138µm. Hence this impacts the measurements of the speed which we need to correct accordingly. Also, as the refractive index of IPA changes with temperature, an error can be introduced by temperature changes. Therefore we have:

ε v = v ∂n ∂T (T ), (4.23)
with v the RTS speed, ε v the corresponding error on the speed, n the refractive index and T the temperature. Between 20 and 25 • C, we can consider that ∂n ∂T = 4.6 • 10 -4 C -1 [START_REF] Chu | Densities and Refractive Indices of Alcohol-Water Solutions of n-Propyl, Isopropyl, and Methyl Alcohols[END_REF]. For the air this variation is below 10 -6 C -1 [START_REF] Owens | Optical refractive index of air: dependence on pressure, temperature and composition[END_REF] and we can consider it constant as a first approximation.

As our temperature error is of 0.2 • C, the speed error is under 0.01% which we consider negligible and do not take into account for the total error calculation.

RTS volume and mass estimation

To know the total force acting on the RTS we need to evaluate the weight and the buoyancy force. For this we introduce several values:

• V r is the resist volume of the RTS after the 3D lithography.

• V m is the metal volume on the RTS after the PVD deposition.

• ρ r is the density of the resist used in the lithography process.

• ρ m is the average density of the metal. It is obtained by averaging the density of nickel and chromium weighted by their respective deposit height during the PVD process. In our case ρ m = 1000ρ N i + 200ρ Cr 1200 .

• ρ l is the isopropyl alcohol density. Note that it depends on the temperature [START_REF] Sovilj | Kinematic Viscosities of Binary and Ternary Liquid Mixtures Involving Chloroform, 2-Propanol, and 2-Butanol at Several Temperatures[END_REF].

Therefore the equation of the weight and buoyancy resulting force, with the positive direction opposing the gravity acceleration, can be calculated by the following formula: The RTS is mostly made in a polymer resist during the 3D lithography, unfortunately no indication about its density is given by the manufacturer. Therefore we measured this quantity in our laboratory using the process illustrated in Figure 4.10. For this, the resist needs to have the same properties as the RTS resist. For this reason, we apply the same process as during the lithography which consists of UV polymerization and baking. By definition the volumetric mass density is defined as follows:

Weight + Buoyancy = g(ρ r V r + ρ m V m -(V m + V r )ρ l ). ( 4
ρ r = m r V r , (4.25)
with m r and V r respectively the associated mass and volume of the same quantity of resist. For practical reasons the resist must be cured inside the measuring container, therefore we have to use disposable plastic ones. The direct consequence is that no precise measurement of the volume is possible. To get a precise information on the volume we use purified deionized water which has a known density and we apply the steps from a) to f) presented in Figure 4. [START_REF] Swaminathan | Mechanical Stiffness grades metastatic potential in patient tumor cells and in cancer cell lines[END_REF]. By referring to the notations in Figure 4.10 we have:

m r = m 2 -m 0 , (4.26)
V r = V 1 -V 2 = (m 1 -m 0 ) -(m 3 -m 2 ) ρ water . ( 4

.27)

Here V 1 and V 2 are defined such that the total volume of the containers is the same. In practice we mark the container at the step b) so that the same water level can be set at the step f). To estimate the error made in this measurement, we measure how much water needs to be added for detecting clearly that we are above this mark. In our experiment, the error was 0.03g. We can link the weight measurement to the volume. By weighting the container at the steps a) b) c) and f) we can determine the density of the resist with the following equation:

ρ r = ρ water • m 2 -m 0 (m 1 -m 0 ) -(m 3 -m 2 )
. (4.28)

THEORETICAL BACKGROUND AND MEASUREMENT METHODS

95

The numerical application shows that the volumetric mass of the resist (IPG 780) is 1102.8kg.m -3 . The weighing scale error is 0.1 mg and the error on the water density due to temperature change is below 0.2 mg. Both these values are considered negligible compared to the one made by reproducing the same water level between steps b) and f). Therefore the only considered error appears in the calculation while making the difference between m 3 and m 2 , we name it ε. The expression on the density error is the following:

ρ r + ε ρ r = ρ water • m 2 -m 0 (m 1 -m 0 ) -(m 3 -m 2 + ε) , (4.29)
which can be simplified at the first order by

ε ρ r = ρ r ε (m 1 -m 0 ) -(m 3 -m 2 ) . (4.30)
By making the numerical application, the error is estimated to 8.29kg.m -3 which is below 1% of the resist density value.

RTS volume estimation

In order to calculate the force using the formula given in equation 4.5, we also need to estimate the volume of resist inside the RTS as well as the volume of metal deposited by PVD. For this we perform a numerical simulation of both the 3D lithography process and the PVD process.

In the real process the 3D lithography moves a laser into a resist and polymerizes it. For a given position the laser focal is a point, the resist around this point is polymerized and an approximately ovoid shape of cured resist is formed. This volume element is referred as "voxel" (for volume element). The voxel has a shape close to a symmetric ovoid, which can be defined as the rotation of an ellipse around a main axis.

For the estimation, we first need an estimation of the voxel size and shape. For this, we designed a structure where an elevated cross is patterned with one passage of the 3D lithography laser focal. Therefore the branches of this cross have a section which can be modeled by an ellipse. The parameters of this ellipse define our voxel model. Hence, by imaging this structure we can measure the voxel ellipse parameters. To elevate this cross for the measurement, a more massive part of resist holds it in the center. Figure 4.11 a) shows this structure from nearly a side view (85 • tilt from perpendicular view). However as the real voxel does not exactly have an ovoid shape and in order to take account of the measurement uncertainty, we bond the voxel inside two ellipsoid voxels. The first one corresponds to a low approximation of the real voxel and whose section is contained inside it. The second corresponds to a high approximation. In this case the real voxel section is contained inside this ellipse. We performed this measurement on five different structures. To be sure not to underestimate the error, the largest dimensions of the high estimation and the lowest dimensions of the low approximation are taken to define two extreme voxels. These two extreme voxels will be used for the simulation to give respectively a maximum and a minimum possible value of the RTS volume. Moreover our SEM imaging has a 5% error on the dimension, thus these values are respectively increased and decreased by 5%. By making the assumption that the voxel has the same dimension on both horizontal axis, we can guarantee that the real voxel is contained between these two extreme ovoid shapes. The ellipsis parameters of our 3D lithography machine are presented in Table 4 To simulate numerically the lithography process of the RTS, we choose to represent the resist environment by a 3-dimensional binary matrix with coordinates proportional to the space dimensions. Each element of this matrix corresponds to an elementary cube of resist. We call d the edge length of these cubes. It corresponds to the resolution of our simulation. If an element has the value 1, it means that the resist associated with this elementary cube is polymerized. If it is 0 it means it is not polymerized and will not be part of the RTS. To simulate the polymerization by the laser at a given position, the value of the matrix elements in the surrounding region inside the voxel are set to 1. Thus to simulate a structure, the same path as the one sent to the 3D lithography machine is simulated. In the simulation the step between two positions of the laser insulation simulation along this path is d. A 2D simplified version of this process is illustrated in As an indicator for this precision we choose 1/d to simplify the graphic reading. This graphic shows that the value of the volume seems to converge to a constant value. To get a more precise estimation of the converging value, simulations with 1/d > 100 should be necessary. However more than 50 gigabytes of memory are required to get the simulation to run for d less than 0.01µm (precision > 100 µm -1 ). This reaches the limit of a classic desktop computer. For this reason we decided to use the value for 1/d = 0.01 µm and to add an error of 1µm 3 to the computed result for the high simulation and to subtract 1µm 3 to the computed result for the low approximation.

Finally, we need to estimate the volume of metal added to the RTS during the PVD process. It is difficult to estimate how much metal is deposited on a precise RTS location. Moreover half of the PVD process is made with a 75 • tilt angle with a rotation around an axis parallel to the vapor flow. This is performed to make the deposition more homogeneous. Therefore, to estimate the volume of the deposited metal, the simplest solution is to consider the shadow of the RTS. As shown in Figure 4.13, the amount of metal deposited on the RTS is equal to the amount deposited on a flat surface multiplied by the area of the RTS shadow. To simulate this shadow we take the same matrix as the one used to determine the volume. Then we make the projection of this matrix depending on the tilt angle and rotation. This gives us the shadow surface for a given configuration in the PVD machine. The first metallization step is made without tilt. Therefore the total height of deposited metal is multiplied by the projection of the RTS without tilt. In the second step, the RTS substrate has a 75 • tilt angle. In this case we measure the shadow area with this 75 • tilt for all different angles due to the rotation along the deposition flow, with a 1 • resolution. We multiply the average of these shadow values with the metal deposition height to get the amount of metal deposited during the whole 75 • tilt.

To get both a value of the volume and associated error for each RTS model, a simulation of the resist and metal volume is performed for both small and high voxel estimations. Table 4.2 shows the results of the two kinds of RTS used in this chapter which have different helical periods. For the resist and the metal volume, estimations of these values are given by the following formula:

Error estimation of the propulsion matrix coefficients

To give the maximum error related to the force of the RTS depending on its rotation frequency and its speed, we need to evaluate the error on the coefficients a and b defined in equation 4.3. As it is presented in Figure 4.14, this error depends of our measurement error and of the RTS volume and mass estimation error. To get the error on the coefficients a and b we first consider the error on the force acting on the RTS. Using the equation 4.4, the expression of F depending on the mass and buoyancy can be expanded to consider the error terms:

Lithography Voxel

-F -ε F =g((ρ r + ε ρ r )(V r + ε V r ) + (ρ m + ε ρ m ) • (V m + ε V m ) -(V m + ε V m + V r + ε V r )(ρ l + ε ρ l )), (4.33)
with F the force from the fluid on the RTS, ρ r and V r the resist density and volume, ρ m and V m the metal density and volume ρ f the fluid density, ε the error associated with each single value.

By making a first order approximation and considering the absolute value of each error term, equation 4.33 becomes:

ε F = g(ε ρ r (V r ) + ε V r (ρ r -ρ f ) + ε ρ m (V m ) + ε V m (ρ m -ρ f ) + ε ρ f (V r + V m )). (4.34)
As shown in the equation 4.6, the coefficient a is deduced from the force F . By taking into account the error term, this equation becomes:

a + ε a = F + ε F (ν + ε ν )(v 0 + ε v 0 ) . ( 4

.35)

By continuing the first order approximation and considering the absolute value of each error term, equation 4.35 becomes:

ε a = ε F + ε v 0 (aν) + ε ν (av 0 ) νv 0 , (4.36)
with v 0 the experimentally measured speed at 0Hz. Finally, the error on the equation 4.8 for b does not need any first order approximation and directly gives

ε b = ε a m + ε m a, (4.37)
with m the experimental linear relation between the rotation frequency and RTS speed found experimentally.

Attempt to measure the torque coefficient

Principle and challenges

The torque produced by the RTS on the fluid during its rotation can also be deduced from the propulsion matrix. Identifying this value could allow for example to quantify the maximum torque provided to the RTS by the rotating magnetic field. We could thus deduce the magnetization of the RTS. With this, we could explore the RTS ferromagnetic behavior which is for now hardly repeatable at low frequency. Understanding and quantifying this magnetization phenomenon could allow to improve significantly the RTS design and to use the cut-off frequency to measure fluid or environmental parameters [START_REF] Pedaci | Excitable particles in an optical torque wrench[END_REF][START_REF] Salmon | Swimming property characterizations of Magnetic Polarizable microrobots[END_REF]. Moreover it would become possible to perform torque measurements at microscale associated with the advantage of a mobile untethered sensor. This could enable for example to research towards the torque measurement of a biological motor on the bacteria surface.

To get this torque we must identify the parameters c and d of the propulsion matrix presented in equation 4.2, i.e.:

N = cv + dω, (4.38)
with v and ω the speed and rotation frequency of the RTS, and N the torque from the fluid on the RTS.

As the propulsion matrix is symmetric (c = b), and be can be computed with equation 4.8, d is the only parameter to determine in this expression. A classical approach is to perform a free drop test. In this test, we turn off the magnetic field and let the magnetic object that we want to characterize fall freely inside the fluid. As the magnetic field is cut, there is no external torque left on the object. Therefore d can be expressed in function of c in the equation 4.38. Hence

d = cv ω . (4.39)
As c is already known, the two parameters to measure during the free drop test are the speed v and the rotating frequency w of the RTS. This technique of test has been demonstrated on helical microrobots by Zhang et al. [START_REF] Zhang | Characterizing the swimming properties of artificial bacterial flagella[END_REF] but unfortunately this test seems to have been performed only once and no information on the precision of the measurement is available. This measurement is very delicate as the rotation of such helical object in free dropping conditions is very slow. The authors report an experiment time of 4.9 seconds for a rotation of only 80 degrees. Therefore we first tried to reproduce this test with the most important drop test distance allowed by our microfluidic chip height. Indeed the RTS falls freely to the bottom of our microfluidic chip in approximately one minute. This leaves it more time to rotate.

Free drop test

The first free drop test experiment suffered from a misalignment of the RTS with the vertical axis. Indeed to perform a relevant drop test, the helical microrobot must be aligned with the falling speed. But the RTS cannot remain vertical during the drop test without providing an alignment torque by a constant command of the magnetic setup. This torque blocks its rotation and thus prevents from the measurement of c. In fact, there are two reasons for an immersed 100 CHAPTER 4. ROBOT CHARACTERIZATION FOR FORCE MEASUREMENT object to be stable and aligned into a preferred direction. The first one appears when the gravity center is different from the buoyancy center. As these forces are in opposite directions, a torque is created and aligns the two centers on an axis parallel to the gravity acceleration. A hot air balloon illustrates well this phenomenon. Such a balloon is stable because the weight is placed on the low part in the passenger basket and the center of buoyancy is above the mass center, approximately at the center of the balloon. The second reason appears when the object moves in the fluid. In this case if the center of the fluid drag force is different from the gravity center an alignment torque also appears. This is the goal of the tails at the back of a dart or a plane.

However even if the helical tail is by definition not symmetric, it can be considered as such for the two physics phenomena above. Moreover the RTS fabrication materials are homogeneous. Therefore the gravity, buoyancy, and drag center points are relatively close. So in practice, no torque stabilizes the RTS in the vertical direction. We need to provide an alignment torque with the magnetic setup for the RTS to remain vertical as we do for measuring the falling speed at 0Hz. But this magnetic torque is incompatible with the torque measurement as it blocks the RTS rotation. Consequently another solution was investigated.

Glass tube drop test

To keep the RTS aligned with the falling direction we decided to perform the test inside a glass tube. This solution was already proposed for centimeters scale helical swimmers [START_REF] Xu | Propulsion Characteristics and Visual Servo Control of Scaled-up Helical Microswimmers[END_REF]. The inner dimension of the glass tube was approximately 10µm. For handling and adhesion into the chip this tube was placed inside a PDMS block. Details on the fabrication of this glass tube and its integration on the chip are presented in Appendix G. Figure 4.15 a) shows where we place this tube inside the microfluidic chip. It is integrated during the chip fabrication. We also had to develop a side view to get a more precise information on the RTS rotation. Thus, we designed a 45 • slope on the PDMS part of the microfluidic chip. Then a small surface of glass covered with gold is bonded and acts as a mirror. It was then possible to get a side view by looking with the setup microscope on this mirror as shown in Figure 4.15 a).

To put the RTS inside the tube, we first move it on the PDMS surface near the tube entrance as it is shown in Figure 4.15 b). We use a swimming motion to place the RTS above the tube entrance, then we reverse the thrust to push the RTS inside the tube. After these steps we move the stage on the side mirror to get a side view of the tube and the RTS. Figures 4.15 c) and d) show side view snapshots at the beginning and end of a drop test. There are 48 seconds between these two pictures and the RTS moves of 160µm. During this time no significant rotation along its axis was observed.

Discussion on the results

There are two main hypotheses to explain this absence of rotation. The first one is that the earth magnetic field interacts with the remaining magnetization of the RTS. To justify this hypothesis we tried to estimate the torque order of magnitude created by the earth magnetic field. We first needed to get the RTS magnetization order of magnitude and multiply it by the earth magnetic field intensity. But for this, we needed an estimate of the coefficient d. A reasonable order of magnitude for the free drop test result is to consider that the RTS will make one turn on itself when falling from 100µm. If we assume this, by using the equation 4.38 with the torque equal to zero, we have:

d = c • 10 -4 .
Then if we consider the maximum possible torque, the angle between the magnetization intensity (M ) and the magnetic field intensity (B) is 90 • and M can be estimated by

M = N B = cv + dω B , (4.40)
with v the falling speed of the RTS and ω its rotation speed while falling.

From our various experiments we know that the cut-off of the RTS happens around 180Hz. At this frequency the speed is approximately 80µm • s -1 and our setup loses half of its maximum power. So from the setup characterization made in Chapter 2.3) we can deduce that B ≈ 7mT . Finally, we know that c = b and is determined by the drop test experiment presented in If we assume that the RTS stays fully magnetized when the field is cut, the estimation of the resulting maximum earth magnetic field is:

N earth = M B earth ≈ 1.5 • 10 -17 N.m -1 .
Finally, this value needs to be compared to the maximum torque produced by the fluid during the free drop test. For this we assume that the rotation is blocked. The equation then 4.38 gives:

N fluid = cv ≈ 1 • 10 -19 N.m s -1.
with v the speed during the free drop test inside the glass tube (≈ 3µms -1 ).

Hence the torque applied by the earth magnetic field is higher by two orders of magnitude than the minimum field necessary to block the RTS rotation. Of course this result needs to be taken with serious precautions. Indeed the hypothesis on the value of d as well as the assumption that the magnetization of the RTS does not decrease when the field is cut brings possibly an error of several orders on the final result. However this proves that the earth magnetic influence can be considered as a serious hypothesis to explain the non-rotation of the RTS.

To reduce the impact of the earth magnetic field, we compensated it with the Helmholtz coils of the setup. But by performing the same experiment as the one presented in Figure 4.15, no RTS rotation was observed. Due to the lack of precision of our actuating and tuning of the Helmholtz coils for a magnetic field of small intensity, the hypothesis of the earth magnetic field 102 CHAPTER 4. ROBOT CHARACTERIZATION FOR FORCE MEASUREMENT blocking the rotation cannot be excluded. Indeed we estimated that we could reduce only 90 % of the earth magnetic field.

The second hypothesis is that the friction created by the tube on the RTS prevents the RTS from rotating. To be able to choose between these two hypotheses we propose the following perspectives.

Perspectives

Before upgrading the setup to compensate with more precision the earth magnetic field, it is needed to exclude the hypothesis of the wall friction. For this we suggest designing a RTS which is naturally stable and stays aligned during the drop test. To do so, the symmetry of the RTS needs to be broken, either by adding a denser component at one extremity, or by designing a tail shape that will stabilize the RTS through the viscous drag. By doing so, it could be possible to perform experiments without a tube and to see if the RTS can rotate in this case.

Another way could be to use the cut-off of the RTS to get the value of the coefficient d. By assuming that the magnetization of the RTS is constant for a given magnetic field intensity, it could be possible to compare ascending and descending speeds and frequencies just below the cut-off of the RTS rotation. Indeed in this case the angle between the RTS magnetization and the magnetic field is equal to 90 • in both experiments. Therefore the torque is the same for the two cases. So the equation 4.38 will give:

N = cv a + dω a , (4.41)
N = cv d + dω d , (4.42)
with v a and ω a the values of speed and frequency just before the cut-off in ascending speed and v d and ω d the values of speed and frequency just before the cut-off in descending speed. Therefore by subtracting equation 4.41 to equation 4.41 we have:

d = c v d -v a ω a -ω d . (4.43)
However the assumption that the RTS magnetization is constant with time does not seem realistic with our current design. Also a very good precision on the speed is required, which is particularly difficult in z-axis. For these reasons no pertinent result was obtained with this technique. Therefore a better understanding of the RTS magnetization is required to allow the performance of such dynamical method to identify the value of d and thus control quantitatively the torque generated by the RTS.

Environment control with a microfluidic drop test chamber

To obtain repeatable and quantitative measurements, it is essential to control the impact of the environment on the measure. The goal of this section is to present how the experimental design can be adapted for this purpose. This is essential both for a precise measurement and also to reach a pertinent analysis of our results. Therefore in this section we analyze the impact on the RTS characterization of the convection flow, the leaks and the absorption flows, the experimental boundary conditions and the field intensity.

Suppressing parasite flows due to thermal convection

To detach the RTS from the fabrication substrate with a tip, we need an environment accessible from the exterior. The simplest solution to actuate and characterize the RTS is to use an open environment, for example a Petri dish. However in such open environment the liquid evaporation is important especially as we use isopropyl alcohol medium, which is very volatile. This evaporation creates a lot of perturbations that result in the impossibility to characterize or even actuate the RTS. Moreover, we are in this case unable to control the temperate and its gradient by blowing air at a constant temperature in the experiment area. This will result in even more evaporation. This is crucial as the electromagnet temperature can reach a maximum For these reasons, the characterization of the RTS inside microfluidic chip was required to get quantitative and reproducible measurements. Indeed the closed environment of the chip limits the evaporation of the liquid medium and therefore the parasite flows. Moreover it is possible to blow air around the chip without inducing more evaporation which allows a temperature control. Then it is possible to suppress the drift related to the temperature. This is part of the setup 2 presented in Chapter 2.3.

However even inside the microfluidic chip with temperature controlled conditions, some important drifts can occur. They are responsible for the high standard deviation in the measurements presented for the swimming motion in Chapter 3.1.3. These drifts are firstly hard to predict as the absorption of the fluid through the wall at some places can result in an important current in another place. Secondly, it is hard to detect if it occurs in the vertical axis. In fact this is the main concern as a constant vertical flow in one location will impact the whole characterization of the RTS. Hence, it is crucial to limit and evaluate this drift in order to guarantee the estimation of the RTS force.

For this, we design a small cylindrical chamber inside the chip which has a diameter of 400µm and a height of 1mm. The RTS can access this chamber through a square microchannel with 80µm side and 1mm length. In the future, we will refer to this chamber as the drop test chamber. Figure 4.16 shows a 3D simulated view of this chamber. Its principal particularity is to be a dead end part of the fluidic circuit. This implies that the fluid speed inside this chamber is not affected by the speed distribution outside the chamber. Therefore even if a strong absorption of the fluid occurs at multiple locations, this will have no effect on the flow inside the drop test chamber. Hence only the absorption of the fluid inside the chamber will impact the flow distribution.

Another benefit from the small size of the chamber is that it decreases the temperature convection effect over the diffusive effect. To quantify this phenomenon we evaluate the Rayleigh number (R a ) which is defined by the ratio between the heat transfer by convection and conduction. If R a is less than 1000, the heat transfer is purely conductive [START_REF] Harris | Critical {R}ayleigh numbers for natural convection of water confined in square cells with L/D from 0.5 to 8[END_REF]. This means that there is no convection flow. The expression of R a is the following:

R a = ρgβ να (T s -T inf )L 3 , (4.44)
with ρ the density, β the thermal expansion, ν the dynamic viscosity and α the thermal diffusivity of the fluid, g the acceleration due to earth gravity, T s the surface temperature and T inf the temperature inside the liquid. Here we consider this difference as the maximum temperature gradient possible. L is the height of the chamber. We estimate the order of magnitude of R a inside the drop test chamber. As thermostatic air is around the chip, the maximum possible temperature gradient will be below the maximum error of the thermostatic flow. Therefore we make the calculation with (T s -T inf ) = 0.2 • C. For the drop test chamber the characteristic length is 1mm and Ra ≈ 10 -2 . This guarantees that there is no flow inside the drop test chamber due to temperature gradient.

Parasite flow due to PDMS absorption

The design of the drop test chamber inside the microfluidic chip is not sufficient to stop by itself all parasite flows. At first we were convinced that this parasite flow could only come from the PDMS absorption. Therefore we estimated this value order of magnitude inside the drop test chamber by using the RTS as a marker to measure the flow rate in the drop test chamber inlet. In this way, we made an evaluation of this parasite flow and concluded that it was negligible. Our model assumed that the absorption could only happen from the liquid to the PDMS and that there was no reject from the PDMS to the liquid. However we discovered experimentally that this assumption was not verified. Indeed, Figure 4.17 a) shows one of our first RTS characterization attempts. We made two drop test experiments performed at different times inside a simple drop test chamber. We can see that these two curves seem to be shifted from a constant value. This result can be explained by a 4.3. ENVIRONMENT CONTROL WITH A MICROFLUIDIC DROP TEST CHAMBER 105 vertical constant flow which appeared during one of the two tests. In fact this phenomenon could not be easily justified by a change in the RTS mechanical properties. Indeed it seems improbable that the response of the RTS to the magnetic field changes such that the ascending speed is decreased when the descending speed increases. We concluded that the most probable way to explain the non-repeatability of these two drop test experiments was the existence of a remaining vertical flow. Figure 4.17 a) shows the difference for only two different characterizations of the same RTS but a similar shift was obtained in all our experiments with this simple design for the drop test chamber.

Thus we concluded that our hypothesis to consider that the PDMS can only absorb the liquid and not reject it inside the drop test chamber was not verified. The justification of this hypothesis was to consider that when an element of volume was absorbed by the PDMS it was impossible that this element passes through the fluid again to leak outside. This could be justified if the fluid resistivity to get from one surface element to the outside of the chip through PDMS absorption was the same everywhere.

However we think that the chip leaks much more from the bonding interface, especially because this surface is quite rough due to our micromilling process explained in Chapter 2.1.2. Therefore we formulated a new hypothesis: the PDMS is storing liquid during the time before the experiment. In fact we leave all the chips in a liquid bath to saturate the PDMS in liquid before the experiments. Then during the experiments the PDMS rejects some liquid inside the drop test chamber. This liquid will mostly leak through the bonding interfaces which is the less resistive path to the outside. This phenomenon is illustrated in Figure 4.17 b).

To avoid these leaks through the interface around the drop test chamber, we decided to isolate the drop test chamber. For this we put it such that there is no path from the drop test chamber to the exterior through the bonding interface. In an electric analogy, this corresponds to short circuiting the leak from the chamber with the drop test chamber inlet. Figure 4.17 c) and d) shows our new design.

Moreover for the PDMS to reject the absorbed liquid, the pressure must be lower inside the chamber. This is possible with the current design presented in Figure 4.17 b) as the microfluidic chip connections are closed and the fluid volume decreases due to leaking. We decided to also connect the inlet of the chip during the drop test experiments and to apply a small pressure of 10 mbar above the outside ambient pressure to prevent the PDMS to reject liquid. We also bond a small glass with a 300µm thickness above the drop test chamber during the fabrication step. This limits the liquid evaporation through the PDMS.

Finally, we need a way to verify that this modification reduces parasite flow enough. For this we use the fact that this parasite flow does not produce a constant flow in the whole drop test chamber. To prove this, we need to study Figure 4.18 a) which displays records made in a simple drop test chamber where leaks to the outside through the bonding interfaces were possible. In the second series of tests displayed in green, we re-centered the robot after the ascending test at 70Hz (between the numbers 5 and 6) due to the presence of a lateral flow. We can see that the linear shape of the curve changes from the measurement number 6, both for ascending and descending speed. This shows that the parasite flow depends on the location as re-centering the RTS changes the ascending speed value. We are not surprised to find that the parasite flow depends on the position. Indeed in this small environment the flow is governed by its viscosity and the flow speed decreases slowly as we approach a wall to match the boundary conditions.

At the end, we make the assumption that if no speed difference in 0Hz experiments appears between the five different locations of the chip presented in Figure 4.18 b), there is no parasite flow. By performing this experiment with one RTS we find an average value of 7.45µm • s -1 with a standard deviation of 0.125µm • s -1 and a maximal error of 0.17µm • s -1 deviation. This small error is probably due to our measurement method so there should be no significant parasite flow in this case. This validates the efficiency of the drop test chamber design surrounded by the main fluidic chamber and with a top cover glass to eliminate parasite flows.

To check the absence of parasite flow in our experiments, we performed this test before each characterization. In fact it is also how we measured the falling speed at 0Hz (v 0 ) for the characterization. Therefore the potential error due to small parasite flows is taken into account when we calculate the error on v 0 .

Wall proximity influence

The proximity of the walls of the chip has an influence on the RTS swimming. Indeed when the surroundings are free from any obstacle, the flow distribution is such that it needs to meet a null condition at an infinite distance. However when a wall is present, this null condition is on this wall and not at infinite distance. Therefore the flow velocity decreases quicker to match the null velocity condition of the wall. As the fluid drag on a surface is proportional to the normal gradient of the flow speed at this surface, it will increase with the wall proximity leading to an increase or direction change of the RTS propulsion. We noticed this phenomenon during the drop test in the horizontal axis. Indeed a change in the RTS propulsion happens when it is in vertical position and is not centered in the drop test chamber. In this case the wall proximity distance produces a drift that makes the RTS move on 4.3. ENVIRONMENT CONTROL WITH A MICROFLUIDIC DROP TEST CHAMBER 107 a circular path around the middle of the chamber. This phenomenon is relatively slow in our drop test chamber and the maximum drift reaches a maximum around 8µm • s -1 . However this phenomenon is more important in smaller channels when the diameter is of the same order of magnitude as the RTS as will be shown in Chapter5. [START_REF] Hagiwara | Precise Control of Magnetically Driven Microtools for Enucleation of Oocytes in a Microfluidic Chip[END_REF].

Therefore our concern is to determine if the lateral position of the RTS inside the drop test chamber has an impact on the ascending speed measurement. To do so we performed five speed measurements at a given frequency in each of the three different locations illustrated in Figure 4. [START_REF] Zhong | Fractured polymer/silica fiber surface studied by tapping mode atomic force microscopy[END_REF].

The average speed measurement does not significantly change for the three different positions. Therefore we conclude the walls have no impact on the RTS characterization if the distance from the center remains inferior to 180µm. So for the characterization to be valid we will perform measures while keeping the RTS in this center region of the chamber. We also need to see if the altitude at which the experiments are performed has an influence on the RTS speed. For this we performed three different speed measurements in three different regions. As displayed in Figure 4.20 a), there is one region in the lower part of the drop test chamber, one in the middle and one on the top. In this case we narrowed the region size used in the speed characterization from 550µm to 275µm to identify this precise region. For this experiment the drop test chamber height was 1200µm.

Altitude influence

Bottom

From the results of Figure 4.20, we see that there is some difference in the ascending speed depending on the altitude. The top of the chamber leads to a higher speed. However these differences are probably not linked to the geometry of the chamber. A first reason is that these results are not repeatable. Other identical experiments displayed lower speed for the top part of the chamber. Secondly, no significant difference in speed can be seen for the experiment at 0Hz. These experiments at 0Hz were performed at the same time as the one performed at 80Hz. Indeed during a series of experiments, the RTS goes up and down three times. It goes up at 80Hz and goes down at 0Hz. Therefore the absence of altitude influence on the free drop tests reveals that the difference for 80Hz cannot be due to an increase of the fluid drag in this region, a parasite flow, or an optical deformation due to the chamber configuration.

We therefore conclude that the altitude in the drop test does not significantly impact the speed measurement. The difference in the result of Figure 4.20 b) could be due to the magnetization history of the RTS impacting its propulsion. This error might be particularly visible in this experiment because some time was required to configure the correct altitude in the test presented in this section. Hence, the RTS had time to lay horizontally on the surface which increases its chance to have a different magnetization direction when the field is turned on again for the next characterization altitude. This error is developed in more detail in Section 4.4.3. Normally if the torque created by the magnetic field to the RTS is sufficient to make it rotates, there is no reason for it to influence the RTS speed. In fact, it will just impact the phase shift between the RTS and the magnetic field rotation angles. However as we presented in Section 3.1.1, the amplitude of the field has an influence on the RTS stability. This could influence the rotation axis of the RTS. Therefore we need to check this possibility experimentally.

Magnetic field intensity influence

Figure 4.21 displays the results of these experiments. We see that there is no strong influence of the magnetic field amplitude on the RTS speed. At 8.8mT , it seems that the speed is slightly increased in both ascending and descending speeds. This could suggest that the strongest field tends to change the magnetization direction so that the RTS has a more efficient rotation direction. Indeed the rotation direction is not purely longitudinal and a small wobbling is always present. However this deviation is small and we consider it negligible.

RTS characterization results

Now that we found a way of controlling the experimental environment, we propose a protocol to characterize the RTS. Then we discuss the error, repeatability and influence of different RTS designs on this characterization. Finally, we summarize the results in Table 4.3 which gives the force developed by the RTS depending on its frequency with the associated errors.

Experimental protocol

The different steps performed for the determination of the coefficients a and b of the RTS propulsion matrix are summed up here.

RTS CHARACTERIZATION RESULTS

109

Steps performed only once: Steps performed once for each RTS:

• Integration of the RTS inside the microfluidic chip. It is presented in more details in Chapter 3.

• Displacement of the RTS into the drop test chamber.

• Saturation of the PDMS by isopropyl alcohol. This is to limit the parasite flow due to the PDMS absorption. During the characterization the microfluidic chip and the RTS are put for minimum 24 hours in an isopropyl alcohol bath.

Steps performed once for each measurement series:

• Temperature adjustment. The microfluidic chip is placed on the setup 2 (presented in Chapter 2.3.2). The fan and the temperature control flow are set on. We wait 5 minutes for the temperature to be homogeneous inside the chip.

• Parasite flow determination and v 0 measurement. Five drop tests at 0Hz are performed by keeping the RTS vertical with a small constant horizontal field. These five drop tests are performed in the center and in four positions at 150µm from the center forming a square (see Figure 4.18 b) ). The speed v 0 and its error are deduced from these measurements. If the error is larger than 0.3µm • s -1 we conclude that there is a remaining parasite flow due to PDMS absorption. In this case we apply a positive pressure inside the chip of 200 mbar above ambient pressure for at least two hours before trying the test again (see Section 4.3.2 for details).

• Focal plane setting. The first plane is set to approximately 275µm above the glass surface of the chip, the second plane precisely 550µm above the first plane.

• Dynamical drop tests. We set the frequency at 50Hz and the focal on the first focal plane. We move up the RTS vertically until it crosses the focal plane and gets out of focus. Then the focal is moved to the second focal plane position by commanding the stage platform with the control software and we wait again for the RTS to pass through the focal plane.

The reverse steps are made by moving the RTS down to get descending speed. These steps are generally repeated for the frequencies from 50Hz to 110Hz with a 10Hz step (see Section 4.2.2 for details).

• Video analysis. We analyze the video of the experiment and the computer automatically detects the time corresponding to the RTS crossing the focal plane. The ascending and descending speeds are plotted depending on the rotation frequency of the RTS (see Section 4.2.2 for details).

• Force determination. We calculate the coefficients a and b of the propulsion matrix and therefore the relation between the force created by the RTS for a given frequency. We also compute the error of this measurement (see Section 4.2.2 for details).

After a series of measurements, the RTS is left in the drop test chamber. The chip is then stored inside an isopropyl alcohol bath for the eventuality of a new characterization series. The calculation sheet and the protocol to get from the experimental video measurement to the identification of the coefficients a and b are presented in Appendix H.

CHAPTER 4. ROBOT CHARACTERIZATION FOR FORCE MEASUREMENT

Difference between v 0 and v0

By applying the protocol presented above we can obtain the speed characterization of the RTS. This characterization is guaranteed free from any perturbation due to parasite flow or wall proximity influence thanks to the different methods presented in Section 4.3. Before using the equations 4. At first sight, our linearity assumption seems to be verified. First the ascending and descending speeds are linear. Second they seem to intersect roughly in the same point at 0Hz. This is what we expected from the propulsion matrix model. But the difference in the intersection point is not completely negligible. Indeed a zoom shows that thanks to the precision of our measurement, the difference between the speed at 0Hz extrapolated from the ascending speed ( v0a ) and descending speed ( v0d ) is significant. Moreover the average of these two values seems to correspond roughly to the v 0 value measured directly in the drop test experiment at 0Hz. Normally the two curves should intersect exactly at this value. Unfortunately due to the wobbling phenomenon, it is impossible to perform pertinent drop tests between 0Hz and 50Hz to get the ascending and descending speed evolution close to 0Hz.

This phenomenon cannot be due to the parasite flow or wall influence, as we guaranteed that there were negligible. Moreover a parasite flow would only translate the curve vertically by adding some offset. The wall proximity would affect the propulsion proportionally to the rotating frequency ω due to the linearity of the flow. But the particularity of this anomaly it that it behaves exactly as if a constant force opposing the RTS speed was present. This would result in moving down the ascending speed curve and moving up the descending speed curve. To analyze where this error comes from, let us write the expression of v 0 from the equation 4.6

v 0 = F a , (4.45)
with a the first propulsion matrix parameter and F the sum of the forces applied on the RTS. If the value of v 0 changes, F or a (or both) changes as well. Normally a should be constant for each RTS. Nevertheless for the same rotation frequency, the descending speed is larger than the ascending speed. So, the alignment of the RTS could change, thus impacting the coefficient a, and leading to two different a coefficients, one for each speed curve. But such change would result in different absolute slope coefficients, which are normally equal to b/a, with b a coefficient of the propulsion matrix. But the observed slope coefficient are almost equal, whereas there should differ from at least 30 % because of the difference between v0a and v0d . And a similar change in b compensating exactly the change in a does not seem reasonable.

Therefore the other solution involves a change in F . Normally if the RTS is free in the fluid, F is only the sum of the RTS weight and buoyancy. But this is true only if the magnetic field is perfectly homogeneous. Indeed let us recall equation 3.2 that defines the magnetic force due to the magnetic gradient:

F m = ∇(µ r • B),
with F m the magnetic force, µ r the RTS magnetization and B the magnetic field at the RTS location. One of our hypotheses was that our magnetic setup was a linear system. However it is probably only a rough estimation as the coils may interact with each other. Therefore we cannot guarantee the absence of a small magnetic gradient. If this gradient evolves with the direction of the rotating field, being in the opposite direction to the RTS both in ascending and descending experiments, it could explain the difference between v0a and v0d . As it seems for now the only possible explanation, we keep this hypothesis to explain this small anomaly. However in the future, we should use a field sensor position with micrometer resolution with high feedback speed to measure the rotating field and measuring its gradient. Another test could be to design a RTS with an inverted chirality (opposite helix direction) and to see if this phenomenon is reversed.

In practice to determine a with the equation 4.6, we keep using the value v 0 determined by five drop tests at 0Hz. For b defined in equation 4.8, we use the slope coefficient of the ascending speed as it is not impacted by a potential translation of the characterization curve.

RTS characterization repeatability

Before being able to draw a conclusion on the force of a RTS with a drop test speed characterization, we first need to evaluate how repeatable this experiment is. For this we repeated the protocol presented above several times using the same RTS in the same drop test chamber. To see the effect of time on the repeatability, we performed two characterizations on one day, two others one day after and a last one the following day. This last characterization is performed up to the cut-off frequency (above 200Hz ) to show that the RTS propulsion remains linear and therefore that the propulsion matrix model is valid up to this frequency. After the cut-off the RTS is still propelled but it is rotating at a lower frequency and its perpendicular axis is not aligned with the magnetic field any more. This results in the lower speed measurement at 210Hz. Figure 4.23 b) displays the extrapolate speed v0 at 0Hz, and slope coefficient resulting from the linear fitting of the measures. They are displayed both for ascending and descending speed. The error bar represents the confidence interval at 90% of these measurements.

Note that the error is globally more important for the descending speed than for the ascending speed. This is probably due to the fact that descending speeds are larger. As the speed is obtained by measuring the time for the RTS to go from one focal plane to the other, a constant error on this time measurement will have a bigger influence at high speed and therefore on the descending speed. To lower the global error, we use the ascending speed measurement for the characterization.

The slope coefficients are quite repeatable over the different experiments. However some measurements have more errors linked to the linear fitting than others. This means that the evolution of the speed with the frequency is more linear in some cases. Some differences between the measurements (especially between t=1h30 and t=22h30) cannot be explained only by the error inside each of these measurements. This means that some parameters of the environment or the RTS have changed between these two experiments.

But the hypothesis of a parasite flow inducing this error can be rejected. Indeed a parasite flow cannot have any effect on the slope curve as it will just add a constant speed on each measurement point. Therefore the curve would be shifted in the direction of the flow but its slope would remain unchanged. This set of experiments draws the same conclusion as the one on the wall influence presented in Section 4.3.3. The RTS behavior is not exactly repeatable for the same input magnetic rotating magnetic fields. This is probably due to the magnetization history of the RTS. In the wobbling region, we observe that the same frequency does not produce each time the same wobbling angle. In the frequency range in which we are working , these different wobbling phenomena are too small to be seen in the video but probably impact the propelling efficiency of the RTS.

Even if we are quite confident on this hypothesis, it still needs to be experimentally proved. For this, the setup could be arranged to deliver a certain strong magnetic field pattern that could repeatedly put the RTS in a particular magnetization state. If our hypothesis were true, the different characterizations should be more repeatable. Of course the challenging point should be here to find the correct magnetic field pattern that could reset the RTS magnetization history from any configuration.

In practice we want here to define the maximum possible error made on the slope coefficient during the use of the RTS as a force sensor. This error is defined by the error between these five measurements increased from their corresponding error intervals, computed from the error linear regression and physical parameters identification. It is displayed in the ascending slope coefficient measurement in Figure 4.23 b). From this we estimate that the force applied during a RTS use can vary from a maximum value of 27% of the force obtained during the characterization.

With a large campaign of experiments on the same RTS as well as on other RTS, the accuracy of this error estimation could be further improved. Indeed for now this value only relies on five experiments. But this goes outside the scope of this thesis. Indeed, we chose to work with several prototyping technologies such as PDMS for microfluidic chip and 3D lithography for the RTS design. This was essential to obtain a first working experiment in a reasonable time proposing a

RTS CHARACTERIZATION RESULTS

113

precise characterization of the RTS. The philosophy behind this is to get a working system in a few years development. This system could then be used to identify where are the main challenges and improvement points. For us, this philosophy seems clearly justified as microrobotics is still in an early stage of development. Therefore the first task is to identify where the possible difficulties are.

Because of this, it seems not very interesting to invest time in getting a really precise value of this repeatability error as we are working with a prototype. However what is really important is to know how much this repeatability error impacts the force characterization compared to the other errors and where it comes from. This is essential to decide what improvement needs to be done when we will move forward to a more stable design. In this section we present the force characterization for two different RTS designs. We perform this characterization with two different microfluidic chips but the two RTS were coming from the same fabrication substrate. As shown in Figure 4.24 the main difference between them is the length and number of their helical periods. The plots show that the RTS with a pitch period of 5µm is quicker than the one with a period length of 4µm. However as this difference is at the limit of our error interval, it is not possible to draw any definite conclusion. Nonetheless it seems logical that the speed of the RTS decreases with the helix period length. It was reported several times in the literature [START_REF] Purcell | The efficiency of propulsion by a rotating flagellum[END_REF][START_REF] Xu | Propulsion Characteristics and Visual Servo Control of Scaled-up Helical Microswimmers[END_REF].

Force characterization of two different RTS

Their speed at 0Hz (v 0 ) is measured by five drop tests at 0Hz before the characterization. Their speeds are quite similar: 7.45 ± 0.17 µm • s -1 for the RTS with a 5µm period length compared to 7 ± 0.22 µm • s -1 for the RTS with a 4µm period length. From the slope coefficients and the values of v 0 we can identify the coefficients a and b of the propulsion matrix and therefore determine the force generated by the RTS at a given speed and frequency. These results are presented in Table 4.3 with the corresponding maximal possible error. Details on these calculations and error are presented in Subsection 4.2.2.

The table displays the force range generated by the RTS. This force corresponds to a static RTS pushing an obstacle under the assumption that this obstacle does not change the RTS propulsion matrix. This force is limited at low frequency by the wobbling phenomenon that can happen under 50Hz and changes the propulsion matrix. For high frequencies, the cut-off limits the maximum force generated by the RTS. This cut-off is directly linked to the power of our magnetic setup.

It is difficult to draw a definitive conclusion on the differences between the two RTS. Indeed, the differences between a and b are roughly equal to the maximum error. However these differences seem logical. Indeed the robot with the 4µm pitch has a larger surface. Hence, the drag force will be larger, and the a coefficient as well. Moreover the maximum errors displayed in Table 4.3 are probably overestimated, because they are calculated separately. But the errors in the resist or metal volume calculation will probably be similar, leading to cancellations of errors when considering the difference between the two RTS propulsion matrices. Nevertheless, with the current setup and protocol, we cannot conclude quantitatively on how the parameters a and b evolve with the different RTS parameters.

In order to definitely conclude on the quantitative impact of the RTS difference, we should reduce the errors. The optimization of the setup and RTS for reaching such goal is the topic of the next section. One of the interests is to build a good model that allows us to make a guideline for RTS design. Optimizing the RTS force estimation could also be useful. Some proofs of concept of potential applications are developed in Chapter 5 where we present flow measurements and strategies towards surface friction measurement and cell force stimulation.

Towards a better characterization

One major goal of the RTS force characterization developed in this chapter is to build a working experiment that helps revealing the challenges and important aspects to improve the RTS and setup design towards concrete applications. The identification of these challenges is essential if we want to apply the force sensing ability of a helical microrobot to another field.

This section focuses on estimating the importance of each part of the experiment and to target what needs to be improved. To do so, we assess the impact of each error on the global error linked to the force generated by the RTS. Figure 4.25 a) shows all these errors and where they appear in the determination of the force. Figure 4.25 b) displays an estimation of each error impact on the final force error.

We make this estimation by developing the first order approximation of the error. If we consider the force F generated by the RTS as a function of n parameters named p 1 , p 2 , . . . , p n which are the different values needed for the force calculation (v 0 , slope coefficient of the speed characterization, resist density, ...), the error on F is given by:

ε F (p 1 ,...,p i ,...,p n ) = ε p 1 ∂F ∂p 1 + ... + ε p i ∂F ∂p i + ... + ε p n ∂F ∂p n . (4.46)
The impact on F of a particular parameter p i on the error is ε p i ∂F ∂p i . Therefore to evaluate the impact of a parameter p i on the force error, we calculate this error assuming that the error from p i is null and we compute the difference with the actual error: From this result we clearly see that the main part of this error corresponds to the repeatability error on the slope coefficient. The details of this error estimation value are presented in Section 4.4.3. This repeatability problem is therefore the key aspect to consider to get more accuracy on sensing with helical microrobots. As detailed in Section 4.4.3, this error might come from the RTS magnetization history that can be different from one experiment to another. Therefore the first investigation to reduce this error would be concerned with finding a way to reset in a defined state this history before a characterization or a measurement. For this, imposing a particular strong magnetic field pattern could be helpful. The remaining challenge is to find such magnetic field pattern.

ε p i ∂F ∂p i = ε F (p 1 ,...,p i-1 ,p i ,p i+1 ...,p n ) -ε F (p 1 ,...,p i-1 ,0,p i+1 ...,p n ) .
The other errors are much less important. However if the above solution could reduce the repeatability error, some of them would be worth investigation. This is the case of the RTS volume estimation. This estimation considers both the metal and resist volume and results from the simulation of the 3D lithography process presented in Section 4.2.3. Indeed quite a rough estimation is made by assuming that the voxels is symmetrical with an elliptical section. Improvements could be performed by using a more complex shape, for example a Non-Uniform Rational B-Spline (NURBS). We could also improve the voxel imaging experiment by using a better protocol.

On top of that, an important hypothesis is made during this estimation: by making our metallization simulation we neglect the influence of the surface on the metallic deposition. This surface could have an impact as we do not know exactly how the metal layer between the RTS and the substrate is detached by the tip. Should the volume calculation be improved, it would be necessary to find a way to get a high-resolution view with a Scanning Electron Microscope of a detached RTS to answer this question.

After the volume, the next error to improve would be the one on the evaluation of the drop speed at 0Hz, v 0 . This error is mainly due to the small angle of the RTS with the vertical axis during drop test at 0Hz. Moreover from the experiment image we can see that this angle is not the same between each drop test and varies between 0 and 10 degrees approximately. Understanding the origin of the anomaly between this direct experimental value of v 0 and the one got by linear extrapolation of the speed curves ( v0 ) with frequency could also be a concern. By solving these problems and by reducing the wobbling phenomenon the extrapolation of the speed curves could be a way to obtain a more precise value of this speed.

The measurement of the resist density could be the last error source to easily improve the error even if its contribution is low. This one has been performed with the available equipment. As the error is mainly due to the reproducibility of the water level, great improvement could be achieved by using a dedicated volumetric flask.

From their small contributions to the global error, the temperature control and stage position do not require further improvement for the moment. The error on the temperature is 0.2 • C and the position error is below 0.2µm.

Conclusion

In this chapter we presented a characterization of the RTS force. This requires a good control of the environment to limit parasite flows as well as control the temperature. This was possible only thanks to the microfluidic environment accessible with the RTS integration developed in Chapter 3. Moreover the microfluidic chip allowed us to store a given RTS for a long time. This was necessary for assessing the repeatability of the characterization.

After having introduced the theoretical background, we showed how an estimation of the volume and mass of the RTS was possible with numerical simulations. The precision of this measurement could be guaranteed with a 20% error margin. Then we presented the determination of the force generated by the RTS depending on its speed and frequency, using this estimation of the volume and mass and vertical speed measurements. We also presented a way of estimating the absolute error on this force.

In the following section we showed that an experimental chamber called drop test chamber could guarantee an environment with negligible parasite flow and a negligible influence of the chamber walls on the RTS force characterization. This environment was essential to perform quantitative measurements.

After the characterization of the RTS, we concluded that we can choose to apply a force with the RTS between 10 and 45 piconewtons by tuning the rotating frequency of the RTS. The lower limit is due to the wobbling of the RTS that excludes low frequencies and the upper limit to the cut-off. However the size of the RTS could be adapted to match a particular force range. With the technology used in this thesis, the RTS dimensions could be easily scaled by a factor k varying from 0.3 to 3. This induces a k 2 change in the propulsive force [START_REF] Purcell | The efficiency of propulsion by a rotating flagellum[END_REF] and therefore the force could vary from 1 to 400 piconewtons. Other fabrication technologies like self-scrolling [START_REF] Zhang | Characterizing the swimming properties of artificial bacterial flagella[END_REF], template electrosynthesis [START_REF] Li | Template electrosynthesis of tailored-made helical nanoswimmers[END_REF] and vapor deposition [START_REF] Mark | Hybrid nanocolloids with programmed three-dimensional shape and material composition[END_REF] could be used to reach an even lower force range.

The precision of the force value is around 40 %. For now this is quite large, especially if we compare this with technologies operating in a similar force range. For example, the typical error of the AFM is between 5% and 10% [START_REF] Neuman | Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy[END_REF]. However the characterization platform presented in this chapter was not designed to propose directly the best possible precision but to detect where optimization is required. Therefore we proposed a complete estimation of the error. We detected the most relevant optimizations in order to reach a precise force estimation. We concluded that further efforts should focus on the RTS magnetization repeatability which is for now the principal error source.

Even if these results cannot yet answer the needs for biological applications of helical microrobot force sensors presented in the introduction, the selective on-chip integration of the RTS inside microfluidic chip presented in Chapter 3 and the on-chip characterization of individual RTS presented in this chapter are two major steps in this direction. The need of sensing for physical characterization and improvement of the robot control were also presented in the introduction. Now that we have characterized robots in a well-control environment, we can start answering these questions. This is the topic of the next chapter where proofs of the concept for different sensing RTS applications are presented.

Chapter 5

Towards Helical Microrobot Sensing Applications Introduction: from characterization to applications

The main contribution of the previous chapter was to characterize the RTS and determine the force it produces depending on its rotation frequency. The conclusion was that the RTS, with its actual design, can deliver a force from 10 to 45 piconewtons. By simple optimization of the RTS design and magnetic setup, this range could be extended for applications from 5 to 100 piconewtons. Even if the characterization of the RTS is not yet perfect and that optimization on its design and measurement protocol could be performed to reach more precise values for the force, it is worth starting to look at potential applications. Indeed, the characterization method of the RTS develops a quantitative way of assessing the RTS mechanics. The force characterization of the RTS could be the common base to multiple applications for biology, physics and helical microrobots control. Therefore to prove this point, the goal of this chapter is to demonstrate, by three different proofs of concept, that this characterization is an essential step towards potential applications for on-chip or in-vivo helical microrobots.

These proofs of concept are presented below and in Figure 5.1.

RTS+bead Characterization

Overflow detected 2 Flow sensing for automatic motion adaptation 3 Small channel control presence of a microbead on the RTS force. This bead is placed at the tip of the RTS. This serves two purposes. Firstly, as the robot surface is difficult to change, beads could serve as an interface for friction measurement. As we presented in the introduction, the measurement of the local friction is the most promising force measurement application for helical mircrorobots. Secondly, it could enable us to model the change of the RTS force while pushing into a surface, which is essential to consider applying a known force on any object.

2. Flow sensing for automatic motion adaptation. We show that the characterization of the RTS allows us to deduce the speed of the local flow by making the difference between the theoretical and real speed of the RTS. We also demonstrate that this flow sensing can be used to automatically put the RTS in the safest motion by detecting dangerous flow conditions. This experiment shows that the sensing ability of the RTS is essential to develop a full automatic control that could guarantee the safety of the RTS in unknown conditions. This would be essential to deploy the RTS in a complex environment, as well as for its use by untrained users.

3. Flow simulations for small channels control strategy. The development of the RTS control in channels with a section width below 100µm is essential towards microfluidic chips applications and in-vivo applications. We demonstrate experimentally that a focusing phenomenon happens when the RTS evolves in such small channels with a section width below 100µm. To understand the mechanism of this phenomenon we use numerical simulations based on the RTS characterization parameters. These simulations are finally used to propose a control strategy using 2D in-plane feedback for control inside a microchannel whose direction can evolve arbitrary in 3D.

Robot beads combination towards force sensing applications Introduction

Thanks to the RTS characterization we know that the force produced by the RTS helical tail is in the order of magnitude of 20 piconewtons for a rotation speed around 100Hz. We now wonder what kind of applications could be easily achieved with such RTS. In the introduction, we mentioned that measuring biological cell stiffness is a way to differentiate a cancer cell from a normal one. Therefore using the RTS for stiffness measurement could be a first idea of an application to develop. However by applying a force with a tip of roughly the same size as our robot head, the order of magnitude of the cell wall stiffness is 10 -3 N •m -1 [START_REF] Swaminathan | Mechanical Stiffness grades metastatic potential in patient tumor cells and in cancer cell lines[END_REF]. This means that if the RTS applies a force of 1 piconewton on the cell, this one will be deformed of 1 nanometer. Hence a space resolution below 10 nanometers in the RTS position is required to perform a pertinent measurement. To get such resolution is not impossible. In fact, it is covered by the magnetic tweezers and the AFM [START_REF] Neuman | Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy[END_REF], which are the conventional force sensing tools at this scale. So it could be possible to make the same kind of position feedback by measuring the interference created by a laser focused on one of the robot features designed for this need. But implementing such methods would be as complex as making an optical or magnetic trap control and feedback. Moreover the helical rotation could complicate even more the measurement. This would also suffer from a need of transparent media and from heating damage by the laser. Therefore, this solution would not improve existing solutions, and we did not develop the RTS as stiffness sensor in this work.

In order to propose relevant applications, let us recall first the main advantages of helical microrobot force sensors compared to classical methods. The main one is that the force produced by the robot is not linked to its displacement. Therefore, if the RTS has been previously calibrated, no feedback on the RTS position is needed to get the force, even with piconewton resolution. This allows a relatively reasonable technological setup, as only basic electromagnetic coils, a standard microscope and a standard personal computer are needed. These advantages are shared with the magnetic tweezers. However a helical magnetic microrobot setup has two advantages compared to magnetic tweezers. First, we can apply a force at a precise location,

ROBOT BEADS COMBINATION TOWARDS FORCE SENSING APPLICATIONS 121

whereas with magnetic tweezers, a lot of magnetic beads have to be released and guided by the flow to get few of them attached to the region of interest. Secondly, it works with a low homogeneous magnetic field which makes it easily compatible with an already existing setup as the coils are placed at several tens of centimeters from the microrobot.

Pertinent applications for helical microrobot force sensor should use these advantages. In the introduction we also mentioned that the biology community has an interest in studying the response of animals cells [START_REF] Itabashi | Mechanical impulses can control metaphase progression in a mammalian cell[END_REF], plant cells [START_REF] Lintilhac | Stress-induced alignment of division plane in plant tissues grown in vitro[END_REF][START_REF] Helmlinger | Solid stress inhibits the growth of multicellular tumor spheroids[END_REF][START_REF] Kim | Cyclic mechanical strain regulates the development of engineered smooth muscle tissue[END_REF] and small organisms [START_REF] Kawahara | On-chip microrobot for investigating the response of aquatic microorganisms to mechanical stimulation[END_REF] to external force stress stimuli. This could really benefit from both the low setup requirements and the selectivity of the RTS. Indeed thanks to its mobility and control, the microrobot could adapt directly to apply force on a cell culture without any particular preparation of the environment. Such measurements could be performed in conditions closer to the real in-vivo ones. Moreover, as the RTS can target a precise location for the force, the control cells or micro-organism group of a study could be placed close to the tested one to avoid potential bias resulting from different environmental conditions. A schematic of such experiment is present in Figure 5.2 a). Another application that does not require precise imaging, is to study the surface friction. Generally, the AFM is used for this purpose. But this tool cannot access inside a microfluidic chip. Therefore the development of on-chip surface measurements with a microrobot seems interesting. Moreover optical tweezers are also difficult to use for such applications because a not perfectly transparent surface can interact with the optical trap.

Such friction measurements with the RTS could be made by dynamically measuring the speed of the RTS with a given propelling force to reveal its friction force with the surface. Preliminary tests were made with spintop motion and are presented in Chapter 3.2. This test shows that different speed behaviors due to different force interactions with the surface are possible. Therefore this demonstrates that the analysis of the RTS motion can reveal information on the surface. However no clear correlation between the material of the surface and the speed have been revealed in this experiment. Hence the main challenge for now is to understand the physics behind the surface interaction, in order to use these friction based measurements.

Therefore we propose to use micrometric beads (microbeads) as an interface between the robot and the surface. Indeed a wide range of surface treatments is available for such microbeads, and it has been an active area of research for the past decades. Let us cite few examples. Biotinstreptavidin bonds can be used to fix DNA molecules on a polystyrene bead [START_REF] Hess | Clinically meaningful blood pressure reductions with low intensity isometric handgrip exercise. A randomized trial[END_REF]. Another possibility is to create a bead by the copolymerization of two different monomers [START_REF] Men | Magnetic polymer particles: Synthesis and properties[END_REF]. One of the monomers provides the functional group to start fixing other molecules. Polymers can also be used to attach chemical compounds directly by covalent attachment, adsorption or by direct trapping [START_REF] Roca | Progress in the preparation of magnetic nanoparticles for applications in biomedicine[END_REF]. Therefore a particular type of bead coating could be chosen depending on the desired surface measurement, without changing the RTS design. Moreover this solution is simpler than directly trying to control the surface of the RTS, which would result in more delicate fabrication steps.

The different possible friction measurements presented above could be adapted to work with a microbead effector with a known physical interaction with the surface, placed at one extremity of the robot. In Figure 5.2 a) we show how the bead could be laterally pushed by the RTS to measure the dynamical friction between the bead and the surface. In Figure 5.2 b) and c) we make the hypothesis that the bead is stuck to the surface. In this case, we could measure the minimal force needed to detach the bead, either by pushing laterally (b) or by pulling it (c). For pulling the bead from the surface, a permanent bonding between the bead and the RTS should be possible. Finally, Figure 5.2 d) illustrates how mechanical stress tests could be performed on a desired cell.

But both the cell mechanical stress application and the surface friction analysis through microbeads raise the following question: are the values obtained during the RTS characterization still valid when it pushes an object? Indeed this object will probably deform the flow speed and therefore impact the RTS propulsion. If it is the case, it is essential to correct the RTS characterization to be able to propose microbead based friction measurements or for pushing cells applications. Hence, this section presents an experiment to analyze and discuss how the robot characterization can be adapted to a robot-bead combination or to the case where the robot pushes a spherical cell. For this we will adapt the protocol used for the RTS characterization to include the characterization of the RTS combined with a polystyrene microbead. We will also show how this protocol can be adapted to avoid suffering from the RTS repeatability error due to changes in its magnetization.

In this section we first present the theoretical background on the linearity of the propulsion matrix. This is essential to later analyze rigorously the impact of the bead on the RTS propulsion force. In this analysis, we assess the difference between the real propulsion of the RTS-bead combination and the propulsion deduced by the sum of the RTS and bead propulsion matrices. Then we present how microbeads can be placed at the extremity of the RTS to be manipulated inside microfluidic chip and to be characterized. Finally, the measurement protocol is presented and the associated results are discussed concluding on the impact of the bead on the RTS propulsion and drag force.

Theoretical background

General principle

In the introduction, we mentioned that the two closest applications for the RTS as a force sensor seemed to be the force stimulation on a cell or a micro-organism and the friction measurements through a bead. In these two cases, it is essential to investigate how the spherical shape of the cell or the microbead impacts the propulsive force of the RTS.

To formalize this we need to consider the propulsion matrix coefficients. First let us consider that the robot and the pushed object are physically linked by an infinitely small link, so that the force and torque are transmitted through the link, and far enough from each other so that their flow do not interact as shown in Figure 5.3 a). In this case, the propulsion matrix resulting in the combination of the two objects will be the sum of the propulsion matrix from the robot and the object [START_REF] Purcell | The efficiency of propulsion by a rotating flagellum[END_REF]. But in practice, this infinitely small and long enough link does not exist, instead the RTS is in direct contact with the object as shown in Figure 5 Let us consider, as shown in Figure 5.3, P R the propulsion matrix of the robot, P B the propulsion matrix of the object and P RO the propulsion matrix of the robot and object combination. We will consider ∆P which is defined by: ∆ P = P RB -(P R + P B ).

(

To find ∆P , we need to adapt the characterization protocol to be compatible with the robot-bead combination. As we presented in Chapter 4, our experiment protocol reveals only the first line of the propulsion matrix. However this is sufficient to correct the force measurement. For the pushed object we choose a 10µm polystyrene bead. Depending on this result further experiments should be conducted to build a general model that can adapt to a large variety of objects.

Error calculation

In the following we analyze the value of the maximum error made on ∆P coefficient. A rough estimation of this error could be to simply add the error on a and b on each experiment. However some error affects these coefficients in the same way and therefore cancel each other when we calculate the difference. This is why we need to expand the calculation. We want to assess the value Delta P defined by:

∆ P = P RB -P R -P B , (5.2)
with P R , P B , P RB respectively the propulsion matrix of the RTS, the bead, and the RTS and bead combination. So the corresponding error is:

ε ∆ P = ε P RB -ε P R -ε P B . (5.3)
This expression can be expanded for a' and b' coefficient:

ε ∆ a = ε a RB -ε a R -ε a B (5.4) ε ∆ b = ε b RB -ε b R -ε b B (5.5)
By using equation 4.36 we can expand the first and second term of 5.4:

ε ∆ a = ε F RB + ε v 0RB (a RB ν) + ε ν (a RB v 0RB ) v 0RB ν - ε F R + ε v 0R (a R ν) + ε ν (a R v 0R ) v 0R ν -ε a B , (5.6)
with F RB and F R the gravity and buoyancy force on the RTS bead combination and RTS alone respectively. v 0RB and v 0R the speed at 0 Hz on the RTS bead combination and RTS alone respectively and ν the fluid viscosity.

we introduce F B the gravity and buoyancy force on the bead alone such as: F BR = F B + F R . Therefore as we neglect the error on the bead dropping test we have:

ε a B = ε F B νv 0 B (5.7)
Therefore by using this decomposition, the equation 5.6 can give a better approximation of the error on ∆ a :

ε ∆ a = ε F R 1 v 0RB ν - 1 v 0R ν + ε F B 1 v 0RB ν - 1 v 0B ν + a R ε v 0R v 0R + a RB ε v 0RB v 0RB + ε ν ν (a R -a RB ) (5.8)
Similarly ε ∆ b can be expanded by using equation 4.37:

ε ∆ b = ε a R m R + ε m R -ε a RB m -ε m RB -ε b B , (5.9)
with m R and m R B the slope coefficient of the linear relation between the rotation frequency and the speed of the RTS bead combination and RTS alone respectively. Errors on this slopes are deduced from the standard deviation of the experiment. By introducing δ m such as m R + δ m = m RB the error on the difference of b coefficient can be given by:

ε ∆ b = m R (ε a R -ε a R B ) + δ m ε a RB + a R ε m R + a RB ε m RB + ε b B (5.10)

Bead manipulation

In Chapter 3.1.4 we demonstrated how to move beads by spintop. This was possible thanks to the flow around the RTS creating a vortex with closed flow lines. In this bead transportation method, there is no direct contact between the bead and the RTS, thus it is not possible to transfer the force created by the corkscrew motion to the bead. To transfer the force to the bead, it is preferable to put the bead at the extremity of the RTS head. Fortunately it seems that the flow around the rotating RTS can trap the bead in a stable equilibrium at the end of the head. Figure 5.4 shows the easiest protocol to pick a bead on a surface with the RTS and to move it. Between the steps 1 and 2 the robot swims just above the bead and then swims down while aiming at the bead. When the robot touches the bead it remains on the top. Then between steps 2 and 3 the pitch is changed to push the bead vertically.

ROBOT BEADS COMBINATION TOWARDS FORCE SENSING APPLICATIONS 125

Usually, with the polystyrene bead used for the experiments, the adhesion with the surface was sufficient to keep the bead at the same place. However sometimes the robot-bead combination starts to move in a spintop motion way. Between steps 4 and 5 the pitch angle is further increased to make the robot-bead combination take off. This is the most critical point as the release of the bead from the surface can generate a perturbation that removes it from the top of the head. Then step 6 shows how the bead can be moved through a microchannel. This is used to pick a bead in the main chamber of the microfluidic chip and to isolate it inside the drop test chamber for characterization. In all these steps, it is essential to keep the RTS rotating otherwise the bead detaches from the head of the RTS.

Sometimes and especially when the bead is stored in the drop test chamber for several days, the stiction between the bead and the surface increases. In this case it is possible to make the measurement proposed in Figure 5.2 b) by stopping just before step 4 and by increasing the rotating frequency until the bead detaches. This phenomenon was not repeatable enough to present clear measurements but the corresponding force needed to detach the bead was around 20 piconewtons.

robot-bead combination characterization

Protocol

The result of the RTS characterization presented in Chapter 4.5 left us with the problem of the measurement repeatability. Indeed it was found that if the rotating frequency of the RTS was cut a long enough time for it to sediment on the surface, the magnetization of the RTS could change and impact significantly the ratio between the force and the frequency. To solve this issue, we suggested to find a certain magnetic field pattern that could reset the magnetization of the RTS or to change the fabrication techniques to get a more repeatable design.

But even if this problem should be solved in order to offer a simple force sensing application protocol, we want to bypass it for now to perform our measurements. Therefore, we use a protocol where the robot is characterized in a row with and without bead. For this, the measurement of the robot-bead combination is firstly made at one frequency, then the propulsion of the RTS is reversed for few seconds to detach the bead. Finally, the characterization of the RTS without bead is performed. In this way the magnetization of the RTS should not change. To be certain of this, we repeat the measurement several times and compare the results.

It is also essential to perform a drop test of the robot-bead combination at 0Hz. As the robot is not rotating here, its magnetization state does not need to be controlled and this experiment can be performed after the other ones. In this experiment it is important to put the robot on top of the bead. Indeed the robot falling speed is quicker than the bead. Therefore if it is placed under the bead they will detach and fall at different speeds. For further tests with heavier or larger beads, this order could be reversed.

To assess how linear the combination of the bead and the RTS is, we also need to get a characterization of the bead. As we consider only the first line of the propulsion matrix, we need to know the relation between the drag force, the speed and the rotating frequency. Therefore, as we defined in equation 4.3 we need to identify a and b such that

F = ν(a v + b ω), (5.11)
with F the drag force, ν the fluid viscosity, v the speed and ω the rotating speed.

As the sphere has 3 axes of symmetry, its b coefficient is null [START_REF] Purcell | The efficiency of propulsion by a rotating flagellum[END_REF]. This result is intuitive as it means that a spinning sphere will not produce a corkscrew force. The drag on a sphere in a viscous medium is well known and the value of a is the following a = 6πr, (

with r the radius of the sphere that can be measured directly with the microscope. Therefore it is possible to get the coefficients a and b of the sphere propulsion matrix without any experiment. However the mass of the bead is not known precisely. So we perform a drop CHAPTER 5. TOWARDS HELICAL MICROROBOT SENSING APPLICATIONS test with the bead only to measure it. In this drop test the weight is compensated by the fluid drag. We deduce the mass of the bead with the following equation:

m = 6πrvν g , (5.13)
with m the mass of the bead and g the gravity constant at earth surface. The different characteristics of the bead are available in Appendix I.

Top focal plane

Bottom focal plane

RTS+Bead: 80 Hz RTS: 80 Hz RTS+Bead: 0 Hz Bead: 0 Hz All the preparation steps for the microfluidic are similar to the ones presented in Section 4.4.1. The only difference is that the polystyrene microbeads are injected with the input of the microfluidic chip while the RTS is protected from the flow in the drop test chamber. Then the fluid input and output of the chip are closed and the RTS picks a bead and brings it inside the drop test chamber. The measurement protocol is described in the following list. These steps are also illustrated in Figure 5.5.

1. Four drop tests of the RTS at 0Hz are performed in different locations of the chamber to verify that there is no parasite flow.

2. The RTS picks the bead. The rotating frequency is set to 80Hz.

3. The RTS-bead combination is characterized during the ascending of the drop test chamber (see Section 4.2.2 for more detail on the measurement method).

4. At the top of the drop test chamber, the RTS rotating direction is reversed for one second to detach the bead.

5. The RTS swims back at the bottom of the drop test chamber.

6. The RTS without bead is characterized during the ascending of the drop test chamber.

7. The RTS picks again the bead to repeat the measurement (the steps 2 to 6 are repeated 3 times).

ROBOT BEADS COMBINATION TOWARDS FORCE SENSING APPLICATIONS 127

8. The RTS picks the bead, brings it to the top of the drop test chamber and aims the ground to place the bead under the RTS. Then the field is cut (0Hz ) and the RTS-bead combination is characterized during the descending of the drop test chamber. This step is repeated 3 times.

9. The RTS picks the bead, brings it to the top of the drop test chamber. The RTS rotating direction is reversed for one second to detach the bead. The bead alone is characterized at 0Hz while it falls naturally at the bottom of the drop test chamber.

Results and Analysis

Figure 5.6 displays the speed measures at 0 and 80Hz, with and without beads. These data were obtained with the protocol presented above. For each measurement point, we made four measurements and we display the standard deviation. For the speed of the bead alone at 0Hz only one measurement is necessary as this phenomenon is reproducible. The speed of the RTS alone at 80Hz presents a relatively low standard deviation. This means that no change in the magnetization has occurred between the measurements, hence the force measurement was repeatable. Therefore it is relevant to display all the measurements on the same plot. We first see that the RTS ascending speed reduces when it pushes the bead. This seems intuitive as the bead adds weight and drag without bringing extra propulsion. At 80Hz the measurement with a bead has an important standard deviation compared to the others. This is probably due to an instability in the bead trapping at the head of the RTS. Indeed during the experiments we observed that the bead gets misaligned with the RTS and the occurrence and duration of this phenomenon was not repeatable on every experiment.

What seems less intuitive is that the falling speed at 0Hz of the robot-bead combination is faster than both the bead and the RTS falling speed. This reveals that the propulsion matrices of the two objects do not add linearly. To quantify this difference we calculate the propulsion matrix coefficients a and b for both the RTS and the RTS-bead combination. Their value and Table 5.1 -a and b coefficients of the RTS, the bead and the combination of the two objects. the difference compared to the linear solution are presented in Table 5.1. In this table we present also the difference between the experimental solution (P RB ), the linear solution (P R + P B) and the difference between the two (∆P = P RB -P R + P B).

For a the difference represents 30% of the value obtained by linear addition of the propulsion matrices. The error is estimated to 4%. As a is always negative, a smaller value corresponds to an increase of the drag. Therefore a positive value for ∆a means that the fluid drag increases less than it should in a linear behavior. This makes sense as the bead protects the RTS from the relative flow and so reduces the fluid drag on the RTS when there are combined together.

For b the difference represents 15.5% of the total value and is negative with an error estimated around 13.5%. This means that the force delivered by the RTS is reduced when a bead is present at the RTS head and deforms the flow. This makes sense at it is hard to consider that the bead presence could increase the force of the RTS. This change mean that the force obtained by the characterization of an helical microrobot should be corrected when this one push an object as this force is given by: F = νb ω.

(

However the large error on b do not allow to deduce a precise value of the propulsion reduction. To study this, increasing the stability of the bead trapping could help to get more reproducible data leading to reducing the error during the calculation.

Conclusion and perspectives

In this section we have suggested two potential applications on microfluidic chips where an helical microrobot could be used as a force sensor. The first one is cell stimulation where the RTS could be used to study the reaction of a cell to an external force. The second is surface friction measurement. We suggested to use microbeads as an interface between the RTS head and the surface to benefit from their simple geometry and their surface treatment possibility. In these two applications it is essential to study how the force created by the RTS evolves close to a spherical shape, which can be a cell or a microbead. Therefore we proposed a protocol to reveal the impact on the propulsion using a drop test characterization inside the controlled environment of a microfluidic chip. A helical robot with a diameter of 5.5µm and a length of 55µm loses 6 % of it propulsion force while pushing a sphere of 10µm.

As a short-term perspective for this work, it seems essential to see the influence of the size of the bead. This will allow the construction of a predictive model on the impact of the propulsive and drag force depending on the bead radius which could be used to correct the force and drag applied on a RTS pushing a spherical object. If this model becomes too complex and leads to imprecise corrections then the geometry of the RTS could be adapted to reduce the non-linearity of the b coefficient in the RTS-bead combination propulsion matrix. Both the impacts on the drag (a coefficient) and on the propulsive force (b coefficient) may be reduced by increasing the size of the RTS head, hence providing more space between the corkscrew shape and the bead. Moreover this difference might be largely due to the instability of the bead positioning on the RTS head. Therefore by solving this instability this non-linearity could maybe further reduce.

It is also essential to consider the link between the RTS and the bead more in detail to increase its stability and get more repeatable measurements. For this, a change in the shape of the RTS could help bringing a stable equilibrium directly by physical contact between the bead and the head of the RTS [START_REF] Tottori | Magnetic helical micromachines: Fabrication, controlled swimming, and cargo transport[END_REF]. A way of making a strong or a permanent bond between the RTS and the bead should also be investigated to allow force measurements, by measuring the required force for the RTS to take off with the bead stuck to the surface as displayed in Figure 5.2 c).

FLOW MEASUREMENT FOR AUTOMATIC CONTROL STRATEGY 129

Then real force measurement experiments could be performed. First it seems simpler to start with non-biological measurements, for example the analysis of some surface property change like oxidation or adsorption of a particular molecule on a surface. For this, special care should be given to the choice of the bead and its surface in order to interact with the surface to measure.

Finally, making the RTS biocompatible would allow us to apply measurements to biological studies. As mentioned earlier, stimulating cells or micro-organisms could be one application.

Here surface friction analysis with a bead coated with antibodies or a pertinent protein could for example allow the scanning of several cells and detect one with a particular property.

Flow measurement for automatic control strategy Introduction

Sensors on robots can serve two purposes. The first one is to perform a measurement and to send back this information to the user. This is particularity useful when this environment is difficult to access directly with a sensing probe. This is the case for closed environments such as microfluidic chips where non-robotic sensors must be embedded during the fabrication and can only access predefined locations. The second purpose is to gather information on the environment condition to provide a better autonomous control strategy. If some robots are not aimed at performing measurements, all of them must use sensors in order to control themselves autonomously.

Helical microrobots are for now far to be autonomous and they mostly rely on direct human control. Currently, human control is the best way to deal with the new problems constantly emerging from the displacement of such microrobots in uncontrolled environments. However it depends a lot on the skills of the operator, and an untrained user can easily put the robot in dangerous situations where it can be destroyed or lost. Figure 5.7 illustrates the main dangerous situations arising from the RTS control. In surface motion, like spintop, the robot can be blocked by obstacles or stuck on a surface with an uncontrolled composition. In swimming, an important flow can carry away the RTS resulting in its loss whereas spintop motion is much more robust to the flow. In Chapter 3.1.2 we showed that the RTS could have an important robustness thanks to its multiple motions. However as no concrete feedback information was possible, the decision to choose between the different motions was totally left to the users who had to rely on their intuition to choose the most pertinent motion. But now, the characterization of the RTS allows us to have information on the flow speed. Indeed as the robot is characterized, we know its theoretical speed depending on our command input. Therefore the flow speed amplitude and direction can be obtained by subtracting the theoretical speed to the real speed of the robot which is available thanks to the visual tracking. This flow speed measurement can then be used as a feedback to automatically switch between the surface motions and the swimming motion. An automatic motion adaptation has the advantage to provide safe control for untrained users and to react within a very short delay compared to a human.

Moreover enabling a flow sensing inside a microfluidic chip could be interesting in itself. For now several technologies exist to measure the total average flux in a microchannel. For example, thermal probe [START_REF] Branebjerg | A micromachined flow sensor for measuring small liquid flows[END_REF][START_REF] Lammerink | Micro-liquid flow sensor[END_REF] assesses the flow speed by measuring the diffusion profile of a heat wave. Electrohydrodynamic flow sensors [START_REF] Fuhr | Pumping of water solutions in microfabricated electrohydrodynamic systems[END_REF] can also be used. Direct drag force measurement was proposed as well [START_REF] Gass | Nanofluid handling by micro-flow-sensor based on drag force measurements[END_REF], with the advantage of leaving the fluid properties unchanged. Other methods such as tracer injection and flow pressure measurements at different positions are also possible [START_REF] Gravesen | Microfluidics-a review[END_REF]. However all these methods give information on the total average flow but cannot give information of the flow speed at a particular position.

To address this need, Particle Image Velocimetry (PIV) was proposed at the microscale [START_REF] Santiago | A particle image velocimetry system for microfluidics[END_REF] and applications on characterizing biological flows were presented [START_REF] Lima | Confocal micro-PIV measurements of three-dimensional profiles of cell suspension flow in a square microchannel[END_REF][START_REF] Lima | In vitro blood flow in a rectangular PDMS microchannel: Experimental observations using a confocal micro-PIV system[END_REF]. This technology consists of injecting multiple particles inside the microfluidic chip. Each particle behaves like a tracer in the flow, so to have a good resolution and to be sure to cover any position, a large amount of particles needs to be injected. Therefore helical microrobots could present at least two advantages compared to PIV. First the RTS can go to any location, whereas in PIV a large amount of particles is required to be sure to have one at the desired location. Thus it could be interesting in the case of microfluidic chips where particle contamination needs to be avoided. Secondly, the particles need to have a perfectly neutral buoyancy (meaning that the buoyancy force compensates exactly the weight). It could be particularly interesting to study cyclic flows such as convection loops for a long time. Indeed in this case particles can settle with time either on the top or the bottom of the chip whereas a RTS could always be sent at the desired location for the measurement.

So in this section we first want to demonstrate that the RTS is able to measure the value of the flow via visual feedback. To prove this we propose to measure the flow profile inside different rectangular microchannels and to compare these results with numerical simulations. Then we want to apply this flow measurement to perform a closed-loop control that decides the best motion by automatically switching between spintop and swimming depending on the flow conditions. For both these applications, it is essential to develop a closed-loop system for the swimming motion. Indeed to make the microchannel profile measurement, the RTS needs to be controlled along a given path in three dimensions. Then to demonstrate the automatic adaptation to the flow, both the closed-loop in spintop presented in Chapter 3.2.2 and a closed-loop in swimming will be used.

We first present the swimming closed-loop control as it is a required tool for the rest of the section. Then we explain the flow measurement principle and assess its validity by measuring the flow profile in a microchannel with a rectangular section. Finally, an algorithm to automatically adapt the RTS motion along a predefined path is proposed and fully tested with different flow conditions. The pitch, yaw angle and frequency are sent to the thread that generates the command of the magnetic field. This command substitutes the manual command.

Swimming closed-loop control

To enable reproducible measurements it is simpler to automatize the measurement process. Moreover we want to use flow measurement to feedback information to an automatic control 5.3. FLOW MEASUREMENT FOR AUTOMATIC CONTROL STRATEGY 131 system which will decide the best strategy between surface motion and swimming motion. A primary required step is to develop a closed-loop control for the swimming motion.

Swimming motion is by nature a 3D motion. However as already mentioned our tracking is limited to the 2D horizontal plane. For now, we propose a closed-loop control on this plane while an open-loop maintains the RTS at the same altitude by compensating its weight. As this is an open-loop, we cannot prevent from a small drift and the RTS will slightly change altitude with time.

Figure 5.8 presents our control strategy. In order to use a simple Proportional Integrative and Derivative (PID) controller based solution, we decouple each direction of space (x, y, z). On each of these directions we express the propulsion force in the corresponding rotation frequency (ω x , ω y , ω z ). ω x and ω y are calculated with a PID controller fed with the error on x and y between the track position and the command position. For ω z we used the characterization of the RTS to determine the needed value to overcome gravity corresponding to ω z = mg b ν with b the second term of the propulsion matrix and ν the fluid viscosity. Then these terms are processed to give the corresponding value with frequency (ω), pitch (θ) and yaw (ψ) angle to the thread commanding the magnetic setup.

Figure 5.9 a) presents a photomontage of the experimental view during a swimming closedloop on a rectangular path. During the experiment a flow around 5µm • s -1 was pushing the RTS opposing the y direction. This explains why the real path is always below the command path for y. Figure 5.9 b) displays the evolution of the command and real position with time during this experiment. We see that the RTS converges to the command position when it stops moving. But a relative important error and delay are present for a moving command. Unfortunately we saw experimentally that a more reactive system presents a risk of being unstable and therefore the PID controller could not be tuned to reduce more this error. This is mainly due to our tracking system. A brief explanation on this tracking principle is here necessary to fully understand where the instability can come from. The tracking works by detecting connected pixels with the similar gray level. The gravity center of these pixels is computed to obtain the robot center position. The software then calculates the RTS position and speed. However, the physical center of rotation of the RTS might not correspond to the gravity center of the detected image by tracking. In this case the rotation of the RTS will produce a displacement of the tracking gravity center resulting in a change of position. With low reactive PID tuning, this error is negligible. But if the PID parameters are increased to reduce the error and phase shift, it can trigger instability in the robot behavior. If they are pushed further, the position control becomes unstable.

This problem could be solved by a more sophisticated tracking algorithm. For example, detecting features such as the two heads of the RTS could greatly help detecting the real gravity center of the RTS and reducing the link between the position and rotation of the RTS. However the creation of such a robust tracking is not straightforward as it needs to work for every RTS configuration in space. Hence this kind of optimization is beyond the scope of this thesis and could be premature, especially because the shape of the RTS and the feedback method could change for different applications.

Flow measurement principle

With the RTS characterization presented in Chapter 4, it is possible to estimate the speed of the robot relative to the fluid from the input command. Indeed from this characterization the speed of the RTS can be deduced from the frequency using the formula presented in equation 4.3. If the RTS is only surrounded by liquid this equation gives:

V = - bω a r - mg a z, (5.15)
with V the speed, ω the rotation frequency, a and b the two first coefficients of the propulsion matrix given by the characterization, m the weight of the RTS, r a unitary vector parallel to the RTS and z the unitary upward vertical vector. Figure 5.10 shows how we can deduce the speed of the flow from the knowledge of the RTS theoretical speed. For this, we use a measurement of the absolute speed thanks to the image tracking of the camera. Then we subtract this speed to the theoretical speed which is modeled thanks to the RTS characterization. The obtained difference corresponds to the flow speed.

Figure 5.10 also explains how this calculation is made in our control software. It is important to note that for more precision on the theoretical speed we directly use the tracking information of the yaw angle from the tracking instead of the commanded one. Indeed as the amplification and electromagnetic coils stage does not have a perfectly linear behavior small errors in the command direction can happen.

As shown in the equation 5.15, this method is not limited to the horizontal plane and could perfectly work in 3D as the weight of the RTS is estimated. This speed estimation could work even without the robot weight knowledge as the equation 5.15 corresponds to the experimental speed curve given by the drop test performed for the characterization. In this case only the ratios bω a and mg a are needed. However because of the limitation of our setup, we have only implemented this method in the horizontal plane. To get an estimation of the vertical flow speed, a way of tracking the RTS altitude is required. The implementation of such tracking based on the focus of the RTS is for now one of our main perspectives as it will also allow 3D swimming closed-loop control.

Flow profile measurement

To demonstrate the flow sensing ability of the RTS, we propose to analyze two different flow profiles due to different channel geometries inside the microfluidic chip. Figure 5.11 displays the geometry of these two profiles. They are both rectangular section channels with a 1mm height. The width, represented by e in Figure 5.11, is the only difference between the two channels. One has a width of 0.3mm and the other of 3mm. Both sides of the channel are respectively connected to the microfluidic input and output. These connections are connected to two reservoirs with different pressures. Therefore this generates a pressure difference between the microfluidic input and output which results in a flow inside the channel.

This geometry has the advantage of having a flow speed component only in the horizontal plane. This is required as our closed-loop system only works on the horizontal plane and we can only measure speed along this plane. In Figure 5.11 the path of the RTS is displayed in red. This path is in the middle of the channel and goes from the bottom to the top. The closed-loop control maintains the RTS centered on this path, the vertical component of the propulsion is set constant. Therefore the vertical speed of the RTS can be considered also constant. In a post-process step this speed is measured precisely by determining the time when the RTS hits the upper wall of the channel. During the experiment the altitude of the platform is moved manually to keep the RTS in the optical focus plane. As we concluded in Chapter 4, the change of magnetization of the RTS with time can lead to the evolution of its characterization properties. To quickly solve this problem while a permanent solution is investigated to stabilize the RTS magnetization, we use the same method as for the bead measurement. We perform a quick characterization of the RTS right before starting the closed-loop. For this we close the input and output of the chip to ensure that there is no remaining flow. Then we measure the horizontal RTS speed at a given frequency. This is partially automatic and the user only has to drive the RTS in a straight way for few seconds while pushing a certain key on the keyboard. Then the new characterization is directly updated in the control code for the closed-loop system to be efficient. The characterization at 0Hz corresponding to the falling speed of the RTS is not impacted by the magnetization and is only made once in the drop test chamber.

Figures 5.12 a) and b) show the flow profiles measurement for the two different channel widths e. As expected, a parabola shape is obtained for e = 3mm. Indeed in this case the lateral walls are too far to have an influence on the flow and the solution is close to the 2D one with infinite e value. For e = 0.3mm, the walls have an important influence and the solution is closer to a square shape flow. To provide a comparison, we simulate with the finite element software Comsol the expected flow profile for the two channels. The Stokes equation was used to compute the flow by taking the IPA viscosity at 20 • C. The obtained profiles are scaled to match the maximum value of the experimentally measured profiles. Therefore, as the flow is linear,the flow profile is the same for any pressure shift between P 0 and P 1 . We take it equal to 1 bar. We see that the measured shapes fit well the simulated ones. The small difference between experiment and simulation and the relatively important noise can be attributed to the tracking algorithm. As presented with the swimming closed-loop, the change in RTS direction impacts the tracking position. Therefore an error is made on the RTS speed when its direction changes. Moreover if the focal plane is not perfectly set in the middle of the RTS, either the top or the bottom will be more in focus thus resulting in the displacement of the tracking center. This error can also be important as we manually track the optical plane which creates another artificial speed of the RTS added directly to the measurement.

Solutions to improve the flow sensing should mainly focus on a better image tracking. But these results seem satisfactory enough for a proof of concept. As we concluded for the swimming closed-loop, optimization is beyond the scope of this thesis which focuses on evaluating the RTS sensing possibilities. Further developments might be premature as long as no concrete applications are directly aimed at.

Figures 5.12 c) and d) show the horizontal error along the path during the measurement. This error is mainly caused by the difficulties of the PID controller to keep the RTS at the same position as the flow intensity changes with the altitude. This explains why the error on y is almost null: there was no flow on the y axis. This error is more important for the solution with e = 0.3mm because the flow speed was more important in this case.

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135

Control strategy adapted to flow speed

Principle

To limit the risk of the RTS to be carried away by the flow and to improve its robustness, we want to develop a semi-automatic control. The user could benefit from his/her high level understanding of the physics and the situation in order to define the best path in the chip. Then the RTS control system could compute the safest motion along this path. Therefore we propose here to develop such algorithm ensuring the safest RTS displacement along a predefined path. To design this algorithm, we first need to see how the dangerous situations presented in Figure 5.7 can be avoided. Unfortunately the surface stiction is for now difficult to detect in advance. We hope that further research on the friction between the RTS and the surface will propose a solution to evaluate the stiction probability of the RTS. However, an excessive flow can easily be detected. Therefore the best motion decision algorithm can be summarized for now in the following sentence: "If swimming is possible then use swimming." Figure 5.13 explains how this algorithm is implemented with our current system. In swimming motions the RTS follows the path by closed-loop control. Then if the flow measurement exceeds a given threshold the state changes and the RTS switches to "swimming to spintop" mode. In this state the RTS aims the ground at the fastest speed. The collision with the ground is detected by evaluating the difference between the axis of the RTS and its direction. In swimming this difference is close to zero whereas it is close to π 2 in spintop. In order not to interfere with this measurement, the direction of the robot is set constant. The last measured flow speed is used to determine a direction that will compensate the flow drift.

Spintop

When spintop is detected the closed-loop on the path is restored and the RTS continues its way. The decision of trying to come back to swimming is for now made by the user. Indeed CHAPTER 5. TOWARDS HELICAL MICROROBOT SENSING APPLICATIONS he/she is in the best position to determine if the flow speed has reduced. But to reduce even more time in spintop and therefore the probability of getting stuck to the surface, triggering periodically the command to come back in swimming could be an alternative solution.

When the user pushes a specific key, the RTS switches to the "spintop to swimming" state. In this state the RTS will try to go to 100µm altitude for swimming. As we do not have yet an altitude tracking, we evaluate this altitude by the time. Indeed the speed along the vertical axis is controlled with an open-loop thanks to the RTS characterization. No feedback on the RTS altitude is possible for now. Therefore this vertical speed is set to 20µm•s -1 and a timer is started at the beginning of this state. When the timer reaches 5 seconds the RTS comes back to the swimming state and continues to follow the path by closed-loop control. A constant horizontal position during the "spintop to swimming" state is maintained by the swimming closed-loop algorithm. Indeed even if the vertical position is controlled in an open-loop way, the swimming closed-loop is possible only for horizontal command. Therefore the RTS compensates the flow and is maintained in the same x and y position during the "spintop to swimming" state. As the RTS is in swimming mode during the ascension, the flow can be measured. If it becomes larger than the flow threshold, the RTS comes back to the ground by switching to the "swimming to spintop" state. Therefore trying to switch to swimming is guaranteed without risk of losing the RTS on the flow and can be tried as often as one wants. As the flow measurement is a bit perturbed when the RTS takes off, we wait one second before checking for overflow in this state.

Experiments

To test this algorithm we propose to command several paths of a rectangle. This repetition of path is required as we do not have implemented a moving platform to follow the RTS on the chip on a long closed-loop path. This gives us time to tune the flow in order to test the motion adaptation algorithm. To precisely tune this flow, the input reservoir is put on a platform where the altitude can be set manually with millimeter precision. As both input and output reservoir surfaces are connected to the ambient pressure, the elevation of the input reservoir creates a pressure difference that generates a flow. To reduce the noise of the flow measurement by the RTS, we perform an averaging of its value on one second.

Figure 5.14 shows the results for this path. In this figure, experimental screenshots are taken at different times. As we do not have an altitude tracking system, the focus is set manually. At first the RTS follows the path by swimming closed-loop as it can be seen in the picture a). The altitude is around 100µm. At the end of the first path on the rectangle we start to increase the flow gradually. At the beginning the RTS can continue to perform the swimming motion and the PID controller automatically compensates the drift due to the flow. The picture b) is taken at this time. We see that the RTS is not parallel to the path to compensate the flow drift. Then the flow value reaches the threshold which is set to 15µm • s -1 . This triggers the transition to spintop and the RTS control switches to the state: "swimming to spintop". The closed-loop control is stopped and the RTS aims for the ground. Even if the direction of the RTS is set to compensate the flow, some errors in the position appear in the y position.

When the RTS touches the ground, the closed-loop is restored in spintop. The details on this closed-loop control are presented in Chapter 3.2.2. As the propulsion is controlled by the pitch angle in this motion, the frequency is set to 100Hz. The flow measurement becomes impossible and is therefore stopped. The picture c) is taken during this spintop closed-loop control. To test the ability of the RTS to come back to swimming, we reduce the flow. Then we manually trigger the transition to the "spintop to swimming" state which restores the swimming closedloop. The picture d) is taken during this state. The horizontal position is kept constant as the vertical speed is set to 20µm • s -1 to reach an altitude around 100µm. After one second in this state, the flow threshold is reactivated to detect potential overflow. As it can be seen on the flow measurement curve, the take-off from spintop to swimming creates perturbations that increase the flow estimation artificially. This justifies waiting one second before restoring the flow threshold. After five seconds the wanted altitude of approximately 100µm is reached, because we set the ascending speed to 20µm • s -1 in the altitude open-loop. Then the closed-loop on x and y is set to follow the path and the altitude open-loop on a 0 µm • s -1 speed. As it can be seen in Figure 5.14 e) the swimming state is restored. In some cases where we would like to restore the swimming motion, the flow speed is still over the threshold and too dangerous for swimming motion. Therefore it is important to prevent the RTS from reaching the swimming state and to be carried away by the flow. Figure 5.15 a) shows a record corresponding to this situation. Here the RTS first follows the rectangular path with the closed-loop of spintop motion. Then the user triggers the transition to swimming and the RTS control switches to the "spintop to swimming" state. After one second the flow threshold is set and then the measurement flow reaches this threshold. This triggers the transition to the "swimming to spintop" state until the RTS reaches the ground and returns to following the path by spintop closed-loop.

Finally, Figure 5.15 b) shows what happens if the RTS control does not perform motion adaptation. In this experiment the RTS follows the path by swimming motion and the flow is continuously increased. At first, the RTS control can compensate the flow drift but as the necessary frequency gets larger than 200Hz, the RTS reaches its cut-off frequency and the speed no longer increases with the frequency. On the contrary the RTS speed decreases brutally after the cut-off (see Chapter 3.1.3). This results in an almost immediate loss of the robot from the frame and a potential definite loss. The rapidity of this phenomenon demonstrates the need of automatic motion control as a human user cannot monitor at all times the motion of the RTS to avoid this phenomenon. It can be seen on these three different experimental records that the flow measurement presents important fluctuations and noise. This error is due to perturbations during the brutal change of direction of the RTS while following the rectangular path. Therefore to reduce it, the solution would be to improve the tracking precision exactly as we presented for the absolute flow measurement in Section 5.3.4.

Conclusion and perspectives

In this section we first proposed an automatic control of the swimming motion. This automatic control relies on two closed-loop controls for the x and y coordinates and one open-loop control based on the RTS characterization for the z coordinate. This open-loop was necessary as we have currently no way to track the RTS altitude online. The automatic closed-loop was then used to measure the flow profile in rectangular channels with different widths. These flow profiles obtained by the RTS were shown to match the shapes obtained by numerical simulations. Then we showed that a semi-automatic algorithm with minimum user intervention is able to control the RTS along a path in swimming and to detect overflow to continue on this path with the spintop motion. As no information on the flow can be obtained, the signal to trigger the come back to swimming motion remains the only manual step. However if the user triggers this signal while the flow is still too important for the RTS to perform safely swimming, the RTS aborts automatically the transition to swimming motion and comes back to spintop.

CONTROL STRATEGY IN A MICROCHANNEL UNDER 100 MICROMETERS

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In the near future, it would be necessary to perform an altitude tracking of the RTS by analyzing the focus. This would enable the automation of swimming motion by providing a closed-loop on the vertical axis. With this feature, it will be then possible to also measure the vertical flow inside a microfluidic chip at any place reachable by the RTS. As mentioned several times in this section, a better tracking is essential to improve the measurement precision. However it should be wiser to invest in such tracking only when clear applications will be investigated in order to match exactly their needs.

To continue improving the robustness of the RTS, the motion algorithm could include the rolling motion. As presented in Chapter 3.1.3, the RTS presents more chance of being stuck to the surface while rolling than in spintop motion. But while rolling, it is even less sensitive to the flow. To do this, the impact of the flow on the spintop motion should be investigated in more detail. In fact, we saw experimentally that the flow has an influence on this motion. Therefore a rough estimation of it should be possible from the spintop motion. This estimation could then be used to choose if rolling is a more appropriate motion than spintop.

The final goal of this work is to propose an easy way to control helical robots with no prior knowledge of the robot control and problems. The user should be able to only enter the place where he/she wants to displace the RTS on the screen. Then the system should choose the best motion to safely go to this location. If this location is too dangerous to be reached, the displacement should be stopped and a warning displayed to the user.

Control strategy in a microchannel under 100 micrometers Introduction

Integrating helical microrobots inside microfluidic chips make them closer to potential application as microfluidics could benefit from these mobile characterization tools. However for now, in order to not suffer from surface perturbation, we mostly presented the RTS motions in wide environments with dimension close to the millimeter. But conventional microfluidic chips mostly deal with dimensions closed to 10 to 100µm. In this section we therefore discuss what happens and how the RTS can be controlled in a microchannel with a characteristic size closer to the RTS diameter.

Controlling a helical microrobot inside a small channel might seem difficult at first sight. Indeed for the same reason that it is harder to drive on a smaller road, it seems that a very high precision on both the microrobot direction and gravity compensation is required to align its direction with the channel. And avoid unintended touching of the wall that could result in permanent stiction of the RTS might be difficult. However, research on particles inside microchannels shows that the proximity of the surface could guide neutral buoyancy particles through the channel. Moreover this particles are focused in a precise position on this channel cross-section [START_REF] Di Carlo | Continuous inertial focusing, ordering, and separation of particles in microchannels[END_REF]. These phenomena were demonstrated theoretically [START_REF] Asmolov | The inertial lift on a small particle in a weak-shear parabolic flow[END_REF] and proved to be useful to sort the different components of a blood sample [START_REF] Di Carlo | Equilibrium separation and filtration of particles using differential inertial focusing[END_REF]. For other particles, micro patterns on the channel was proved to induce different particles location depending on their size [START_REF] Choi | Continuous hydrophoretic separation and sizing of microparticles using slanted obstacles in a microchannel[END_REF]. Therefore, with these results we can wonder if comparable phenomena arise on a microrobot moving inside a microchannel and how we can use these phenomena to improve the microrobot control. Of course, the conditions are not the same as in our case the microrobot is moving in a motionless flow and produces a rotation along the channel axis, whereas in the case of particles, they produce no flow but an external flow is applied on the channel. Nonetheless, the physical configurations involved are the same, and therefore similar phenomena on the microrobot could happen.

To investigate this question we first send the RTS through microchannels with size under 100µm. From this prospective experiment, we saw that as the RTS advances in the channel, it starts rotating around the channel center line resulting in a helical trajectory. From this observation, we proposed the control strategy displayed in Figure 5.16 to guide the RTS in any 3D microchannel with a 2D feedback.

The major advantage of this control strategy is that, as the RTS is rotating around the channel center, a 2D imaging system could be enough for the control. Indeed, on this 2D image the helical trajectory of the RTS inside the channel becomes sinusoidal. As the RTS position in the channel cross-section orbits around a position close to the channel center, the amplitude of the sinusoidal trajectory on the 2D image is enough to give a good estimation on the RTS position with respect to the microchannel center. Therefore there is no need of a 3D imaging and position estimation to develop a control that guides the RTS through an in-plane microchannel by only controlling the yaw angle (ψ).

However if this microchannel direction starts moving in 3D dimension which would be the case for in-vivo situation, such as blood or lymphatic vessels, one would need to control the pitch angle (θ) of the helical robot. Therefore this section focuses on proposing a numerical model to prove that the control of the yaw angle (ψ) is sufficient to guide the RTS through an in-plane microchannel, while focusing it on the center of this channel. Then this model will be used to find a way of getting information on the vertical misalignment of the RTS with the microchannel, in order to propose a control scheme for the pitch angle (θ). We will first describe how this model is built. Then we will compare the model results with various experimental cases in order to assess its validity and its limits. Finally, results on the implementation of the simulated 3D control scheme will be discussed.

Numerical simulation protocol

To propose a control strategy inside a microchannel, we need to get a better understanding of the rotation of the RTS in the channel cross-section plane. For this we model the RTS position in the cross-section of the channel with numerical simulations. To simplify, we consider the RTS as an infinite cylinder perfectly aligned with an infinite microchannel. A cylinder does not take into account the corkscrew shape and therefore does not simulate the flow parallel to the RTS producing propulsion. However we make this strong assumption as we are not interested in this propulsive flow but only the flow in the cross-section plane. Indeed, this flow is the one that can produce a fluid drag perpendicular to the RTS and the channel direction. The decoupling of these two problems is justified by the low Reynolds conditions that guarantees the linear addition Thanks to this assumption, we consider only the 2D problem in the cut plane defined by the microchannel cross-section. In the numerical simulations, we solve the Stokes equation given by: ν∇ 2 u -∇P = 0, (5.16) with u the speed of the flow, P the pressure and ν the dynamic viscosity. The boundary conditions are such that the flow speed is null on the microchannel wall and is equal to the RTS rotation speed on its surface. We used the software Freefem++ [START_REF] Hecht | New development in freefem+[END_REF] to perform the simulations. As explained in Figure 5.17, some other steps are required to get from these simulations to the reproduction of the RTS path in the microchannel cross-section. First the simulation of the flow is performed with the RTS at different places on the channel cross-section. We create a 100 by 100 grid that equally divides this cross-section and the simulation is run with the RTS positioned at each node. For each of these simulations we integrate the fluid drag on the RTS surface, this drag is given by the following formula:

F = s ∂U ∂n ds, (5.17)
with U the fluid speed, n the normal to the surface and s the total RTS surface. This integral is computed by FreeFem++. The integral of the pressure force on the RTS surface were not computed as they were negligible. By performing a linear interpolation of these data we can reconstruct a map of the fluid drag on the RTS. This map gives the associated perpendicular fluid drag created by the RTS rotation for any position inside the channel cross-section. This drag is a force and as any force applied on a free body, it creates a displacement. As seen in Section 4.2.1, the inertia of the RTS can be neglected, therefore we can consider that the speed of the RTS at a given time only depends on the sum of the forces at this same time. Moreover as we are in a low Reynolds number condition, we have a linear relation between the speed (v) and the force (F ) such that:

v = F a , (5.18)
where a is the drag coefficient and corresponds to the first coefficient of the propulsion matrix. However it is not the same as the one measured in Chapter 4 during the RTS characterization.

Indeed in our simulation, the RTS moves laterally in the cross channel section. Therefore we need to obtain the drag coefficient corresponding to this movement and not the one corresponding to the movement perpendicular to its direction produced by the helical rotation.

To bring the simulations closer to reality, we chose to measure this coefficient directly on the RTS. For this we perform a drop test at 0Hz following the protocol described in Section 4.4.1. However instead of keeping the robot vertically in the direction of the relative flow, we put it perpendicularly. By performing this test we find the following value for the lateral drag coefficient:

a = 8.40 • 10 -7 ± 0.2N • s • m -1 . (5.19)
We divide this value by the RTS length to fit our 2D model and inject it in the equation 5.18 to get a speed map of the RTS inside the channel cross-section.

Finally, a starting position on the channel cross-section can be chosen and the path can be integrated thanks to the speed map. This integration is made using a second order Runge-Kutta method and it is implemented in Python.

The protocol to reproduce this simulation and the associated codes are available in Appendix J.

Perpendicular rotation phenomenon inside a microchannel To study experimentally the behavior of the RTS inside a microchannel, we made a microchip containing microchannels of different dimensions. For fabrication simplicity, these microchannels have square sections and their edges vary from 100µm to 10µm. By moving the RTS inside these channels we first note that the wall proximity has an influence on the propulsion. As shown in Figure 5.18 a), a force perpendicular to the channel direction is applied on the RTS and translates it. This force seems to depend on the RTS position in the channel as a rotation phenomenon appears. This rotation phenomenon transforms the path of the RTS inside the microchannel from a line to a helical trajectory around this line. Indeed in Figure 5.18 a) the RTS moves to the top of the picture between 2 and 4 seconds. Between 4 and 6 seconds it seems not moving but the focus of the RTS change reveals a change in altitude. Then between 6 and 8 seconds, it moves to the bottom of the picture. During the experiments, we could clearly see that this phenomenon is periodic and that the RTS position inside the channel cross-sections evolves when it advances in the channel.

Figure 5.18 b) shows the results of this simulation with the starting positions of the RTS gradually increases from the center to the side of a 50µm channel. The trajectories represent the evolution of the RTS center. For starting points at a distance from the center inferior to 15µm, the trajectories are periodic and oriented in the same direction that the RTS rotation direction. This rotation corresponds to the one observed experimentally. For distance larger than 15µm, the trajectory center moves closer to the wall and the rotation is reversed. Indeed when the RTS is close to the wall, the direction of the perpendicular drag force changes and increases brutally. This may correspond to the friction with the wall creating a propulsive force similar to the propelling force in surface motions. This inversion of the force direction leads in the simulation to a stable equilibrium point (as the one displayed in green in Figure 5.18). However this model should not be valid for a position close to the wall because the 2D nature of our model neglects the relative flow of the RTS. This relative flow could create lift forces in this region [START_REF] Zeng | Wall-induced forces on a rigid sphere at finite Reynolds number[END_REF]. It is therefore difficult to conclude on the reality of the equilibrium for a distance to the channel center larger than 15µm. Therefore we investigated a way of proving that our simulations were valid for a distance from the channel center less than 15µm. For this, we chose to analyze the frequency evolution of the perpendicular rotation phenomenon with the microchannel size. Experimentally, we drive the same RTS into different square channels with an edge size from 18 to 85µm. Then we measure the rotation frequency by manually analyzing the video record of the experiment. For the measurements under and close to 20µm, the equilibrium was difficult to reach inside the channel. This seems to agree with the numerical simulations concluding that no stable regime exists under this channel size for this RTS diameter.

With the simulated model, several sizes of microchannels were studied. We first noted that the starting-point distance from the center has only few influence on the rotation period as it is displayed in Figure 5.19 a). Therefore we use the average value of the frequency to compare to the experimental data. Figure 5.19 b) displays the evolution of this frequency with the channel size for both simulated and experimental data. Even if the simulation seems to underestimate a bit the frequency value, the general tendency of the evolution is similar. This confirms the validity of the model which seems precise enough for qualitative measurements and to estimate the order of magnitude of the different phenomena for trajectories close to the channel center.

CHAPTER 5. TOWARDS HELICAL MICROROBOT SENSING APPLICATIONS

It is interesting to note that the frequency of the perpendicular rotation is correlated to the channel width but not to the starting position of the RTS inside the channel. Indeed it could be used as a tool to measure the channel width of an unknown environment. This could serve both for direct measurement or to improve the control of the RTS in such a confined environment. For example we could detect when the channel width becomes too small for a stable control.

By doing these tests, we also noted that the minimum distance from the wall for the rotation phenomenon to happen is constant and corresponds to a distance between the RTS surface and the wall of around 7µm. This means that the limit channel for this phenomenon is around 20µm in the case of this specific RTS. For smaller channels we can still move the RTS, but no frequency measurement was possible as the microrobot gets too often stuck to the surface. However we observe experimentally that there is still a rotation in the channel cross-section. Therefore a more complex model would be needed to understand more deeply this phenomenon and to control the RTS in such channel.

To conclude, we proposed dimensionless results which can be adapted to other helical microrobots as long as the low Reynolds condition is respected. The rotation phenomena can happen in a square channel if the size of the edge is between 3.3 and 17 times the helical microrobot diameter. This perpendicular rotation phenomenon turns out to be good news for the RTS control as it can guide the RTS through the channel. This means that the RTS follows the channel without touching the wall with a relative tolerance in its propulsion direction. Figure 5.18 illustrates this phenomenon by increasing the pitch angle of the RTS while moving in a 30µm channel. This experiment shows that the pitch angle needs to be increased to 33 • before the RTS touches the wall of the microchannel. Therefore the RTS control inside a microchannel seems to be simplified by the wall impact on the propulsion.

Stability of the perpendicular rotation phenomenon

To understand why the RTS is guided through the microchannel, we decided to add a constant perpendicular force on the trajectory simulation. This simulates a misaligned RTS where some part of the propulsion pushes it to the microchannel wall. For this we have to make the assumption that this force is small compared to the propulsive force. Indeed by working in two dimensions we are keeping a flow simulation where the RTS is aligned with the microchannel. This hypothesis is illustrated in Figure 5.21 a). distant from 8µm to the center are stable. This corresponds to a progressive misalignment of the RTS from the channel direction.

This stable equilibrium explains why the RTS seems to be guided inside the microchannel. However the order of magnitude of this lateral force seems smaller than during the experiments, where the RTS was still stable with a maximum misalignment of 33 • . In the simulations, the maximum force where a stable trajectory exists was found around 1/15 of the propulsive force. This corresponds to a misalignment of 4 • . This difference reveals the limit of our 2D model. Indeed, we assume that the RTS is aligned with the channel and transforms a misalignment into a lateral force. This seems justified for small angle deviations but introduces an important error for a large misalignment. Moreover as mentioned earlier we do not consider the effect of the flow created by the RTS relative speed. This could generate a lift flow [START_REF] Zeng | Wall-induced forces on a rigid sphere at finite Reynolds number[END_REF] keeping the RTS away from the wall. Therefore, further work with 3D simulations should be performed to understand the phenomenon appearing when the misalignment angle is important.

Nevertheless from the similarities between the simulations and experimental data, this model is valid when the RTS is aligned with the channel and distant from the microchannel wall. This model seems still valid even with a small misalignment around this axis in the center region of the channel, which is exactly what we need to propose a control strategy. shows our supposition that ψ can be controlled to produce a force proportional to the RTS distance from the channel center. c) shows with different path simulations the control of ψ is sufficient to control the RTS at a position close to the channel center, even with a small misalignment with the direction perpendicular to the optical plane (θ). d) shows a simulation proving that (θ) can be measured by the RTS focusing position on the channel, a=1/50 of propulsive force, k = 1/50 propulsive force per 30µm stiffness value.

Towards closed-loop in 3D channel with 2D view

In this subsection we demonstrate the theoretical feasibility of a control scheme for the RTS inside a microchannel with a section of 3.3 to 17 times the RTS diameter. To do so we use our trajectory model to simulate this control scheme. For this we need to make some hypotheses presented in Figures 5.22 a) and b). First to use our model, we assume that both misalignment on the yaw (ψ) and pitch angle (θ) can be modeled by adding a lateral force to a RTS with a direction aligned with the direction of the microchannel, which seems reasonable if these angles remain small. Then we also assume that the lateral RTS position on y compared to the channel center is measurable. This also seems reasonable for any feedback system that can detect both the microchannel wall and the RTS position. Figure 5.22 b) shows our control scheme. As we can measure the difference between the RTS and the center of the microchannel projected on the y-axis, we propose to adapt the pitch angle such that a resulting force tends to bring back the RTS to the center regardless of its z position. In our simulations, this force is proportional to the distance between the RTS and the channel center in the y coordinate. Moreover a constant force on the z-axis is set to push the RTS down and simulate a misalignment with the channel on θ. The result of this simulation is displayed in Figure 5.22 c). It shows that this linear control is sufficient to make the RTS position in the microchannel cross-section converge in a position close to the center. Therefore the RTS can remain controlled far from the wall inside the microchannel even with a minor misalignment on θ.

Furthermore Figure 5.22 b) illustrates that the change of θ and therefore of the misalignment force on the z-axis displaces the converging point of the RTS position in the cross channel on the y-axis. Indeed in this trajectory simulation the starting point is the same but the force on the z-axis varies from -1/50 to -1/50 of the propulsive force. The effect is that the converged position equilibrium of the RTS varies mostly along the y-axis. This means that the information needed on the z-axis can be indirectly measured on the y-axis, thus allowing us to control the 3D orientation of the RTS only with a 2D image. We therefore propose to control θ by correcting it from a distance projected on the y-axis between the RTS converging point and the center of the channel.

Even if the RTS control with ψ is robust to small misalignments of the θ angle, the control of θ is essential for evolving in a complex microchannel with a 3D direction evolution. This scenario is typically the case for in-vivo applications, where the helical microrobot could evolve inside blood or lymphatic vessels which are not straight. Moreover, we think that this theoretical control proposition could be really interesting for such applications because it does not require any complex 3D imaging system and it does not require high-imaging resolution as only the average position of the microrobot is sufficient. Indeed those requirements on the optics could be difficult to match with in-vivo applications with larger footprints than a microchip. Moreover obtaining 3D positioning of the robot through stereo imaging is difficult. As for the resolution of the image,in-vivo media could potentially be optically non-transparent and therefore require imaging technology such as ultrasound or MRI, which do not provide the same image quality as optical imaging.

Conclusion and perspectives

In this section we presented the effect of the wall proximity to the RTS propulsion in a microchannel both experimentally and with numerical simulations. We deduced that a rotating phenomenon is making the helical microrobot position move with a periodical pattern in the channel cross-section which results in a helical movement along the channel. The frequency of the pattern was shown to be proportional to the channel cross-section dimension regardless of the microrobot starting position. We showed that this phenomenon starts in a square section channel where the edge dimension is below 17 times the helical robot diameter and stops for a dimension below 3.3 times its diameter. We proved experimentally and by numerical simulations that this phenomenon helps the RTS avoiding the microchannel wall even when it is misaligned with the channel direction. From the difference between our model and the experiments we concluded that for a high misalignment angle, other forces were preventing the RTS from colliding into the channel wall but the 2D nature of our simulation could not simulate them. Finally, we demonstrated with the numerical simulations that a 2D feedback could be sufficient to perform a stable control of the RTS even if the microchannel direction evolves in 3D.

Proving experimentally the relevance of the RTS control strategy inside a microchannel should be the next important step. The main technical challenges concern the tracking of the RTS on the image. Indeed for now the tracking system is based on the propagation of an area having the same gray level. This tracking fails when other features such as the channel boundary comes close to the RTS position. This makes the tracking impossible in small channels.

A better understanding of the perpendicular rotation phenomenon is also needed to enhance control strategy. Understanding why the phenomenon seems more robust to misalignment in the experiments than in the simulations should be the starting point. For this, flow simulations with a 3D model is essential. It would avoid the errors due to the 2D assumption, which does not evaluate the effects of the relative flow created by the RTS speed.

After understanding the flow around the RTS and its control inside a microchannel, we should investigate what happens in the friction regime inside channels with diameters smaller than 3 times the RTS diameter. For this, a first step could be to send into a microchannel a helical microrobot pushing beads slightly smaller than the microchannel and with different surface treatments.

Conclusion of the chapter

This chapter presented different axes of development towards concrete applications directly coming from the RTS characterization inside a microfluidic chip. We first suggested using microbeads as an interface between the robot and the surface for friction measurements in order to benefit from the wide range of potential bead surface treatments. Another force application could be to apply stress on cells in a selective way. For both these methods it was essential to investigate how the propulsion matrix of the RTS was impacted by the proximity of a spherical object. After performing experiments, we concluded that the RTS propulsion matrix does not add linearly with a spherical object propulsion matrix and that the propulsive force is significantly reduced while pushing a 10µm diameter bead.

Another possible application is to measure the flow inside the microfluidic closed environment. We first demonstrated the measurement of the flow profile on different channels with a 1mm height. This measurement was proved to qualitatively match simulations. Then we proposed an algorithm that adapts the motion according to the measured flow value by switching between closed-loop in spintop and in swimming motion. The swimming motion closed-loop was experimentally demonstrated as well as this algorithm in different flow conditions.

Finally, we investigated experimentally and with simulations what happens when the RTS evolves inside a microchannel as it is an essential environment towards applications inside a microfluidic chip. We demonstrated experimentally that the RTS could be easily controlled inside such small channel thanks to a phenomenon we call "the perpendicular rotation phenomenon" that guides it through the channel. Simulations were performed to understand this phenomenon. These simulations were validated by comparing them with the experimental data for the rotating frequency evolution and order of magnitude of the phenomenon. Finally, the simulations were used to demonstrate the theoretical feasibility of a simple control scheme for the RTS evolving into a 3D microchannel with only a 2D feedback.

Chapter 6

Conclusion and Perspectives Conclusion

While many applications, such as drug delivery, minimal invasive biopsy, local sensing or cell manipulation have been proposed for microrobots, only few working examples seem ready to be used in real conditions. Indeed only a few microrobots succeeded to bring more than a proof of concept and proved themselves useful to another field. We can refer for example to a rolling robot manipulating delicately micrometric crystal in a fluid medium [START_REF] Tung | Protein crystal harvesting using the RodBot: A wireless mobile microrobot[END_REF]. Thanks to this, the crystal can be placed in condition for X-ray analysis without being damaged by the physical contact of the tweezers. For sensing, which is even more challenging than actuation as it requires quantification, we can refer to a millimetric force sensor robot able to study the force reaction of micro-organisms on a microfluidic chip [START_REF] Kawahara | On-chip microrobot for investigating the response of aquatic microorganisms to mechanical stimulation[END_REF].

Therefore it seems that the gap between the current state of the art and concrete applications is for now important. As a result, many attempts to present applications are limited to a proof of concept working only for very specific conditions. These results are valuable as they shed light on possible applications in a domain where physical models are not yet perfectly known. However due to these very specific conditions, the improvement to go from this proof of concept to a repeatable and useful process is difficult.

This explains why we did not choose to aim one specific application. We rather focused on the development of a multipurpose force sensor based on microrobot technology. By doing so, we constrained ourselves to remain general. We also refrained from early specific optimization that could lead to an overconstrained design too specific for real applications. In other words, as jumping directly from the state of the art to applications seems too difficult for the moment, this thesis focused on a more general development of the microrobot knowledge, in order to reduce this gap and allow future realistic applications. For this, we chose to develop an on-chip mobile microrobot force sensor. Indeed this microfluidic platform is a great way of controlling the environment to study the physics of the microrobot. Furthermore this platform is in need for mobile force sensors that could apply and measure a force in a specific location, identify a surface state by measuring its friction or analyze the inner flow structure. Therefore the work on the integration of the RTS in such an environment would be the first step towards more concrete applications.

Chapter 2 presents the design and realization of the system. As we are free from constraints coming from specific applications, our technical solutions rely heavily on prototyping technologies. Indeed, this freedom allows us to quickly explore the parameters of each part of the setup and to assemble all parts in a reasonable amount of time into a working system. More precisely, the 3D laser lithography based two-photon polymerization which is already known for the fabrication of helical microrobots [START_REF] Tottori | Magnetic helical micromachines: Fabrication, controlled swimming, and cargo transport[END_REF] associated with Physical Vapor Deposition (PVD) was used for the fabrication of the RTS. This offers a great versatility of design as we are only limited by the laser voxel resolution of the machine. We then proved that the RTS could be selectively detached by a tip with a 10µm diameter from their fabrication substrate where they are mass-produced. To move the RTS, we conceived a design with three pairs of Helmholtz electromagnets in the x,y and z directions. The electromagnet supports and frames were built thanks to a 3D printer. It 150 CHAPTER 6. CONCLUSION AND PERSPECTIVES allowed us to easily adapt this design in a second setup with better resolution and temperature control when the need appeared. A C++ software was programmed to generate the rotating command for the electromagnetic coils. This software was interfaced with an image analysis module (OpenCV and VISP). These modules perform the real time tracking of the RTS. This setup allows semi-automatic measurements which were essential to efficiently characterize and explore RTS motions. The microfluidic chip fabrication also followed the prototyping technology in order to rapidly test many designs needed to reach the solutions presented in Chapters 3 and 4. For this we chose a PDMS chip bond on glass for its quick and easy fabrication process. As we did not need high features resolution but a complex 3D geometry, we chose to use a micro-milling machine to perform the mold. This choice of using several flexible prototyping technologies has several drawbacks. For the RTS design it leads to a low magnetization as for the magnetization of the RTS only a thin layer of nickel is deposed on the polymer microrobot. Moreover the surface condition is not optimized. This led us to experiment in isopropyl alcohol to limit the stiction of the robot with the surface. The 3D printed plastic frames of the electromagnets suffer from deformation with the heating. Furthermore, these plastic parts do not support the integration of an internal cooling system. Finally, the PDMS of the microfluidic chip is porous which creates a parasite flow. Therefore, this approach is a trade-off between the ease to adapt to new challenges emerging from the RTS force characterization and the low optimized quality of the prototype setup. This makes possible the early identification of the real needs for optimization and prevents from losing time in unnecessary developments.

Chapter 3 shows how we could benefit from this system to perform the integration of the microrobot inside microfluidic chips. This is an essential step because untethered force sensors could be used in closed small environments such as microfluidic chips, where conventional tethered probes cannot access. Moreover microfluidic chips are a way of controlling the experimental conditions such as temperature gradient, fluid flow and wall proximity which are indispensable for the RTS characterization. To do this, we identified three different RTS motions: the swimming motion, where the RTS is propelled by its corkscrew motion and evolves in 3D in the fluid; the rolling motion where the robot touches the surface on all its length; and the spintop motion where the RTS touches the surface only with one of its extremities. Rolling and swimming motions have already been demonstrated on such microrobots but spintop motion was presented here for the first time. Therefore we investigated this motion and revealed two kinds of states: a first one where the contact between the head and the surface seems to obey a Coulomb friction model and another one where it presents a lubricated friction model. Unfortunately it was impossible to conclude on the reason that triggers the RTS in one or the other state.

This chapter also demonstrates that each of these motions have complimentary advantages and drawbacks. In a swimming motion the microrobot can evolve in 3D but is impacted by the flow. When rolling the robot is very robust to flow speed but not on the the surface condition. The spintop motion is a compromise between the two and has also the advantage of being precise and simple to control. To prove this, automatic closed-loop of the spintop motion control was demonstrated. By combining these three motions, the RTS was able to benefit from all these advantages while being less dependent on a particular drawback. This boost in mobility was the needed element for the robot to self-integrate and evolve inside a microfluidic chip. Indeed the path from the fabrication substrate to the inside of the microfluidic chip presents an altitude difference between the bottom of the chip and the fabrication substrate which requires a 3D displacement. It also presents some flow between the inside of the microfluidic chip and the open part where the robot is detached. That required the surface motion to be be robust to the flow speed. A specific protocol with an associated chip design and RTS control was elaborated for the RTS self-integration. This protocol is not limited on a particular type of RTS or microfluidic chip and it could be adapted for the general integration of helical microrobots inside microfluidic chips. We also developed a way of storing the RTS inside the microfluidic chip for long-term purposes and drying of the chip. The major difficulty was to deal with the high surface-to-volume ratio of the RTS which makes it very impacted by the drying interface between liquid and gas. Even if we found a solution, we could not prevent the RTS from being slightly damaged by this front, resulting in the change of it characterization properties.

The major contribution of Chapter 3 is to propose a way of integrating one specific helical microrobot into a microfluidic chip whereas a conventional way is to inject a solution with a large amount of microrobots inside this chip [START_REF] Ding | Microfluidic-based droplet and cell manipulations using artificial bacterial flagella[END_REF]. The selectivity is here crucial as the ability to tune individually each RTS is necessary to use it as a force sensor. Moreover it limits the perturbation that could result from the integration of several helical robots moving at the same time. This was an essential step both to bring the RTS on a platform that allows a control the environment for a precise characterization and to bring the RTS closer to potential on-chip applications. Chapter 4 presents the force characterization of the RTS. The main challenge of this chapter was to find a system and a protocol guarantying that the RTS could be characterized without any parasite flow. For this, we used a microfluidic chip, because its closed conditions limit the evaporation and the small dimensions limit the convection flow. As the characterization of the RTS needs to be vertical in order to use its weight as a reference force, we first designed a method to measure the vertical speed. This was performed by moving the optical plane of the microscope and analyzing the focus of the image during a post-process step. Then we designed a vertical drop test chamber inside the microfluidic chip. This chamber is a cylinder with a height of 1mm and a diameter of 400µm. To access it, a small channel with a square section of 80µm was designed. As only one channel connects this chamber to the rest of the chip, the parasite flow created by a leak or a difference of pressure between the input and the output are largely reduced. Moreover we demonstrated theoretically that the dimensions of this chamber guaranty the absence of thermal convection flow. Finally, to suppress any residual parasite flow due to leaks through the walls of the chamber, it was necessary to design this drop test chamber in the middle of a larger chamber. To check that there was no parasite flow we measured the falling speed of the RTS at 0Hz in different positions of the chamber at the beginning of every experiment. To prove that the drop test chamber geometry did not impact the RTS characterization, characterization tests were performed at different positions inside the chamber without finding any relative difference. For the characterization we needed to know the mass and volume of the RTS. We therefore simulated the 3D lithography and metallization process to get an estimation of these values and their associated error.

In this chapter we also made an attempt to measure the torque produced by the RTS. However we concluded that this measurement was not possible with our RTS as a small constant magnetic field is needed to keep the robot aligned with the flow during such measurement. This magnetic field also prevents the RTS from any rotation and therefore from any torque measurement. Further analysis should be made with different RTS geometries that can provide a stable position in the flow. Therefore, we could suppress the magnetic field and let the RTS freely rotates during the characterization.

Finally, we proposed a protocol to characterize a RTS and got an estimation of the force error. We concluded that the force delivered by a RTS could vary from 10 to 40 piconewtons depending on the frequency or pitch of the RTS. Several characterizations on the same RTS exhibit an important variation from two characterizations made at different times. This repeatability error has been estimated to have a maximum impact of 27%. However this value could be underestimated as only four measurements on the same RTS have been made due to their relative complexity. The main explanation for this difference is that the magnetization property changes with the RTS history leading to different propulsion efficiencies. We conclude that changes could happen when the robot is left for a long time and settled on the surface. On the contrary no change were observed when the RTS was constantly used and when brutal contacts with the surface were avoided. This is what leads us to conclude that the main hypothesis is a change of the RTS magnetization state. Indeed this change seems to happen when the surface contact causes an exposition of the RTS to the magnetic field in a different direction than the usual one. This could result in different parasite remanent magnetization that impacts the RTS characterization. However, the loss of ferromagnetic material and the evolution of the RTS structure with time cannot be totally excluded. Further studies on the RTS magnetization should be performed to definitely assess the hypothesis of a parasite remanent magnetic field. This result is an important conclusion of Chapter 4, and validates our approach based on prototyping technology. Indeed by allowing us to develop in a reasonable time a working microrobot system and measurement platform we could quickly build a first working solution. Then this solution was used to identify where optimization is really pertinent, which was impossible to know beforehand. Here the conclusion is that research on the RTS design and control to guaranty a constant magnetic property should be investigated.

As we explained at the beginning of this section, we have chosen to develop force sensing in general in order to avoid the constraints relative to specific applications. Indeed we think that to consider such constraints is premature and is too specific to benefit to long-term development of helical microrobots. However as our goal was to tighten the gap between the current state of the art and potential applications, it was important to investigate few application directions to prove that the RTS characterization performed in Chapter 4 really brings us closer to real applications. Therefore, some proofs of concept that rely on the RTS characterization were investigated in Chapter 5. To avoid the non-repeatability of the RTS characterization, we proposed a way to make a quick characterization just before the RTS use. However a full characterization is still necessary because the quick characterization does not provide the falling speed of the RTS at 0Hz. Moreover error estimation is not possible in the quick characterization. Anyway, we proposed coherent proofs of concept. But improving the design and control to solve the repeatability issue should be an important concern to reach a more precise force measurement.

We first suggested to use the force characterization of the RTS to investigate surface friction and stiction forces. For this, the simplest solution seems to use microbeads between the RTS and the surface as their surface properties are well-known and can be well-controlled. Therefore it should be easier to study surface properties with microbeads than the head of the RTS. Modeling the surface contact should also be simpler as the beads are spherical. Therefore, we firstly showed that we could place a bead at the tip of the RTS. Then thanks to our characterization protocol, we could evaluate the impact of the bead proximity on the RTS force, and thus correct this force. We find that a 10µm diameter bead placed at the head of the RTS decreases the propulsion of the RTS by 15.5%. However the estimated maximal error on this calculation is 13.5%. Therefore to apply a quantitative correction, reducing this error by achieving a more stable trapping of the bead by the RTS seems inevitable. By making tests on different bead diameters, this correction could also be used in the future for cases where the RTS applies a force on any spherical object, for example a cell. Another potential application is the measure of the flow speed at a specific location by analyzing the difference between the experimental speed of the RTS and the theoretical speed given by the characterization. To illustrate this we proposed a proof of concept in 2D by measuring the flow profile of a fluid channel. Finally, we showed how this flow speed information can help the automatic control of the RTS by detecting dangerous situations in which the RTS could be carried away by important flows. To demonstrate this, we proposed and tested an algorithm that chooses the best motion (swimming or spintop) according to the environment, by using the flow measurement.

But a major interrogation towards the development of microfluidic applications was still blurring the perspectives of this work. Indeed the chip we made for the RTS characterization and various tests had larger dimensions than standard microfluidic chips. This was made in the first place to guarantee that the proximity of the wall did not have any impact on the RTS motions. However as we would like the RTS to be deployed in conventional microfluidic chips, it was essential to investigate if the RTS was controllable in small channels with diameters below 20 times the RTS diameter. We proved that such control was possible and that a stabilization phenomenon guides the RTS through the channel up to a diameter around 3.3 times the RTS diameter. This phenomenon is due to the wall interaction on the flow distribution that makes the RTS rotate on the cross-sectional plane as it evolves into the channel, leading to a quasi-helical trajectory. Simple 2D simulations were performed to explain this phenomenon. The lateral drag on the RTS is an important input of this simulation and we evaluated it with the same protocol as the one used for its propulsion characterization. Finally, a control scheme was proposed to control a helical microrobot with a 2D feedback in any curved microchannel evolving in three dimensions. This control worked theoretically on our model simulations.

To sum up, the major contributions of this thesis are the following:

• Development of a helical microrobot that could be integrated selectively in a microfluidic chip.

• Enhancement of the 3D mobility of on-chip helical microrobots by using several motions.

• Design of an on-chip force characterization platform and protocol for helical microrobots through the identification of the parameters of the propulsion matrix.

PERSPECTIVES

153

• Propositions of on-chip force sensing application protocols.

As a result, we are now closer to the force sensing based applications using helical microswimmers. The perspectives will be discussed in the next section. After this exhaustive summary of the achievements of this thesis, we can motivate the relevance of choosing force sensing as an axis of development for the RTS. The first reason we advanced in the introduction was that it could answer many needs in microfluidics by proposing an untethered force sensor inside a closed microfluidic chip. This force sensor could serve physical and biological needs as well as improving the robot control as we showed in Chapter 5. However many other applications could benefit from the development of the RTS as an actuator, for example cargo transport, micro-assembly, drug delivery or gene transmission. The second reason that brought us to research in the path of sensing applications was because it encouraged us to develop a quantitative measurement platform. Indeed even if the propulsion matrix estimation of helical microrobots has already been proposed, it was never associated with an error estimation or any measurement repeatability assessment. Those features are particularly important to optimize the robot design and to study both the helical robot mechanics and its interactions with its environment.

In conclusion, this work not only aimed at proposing a characterization of helical microrobots, but aimed also at offering a platform and a method to quantitatively investigate microrobot physics with a microfluidic drop test chamber and a robot integration. This is an important contribution as without quantitative values it is really difficult to extend an experiment from a proof of concept to real a application. Indeed the parameters to optimize are usually unknown or one does not know how to optimize them.

Another way of seeing this is that it allows more fundamental research and knowledge on the helical microrobot design which is for now an essential step before reaching concrete applications. Moreover to develop force characterization, we developed a setup that can investigate the influence of physical parameters such as temperature, flow speed and wall proximity. The control of these parameters are also essential to perform any kind of quantitative measurement on microrobots. The conclusion of Chapter 4 on the non-repeatability of the measurement illustrates well this advantage. Indeed without controlling physical parameters it would have been impossible to clearly identify the sources of the non-repeatability problem. Therefore it would have been impossible to conclude that further development on the RTS should focus on the RTS magnetization stability.

Perspectives

Our platform and protocols developed for the force characterization present certainly some imperfections, and important hardware development would be required to tune any kind of measurement. As we explained before, all the components are mostly based on prototyping technologies. Therefore a more stable design of the robot to control the magnetization, a microfluidic chip fully in glass to suppress parasite flows from PDMS leak and an automatic control of the RTS characterization could be a short-term development simplifying and improving the RTS characterization. It could also be useful to extend the platform to other measurement needs. However, an important step of this thesis is that our method connects helical microrobot to all the technologies available on microfluidic chips. Therefore it offers a common basis for the design of various experiments. This could be used to investigate helical microrobots more fundamentally or to optimize them towards specific applications.

Let us illustrate this point with three different concrete perspective examples that could benefit from this work. These perspectives are also represented in Figure 6.1 as well as a dependency graph of the different elements of this thesis.

1. Selective cells force stimulation. Firstly, as for any force sensing applications with the RTS, the problem of the non-repeatability of the force should be solved. This should be done by testing new designs and control strategies that could reduce the magnetization history effect of the RTS. To assess these solutions, the standard deviation of the characterization parameters could be a pertinent indicator. From Chapter 5 we already know that the proximity of an object impacts the RTS propulsion force. However we still need to evaluate the evolution of this phenomenon with the size of the pushed object. For this, the drop test chamber could be directly used to characterize different RTS designs pushing different sizes of beads in order to model the RTS force evolution. Numerical simulations could help studying faster the impact of such parameters, but experiments will always be necessary as the simulations validity needs to be assessed by reference experimental results.

State of the Art

Then the compatibility with the biological medium should be checked. Without quantitative measurements this evaluation is limited to see whether the RTS can be displaced in the medium or if it gets stuck to the wall. However by evaluating the RTS characterization evolution with time, more information on the interaction between the robot surface and the medium could be obtained. This could be done by evaluating the evolution of the propulsion matrix parameters. Such increase in precision could lead to understanding the inner physical reaction and could help to propose a bio-compatible solution. It would also be a way of validating more drastically compatibility with the medium by detecting change in the characterization with time, thus preventing from further problems emerging from this issue. Attempt to measure the RTS in two different fluids are presented in Appendix K.

Finally, the stability of the RTS pushing on a spherical surface should be investigated. Indeed we saw in Chapter 5.2 that the robot-bead combination was sometimes unstable which led to small repeatability errors in the characterization. The standard deviation of these measurements could be used as an indicator for guiding the research of a good RTS design with a stable link with the pushed surface. This would be more efficient than subjective experimental analysis of the video record only. Therefore we could optimize the RTS design to guarantee that it could push on a any cell size without sliding on the wall.

2. Robust microfluidic manipulator. As for the selective cell stimulation, the manipulation of objects will require to study the stability of the robot-object combination and will therefore benefit from the quantitative robot characterization. In order to manipulate objects it is also important to be able to safely move inside the microfluidic chip. As we explained, the main dangerous situations for such robots appear when they are carried away by the flow or stuck on the surface. As it was demonstrated in Chapter 5.3, strong flow can be measured by estimating the difference between the current RTS behavior and the theoretical one. We believe that studies on the RTS surface motion could give us indications on the stiction probability and how to avoid it. Indeed in Chapter 3.2, experiments suggested that for the spintop motion, different friction mechanisms between the RTS head and the surface could happen. But the triggering reasons of these different states remain unknown mostly because the environment of the measurement was presenting parasite flows, which did not allow us to conclude on this point. Therefore the microfluidic conditions should be tuned for a proper experimental environment. With this we could get a better understanding of the surface motion mechanisms and thus use this knowledge for developing safer control strategies.

Evolving inside a microfluidic chip also requires to move through small channels. As we demonstrated in Chapter 5.4, the swimming mechanism is perturbed by the confined environment. Even if we have started to investigate this phenomenon we do not know exactly what the 3D flow distribution is and most importantly for this perspective, which mechanisms govern the physics when we push an object through the microchannel. To reach a deep understanding of the phenomenon, computer simulations seem to be a great tool as precisely mapping the flow around the RTS is too difficult experimentally. To make this relatively simple simulations correspond to the real conditions, it is mandatory to get coefficients from the experiments as we did for the lateral drag coefficient in Section 5.4. It is also important to confront the results of the simulations with experimental values. Therefore to fully understand the phenomenon and propose a stable control strategy inside a microchannel the quantitative measurement of the drag and propulsion of the RTS is essential before performing simulations and checking model validity.

This could help to propose a more sophisticated automatic motion adaptation algorithm that will adapt to the environment conditions. Indeed we think that the control and action of a helical microrobot inside microfluidic should be intuitive to be achieved safely for the robot by untrained users. Using a more developed tracking algorithm should also be a key in order to track the robot position in altitude with the focus and independently from the surrounding conditions.

3. In-vivo integration. An important amount of research will be required to move the current technology to in-vivo applications such as minimally invasive surgery. It is therefore too soon to foresee all the future challenges. However we strongly believe that having a fully characterized RTS on a microfluidic chip is an important step towards this goal. The microfluidic platform is the most suitable to simulate the conditions close to the one present in blood or lymphatic vessels. Indeed we can design microchip channels with dimensions and shapes close to those of the vessels. Those channel surfaces could be covered by cells [START_REF] Lu | Microfluidic shear devices for quantitative analysis of cell adhesion[END_REF] to simulate surface conditions and a flow could be provided to simulate blood or lymph circulation.

• Load a g-code that make a flat surface (1 pass at same level).

• Select speed = 10 %.

• Move around the design to verify that the drill is never out of the substrate and that you will not touch anything during fabrication.

• Make Z zeros.

• Go up of 1mm.

• Launch the program.

• Launch the first design.

To keep the original surface you need to localize precisely the Z zero :

• For this make a dichotomous search of the substrate altitude. It is possible to move at 10 % laterally to see if the mill is in the material. Use the "goto" function to be precise (goto work in relative coordinate around the zero).

• When you locate the substrate with good enough precision set Z zero on the upper limit (not in the substrate).

• Move around the design to verify that the drill is never in the substrate and that you will not touch anything during fabrication.

• Launch the fabrication.

During the milling

During the milling it is possible to add oil at the last milling step to get better surface quality.

Change the milling tool

This is useful when different resolutions are needed on a design.

• Measure the difference in Z coordinate from your mill tip to your material surface. For this you can use the contact detector which is fixed on the table, when it enters in contact with the mill tip it will display a green light on the control software above Z coordinate displayed box. You will have to measure the Z coordinate where there is exactly the rising front of the captor. The precision is around 0.4µm.

• Apply the step presented above to change the mill.

• Find the rising front of the altitude captor for your new tip. Then, set the altitude as the difference between this captor and the surface that you measured in the first step.

After the milling

• Move the drill up.

• Shut down the spin of the drill and the displacement.

• Remove your substrate.

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"""PASSED PARAMETER ( IF THEY EXIST) """ """ s y s . argv [ 0 ] i s t h e name o f t h e program """ t r y : e n d p i c t u r e = i n t ( s y s . argv [START_REF] Terry | A Gas Chromatographic Air Analyzer Fabricated[END_REF] ) # t h e number o f t h e p i c t u r e where t h e a n a l y s i s i s s t o p s t e p =i n t ( s y s . argv [START_REF] Macdonald | Microfluidic sorting in an optical lattice[END_REF] ) # s t e p i n p i c t u r e between two a n a l y s i s ( put 1 f o r maximum p r e c i s i o n ) s r c f i l e n a m e = s t r ( s y s . argv [START_REF] Gossett | Label-free cell separation and sorting in microfluidic systems[END_REF] ) #name o f t h e f i e l were t h e p i c t u r e a r e . f o r y i n r a n g e ( 0 , a [ 0 ] -1 ) : norm= norm + img . g e t p i x e l ( ( x , y ) ) """ imarray = numpy . a r r a y ( img ) fimg= f f t s h i f t ( f f t 2 ( imarray ) ) """ debug """ #t e s t = Image . f r o m a r r a y ( abs ( fimg ) ) #t e s t . show ( ) #f f i m g= i f f t 2 ( i f f t s h i f t ( fimg ) ) #t e s t t=Image . f r o m a r r a y ( abs ( f f i m g ) ) #t e s t t . show ( ) f r e p a r t i t i o n = [ 0 . 0 ] * max( a ) f o r x i n r a n g e ( 0 , a [ 1 ] -1 ) :

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""" m u l t i p l y r e p a r t i o n by a f u n c t i o n with v a l u e e q u a l 1 between f s t a r t and f s t o p and 0 e l s e w h e r e """ from o p e r a t o r import mul f s t a r t = 5 f s t o p =15 a=l e n ( r e p a r t i t i o n ) f c t = [ 0 . 0 ] * a f o r i i n r a n g e ( f s t a r t , f s t o p ) : f c t [ i ]=1 out = ( ( sum (map( mul , r e p a r t i t i o n , f c t ) ) ) / ( a / 2 ) ) r e t u r n out d e f smoother ( s i g n a l , d e g r e e ) : """ smooth a s i g n a l with f f t , d e g r e e =0 i s no smoothing , d e g r e e = 1 i s n u l s i g n a l """ f s i g n a l = r f f t ( s i g n a l ) h s i z e= i n t ( l e n ( s i g n a l ) / 2 . 0 ) c u t=i n t ( h s i z e * d e g r e e ) f o r n i n r a n g e ( h s i z e -cut , l e n ( f s i g n a l ) -1) : f s i g n a l [ n]=0 s s i g n a l= i r f f t ( f s i g n a l ) r e t u r n s s i g n a l d e f find max ( l i s t ) :

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""" f o r c e a r r a y . s i z e t o be odd by adding z e r o a r e t u r n a s u b a r r a y o f t h e odd c o o r d i n a t e s v a l u e """ l i s t o u t = [ ] s t a r t =1 i f a r r a y . s i z e %2 == 1 : s t a r t =0 f o r n i n r a n g e ( s t a r t , a r r a y . s i z e , 2 ) : l i s t o u t . append ( a r r a y [ n ] ) r e t u r n ( np . a s a r r a y ( l i s t o u t ) )

""" S t a r t main code """ f o c u s = [ ] f o r n i n r a n g e ( s t a r t p i c t u r e , e n d p i c t u r e , s t e p ) :

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i f l i s t [ i ]>=a : r e t u r n ( i +1) r e t u r n ( 0 ) d e f t h c u t s ( l i s t , t t h , v th , t ) :

""" r e t u r n t h e l s i t with va lue <v t h . V i s a l i s """ f o r c e a r r a y . s i z e t o be even by adding z e r o a r e t u r n a s u b a r r a y o f t h e even c o o r d i n a t e s v a l u e """ l i s t o u t = [ ] s t a r t =0 i f a r r a y . s i z e %2 == 1 : l i s t o u t . append ( 0 ) ; s t a r t =1 f o r n i n r a n g e ( s t a r t , a r r a y . s i z e , 2 ) : l i s t o u t . append ( a r r a y [ n ] ) r e t u r n ( np . a s a r r a y ( l i s t o u t ) ) d e f e x t r a c t o d d ( a r r a y ) :

""" f o r c e a r r a y . s i z e t o be odd by adding z e r o a r e t u r n a s u b a r r a y o f t h e odd c o o r d i n a t e s v a l u e """ l i s t o u t = [ ] s t a r t =1 i f a r r a y . s i z e %2 == 1 : s t a r t =0 f o r n i n r a n g e ( s t a r t , a r r a y . s i z e , 2 ) : l i s t o u t . append ( a r r a y [ n ] ) r e t u r n ( np . a s a r r a y ( l i s t o u t ) ) """ p l o t f i g u r e """ p l t . f i g u r e ( f i g n a m e ) p l t . h o l d ( ) p l t . h o l d ( True ) p l t . p l o t ( t , f o c u s , l a b e l= ' raw data ' ) #r u n n i n g i n 24 f r a m e s p e r s e c o n d ( t h i s i s s e t i n m p 4 t o t i f f ) p l t . x l a b e l ( ' Seconds ' ) """ smoothing """ p l t . p l o t ( t [ 0 : l e n ( s 2 ) ] , s2 , l a b e l= ' smooth =0.8 ' ) p l t . p l o t ( t [ 0 : l e n ( s 3 ) ] , s3 , l a b e l= ' smooth =0.9 ' ) p l t . p l o t ( t [ 0 : l e n ( s 1 ) ] , s1 , l a b e l= ' smooth =0.95 ' ) p l t . l e g e n d ( ( ' raw data ' , ' smooth =0.8 ' , ' smooth =0.9 ' , ' smooth =0. """ end p a s t """ """ p l o t path """ t h e path s e l f . path=path s e l f . s t e p=s t e p s e l f . p o s i t i o n= path [ 0 ] s e l f . p a t h p o i n t =0; s e l f . e n d o f p a t h=F a l s e ; s e l f . p a t h l e n g t h =0; s e l f . w r i t i n g = True ; d e f n e x t p o s i t i o n ( s e l f ) : i f s e l f . p a t h p o i n t +1 == np . s i z e ( s e l f . path ) / 3 : # end o f path d e t e c t e d s e l f . e n d o f p a t h=True e l s e : v e c t o r = [ s e l f . path [ s e l f . p a t h p o i n t + 1 ] [ k ] -s e l f . p o s i t i o n [ k ] f o r k i n r a n g e ( 0 , 3 ) ] i f norm ( v e c t o r ) < s e l f . s t e p : #c h e c k i f new s t e p p o i n t d e f i n i t i o n i s r e a c h e d s e l f . p a t h p o i n t = s e l f . p a t h p o i n t +1; s e l f . p o s i t i o n = s e l f . path [ s e l f . p a t h p o i n t ] i f s e l f . p a t h p o i n t < np . s i z e ( s e l f . path ) /3 -1: i f s e l f . path [ s e l f . p a t h p o i n t + 1 ] [ 0 ] < 0 : #c o d e f o r p e n c i l up . i f t r u e s k i p on p o i n t s e l f . p a t h p o i n t = s e l f . p a t h p o i n t +2; s e l f . p o s i t i o n = s e l f . path [ s e l f . p a t h p o i n t ] e l s e :#no new p o i n t d e f i n i t i #p r i n t ( " path l e n g t h i s " , s z ) s e l f . p a t h l e n g t h =s z / s e l f . s t e p r e t u r n s z / s e l f . s t e p p o s i t i o n = Path ( path , dpath ) # c r e a t e a v a r i a b l e o f c l a s s path p o s i t i o n . f i n d p a t h l e n g t h ( ) #p r i n t ( p o s i t i o n . p a t h l e n g t h ) #p r i n t ( " path i n i t i a l i s a t i o n f i n i s h e d " ) """ U n i v e r s c r e a t i o n """ #f i n d u n i v e r s d i m e n s i o n """ s t a r t i n g i t e r a t i o n """ #p r i n t ( " s t r a t i n g w r i t i n g " ) i =0; p r o g r e s s i o n =0; w h i l e p o s i t i o n . e n d o f p a t h == F a l s e : #e x t r a c t u n i v e r s on t #n e x t p o i n t c a l c u l a t i o n and np . d i s p l a y p o s i t i o n . n e x t p o s i t i o n ( ) i=i +1 #p r i n t ( i ) ; i f p r o g r e s s i o n != i n t ( f l o a t ( i ) / p o s i t i o n . p a t h l e n g t h * 1 0 ) : p r o g r e s s i o n = i n t ( f l o a t ( i ) / p o s i t i o n . p a t h l e n g t h * 1 0 ) p r i n t ( p r o g r e s s i o n * 1 0 , "%" )

""" C a l c u l a t e volume """ #p r i n t ( " Counting u n i v e r s " ) a=u n i v e r s . sum ( a x i s =0) b=a . sum ( a x i s =0) volume = b . sum ( a x i s =0) ; volume=volume * d * * 3 p r i n t ( " f o r d =" , d , " , vz = " , vz , " , vx = " , vx , " , vz = " , vz , " , vy = " , vy , "The c a l c u l a t e d volume i s " , volume , " micometer cube " ) p l t . imshow ( u n i v e r s . sum ( a x i s =0) ) ; p l t . show ( ) ; #s a v e u n i v e r s s t r d= s t r ( d ) s t r v z=s t r ( vz ) p r i n t d= ' d= ' p r i n t v z= ' vz= ' s u f f i x e= ' . p i c k l e ' PVD simu.py """ -------------------------------------Path c r e a t i o n -----------------------------1 argument : name o f f i l e a s i n p u t ( s h o u l d be a * . p i c k l e , o u t p u t o f n a n o s i m u l a t o r . py ) 2 argument : m e t a l i s a t i o n t i l t a n g l e ( d e f a u l t one i s 7 0 ) 3 argument : mesh s i z e o f i n p u t f i e l ( d e f a u l t 0 . 0 5 ) """ name="d =0.05 vz = 1 . 6 6 9 . p i c k l e " t i l t =70 # i n d e g r e e d =0.05 t r y : name = s y s . a r g v [START_REF] Terry | A Gas Chromatographic Air Analyzer Fabricated[END_REF] ; # mesh p r e c i s i o n i n m i c r o m e t e r cube p r i n t ( " name =" , name ) e x c e p t : p r i n t ( "WARNING : No argument was p a s s e d t o t h e program , r u n n i n g w i t h d e f a u l t v a l u e ( d=" , d ) t r y : t i l t = s y s . a r g v [START_REF] Macdonald | Microfluidic sorting in an optical lattice[END_REF] ; # mesh p r e c i s i o n i n m i c r o m e t e r cube p r i n t ( " t i l t =" , t i l t , " d e g r e e " ) e x c e p t : p r i n t ( "WARNING : No s e c o n d argument was p a s s e d t o t h e program , r u n n i n g w i t h d e f a u l t v a l u e ( t i l t =" , t i l t , " d e r g r e e " ) The information contained in this section covers many of the frequently asked questions about polystyrene microspheres. Please contact us with any further questions you might have.

GENERAL CHARACTERISTICS

PARTICLE HANDLING AND PRINCIPLES

Microsphere Monodispersity

The following chart lists our specifications for the uniformity of our Polybead ® microspheres, expressed as the coefficient of variance (CV). The actual diameter (D) and the standard deviation (SD) for each lot are printed on the label. The % CV is expressed as the SD/D x100.

Diameter

Microsphere Size

Diameters specified in product descriptions reflect nominal sizes. For most products, the specific diameter and standard deviation will be printed on the label.

Microsphere Stability

Polysciences offers a one year shelf life. Unless noted, neither biocides nor stabilizers are added and the particles are shipped in DI water with residual surfactant. All polystyrene products should be stored at 4˚C to deter microbial growth. Microsphere suspensions must be protected from freezing to safeguard against irreversible aggregation. If long term storage is required, the addition of biocide is recommended.

Particle Suspension

Most of our products are supplied at 2.5% solids, i.e. every 100ml of the latex suspension contains 2.5 grams of polymer spheres. Higher concentrations are available for bulk shipments. Weight to volume packaging means that the number of particles per ml will vary with the diameter of the particle. The approximate number of particles per ml for common diameters follow. Bead counts were calculated using the nominal diameter and equation provided below. // r e s o l u t i o n i n XY under t h e r o b o t . 5 f o r q u i c k c o m p i l a t i o n 30 f o r r e s u l t s // F o r c e c a l c u l a t i o n i n t s t e p =100; // number o f s i m u l a t i o n between t h e c e n t e r o f t h e c h a n n e l and t h e s i d e . i n t n =100; // number o f p o i n t s a l o n g t h e c i r c l e p a r a m e t e r t o p e r f o r m t h e d r a g c a l c u l a t i o n . r e a l dr =0. o ut << " s t e p " <<" ; "<< s t e p <<" ; "<<e n d l ; o ut << "x"<<" ; "<< "y"<<" ; "<< "Fx"<<" ; "<< "Fy"<<" ; "<< e n d l ;

Diameter (µm) Particles

f o r ( j j =round(-s t e p / 2 ) ; j j <round ( s t e p / 2 ) ; j j ++) // b e g i n i t e r a t -----------------------------START SOLVING-------------------------------------f //----------------------P l o t --------------------------------s t r i n g f i l e n a m e = " r e s u l t s q u a r e / hemi x="+o f f s e t x+" y="+o f f s e t y+" . e p s " ; // s p e e d // p l o t ( [ u , v ] , w a i t =0 , v a l u e=t r u e , c o e f = 0 . 0 0 0 0 5 , ps=f i l e n a m e ) ; // s a v e e v e r y s i m u l a t i o n ( heavy s o l u t i o n ) p l o t ( [ u , v ] , w a i t =0 , v a l u e=t r u e , c o e f = 0 . 0 0 0 0 5 , ps=" b u f f e r s q u a r e 2 0 . e p s " ) ; // s a v i n g o n l y l a s t p l o t //------------------------L a t e r a l d r a g f o r c e on t h e RTS J.3. TRAJECTORY.PY

211

----------------------------------// i n s i d e v a r i a b l e r e a l [ i n t ] F x t a b l e ; r e a l [ i n t ] F y t a b l e ; r e a l Fx = 0 ; // f o r c e on x r e a l Fy = 0 ; // f o r c e on y r e a l xdr , ydr , xx , yy ; // x , y p o i n t xx , yy normal v e c t o r r e a l dun ; // d e r i v a t e a l o n g t h e normal i n t d t h e t a ; // I n t e g r a t e e l l e m e n t a r y d r a g f o r c e on a l l t h e p e r i m e t e r DF=nu dv /dn , w i t h F t h e d r a g f o r c e , nu t h e v i s c o s i t y , v t h e speed , n t h e s u r f a c e ' s normal . * d e r i v a t i v e ) // ou t << d t h e t a * 2 * 3 . 1 4 1 5 / n <<";"<<xx<<";"<<yy<<";"<<xdr <<";"<<ydr <<";"<< dun <<e n d l ; } // p l o t f o r c e and s a v e i n f i l e c o u t <<" F o r c e on t h e RTS ( a t x ="<< o f f s e t x <<" and y ="<<o f f s e t y <<" ) "<< "Fx ="<< Fx <<" Fy ="<< Fy <<e n d l ; o ut << o f f s e t x <<" ; "<< o f f s e t y << " ; "<< Fx<<" ; "<< Fy<<" ; "<< e n d l ; } // end i f i n s i d e t h e t h e c h a n n e l e l s e { o ut << o f f s e t x <<" ; "<< o f f s e t y << " ; "<< 0<<" ; "<<0<<" ; "<< e n d l ; } } // end i t e r a t i o n on x } // end i t e r a t i o n on y c o u t << "END OF ITERATION" << e n d l ;

trajectory.py i m p o r t c s v i m p o r t m a t p l o t l i b a s mpl i m p o r t numpy a s np i m p o r t m a t p l o t l i b . p y p l o t a s p l t i m p o r t math a s mt """---------p a r a m e t e r s -------------""" f i l e n a m e= ' s i m u r e s u l t . c s v ' e=20e-6 # Width o f t h e s q u a r e c h a n n e l s t e p =8e-2 #s e c o n d a =8.4 e -7/42e-6 #s -1 * N-1 ( d r a g c o e f f i c i e n t from l a t e r a l drop t e s t ( a=( w e i g h t+buyancy ) / vo ) , T h i s v a l u e i s d i """ f i r s t i t e r a t i o n """ p0=np . a r r a y ( [ x , y ] ) #p r i n t ( " 1 " ) dp=s p e e d a t x y ( x , y , g , X, Y, FX, FY, a ) #p r i n t ( dp ) """ h a l f d i s a n c e c a l c u l a t i o n """ p12=p0+dp * s t e p /2 #p r i n t ( " 2 " ) dp12=s p e e d a t x y ( p12 [ 0 ] , p12 [START_REF] Terry | A Gas Chromatographic Air Analyzer Fabricated[END_REF] , g , X, Y, FX, FY, a ) #p r i n t ( dp12 ) """ p o i n t c a l c u l a t i o n """ p1=p0+dp12 * s t e p r e t u r n p1 Résumé : Au cours des dernières décennies, l'étude des puces microfluidiques capables d'exécuter des processus chimiques et biologiques sur quelques centimètres carrés a été un domaine de recherche actif. De telles plateformes offrent un environnement fermé et contrôlable qui permet une mesure reproductible et évite toute contamination externe. Cependant, ces environnements sont fermés, ce qui empêche l'utilisation de sondes de mesure ou d'effecteurs fixés à l'extérieur de la puce microfluidique. Pour répondre à ce besoin, nous proposons d'utiliser des microrobots rotatifs hélicoïdaux évoluant dans un fluide. Les microrobots proposés sont conçus grâce à la lithographie 3D par laser. Ils présentent une forme hélicoïdale de 5.5 µm de diamètre et environ 50 µm de longueur. Une couche mince ferromagnétique déposée sur ces microrobots permet de les propulser et de les contrôler grâce à un champ magnétique tournant homogène. Le premier défi est l'intégration stable de microrobots à l'intérieur d'un environnement microfluidique. Dans cette thèse, nous avons donc d'abord prouvé que ces microrobots peuvent utiliser leur propre mobilité pour s'intégrer individuellement à l'intérieur d'une puce microfluidique en utilisant un microcanal relié à un réservoir ouvert. Pour cela, nous avons développé un mouvement 3D où le microrobot évolue dans le fluide et deux mouvements 2D où il évolue sur une surface. En passant facilement d'un mouvement à l'autre, les microrobots peuvent utiliser les différents avantages de chaque mouvement pour obtenir une mobilité suffisante à cette intégration. Nous avons nommé ce modèle de microrobot "Roll-to-Swimm"(RTS). Ensuite, pour utiliser un microrobot comme capteur de force sur puce microfluidique, il est nécessaire de caractériser la force générée par l'hélice de chaque RTS. Une méthode de caractérisation est proposée, dans laquelle les différents paramètres d'environnement tels que le flux parasite, le gradient de température et l'impact des surfaces, sont contrôlées avec précision grâce à l'environnement microfluidique. Nous en concluons que le modèle de microrobot "RTS" peut appliquer une force de 10 à 45 piconewton avec une erreur maximale de 38 %. La composante principale de cette erreur (73 %) est due à l'évolution de l'aimantation du RTS. Par conséquent, les efforts visant à réduire cette erreur doivent d'abord se concentrer sur la propriété de magnétisation du RTS. Cette erreur peut également être temporairement réduite en caractérisant la RTS juste avant son utilisation dans une expérience. Enfin, nous présentons trois preuves de concept pour démontrer que notre méthode de caractérisation rapproche les microrobots hélicoïdaux des applications potentielles. Tout d'abord, nous mesurons la diminution de la force du RTS lorsqu'il pousse une microbille. Cette mesure est essentielle pour connaitre la force appliquée par le RTS sur un objet ou pour mesurer l'état de surface en utilisant des billes comme interface. Nous concluons, qu'une microbille de 10 µm de diamètre à la pointe du RTS réduit la propulsion d'environs 15 %. Deuxièmement, nous utilisons la caractérisation du RTS pour mesurer la vitesse locale de l'écoulement dans un canal. Puis nous proposons d'utiliser cette mesure de vitesse pour le contrôle du microrobot grâce à un contrôle automatique du RTS qui adapte le type de mouvement en fonction de la vitesse de l'écoulement. Ce contrôle a été testé expérimentalement avec différentes conditions d'écoulement. Troisièmement, nous utilisons la caractérisation du RTS pour effectuer des simulations numériques afin de trouver une stratégie de contrôle dans des microcanaux de taille inférieure à 20 fois le diamètre du RTS. Le modèle de cette simulation a été validé en comparant ces résultats avec des données expérimentales. Finalement, nous proposons un système de contrôle permettant de maintenir le RTS centré à l'intérieur de microcanaux courbes évoluant en 3D, en utilisant seulement une acquisition d'image en 2D. Abstract: Microfluidic chips that could perform chemical and biological processes on a few centimeter square footprint have been an active area of research in the past decades. Among other advantages, this platform offers a closed and controllable environment that allows reproducible measurements and avoids external contamination. However, such closed environments prevent the use of tethered probes to measure or apply a specific force on an element inside the microfluidic chip. Therefore we propose to use a helical rotating microrobot inside a microfluidic chip to answer this need. The proposed microrobots are designed with 3D laser lithography, and have a helical shape of 5.5 µm in diameter and around 50 µm length. A thin ferromagnetic layer is deposited on these microrobots which allows us to propel and control them with a homogenous external rotating magnetic field. The first challenge is the stable integration of these microrobots inside microfluidic environments. Therefore, in this thesis we first proved that these microrobots can use their own mobility to integrate themselves selectively (one by one) inside a microfluidic chip through a microchannel connected to an open reservoir. For this, we have developed a 3D motion where the microrobot evolves in the fluid and two different 2D motions where it evolves on a surface. By switching easily from one motion to another, the microrobots can use the different advantages of each motion to get sufficient mobility required for this integration. We named our microrobot design Roll-To-Swimm (RTS) in reference to this characteristic. Then in order to use a microrobot as on-chip force sensor, a precise characterization of the force generated by the helical shape is necessary for each RTS. A characterization method is proposed, where the different environment parameters (parasite flow, temperature gradient and impact of near surfaces on the flow) are controlled precisely thanks to the microfluidic environment. The characterization shows that the force range of the RTS is between 10 and 45 piconewton with a maximum error of 38 %. We also conclude that the main component of this error (73 %) is due to the evolution of the RTS magnetization. Therefore the efforts to reduce this error should first focus on the magnetization property of the RTS. This error can also be temporarily reduced by characterizing the RTS just before its use in another experiment.

Finally, we present three different proofs of concept to demonstrate that our characterization method brings helical microrobots closer to potential on-chip force sensing applications. Firstly, we show that it is possible to measure the diminution of the RTS force when it is pushing a micro spherical bead. This is essential toward applying force on an object or to use beads as an interface between the RTS and the surface to measure friction forces.We conclude that a microbead with 10 µm in diameter at the tip of the RTS reduces the propulsion of approximately 15 %. Secondly, we use the RTS characterization to measure local flow speed. We demonstrate this feature by measuring flow profiles in fluid channels. We show the potential use for of microrobot control by proposing an automatic control of the RTS that adapts the motion to the measured flow. This control has been tested experimentally with different flow conditions. Thirdly, we use the characterization of the RTS to perform numerical simulations in order to find a control strategy in small microchannels. Indeed we demonstrate that for microchannels below 20 times the RTS diameter, the channel walls have an impact on the RTS motions. The model of this simulation is validated by comparing results with experimental data. Finally we propose a control scheme for maintaining the RTS centered in a curved microchannel by only using a 2D image feedback.

Figure 1 -

 1 Figure 1 -Vue au Microscope Électronique à Balayage (MEB). a) est une vue du microrobot, b) représente le substrat de fabrication où plusieurs microrobot sont présents.

Figure 2 -

 2 Figure 2 -Récapitulatif des différents enjeux relatifs à l'intégration du robot sur une puce microfluidique, à sa caractérisation et à son utilisation comme outil de mesure.

18 CHAPTERFigure 1 . 1 -

 1811 Figure 1.1 -Schematic representing the need of untethered force sensor on microfluidic chip for local sensing. In this thesis we propose to answer this need by using microrobots.

Figure 1 . 2 -

 12 Figure 1.2 -Schematics of the different sensors use for force sensing under millinewton. a) isthe AFM: at the contact of the tip with the surface the beam bends. A laser reflecting on the cantilever surface detects this bending, by determining the cantilever stiffness the bending can be linked to the applied force. b) is the optical tweezers: the radiation pressure of the focalized light beam traps the particle. The difference between the particle position and the center of the trap gives an information about the external force applied on the particle. A linear approximation is used to link this displacement to a force. c) is the magnetic tweezers: the magnetic gradient applies a force on a ferromagnetic or magnetic bead. This magnetic gradient is either created with permanent magnet or electromagnet. d) is the comb drive: when the tip touches the surface, its fixations with the frame act like a spring thus the force is proportional to the displacement. The displacement is measured by the electrical capacitance change in the comb.

Figure 1 .

 1 Figure 1.3 illustrates the difference force ranges in function of the accessibility of the presented sensors. First, note that there exist solutions to apply forces from 100 millinewtons to the femtonewton without discontinuity. Of course, force in the Newton scale and above are covered by conventional force sensors in open environments.When the accessibility becomes constrained by considering the access inside a microfluidic chip, some technologies are not compatible. As we already mentioned, this is the case for the AFM and the comb drive actuator because the sensing part of these two technologies are tethered to a macroscopic frame. Magnetic tweezers offer a large spectrum of force. But even if their integration in microfluidic chips is possible, it is largely restrained by the proximity of the electromagnetic coil tip of the magnet. Moreover the system gains in complexity for each supplementary degree of freedom. Thus as the environment becomes even more confined, integrating multiple magnets or electromagnet tips is difficult and the manipulation becomes more difficult. Optical tweezers do not suffer from these proximity footprint problems and they have the advantage of being highly compatible with microfluidic technologies. The only requirement is that the microfluidic chip needs to be transparent for the trapping laser. As only optical trapping is feasible in small microchannels, it is not possible to measure the deformation of an object with a constant force except by doing a complex closed-loop system.But a comparison between these technologies is more complicated than what can be presented by only considering force range and accessibility. Therefore in Table1.1, we present the other notable characteristics and specificity of each technology. The main technology to consider here is the optical tweezers as it is the only technology that can easily be implemented in a small microchannel.[START_REF] Enger | Optical tweezers applied to a microfluidic system[END_REF][START_REF] Wang | Robot-assisted automatic cell sorting with combined optical tweezer and microfluidic chip technologies[END_REF]

Figure 1 . 3 -

 13 Figure 1.3 -Domain of uses of different force sensor systems. The x axis represent accessibility of the devices and the y axis the force range of use.

Figure 1 . 4 -

 14 Figure 1.4 -Helical force robot schematic. The helical part on the middle pushes the liquid and transform the rotation into a force. a and b are the propulsion characteristics and depend on the robot geometry.

Figure 1 . 5 -

 15 Figure 1.5 -Schematic of the helical microrobot sensing process inside a microfluidic chip.

Figure 2 . 1 -

 21 Figure 2.1 -Schematic of the torque induced by the rotating magnetic field onto the RTS.

Figure 2 . 32 CHAPTERFigure 2 . 2 -

 23222 Figure 2.2 -Overview of the RTS control sequence path inside a microfluidic chip.

Table 2 . 1 -

 21 Presentation of the different technical solutions with their advantages (+) and drawback (-) to build microhelical structure. The solutions are sorted by size. The red colored row represents the chosen technology in this thesis.

Figure 2 .Figure 2 . 3 -

 223 Figure 2.3 -RTS fabrication. (a) Fabrication steps, (b) Scanning Electron Microscope (SEM) photographs of one RTS and of one field of RTS.

Figure 2 . 4 -

 24 Figure 2.4 -Three pictures from the RTS detachment process. On a) the RTS is still attached to the substrate, on b) the RTS is detached from the substrate and touches the tungsten tip, on c) the tip is removed.

Figure 2 Figure 2 . 5 -

 225 Figure 2.5 -CAD model of the challenging structure needed in the mold. a) represents the drop test chamber. This structure is used to limit parasite flows during the RTS characterization. b) shows a 45 • slope angle, needed to support a mirror for side view of the RTS, c) shows different channels with increasing sizes from 8µm to 100µm, d) shows a round channel that can be easily closed by applying pressure on it.

Figure 2 . 6 -

 26 Figure 2.6 -Picture of the micro-milling machine in LPN-CNRS.

Figure 2 . 7 -

 27 Figure 2.7 -Microfluidic chip fabrications steps. Steps 1-3 are done only once for each new model as the mold can be reused multiple times.

Figure 2 . 8 -

 28 Figure 2.8 -Optical microscope picture of the PDMS microfluidic chip. a) shows the drop test chamber linked to the big chamber by a 80µm square channel. b) represents the smallest microchannel. c) represents the same microchannel but after bonding the PDMS to a glass substrate. d) is the profile measurement of b) on the slice marked by the A-A line. The measurement is made with a spherical 5µm diameter tip which explains the larger width of the measured channel.

Figure 2 . 9 -

 29 Figure 2.9 -The pressure valve system. a) is a picture of the system on the chip, b) is a side schematic view of the microfluidic valve with screw actuation in open and closed position.

Figure 2 . 10 -

 210 Figure 2.10 -Schematic of the fluid circuit. Atm stands for ambient pressure and Pi for the controlled pressure.

Figure 2 . 11 -

 211 Figure 2.11 -Shematic of the RTS command loop.

Figure 2 .

 2 Figure2.11 brings an overview of the command path we designed. In manual control, a computer software reads, in real time, the command of the user through the keyboard. From this command, it produces an associated signal to generate a rotating magnetic field. This signal is then amplified and sent to three pairs of electromagnets. Note that this assumes that the coils behave linearly, which means that the magnetic field direction and amplitude can be reconstructed by adding the magnetic field generated by each coil pair. Moreover these electromagnets are designed to guarantee the Helmholtz conditions. Therefore the magnetic field is approximately homogeneous (i.e. with no gradient) at the center of setup, where the RTS is placed inside the microfluidic chip.A camera mounted on a microscope sends back the image of the robot to the software which displays it on the screen for the user. The software can also track the robot position on the screen and store it. This is especially used for automated speed acquisition during the RTS characterization. This tracking information can also be used to perform closed-loop position control and generate a command that replaces the user.

Figure 2 .

 2 Figure 2.12 -CAD schematic and picture of one of the three-axes electromagnet device. The different parts are made in ABS with a 3D printer and wired with copper wire.

Figure 2 . 13 -

 213 Figure 2.13 -Schematic of the rotating magnetic field direction. Axes of two different frames are represented. The frame "RTS" is aligned with the rotation direction of the ferromagnetic RTS.The frame "coils" is associated with the three different electromagnet pairs. The angles θ and ψ represent the difference between these two frames.

Figure 2 . 14 -

 214 Figure 2.14 -Schematic of the two code threads.

Figure 2 .

 2 Figure 2.15 -RTS experimental view with different setups. a) setup 1 b) setup 2.

Figure 2 .

 2 Figure 2.8 shows the imaging difference between the two setups. For more details on the specificity of each setup, we refer to Section 2.3.1.

Figure 2 . 16 -

 216 Figure 2.16 -Schematic side view representing the optical path of the two setups.

Figure 2 . 17 -

 217 Figure 2.17 -Picture of the setup 1

Figure 2 . 18 -

 218 Figure 2.18 -Evolution of the magnetic field amplitude with the frequency for the three Helmholtz pairs in setup 1. a) is without tuning and b) is after tuning with an ampere metric clamp.

Figure 2 . 19 -

 219 Figure 2.19 -Picture of setup 2. Main features are good image quality and temperature controlled.

Figure 2 . 20 -

 220 Figure 2.20 -Temperature evolution in the setup 2 in working conditions. At t=0, the two cooling systems and the electromagnetic coils are turned on to simulate RTS characterization condition.

3 .

 3 It allows to explore the physics of the RTS propulsion too. Indeed, we use the microfluidic chip to assess the repeatability of the RTS propulsion in Chapter 4.4.3. We also use it to explore the fluid influence on the RTS propulsion in a closed environment in Chapter 4.3. The different reasons of integrating the RTS inside a microfluidic chip are illustrated in Figure 3.1.

Figure 3 . 1 -

 31 Figure 3.1 -The three goals of integrating the RTS in microfluidic chips.

Figure 3 . 2 -

 32 Figure 3.2 -Schematic of a single motion robot limitations. On a) the robot can only use surface motion, on b) it can only use swimming motion.

Figure 3 .Figure 3 . 3 -

 333 Figure 3.3 -Schematic of the rotating magnetic field and resulting magnetization of the RTS.µ r is the magnetization, B the magnetic field and β is the angle between the rotation axis of the robot and the rotation angle of magnetic field. α is the angle between µ r and the projection on r ⊥1 .

Figure 3 . 4 -

 34 Figure 3.4 -Presentation of the RTS three possible motions and their specificity. a), b) and c) display a schematic of each motion. d), e) and f) present the frequency domain and parameter of the actuations of RTS in each mode. Finally, g),h) and i) present the particular advantages of each motion.

CHAPTER 3 .Figure 3

 33 Figure 3.5 -a), b) show how swimming can be used to go on a top surface and how spintop can control the RTS on this surface. c), d) a show particle trapping, displacement by spintop motion and releasing of the particle by swimming.

64 CHAPTER 3 .Figure 3 . 6 -

 64336 Figure 3.6 -Speed versus frequency of the RTS in spintop on different materials. On a) the helical part applies a pushing force on the substrate. The behavior (1) follows a lubricated friction model, (2) a Coulomb friction model. On b) the helical part applies a pulling force on the substrate. For each experiment the pitch angle is set to 1.1 Radian (63 • ).

Figure 3 . 7 -

 37 Figure 3.7 -Diagram of the closed-loop system for spintop. The pitch (θ) and yaw (ψ) angles are sent to the thread that generates the command of the magnetic field and substitute manual command.

Figure 3 . 8 -

 38 Figure 3.8 -Accuracy of the spintop motion during closed-loop control. Both the command path (in red) and track path (in blue) are displayed for a 150µm square trajectory. a) shows the error in x positioning, b) in y positioning, c) shows a photomontage of the experimental view with the RTS at different position, the command path is in red. d) shows the distance between the current position and the control position with time. This error is below 2µm for a fixed position command. For this measurement the rotating frequency is set to 60Hz. This experiment was conducted using setup 1 .

Figure 3 . 9 -

 39 Figure 3.9 -Picture of a microfluidic chip. In this work, the closed chamber design can vary depending on the needs. However the open chamber and the microchannel design always stay the same.

Figure 3 . 10 -

 310 Figure 3.10 -Integration of the RTS in the microfluidic chip. a) presents a side view of the chip with the different steps made to integrate the RTS on the chip. b), c), d), and f) are top-view photos of the experiments made by optical microscope. e) is a top-view schematic of the chip. The supplementary video 1 displays a record of this integration.

Figure 3 .

 3 Figure 3.11 -RTS exiting the microfluidic chip. a) shows the pathway for both integration and exiting the chip, b) is a picture of the RTS coming back to its starting point on the fabrication substrate after a journey inside the chip.

Figure

  Figure 3.11 shows an extension of the microfluidic chip integration. In this figure, we explain that the reversed integration steps are possible to exit the RTS from the microfluidic chip and make it come back to the fabrication substrate. The operation follows the same steps as the integration but in reverse order. However one important difference is that the RTS is not diving from the fabrication substrate to the chip. Instead, it has to move up the 1.5mm from the chip to the fabrication substrate. Figure3.9 shows that at the end the RTS comes back only 10µm away from the place it was detached. This ability could be interesting by combining it with trapping to either extract selectively an element of a microfluidic chip or to integrate it from an open chamber to the inside of the chip. The supplementary information video 5 of the paper[START_REF] Barbot | On-chip Microfluidic Multimodal Swimmer toward 3D Navigation[END_REF] presenting the integration of the RTS shows a record of this return travel.

  if the chip is dried Adhesion to some surface after long contact Carried away by the flow

Figure 3 . 12 -

 312 Figure 3.12 -Schematic of problems linked to long-term use of the RTS inside a PDMS chip.

Figure 3 . 13 -

 313 Figure 3.13 -RTS trap actuation methods. a) shows a picture of a microfluidic chip equipped with a trap actuation system. b) presents the two different methods to open and close the trap.

FluidFigure 3 . 14 -

 314 Figure 3.14 -Drying steps of the SU-8 trap. a) the trap is open and the RTS moves inside, b) the chip is closed and dried but a small gap remains due to capillary force. c) The RTS is pushed to the side by the drying frontfrom. d) the trap totally closes and damages the RTS.

Figure 3 . 15 -

 315 Figure 3.15 -Glass trap fabrication and use. a) Schematic of the trap milling. b) Side view of the trap insertion inside the microfluidic chip. c), d) and e) are the different steps during drying. The side view is represented by a schematic and the top view is a screenshot of the experiment.

Figure 3 . 16 -

 316 Figure 3.16 -Speed versus frequency in horizontal swimming for the same RTS. a) displays speed tests after several trappings, b) after drying and one day delay between each drying.

Figure 3 .

 3 Figure 3.17 -A dependence tree of the different technologies developed in this chapter as well as their perspectives.

Figure 4 . 1 -

 41 Figure 4.1 -Principle of obstacle detection by RTS rolling motion. a) shows the test obstacle on which the experiments were performed. b) the principle of the obstacle detection by recording roll and yaw angle perturbation. c) explains how overlapping paths are performed to build a probabilistic map of obstacle presence. d) Shows the result of the obstacle probability map.

Figure 4 .

 4 2 presents the principle of this detection and its results. While performing rolling motion, the RTS is perturbed by the obstacle shown in Figure4.2 a). This perturbation induces a temporary change of the yaw angle, which governs the direction of the RTS in rolling motion.

Figure 4 . 2 -

 42 Figure 4.2 -Principle of obstacle characterization. a) illustrates how the obstacle traps the RTS in spintop motion. c) and d) display the evolution of the minimum pitch angle to escape from the trap versus obstacle height.

Figure 4 . 3 -

 43 Figure 4.3 -Surface angle determination by spintop. a) shows the principle of the angle measurement. b) shows the result.

  obtained values with other models or experiments as well as with numerical simulation results.

Figure 4 . 4 -

 44 Figure 4.4 -The two steps for force sensing. Here F Fluid→RTS is the total viscous effect on the RTS (drag and propulsion).

vFigure 4 . 5 -

 45 Figure 4.5 -Force schematic on an isolated RTS. F and N are the force on the torque apply on this RTS by the fluid, V and ω are its speed and rotation frequency

Figure 4 . 6 -

 46 Figure 4.6 -Force applied to the RTS during the drop test experiment and overview of the characterization protocol. On a) av corresponds to the fluid drag and bω the propulsive force. b) shows the principle of the force characterization, c) shows the principle of the torque characterization. This characterization was not possible in this t hesis but our experimental attempts are presented in Subsection 4.2.5 .

Figure 4 . 7 -

 47 Figure 4.7 -Detection principle of RTS passing through the focal plane detection. a) and b) compare the focus indicator of the RTS position to the focal plane. c) and d) show how the ascending speed is measured for a given frequency with the help of the focus indicator.

Figure 4 . 8 -

 48 Figure 4.8 -Flow chart of numerical treatment from the experimental video records to the speed computation. These steps are mostly done automatically.

.13) 92 CHAPTER 4 .

 924 ROBOT CHARACTERIZATION FOR FORCE MEASUREMENT

Figure 4 . 9 -

 49 Figure 4.9 -Schematic of the optical path presenting the difference between the focal point inside a microfluidic chip filled with air and filled with isopropyl alcohol.

Figure 4 . 10 -

 410 Figure 4.10 -Resist density measurement protocol. The water level in b) and f) is the same.

Figure 4 . 11 -

 411 Figure 4.11 -Simulation of the 3D lithography. a) is a SEM picture of a shape designed to measure the voxel dimension, b) is a 2D schematic of how the volume of polymerized resist is estimated.

Figure 4 .

 4 11 b).

Figure 4 . 12 -

 412 Figure 4.12 -Evolution of the estimated RTS volume in function of the calculus precision. The precision is given by 1/d, with d the edge dimension of a mesh elementary cube.

Figure 4 .

 4 Figure 4.12 displays the estimation of one RTS volume in function of the model resolution d.As an indicator for this precision we choose 1/d to simplify the graphic reading. This graphic shows that the value of the volume seems to converge to a constant value. To get a more precise estimation of the converging value, simulations with 1/d > 100 should be necessary. However more than 50 gigabytes of memory are required to get the simulation to run for d less than 0.01µm (precision > 100 µm -1 ). This reaches the limit of a classic desktop computer. For this reason we decided to use the value for 1/d = 0.01 µm and to add an error of 1µm 3 to the computed result for the high simulation and to subtract 1µm 3 to the computed result for the low approximation.Finally, we need to estimate the volume of metal added to the RTS during the PVD process. It is difficult to estimate how much metal is deposited on a precise RTS location. Moreover half

Figure 4 . 13 -

 413 Figure 4.13 -Schematic of the PVD presenting a tilt angle.

2 - 98 CHAPTER 4 .

 2984 Volume estimations and associated errors for two kinds of RTS.V r = 186.5µm 3 ε Vr = 23.5µm 3 V m = 39.6µm 3 ε Vm = 1.9µm 3 pitch = 4µm V r = 199.5µm 3 ε Vr = 24.5µm 3 V m = 41.9µm 3 ε Vm = 2.7µm 3 The protocol and software codes use to get these values are available in Appendix F. ROBOT CHARACTERIZATION FOR FORCE MEASUREMENT

Figure 4 . 14 -

 414 Figure 4.14 -Flow chart of the RTS force characterization.

Figure 4 . 15 -

 415 Figure 4.15 -Glass tube drop test experiments. a) is a schematic on the specific microfluidic chip. b) is a top-view picture of the RTS just before entering inside the glass tube. c) and d) are snapshots of a drop test record. As the view changes, a reference point displays the same position of the tube in the two different pictures.

4. 3 .

 3 ENVIRONMENT CONTROL WITH A MICROFLUIDIC DROP TEST CHAMBER 103 of 80 • C at a distance of few centimeters from the sample region. This would heat the liquid and perturb the measure by changing the density and viscosity and creating convection.

Figure 4 .

 4 Figure 4.16 -3D simulated view of the drop test chamber and its connection to the rest of the microfluidic chip.

Figure 4 . 17 -

 417 Figure 4.17-Parasite flow due to PDMS absorption and leaks. On a) two different drop tests made at different times demonstrate the presence of a parasite flow. b) shows that leak is the main hypothesis to explain parasite flow. c) and d) show the new drop test design to avoid this parasite flow.

106 CHAPTER 4 Figure 4 . 18 -

 1064418 Figure 4.18 -Non-homogeneity of the parasite flow. a) shows two different experiments made with the same RTS. The numbers displayed the order of the experiment. On the test 2 the RTS had important drift and was put back in the center of the chamber at the point 6. b) shows five different places where we performed drop tests at 0Hz to check for a parasite flow.

Figure 4 . 19 -

 419 Figure 4.19 -Influence of the distance to the drop test chamber center on the RTS speed. a) shows the position of the three different tests, b) shows the average speed of these three tests. The RTS rotating frequency is set to 80Hz.

Figure 4 . 20 -

 420 Figure 4.20 -Influence of the drop test chamber altitude on the RTS speed. a) shows the altitude of the three different test regions, b) shows the ascending speed measurement for a 80Hz rotation, c) is the corresponding falling speed of the RTS at 0Hz. For each value three experiments are performed and the error bars display the standard deviation.

Figure 4 . 21 -

 421 Figure 4.21 -Influence of the magnetic field intensity on the RTS speed.

=

  6 and 4.8 to deduce the parameters a and b of the propulsion matrix, it is interesting to use this speed curve to assess the validity of our different hypotheses made to model the RTS behavior. e n d i n g s p e e d ( m = 0 . 4 8 µ m / s / h z ) D e s c e n d i n g s p e e d ( m = -0 . 4 9 µ m / s / h z ) A s c e n d i n g s p e e d i n t e r p o l a t i o n D e s c e n d i n g s p e e d i n t e r p o l a t i o n

Figure 4 . 22 -

 422 Figure 4.22 -The different ways of getting the RTS speed at 0Hz, v 0 is by making direct drop tests, v0a and v0d by making linear extrapolation on respectively the ascending and descending speed measurements. The error bar on v 0 represents the standard deviation of the measurement series. The error bar on the linear regression corresponds to a confidence interval at 90 % (ε v0 = S v0 t(n -2)), with S v0 the standard deviation of v0 from the linear regression t the t-student distribution and n the sample number[START_REF] Morrison | Obtaining Uncertainty Measures on Slope and Intercept of a Least Squares Fit with Excel's LINEST[END_REF].

Figure 4 .

 4 Figure 4.22 displays an example of these measurement results for one RTS. At first sight, our linearity assumption seems to be verified. First the ascending and descending speeds are linear. Second they seem to intersect roughly in the same point at 0Hz. This is what we expected from the propulsion matrix model. But the difference in the intersection point is not completely negligible. Indeed a zoom shows that thanks to the precision of our measurement, the difference between the speed at 0Hz extrapolated from the ascending speed ( v0a ) and descending speed ( v0d ) is significant. Moreover the average of these two values seems to correspond roughly to the v 0 value measured directly in the drop test experiment at 0Hz. Normally the two curves should intersect exactly at this value. Unfortunately due to the wobbling phenomenon, it is impossible to perform pertinent drop tests between 0Hz and 50Hz to get the ascending and descending speed evolution close to 0Hz.This phenomenon cannot be due to the parasite flow or wall influence, as we guaranteed that there were negligible. Moreover a parasite flow would only translate the curve vertically by adding some offset. The wall proximity would affect the propulsion proportionally to the rotating frequency ω due to the linearity of the flow. But the particularity of this anomaly it that it behaves exactly as if a constant force opposing the RTS speed was present. This would result in moving down the ascending speed curve and moving up the descending speed curve. To analyze where this error comes from, let us write the expression of v 0 from the equation 4.6

  Figure 4.23 a) shows the different characterization curves in ascending speed and descending speed.

Figure 4 . 23 -

 423 Figure 4.23 -Speed characterization repeatability. a) shows the speed characterization curves of the same RTS at different times, b) shows the parameter from the linear regression extracted with these different characterizations. The error in b) corresponds to a confidence interval of 90 %.

Frequency

  e n d i n g s p e e d D e s c e n d i n g s p e e d

Figure 4 . 24 -

 424 Figure 4.24 -Characterization curves of two different RTS. m is the slope coefficient for each curve in µm • s -1 •Hz -1 . This characterization has been performed in isopropyl alcohol.

Table 4 . 3 -

 43 Characterization and force generated for a null speed of two different RTS. The maximal error takes account of the repeatability error of the RTS. The force corresponds to test in isopropyl alcohol (IPA). pN stands for piconewton.

(4. 47 )

 47 Finally we divide this value by the total error to get the pie chart displayed in Figure4.25 b).

Figure 4 . 25 -

 425 Figure 4.25 -Impact of the different errors on the total force estimation. a) is a flow chart of the calculation linked with the identification of the RTS. b) shows an estimation of the different error sources.

Figure 5 . 1 - 1 . 120 CHAPTER 5 .

 5111205 Figure 5.1 -The three different proofs of concept presented in this chapter.

Figure 5 . 2 -

 52 Figure 5.2 -Different potential force sensing applications. a) shows how force stimulation could be applied to a particular cell, b) shows a dynamic friction test with a bead, c) shows a static test where the bead is pushed until detachment, d) shows a static test where the robot pulls on the bead and takes off until it is detached from the surface

Figure 5 . 3 -

 53 Figure 5.3 -Propulsion matrix combination. a) shows the theoretical case where the robot and object propulsion matrices add linearly, b) illustrates the real physical case.

Figure 5 . 4 -

 54 Figure 5.4 -Illustration and experimental view of the protocol to place a bead at the tip of a RTS

Figure 5 . 5 -

 55 Figure 5.5 -Illustration of the protocol used to investigate the impact of the microbead on the RTS propulsion force. The different characterizations are displayed at different places but in reality they were all performed in the center of the drop test chamber. The red squares represent the characterization experiments

Figure 5 . 6 -

 56 Figure 5.6 -Results of the ascending and falling speed characterization at 0Hz of an RTS alone and combined with a 10µm • s -1 polystyrene bead.

a (m) error a b (m 2 • s - 1 •

 21 Hz -1 ) error b Bead (P B ) -0.94 • 10 -4 0 0 0 RTS (P R ) -1.38 • 10 -4 0.12 • 10 -4 4.63 • 10 -11 0.40 • 10 -11 RTS + Bead (P RB ) -1.61 • 10 -4 0.15 • 10 -4 3.91 • 10 -11 0.52 • 10 -11 ∆P = P RB -(P R + P B ) 0.7 • 10 -4 0.08 • 10 -4 -0.72 • 10 -11 0.62 • 10 -11

Figure 5 . 7 -

 57 Figure 5.7 -Illustration on how the right combination of spintop and swim motion can guide the RTS through a complex environment.

Figure 5 . 8 -

 58 Figure 5.8 -Partial flow chart of the swimming closed-loop flow. The pitch, yaw angle and frequency are sent to the thread that generates the command of the magnetic field. This command substitutes the manual command.

Figure 5 . 9 -

 59 Figure 5.9 -Example of the swimming closed-loop with parasite flow on a rectangular path. a) shows a photomontage of the experimental top view superposed with the command and real path. b) displays the evolution of the position on x and y with time. The command path is also displayed.

Figure 5 . 10 -Figure 5 . 11 -

 510511 Figure 5.10 -Online flow measurement principle and implementation.

Figure 5 . 12 -

 512 Figure 5.12 -Results of the channel profile measurement for channel widths of 0.3mm and 3mm. a) and b) display the measured flow speed versus the channel altitude, the comparison with the simulated flow profile is also displayed. c) and d) display the RTS horizontal position evolution during the measurement and command position.

Figure 5 . 13 -

 513 Figure 5.13 -Algorithm to guarantee the safest motion along a path.

Figure 5 . 14 -

 514 Figure 5.14 -Semi-automatic motion adaptation along a cyclic rectangular path. The flow speed increases until the flow threshold is reached and the RTS switches to spintop motion. Then the flow is reduced and the RTS is manually triggered to change to swimming motion. For several time markers, an experimental view is displayed: a) swimming with no flow, b) swimming by compensating the flow, c) spintop, d) transition from swimming to spintop, e) swimming by compensating the flow.

Figure 5 . 15 -

 515 Figure 5.15 -Semi-automatic motion adaptation. a) shows the RTS in spintop with a flow superior to the threshold, preventing any tentative of swimming motion. b) shows the RTS swimming without motion adaptation. As the flow increases the RTS control saturates and the RTS is carried away by the flow.

Figure 5 . 16 -

 516 Figure 5.16 -Control proposition for controlling a helical microrobot in a random 3D microchannel with a 2D feedback. ψ and θ represent the angles between the channel direction and the microrobot direction. The red box represents one goal of this section which is to propose a way to control θ.

5. 4 .

 4 CONTROL STRATEGY IN A MICROCHANNEL UNDER 100 MICROMETERS 141 of the flow solutions.

FluidFigure 5 . 17 -

 517 Figure5.17 -Illustration of the trajectory simulation of the RTS in the cross-section plane of the microchannel. This plane is defined by the section of the channel crossing the RTS center.

Figure 5 . 18 -

 518 Figure 5.18 -Experimental demonstration and simulation of the perpendicular rotation phenomenon. The RTS rotation is 100Hz in the counterclockwise direction a) shows a photomontage of this phenomenon in a 50µm square microchannel. b) displays numerical simulation results on the RTS trajectory in the microchannel cross-section.

Figure 5 . 19 -

 519 Figure 5.19 -Frequency evolution of the perpendicular rotation phenomenon. a) simulation results of the almost constant frequency evolution depending on the starting point position in a 50µm channel. b) shows the important correlation between this frequency and the channel size both experimentally and by simulation.

Figure 5 . 20 -

 520 Figure5.20 -Illustration of the stability of the perpendicular rotation phenomenon to the misalignment of the RTS with the channel direction. In this experiment the RTS evolves in a 30µm square microchannel, the pitch angle is increased until the RTS touches the microchannel wall.

Figure 5 .Figure 5 . 21 -

 5521 Figure 5.21 -Simulation results of the perpendicular trajectory on the cross-section channel with lateral force. For each simulation several starting points are chosen. The simulation corresponds to a 100Hz counterclockwise rotation. a) shows the model hypothesis for the misalignment of the RTS by a lateral force. b) shows the trajectory simulations for a non-perfect aligned RTS by adding a perpendicular force. c) simulates a RTS misaligning progressively with the channel by adding slowly this force from zero during the first two turns (20s).

Figure 5 . 22 -

 522 Figure 5.22 -Proposition for a control strategy in a microchannel. The main advantage of this method is to work only with a 2D image from a single camera. a) shows the model simplification, b)shows our supposition that ψ can be controlled to produce a force proportional to the RTS distance from the channel center. c) shows with different path simulations the control of ψ is sufficient to control the RTS at a position close to the channel center, even with a small misalignment with the direction perpendicular to the optical plane (θ). d) shows a simulation proving that (θ) can be measured by the RTS focusing position on the channel, a=1/50 of propulsive force, k = 1/50 propulsive force per 30µm stiffness value.

Figure 6 . 1 -

 61 Figure 6.1 -Thesis achievements and perspectives dependency tree

  conductivity(w.m-1.k-1) 50 Heat flow by surface (W.m-2) conductivity(w.m-1.k-1) 50 Heat flow by surface (W.m-2) conductivity(w.m-1.k-1) 50 Heat flow by surface (W.m-2) plane of the outer part of the small coil (most constraignant case) check coll ide between small/big and small medium FOCUS IMAGE ANALYSIS CODE # p r e c i s i o n i s not mandatory argument . By d e f a u l f v a l u e i s 2 . i f P r e c i s i o n = 1 : a l l frame w i l l be c o n s i d e r , i f P r e c i s i o n = 2 : one frame o v e r 2 , i f P r e c i s i o n = 3 e t c . . # t o e x e c u t e permanently : chmod +x n o m d u s c r i p t #This s c r i p t t a k e t h e name o f t h e v i d e o t o s p l i t i n t i f f image a s a parameter #d e l e t e and c r e a t e new r e p o s i t o r y rm -r t i f f " $1 " mkdir t i f f " $1 " #put s e c o n d argument a s p r e c i s i o n , i f 1 : a l l frame w i l l be c o n s i d e r , i f : 2 one frame o v e r 2 , i f 3 e t c . . . #d e f a u l t v a l u e i s 2 PREC=$ {2: -2} echo $PREC #c o n v e r t t o bmp ( avconv d o e s not h a n d l e p r o p e r l y t i f f ) avconv -i $1 -f image2 -r 24 t i f f " $1 "/%d . bmp #c o n v e r t bmp t o g r e y s c a l e t i f f #c o n v e r t t i f f " $1 " / * .bmp -n e g a t e -c o l o r s p a c e Gray t i f f /%d . t i f cd t i f f " $1 " n u m f i l e s =( * ) n u m f i l e s=$ {#n u m f i l e s [@] } i =1 w h i l e [ " $ i " -l e " $ n u m f i l e s " ] ; do c o n v e r t $ i . bmp -n e g a t e -c o l o r s p a c e Gray $ i . t i f i=$ ( ( $ i + 1 ) ) echo $ i done #remove . bmp rm * . bmp cd . . #l a u n c h python a n a l y s i s python f o c u s d e t e c t o r . py " $ n u m f i l e s " $PREC $1 $1

  e x c e p t : p r i n t ( "WARNING : No argument was p a s s e d t o t h e program , r u n n i n g with hard coded v a l u e ( u s e r s ' s p a r a m e t e r s ) " ) """FIXED PARAMETER PARAMETERS""" f p s = 24 #frame p e r s e c o n d e o f t h e v i d e o from PIL import Image import m a t p l o t l i b . p y p l o t a s p l t import numpy from numpy import * from numpy . f f t import * import numpy a s np d e f normefocus2D ( img ) : """ Return a l i s t c o r r e s p o n d i n g t o t h e f r e q u e n c y i n t e n s i t y r e p a r t i t i o n """ spy = [ ] a=img . s i z e img=img . c r o p ( [ 1 0 , 1 0 , a [ 0 ] -1 0 , a [ 1 ] -1 0 ] ) #c r o p t o a v o i d b o r d e r problem a=img . s i z e #img . show ( ) norm =0 """ f o r x i n r a n g e ( 0 , a [ 1 ] -1 ) :

  d e f e x t r a c t a r r a y ( array , c o o r d i n a t e s ) : """ r e t u r n an s u b a r r a y o f a r r a y made by t h e c o r r e s p o n d i n g v a l u e o f a r r a y a t t h e c o o r d i n a t e s """ l i s t o u t = [ ] f o r n i n r a n g e ( 0 , c o o r d i n a t e s . s i z e ) : l i s t o u t . append ( a r r a y [ c o o r d i n a t e s [ n ] ] ) r e t u r n ( np . a s a r r a y ( l i s t o u t ) ) d e f e x t r a c t e v e n ( a r r a y ) :

  d e f e x t r a c t a r r a y ( array , c o o r d i n a t e s ) : """ r e t u r n an s u b a r r a y o f a r r a y made by t h e c o r r e s p o n d i n g v a l u e o f a r r a y a t t h e c o o r d i n a t e s """ l i s t o u t = [ ] f o r n i n r a n g e ( 0 , c o o r d i n a t e s . s i z e ) : l i s t o u t . append ( a r r a y [ c o o r d i n a t e s [ n ] ] ) r e t u r n ( np . a s a r r a y ( l i s t o u t ) ) d e f e x t r a c t e v e n ( a r r a y ) :

  d e f sortupdown ( a r r a y ) : """ s o r t e x p e r i m e n t t h e f i r s t max must c o r r e s p o n d t o t h e low f o c a l p l a n e on up xp """ c o l 1 = [ ] c o l 2 = [ ] c o l 3 = [ ] c o l 4 = [ ] a =0; i f ( math . f l o o r ( a r r a y . s i z e / 4 ) == f l o a t ( a r r a y . s i z e ) / 4 . 0 ) : a = a r r a y . s i z e e l s e : a = i n t ( math . f l o o r ( a r r a y . s i z e / 4 . 0 ) * 4 ) +4 c o l 1 . append ( a r r a y . s i z e ) c o l 2 . append ( a ) c o l 3 . append ( 0 ) c o l 4 . append ( 0 ) f o r n i n r a n g e ( 0 , a , 4 ) : i f ( n )<=a r r a y . s i z e -1: c o l 1 . append ( a r r a y [ n ] ) e l s e : c o l 1 . append ( 0 ) i f ( n+1)<=a r r a y . s i z e -1 : c o l 2 . append ( a r r a y [ n +1]) e l s e : c o l 2 . append ( 0 ) i f ( n+2)<=a r r a y . s i z e -1 : c o l 3 . append ( a r r a y [ n +2]) e l s e : c o l 3 . append ( 0 ) i f ( n+3)<=a r r a y . s i z e -1: c o l 4 . append ( a r r a y [ n +3]) e l s e : c o l 4 . append ( 0 ) E.4. OPEN.PY 193 r e t u r n ( np . a s a r r a y ( [ c o l 1 , c o l 2 , c o l 3 , c o l 4 ] ) ) d e f s u p p r e s s i n g d o u b l e r i g h t ( array , th ) : """ s u p p r e s s i n g maxima with d i s t a n c e < th , keep r i g h t maxima """ l i s t o u t = [ ] o l d =0; f o r n i n r a n g e ( 0 , a r r a y . s i z e , 1 ) : i f ( a r r a y [ n ] -o l d ) < th : l i s t o u t . pop ( ) np . d i s p ( " s u p r e s s i n g t o o c l o s e maxima , k e e p i n g r i g h t one " ) l i s t o u t . append ( a r r a y [ n ] ) o l d =a r r a y [ n ] r e t u r n ( np . a s a r r a y ( l i s t o u t ) ) t r y : f i g n a m e = s t r ( s y s . argv [ 1 ] ) # t h e name o f t h e f i l e e x c e p t : p r i n t ( "WARNING : No argument was p a s s e d t o t h e program " ) #l o a d i n g t h e data with open ( f i g n a m e+" . p i c k l e " ) a s f : f i g n a m e , t , f o c u s , s1 , s2 , s 3 = p i c k l e . l o a d ( f )

  95 ' ) ) p r i n t ( " you need t o d e f i n e t h e t h r e s h o l d s . You can make s e v e r a l t h r e s h o l d on d i f f e r e n t r e g i o n u s i n g t h e time t o d e f i n e t h e s e r e g i o n . However you s h o u l d p r o b a b l y t a k e a p i e c e o f paper b e c a u s e you need t o c l o s e t h e f i g u r e t o c o n t i n u e ( s o r r y ) " ) p r i n t ( "CLOSE THE FIGURE TO CONTINUE" ) p l t . show ( ) """ t h r e h o l d i n t e r f a c e """ p r i n t ( " Enter number o f d i f f e r e n t t h r e s h o l d r e g i o n " ) nb th=i n t ( r a w i n p u t ( ) ) h e a d e r=z i p ( * h e a d e r ) a . w r i t e r o w s ( h e a d e r ) #s 3 data=z i p ( * sortupdown ( max1 ) ) h e a d e r = [ [ 0 . 9 5 ] ] ; h e a d e r 2 = [ [ "up" ] , [ " " ] , [ "down" ] , [ " " ] ] ; h e a d e r=z i p ( * h e a d e r ) h e a d e r 2=z i p ( * h e a d e r 2 ) a . w r i t e r o w s ( h e a d e r ) a . w r i t e r o w s ( h e a d e r 2 ) a . w r i t e r o w s ( data ) #s 2 data=z i p ( * sortupdown ( max2 ) ) h e a d e r = [ [ 0 . 8 ] ] ; h e a d e r 2 = [ [ "up" ] , [ " " ] , [ "down" ] , [ " " ] ] ; h e a d e r=z i p ( * h e a d e r ) h e a d e r 2=z i p ( * h e a d e r 2 ) a . w r i t e r o w s ( h e a d e r ) a . w r i t e r o w s ( data ) #s 1 data=z i p ( * sortupdown ( max3 ) ) h e a d e r = [ [ 0 . 9 ] ] ; h e a d e r 2 = [ [ "up" ] , [ " " ] , [ "down" ] , [ " " ] ] ; h e a d e r=z i p ( * h e a d e r ) h e a d e r 2=z i p ( * h e a d e r 2 ) a . w r i t e r o w s ( h e a d e r ) a . w r i t e r o w s ( data ) #t a b l e S 3 p l t . show ( ) 198 APPENDIX F. 3D LITHOGRAPHY VOLUME SIMULATION t r y : d = f l o a t ( s y s . a r g v [ 1 ] ) ; # mesh p r e c i s i o n i n m i c r o m e t e r cube p r i n t ( " d =" , d ) e x c e p t : p r i n t ( "WARNING : No argument was p a s s e d t o t h e program , r u n n i n g w i t h d e f a u l t v a l u e ( d = 0 . 1 ) " ) # ###################### b e g i n path -s i m p l e c o n i c a l head p a t h o f f s e t= 1 #m i c r o m e t e r """ 7 * 5um o r 9 * 4um""" p i t c h =4; # i n m i c r o m e t t e r : a m p l i t u d e p i t c h e s =9; #number o f t u r n p i = 3 . 1 4 1 5 """ c y l i n d r i c a l head """ path = [ ] """ c o n i c a l head """ r t a b = [ 2 .4 , 2 . 3 , 2 . 2 , 2 . 1 , 2 , 1 . 9 , 1 . 8 , 1 . 7 , 1 . 6 , 1 . 5 , 1 . 4 , 1 . 2 , 1 . 1 , 1 , 0 . 9 , 0 . 8 , 0 . 7 , 0 . 6 , 0 . 5 , 0 . 4 , 0 . 3 5 , 0 . 2 , 0 . 1 ] i =0; f o r rmax i n r t a b : f o r r i n f r a n g e ( 0 . 1 , rmax , 0 . 1 ) : f o r p h i i n f r a n g e ( 0 , 6 . 5 5 , 6 . 5 5 / 1 2 ) : x=r * math . c o s ( p h i ) +2.4 z=r * math . s i n ( p h i ) +2.4 y = 4 . 2 -0.2 * i #p r i n t ( " s h o u l d be 0 " ) #p r i n t ( y ) path . append ( [ x , y , z ] ) i = i +1;path . append ([-1-p a t h o f f s e t ,-p a t h o f f s e t ,-p a t h o f f s e t ] ) #w r i t e o f f c o d e """ t a i l """ f o r r i n f r a n g e ( 1 , 1 . 8 , 0 . 2 ) : f o r p h i i n f r a n g e ( 0 , p i t c h e s * 2 * p i , p i / 6 ) : x=r * math . c o s ( p h i ) +2.4 z=r * math . s i n ( p h i ) +2.4 y= p i t c h / ( 2 * p i ) * p h i +3.8 path . append ( [ x , y , z ] ) path . append ([-1-p a t h o f f s e t ,-p a t h o f f s e t ,-p a t h o f f s e t ] ) #w r i t e o f f c o d e """ c o n i c a l head """ o f f s e t = 3 9 . 4 ; i =0; f o r rmax i n r t a b : f o r r i n f r a n g e ( 0 . 1 , rmax , 0 . 1 ) : f o r p h i i n f r a n g e ( 0 , 6 . 5 5 , 6 . 5 5 / 1 2 ) : x=r * math . c o s ( p h i ) +2.4 z=r * math . s i n ( p h i ) +2.4 y = o f f s e t +0.2 * i path . append ( [ x , y , z ] ) #p r i n t ( " s h o u l d be 5 3 . 6 " ) #p r i n t ( y ) i = i +1; k = np . s i z e ( path ) /3 """ path o f f s e t """ #a v o i d t h e v o x e l t o t o u c h t h e b o r d e r o f t h e m a t r i x f o r i i n r a n g e ( 0 , k ) : f o r k i n ( 0 , 1 , 2 ) : path [ i ] [ k]= path [ i ] [ k]+ p a t h o f f s e t ; """ p l o t """ k = np . s i z e ( path ) /3 pathx=np . z e r o s ( k ) pathy=np . z e r o s ( k ) p a t h z=np . z e r o s ( k ) f o r i i n r a n g e ( 0 , k ) : pathx [ i ]= path [ i ] [ 0 ] pathy [ i ]= path [ i ] [ 1 ] p a t h z [ i ]= path [ i ] [ 2 ]

F. 2 .

 2 mpl . rcParams [ ' l e g e n d . f o n t s i z e ' ] = 10 f i g = p l t . f i g u r e ( ) ax = f i g . g c a ( p r o j e c t i o n= ' 3d ' ) ax . p l o t ( pathx , pathy , pathz , l a b e l= ' p l o t ' ) NANOSCRIBE SIMU.PY 199 ax . l e g e n d ( )p l t . show ( ) # ##############################s t a r t s i m u l a t i o n """ p ar a m e t e r s """ #S i z e o f t h e v o x e l vz =1.715 #+/-0 . 0 1 vx =0.533 #+/-0 . 0 0 5 vy =0.533 #+/-0 . 0 0 5 t r y : vz = f l o a t ( s y s . a r g v [ 2 ] ) ; # mesh p r e c i s i o n i n m i c r o m e t e r cube vx = f l o a t ( s y s . a r g v [ 3 ] ) ; vy=vx p r i n t ( " Voxel s i z e : vz =" , vz , " vx =" , vx , " vy =" , vy ) e x c e p t : p r i n t ( "WARNING : No s e c o n d and t h i r d argument p a s s t o t h e program , Voxel s i z e i s d e f a u l t : vz =" , vz , " vx =" , vx , " vy =" , vy ) #path ( l i s t o f 3D p o i n t s ) , NO NEGATIVE VALUE e x c e p t w r i t i n g o f f c o d e ( x=-1) #path = [ [ 0 , 0 , 0 ] , [ 1 0 , 0 , 0 ] , [ -1 , 0 , 5 0 0 ] , [ 0 , 1 0 , 0 ] , [ 0 , 2 0 , 0 ] ] #mesh s i z e ( e d g e o f t h e s q u a r e mesh ) #path d i s c r e

  o n v e c t o r [ : ] = [ ( x * s e l f . s t e p ) / norm ( v e c t o r ) f o r x i n v e c t o r ] #v e c t o r norm i s now a s t e p s e l f . p o s i t i o n = [ s e l f . p o s i t i o n [ k]+ v e c t o r [ k ] f o r k i n r a n g e ( 0 , 3 ) ] r e t u r n s e l f . p o s i t i o n d e f r e s e t ( s e l f ) : s e l f . p o s i t i o n= path [ 0 ] s e l f . p a t h p o i n t =0 s e l f . e n d o f p a t h = F a l s e d e f f i n d p a t h l e n g t h ( s e l f ) : o l d v e c t o r = [ s e l f . path [ 0 ] [ k ] f o r k i n r a n g e ( 0 , 3 ) ] s z =0; f o r i i n r a n g e ( 1 , np . s i z e ( s e l f . path ) / 3 ) : # end o f path d e t e c t e d v e c t o r = [ s e l f . path [ i ] [ k ] f o r k i n r a n g e ( 0 , 3 ) ] d i f f =[ v e c t o r [ k]-o l d v e c t o r [ k ] f o r k i n r a n g e ( 0 , 3 ) ] s z=s z+norm ( d i f f ) ; o l d v e c t o r=v e c t o r ;

200

  APPENDIX F. 3D LITHOGRAPHY VOLUME SIMULATION k = np . s i z e ( path ) /3 pathx=np . z e r o s ( k ) pathy=np . z e r o s ( k ) p a t h z=np . z e r o s ( k ) f o r i i n r a n g e ( 0 , k ) :pathx [ i ]= path [ i ] [ 0 ] pathy [ i ]= path [ i ] [ 1 ] p a t h z [ i ]= path [ i ] [ 2 ] #cr e a t e U n i v e r s u n i v e r s = np . z e r o s ( ( max ( pathx ) /d + i n t ( vx /d ) + 6 , max ( pathy ) /d + i n t ( vy /d ) +6 ,max ( p a t h z ) /d + i n t ( vz /d ) +6) , d t y p e = ' b o o l ' ) """ Voxel c r e a t i o n """ #The v o x e l i s c e n t e r e d on c o o r d i n a t e cx , cy , xz , t h e s e a r e t h e rounded s e m i a x i s cx=i n t ( round ( vx / ( d * 2 ) ) ) cy=i n t ( round ( vy / ( d * 2 ) ) ) c z=i n t ( round ( vz / ( d * 2 ) ) ) #p r i n t ( " r e a d y " ) #c r e a t e v o x e l m a t r i x v o x e l = np . z e r o s ( ( 2 * cx +4 ,2 * cy +4 ,2 * c z +4) , d t y p e = ' b o o l ' ) #For e a c h e l e m e n t i n v o x e l m a t r i x put True i f t h i s e l l e m e n t b e l o n g t o t h e v o x e l f o r x i n r a n g e ( 0 , 2 * cx +4) : f o r y i n r a n g e ( 0 , 2 * cy +4) : f o r z i n r a n g e ( 0 , 2 * c z +4) : #e l l i p s o i d e q u a t i o n i s x ˆ2 / ( vx / 2 ) ˆ2 + y ˆ2 / ( vy / 2 ) ˆ2 + z ˆ2 / ( vz / 2 ) ˆ2 <=1 ( t r u e i f i n s i d e t h e e l l i p s o i d ) i f ( ( ( x * d-(cx +1) * d ) * * 2 ) / ( ( vx / 2 ) * * 2 ) + ( ( y * d-(cy +1) * d ) * * 2 ) / ( ( vy / 2 ) * * 2 ) + ( ( z * d-( c z +1) * d ) * * 2 ) / ( ( vz / 2 ) * * 2 ) <= 1 ) : v o x e l [ x , y , z ]= True #c r e a t e e x t r a c t e d u n i v e r s e x t r a c t e d u n i v e r s = np . z e r o s ( ( 2 * cx +4 ,2 * cy +4 ,2 * c z +4) , d t y p e = ' b o o l ' )

  p o s i t i o n [ 2 ] / d ) + c z ) f o r x i n r a n g e ( xb , xe +1) : f o r y i n r a n g e ( yb , ye +1) : f o r z i n r a n g e ( zb , z e +1) : e x t r a c t e d u n i v e r s [ x-xb , y-yb , z-zb ]= u n i v e r s [ x , y , z ] #w r i t e v o x e l on t h e e x t r a c t e d u n i v e r s e x t r a c t e d u n i v e r s=np . b i t w i s e o r ( e x t r a c t e d u n i v e r s , v o x e l ) #r e p o r t e x t r a c t e d u n i v e r s on u n i v e r s f o r x i n r a n g e ( xb , xe +1) : f o r y i n r a n g e ( yb , ye +1) : f o r z i n r a n g e ( zb , z e +1) : u n i v e r s [ x , y , z ]= e x t r a c t e d u n i v e r s [ x-xb , y-yb , z-zb ]

F. 3 .

 3 PVD SIMU.PY 201 t o u t = p r i n t d+s t r d+p r i n t v z+s t r v z+s u f f i x e w i t h open ( t o u t , 'w ' ) a s f : p i c k l e . dump ( [ u n i v e r s ] , f ) """# l o a d # G e t t i n g back t h e o b j e c t s : w i t h open ( ' o b j s . p i c k l e ' ) a s f : o b j 0 , o b j 1 , o b j 2 = p i c k l e . l o a d ( f ) """

i m p o r t p i c k l e w i tINTRODUCTION

  h open ( name ) a s f : u n i v e r s = p i c k l e . l o a d ( f ) [ 0 ] i m p o r t math i m p o r t numpy a s np i m p o r t m a t p l o t l i b . cm a s cm i m p o r t m a t p l o t l i b . p y p l o t a s p l t #r e t u r n X, Z i n a t u p l e , x and y c o r r e s p o n d t o he c o o r d i n a t e o f t h e RTS a f t e r two r o t a t i o n . t h e t a t h a t r e p r e s e n t t h e t i l t o f t h e m e t a l l i s a t i o n p l a t e f o r m and p s i i t s r o t a t i o n . d e f p r o j ( x2 , y2 , z2 , t h e t a , p s i ) : x = x2 * math . c o s ( t h e t a ) * math . c o s ( p s i ) -y2 * math . s i n ( p s i ) * math . c o s ( t h e t a ) -z2 * math . s i n ( t h e t a ) y = x2 * math . s i n ( p s i ) + y2 * math . c o s ( p s i ) +z2 * 0 a =[x , y ] r e t u r n a #d e f a n t i p r o j ( y2 , z2 , t h e t a , p s i ) :d e f r m h o l l e ( p r o j e c t i o n ) : [ x2 , y2 ] = p r o j e c t i o n . s h a p e f o r x i n r a n g e ( 1 , x2 -1) : f o r y i n r a n g e ( 1 , y2 -1) : s i d e = 1 * p r o j e c t i o n [ x -1 ,y -1] + 1 * p r o j e c t i o n [ x , y -1] + 1 * p r o j e c t i o n [ x -1 ,y +1] + 1 * p r o j e c t i o n [ x+1 ,y +1] i f s i d e == 4 : p r o j e c t i o n [ x , y ] = True r e t u r n p r o j e c t i o n i =0; d p s i = r a n g e ( 0 , 9 1 ) graph=np . z e r o s ( np . s i z e ( d p s i ) ) ; f o r d p s i i n d p s i : t h e t a = t i l t * math . p i / 1 8 0 ; # p s i=d p s i * math . p i / 1 8 0 ; #d i m e n s i o n d e t e r m i n a t i o n [ a , b , c ] = u n i v e r s . s h a p e ; d e t y = [ ] ; d e t z = [ ] ; f o r x i n [ a , 0 ] : f o r y i n [ b , 0 ] : f o r z i n [ c , 0 ] : kg/m³ Start time(s) Stop time(s) speed(µm/s) linear regressi y=mx+b regression error V0 (90 0Polystyrene microspheres are used in many applications, including lateral flow tests, latex agglutination tests, flow cytometry, fluorescence microscopy, and as calibration particles. Polysciences, Inc. offers a wide selection of polystyrene-based microspheres, with diameters ranging from 0.05µm to 90µm within our Polybead ® line. We also offer particles with visible and fluorescent dyes. Both our dyed and undyed particles are available with amino and carboxyl surface chemistries.

  e s o l u t i o n i n XY 10 f o r q u i c k c o m p i l a t i o n 50 f o r r e s u l t s r e a l XYin = 7 0 ;

  2 e -6; // d i s t a n c e from t h e p e r i m e t e r t o c a l c u l a t e t h e f i r s t o r d e r d e r i v a t i o n o f t h e s p e e d on t h e r o b o t s u r f a c e t o g e t t h e v i s c o u s d r a g . . //----------------------------OUTPUT FILE -------------------------------------------of s t r e a m o u t ( " s i m u r e s u l t . c s v " ) ; // f o r s t o r r i n g t h e f o r c e //----------------------------GENERAL BOUNDARY DEFINITION----------------------------r e a l o f f s e t x = 0 ; r e a l o f f s e t y = 0 ; // number from 1 t o 20 a r e a s s o c i a t e d w i t h c o l o r i n t r o b o t = 1 0 ; i n t d o u t s i d e f r e e = 1 5 ; i n t g o u t s i d e f r e e = 2 0 ; i n t kk= s t e p ; i n t j j ; o f f s e t y =10e -6;

  i o n on x { o f f s e t x= B r a d i u s /2 * j j / round ( s t e p / 2 ) ; f o r ( kk =0; kk<round ( s t e p ) ; kk++) // b e g i n i t e r a t i o n on y { o f f s e t y= B r a d i u s * kk / round ( s t e p ) ; // c h e c k i f r o b o t i s i n s i d e t h e c h a n n e l i f ( ( o f f s e t x >-B r a d i u s /2+ R r a d i u s+1e -6) && ( o f f s e t x <B r a d i u s /2-R r a d i u s -1e -6) && ( o f f s e t y > R r a d i u s+1e -6) && ( o f f s e t y <B r a d i u s -R r a d i u s -1e -6) ) // 1 m i c r o m e t e r margin { //----------------------------2D CONSTRUCTION--------------------------------------b o r d e r S ( t =-1,1){ x=B r a d i u s * t / 2 ; y =0; l a b e l=d o u t s i d e f r e e ; } b o r d e r E( t =0 ,1) { x=B r a d i u s / 2 ; y=B r a d i u s * t ; l a b e l=d o u t s i d e f r e e ; } b o r d e r N( t =1,-1){ x=B r a d i u s * t / 2 ; y=B r a d i u s ; l a b e l=d o u t s i d e f r e e ; } b o r d e r W( t =1 ,0) { x=-B r a d i u s / 2 ; y=B r a d i u s * t ; l a b e l=d o u t s i d e f r e e ; } b o r d e r b ( t =0 ,2 * p i ) { x=R r a d i u s * c o s ( t ) + o f f s e t x ; y=R r a d i u s * s i n ( t ) + o f f s e t y ; l a b e l=r o b o t ; } // p l o t ( S ( 2 0 )+E( 2 0 )+N( 2 0 )+ W( 2 0 )+b ( 3 0 ) , w a i t =1) ; / / t o s e e a p l o t o f t h e b o r d e r mesh mesh T h w i t h h o l e = b u i l d m e s h ( S ( XYout / 2 )+E( XYout / 2 )+N( XYout / 2 )+ W( XYout / 2 )+b(-XYin ) ) ; // Uncomment t o d i s p l a y t h e mesh // p l o t ( Thwithhole , w a i t =1 , ps="T h w i t h o u t h o l e . e p s " ) ; //-

  e s p a c e Uh( Thwithhole , P1b ) ; Uh u , v , uu , vv ; f e s p a c e Ph ( Thwithhole , P1 ) ; Ph p , pp ; s o l v e s t o k e s ( [ u , v , p ] , [ uu , vv , pp ] ) = // weak f o r m u l a t i o n o f t h e s t o k e s e q u a t i o n i n t 2 d ( T h w i t h h o l e ) ( dx ( u ) * dx ( uu )+dy ( u ) * dy ( uu ) + dx ( v ) * dx ( vv )+ dy ( v ) * dy ( vv ) + dx ( p ) * uu/nu + dy ( p ) * vv /nu + pp * ( dx ( u )+dy ( v ) ) /nu -1 e -10 * p * pp/nu/nu ) // f o r model s t a b i l l i t y // Boudary c o n d i t i o n s + on ( r o b o t , u=-w * ( y-o f f s e t y ) , v=w * ( x-o f f s e t x ) ) + on ( d o u t s i d e f r e e , u=0 ,v=0) ;

  f o r ( d t h e t a =0; d t h e t a <n ; d t h e t a++) { xx = c o s ( d t h e t a * 2 * 3 . 1 4 1 5 / n ) ; yy = s i n ( d t h e t a * 2 * 3 . 1 4 1 5 / n ) ; xdr = ( R r a d i u s+dr ) * xx +o f f s e t x ; ydr = ( R r a d i u s+dr ) * yy +o f f s e t y ; dun = ( s q r t ( u ( xdr , ydr ) * u ( xdr , ydr ) + v ( xdr , ydr ) * v ( xdr , ydr ) ) -R r a d i u s * w) / dr ; // d e r i v a t e = ( s p e e d (M( x , y ) -s p e e d ( on t h e RTS) ) / ( d i s t a n c e between t h e two ) Fx = Fx + (-s i n ( d t h e t a * 2 * 3 . 1 4 1 5 / n ) ) * R r a d i u s * 2 * 3 . 1 4 1 5 / n * nu * dun ; // f o r c e x = sum ( p r o j e c t o n x ( r d ( t h e t a ) * v i s c o s i t y * d e r i v a t i v e ) Fy = Fy + (+ c o s ( d t h e t a * 2 * 3 . 1 4 1 5 / n ) ) * R r a d i u s * 2 * 3 . 1 4 1 5 / n * nu * dun ; // f o r c e y = sum ( p r o j e c t o n y ( r d ( t h e t a ) * v i s c o s i t y

  v i d e by t h e l e n g t h o f t h e r o b o t t o work i n 2D) n b i t e r =700; # number o f i t e r a t i o n P0=np . a r r a y ( [ 5 e -6 ,10 e -6 ] ) # S t a r t p o s i t i o n m=5.5 e -12/50 e-6 #masse o f t h e r o b o t by s e c t i o n Kg .m-1 g =0; # L a t e r a l f o r c e g =10 mean t h e f o r c e i s e q u a l t o t h e RTS t o t a l w e i g h t t l i m =1 # s e c o n d d e l a y b e f o r e s t a r t i n g t o c h e c k f o r l o o p """-------i m p o r t f i l e -------------""" i m p o r t c s v w i t h open ( f i l e n a m e , ' rb ' ) a s c s v f i l e : s p a m r e a d e r = c s v . r e a d e r ( c s v f i l e , d e l i m i t e r= ' ; ' , q u o t e c h a r= ' | ' ) spam=s p a m r e a d e r . n e x t ( ) #g e t s t e p t s i z e =i n t ( spam [ 1 ] ) s p a m r e a d e r . n e x t ( ) #s k i p s e c o n d l i n f o r row i n s p a m r e a d e r : #p r i n t ( row ) X. append ( f l o a t ( row [ 0 ] ) ) Y. append ( f l o a t ( row [ 1 ] ) ) FX . append ( f l o a t ( row [ 2 ] ) ) FY . append ( f l o a t ( row [ 3 . a r r a y (XX) ) Y=(np . a r r a y (YY) ) FX=(np . a r r a y (FFX) ) FY=(np . a r r a y (FFY) )"""----------F u n c t i o n d e f i n i t i o n ----------------""" d e f f or c e a t x y ( x , y , g , X, Y, FX, FY) : """ i n t e r p o l a t e t h e f o r c e on t h e r o b o t a t t h e g i v e n l o c a t i o n ( x , y ) """ f o r xx i n r a n g e ( 1 ,X . s h a p e [ 0 ] , 1 ) : f o r yy i n r a n g e ( 1 ,X . s h a p e [ 1 ] , 1 ) : i f ( (X [ xx ] [ yy]>x ) and Y [ xx ] [ yy]>y ) : #d e t e c t t h e f i r s t i m e above , i t mean xx , yy a r e t h e c o o r d i n a t e a t t h e t o p r i g h t c o r n e r o f t h e g r i d c o n t a i n i n g t h e p o i n t ( x , y ) dx=(x-X [ xx -1 ] [ yy ] ) / (X [ xx ] [ yy]-X [ xx -1 ] [ yy ] ) dy=(y-Y [ xx ] [ yy -1 ] ) / (Y [ xx ] [ yy]-Y [ xx ] [ yy -1 ] ) #p r i n t ( dx ) #c a l c u l a t e i n t e r m d i a t e p o i n t on xx-1 and xxl i n e f x 1=FX [ xx -1 ] [ yy -1] * (1 -dy )+FX [ xx -1 ] [ yy ] * ( dy ) f y 1=FY [ xx -1 ] [ yy -1] * (1 -dy )+FY [ xx -1 ] [ yy ] * ( dy ) f x 2=FX [ xx ] [ yy -1] * (1 -dy )+FX [ xx ] [ yy ] * ( dy ) f y 2=FY [ xx ] [ yy -1] * (1 -dy )+FY [ xx ] [ yy ] * ( dy ) #c a l c u l a e f i n a l p o i n t f x=f x 1 * (1-dx )+f x 2 * dx f y=f y 1 * (1-dx )+f y 2 * dxF=np . a r r a y ( [ f x , f y -g ] ) r e t u r n (F) F=np . a r r a y ( [ 0 , 0 ] ) r e t u r n (F) d e f s p e e d a t x y ( x , y , g , X, Y, FX, FY, a ) : #Give t h e r o b o t s p e e d i n t h e c h a n n e l s e c t i o n F=f o r c e a t x y ( x , y , g , X, Y, FX, FY) / a r e t u r n F d e f RK2 ( s t e p , x , y , g , X, Y, FX, FY, a ) : #r a n g e k u t t a 2 : r e t u r n t h e p o s i t i o n o f t h e r o b o t a f t e r t h e t i m e s t e p """ #h e r e we assume t h a t t h e f o r c e i s d i r e c t l y p r o p o r t i o n a l ( e g a l f o r now ) t o t h e d i s p l a c e m e n t a s t h e i n e r t i a o f t h e r o b o t i s n e g l i g i b l e and t h e v i s c o s i t y d i r e c t l y compensate t h i s move """

  d e f simu ( P0 , n b i t e r , s t e p , g , X, Y, FX, FY, a ) : """ s i m u l a t e RTS t r a j e c t o r y i n t h e c h a n n e l s e c t i o n , s t o p i f t h e t r a j e c t o r y l o o p """f =0 tX = [ ] tY = [ ] t i m e = [ ] F v a r ia t i o n = [ ] tX . append ( P0 [ 0 ] ) tY . append ( P0 [ 1 ] ) t i m e . append ( 0 ) P=np . a r r a y ( [ P0 [ 0 ] , P0 [ 1 ] ] ) f o r k i n r a n g e ( 1 , n b i t e r , 1 ) : #i t e r a t e p o s i t i o n P=RK2( s t e p , P [ 0 ] , P [ 1 ] , g , X, Y, FX, FY, a ) tX . append (P [ 0 ] ) tY . append (P [ 1 ] ) t i m e . append ( k * s t e p ) i f ( k * s t e p >t l i m ) and ( mt . s q r t ( ( P[ 0 ] -P0 [ 0 ] ) * (P[ 0 ] -P0 [ 0 ] ) + (P[ 1 ] -P0 [ 1 ] ) * (P[ 1 ] -P0

  Microfluidic and lab-on-a-chip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 The needs for on-chip force sensor . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Needs in biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Needs in physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Needs in robotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Review of existing on-chip force sensing technologies . . . . . . . . . . . . . . . . Magnetic actuated helical microrobot for force sensing . . . . . . . . . . . . . . . 1.5 Goals and challenges of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . Presentation of the chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Differences between the two setups . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Setup 1: robot detachment and precise pitch control . . . . . . . . . . . . 2.3.2 Setup 2: high resolution and temperature control . . . . . . . . . . . . . . 2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Robot Motions and Microfluidic Chip Integration 3.1 Characterization of the different robot motions . . . . . . . . . . . . . . . . . . . 3.1.1 RTS actuation principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Presentation of the different motions . . . . . . . . . . . . . . . . . . . . . 3.1.3 Characterization and comparison of the motions . . . . . . . . . . . . . . 3.1.4 Achieving special tasks by combining motions . . . . . . . . . . . . . . . . 3.2 The spintop motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Closed-loop control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Microfluidic chip integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Microrobot storage inside microfluidic chip . . . . . . . . . . . . . . . . . . . . .

	Contents 1 Introduction 1.1 Chapter 1

1.3.1 Atomic force microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Optical tweezers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 Magnetic tweezers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.4 Comb drive actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.5 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 1.5.1 Thesis goals definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.2 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 2 System 2.1 RTS and microfluidic chip fabrication . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 RTS fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 3D microfluidics with screw valve . . . . . . . . . . . . . . . . . . . . . . . 2.2 2.2.1 Magnetic field generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Control software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Feedback path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 3.3.1 Microfluidic chip design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Integration protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4

Table 1 .

 1 1 -Advantages and drawbacks of force sensing techniques.

		Advantages	Drawbacks
	AFM	-High versatility -Commercially available	-Difficult sample preparation -Not compatible with microfluidics -2D limited
	Optical tweezers	-High versatility -3D -Microfluidic compatible	-Not selective -Requires purified and homogeneous medium -Heat and photo damage of trap object
	Magnetic tweezers	-Simple 1D design -Selective -No damage -Compatible with any medium -Constant force with displacement -High field intensity	-Not versatile -3D requires a complicated design -Heating from electromagnet -Complicated microfluidic integration for electromagnet
	Comb drive actuator	-Simple to use (plug & play) forces -Measure axial and longitudinal	-Not compatible with microfluidics
		-3D
		-Microfluidics compatible	-Requires robot integration inside
	Helical	-Constant force with displacement	the chip
	microrobot	-Large medium compatibility	-Under the micrometer, the localization is
		-Works with low field intensity	complicated
		(≈ 10mT )
	refraction index that the liquid.

Table 1 .

 1

2 -Applications of the different force sensing technologies. Helical microrobot are displayed in italic as they represent potential applications.

Table

  1.3 -Different micro and nanorobots designs sorted by average size. The red colored row describes the technology chosen for this thesis.

							CHAPTER 1. INTRODUCTION
					Continued from Table 1.3
		Size	References and picture	Propulsion technique	Control and Locomotion	Existing features	Perspec-tives
	Size	References and picture ≈ 10µm	Propulsion technique	Control and Locomotion	Existing features	Perspec-tives
	> 1mm		[4, 7] [5, 58, 59, 60] permanent magnet both on stage and on robot	rotation 2D + 1	force mea-ation Enucle-and Cell surement
				ferromagnetic
	≈ 1mm			robot by magnetic	3D + 1 rotation	micro assembling
			[43]	gradient
				ferromagnetic		puncture
	≈ 1mm			robot by magnetic	3D +2 rotation	blood vessel in	eye surgery
			[44, 45]	gradient		vitro
	≈ 800µm			reciprocal motion in non Newtonian flow	1D (slow)	in-vivo fluid compatible
			[46]
	≈ 500µm		[47]	flow jet by bubble oscillation	1D	3D possible as well as selective control
	≈ 300µm		[48]	magnet on robot and magnetic rotating field	2D + 1 rotation	cargo transport	micro cristal transport
				ferromagnetic		measuring
	≈			robot by	2D and 1	viscosity
	300µm			magnetic	rotation	and wall
			[49]	gradient		proximity
	≈ 50µm			electro-osmotic propulsion	1D
			[50]
	≈ 50µm	[51, 52, 53, 54, 55]	ferromagnetic robot and rotating magnetic field	3D + 2 rotations	cargo transport	On-chip force sensing (this thesis)
				chemical
	≈			reaction +	2D + 1
	10µm			magnetic	rotation
			[56, 57]	orientation

Table 2 .

 2

	2 -Parameters of the two different magnetic setups
			Setup 1 Setup 2
	Coils radius diameter in mm	Small Medium 77 55 Big 113	55 75 95
		Small	250	110
	Number of wire turns per coil	Medium 350	120
		Big	510	150
	Maximum magnetic power at the center in mT	Small Medium 14 14 Big 14	8 8 8

Table 4 .

 4 .1. 1 -Upper and lower limits of the 3D lithography voxel.

		High	Low
		approximation	approximation
	Vertical dimension	2.001µm	1.626 µm
	Horizontal dimension	0.517 µm	0.371 µm

•

  Resist volume determination. (see Section 4.2.3 for details) • 3D lithography voxel determination. (see Section 4.2.3 for details)

	Steps performed once per new RTS design:
	• Resist volume determination. (see Section 4.2.3 for details)
	• Metal volume determination. (see Section 4.2.3 for details)

  t i s a t i o n (SMALLER THAN D I S USELESS) dpath=d """ path c r e a t i o n """ # I n s e r t a x=-1 p o i n t t o jump t o n e x t p o i n t w i t h o u t w r i t i n g . c l a s s Path : d e f i n i t ( s e l f , path , s t e p ) : #path i s t h e l i n e a r by p i e c e path , s t e p t h e s t e p t o advance i n

  Title: On-Chip Untethered Helical Microrobot for Force Sensing Applications keywords: Robotics, microfluidic, microtechnology

CHAPTER 6. CONCLUSION AND PERSPECTIVES Bibliography 208 APPENDIX I. BEAD CHARACTERISTICS

CHAPTER 6. CONCLUSION AND PERSPECTIVES

When the microrobot will enter an organism, we will be unable to use precise optics to feedback control as living tissues are rarely transparent. Therefore microfluidic chips are needed to get a deep understanding of RTS physics microchannel to simplify the RTS control in order to deal with poor feedback resolution like ultrasound imaging or MRI. We start to propose a theoretical control scheme of Chapter 5.4 but a first start will be to prove it experimentally. Then investigating the shape of the helical microrobot by both simulations and experiments should be considered to find the most simple helical robot geometry to move inside a vessel.

Bio-compatibility will also be a concern and the same method as for the cell characterization could be undertaken. To understand the physical change due to the evolution of the non-Newtonian biological fluid and their consequences on the RTS dynamics, quantitative characterizations of the robot could also be a key tool.

To conclude, we are convinced that both the helical microrobot on-chip integration and the protocol to perform force characterization are not only necessary for force related measurements. They constitute also an important step towards a large range of applications. Indeed we think that bringing the helical robot on a very modular platform where the physics can be fully controlled will allow to perform the quantitative studies required for physics analysis and microrobot optimizations.

List of publications Journal Article

A. Barbot, D. Decanini, and G. Hwang, "On-chip Microfluidic Multimodal Swimmer toward 3D Navigation.," Scientific reports, vol. 6, no. January, p. 19041, 2016

Conference proceedings

A. Barbot

Milling Machine

This annex presents the milling machine characterization and protocol to make the microfluidic mold. This protocol is presented here because it was developed for this thesis by the author for making the microfluidic chip present in the thesis.

Machine characteristics

User manual

The micromilling machine can be used as an alternative for creating a mold for a microfluidic chip. The advantages and drawbacks compared to SU8 lithography solution are the following:

• Advantages:

-Quick process from the idea to the mold (around 2 days).

-Possible multilevel and 3D structure.

important height of design (around millimeters)

• Drawbacks:

-Resolution limited by the 100µm mill -Only one level (top one) will have high optical quality bonding delimited easily on the border of the chip To sum up, for microfabrication the micromilling machine fills the gap between what one could make with classical machining fabrication methods and lithography.

Design part

The design can be made on any CAD software. We used here the Solidwork software. When the 3D design is finished one must export it in "STEP" format and import it on the visual mill.

A complete guide through Visual Mill will not be given as the manual is online and it is possible follow an example. However here the big steps and the tips are not to be found in the manual are given:

• Import the STEP file, move it so the top part is at an altitude z = 0 ( because it will then be the zero of the milling machine)

• Create a "box stock", click an automatic scaling.

• Create a milling operation (if you have no idea of which one select "3D -rough")

• Double click on the milling operation and give information about the mill, the cut speed, the overlapping on each path, the advance at each step and the margin (for the margin put zero if it is the last operation). The compilation of the path sometimes crashes, this means that some parameters are not good.

• Simulate the path to check that everything is fine.

• Right click on your milling operation and export to gcode for the machine Mach 3.

• Send your gcode to the milling machine computer.

Milling machine

First, be safe! The milling machine is a rotating unprotected cutting tools. So remember these two things:

• Wear protection glasses at all time. If the drill breaks, some pieces can go into your eyes.

• Double check that the spin command of the mill is shut down before manipulating it. The emergency STOP button only stops the displacement of the drill but not its spinning.

Now here are the steps to mill an object:

Changing drill

• Set off the position command and the spinning command.

• Unscrew the tip to put the good drill, for this it is recommended to put a glove under the mill pit to avoid breaking if it falls.

• Sometimes the chuck (in french mandrin) is hard to release, in this case use the tweezers to hold the top of the chuck while you unscrew above with the key. This should be enough to release it.

• Put the new drill.

Preparing the substrate

• Clean the surface.

• Fix your substrate.

Starting the drill

• Turn on the position command.

• Turn on the spinning command ( by default put to 10 ). The drill should start turning.

• Launch Mach3 on the desktop.

• Select "mach3 4 axis".

• Press the reset button until it stops flashing. You should be able to control the X and Y axis of the drill with the keyboard.

Making the zeros and launching program

• Load your G code.

• Make X and Y zeros.

• Now one can have a preview of where the design will be on the substrate. To change this position just move with X Y above the substrate and remake X Y zeros when the position suits you.

• Select speed = 10 %.

• Approach to the substrate until you are 1mmabove it.

• Change the speed at 1 %.

• Approach the substrate until you touches it. Now there are two solutions. To make a flat surface follow the following steps :

Mill in glass

Particularities of milling in glass:

• Stick the glass to a metal piece with melt wax to prevent destructive vibrations between the glass and support. This metal piece is then fixed to the mill table. To remove the wax use hot trichloroethylene under an aspiration hood.

• Speed must be below 0.1 mm/min.

• Mill in water condition to avoid heating and remove glass particles.

Appendix B

Mechanical Setup Dimensioning

This appendix presents the iterative protocol associated with the design of the magnetic setup consisting of the three pairs of Helmholtz coils. The major constraint of the design is that the radius of each pair of coils needs to be equal to the distance between these two coils. The following calculation sheet takes the diameter of the coils, the wire diameter, the number of turns, the length of the coils and the input current as input parameters. From this, it computes the magnetic field power at the center of the two coils, the temperature assuming only exchange from natural convection with air and the coil width.

These data are used to manually adjust the input parameters to find the optimal solution. To help this process and check for collisions between the coils, two in plane views are automatically computed. The first view displays a cross-section (corresponding to a tomography view) to check the insertion of the sample in the middle of the coils. This calculation sheet was used for the design of setup 1 and setup 2 as well as other setups currently in use in the laboratory. The displayed figure shows the calculation for the setup 1.

Appendix C Magnetic Setup Tuning Protocol Protocol With a gauss meter

This measure records the response of each coil pairs to a constant input. It is needed to experimentally find the good coils command that allows the expected magnetic field from the design. The steps are the following:

• Launch the modified version of the control program that sends a constant output on each coils pair.

• Send a coils command between 1 to 10 (usually it is safe to start with 1) on one of the coils pair

• Record the corresponding magnetic field.

• Reproduce the same operation for the two other magnets with the same command.

Then the use of this measure can vary depending on the setup. For setup 1, they are just made to check that the magnetic field is the same on every coil pair. Indeed the coils are controlled in current and the design guaranties the same magnetic field for the same input current. Therefore this guarantees that there was no fabrication error on setup 1 as the measurement variations were less than 5 %. Depending on the found value the command can be adapted to reach the desired field.

For the setup 2, the design constraints are such that the same coils command leads to a different magnetic fields. In this case these results are used to tune the output of each pair of coils to deliver the same magnetic field for a constant input. On setup 2 the evolution of the magnetic field power with the frequency was not investigated.

With current clamp

For the setup 1, we want to guarantee that the power delivered by each pair of coils is the same depending on the frequency. This is essential to study the spintop motion evolution with frequency because if the evolution of the power is different on the coil pairs the pitch angle of the RTS will also evolve with the frequency. To do so we use a current clamp. As the power of the field was already found with the gauss meter and that the same relation between the input current and magnetic field is guaranteed, this measure is enough. Therefore the protocol is the following:

• Start the normal control program.

• Set a field direction where the amplitude is fully projected on at least one pair of coil. For example, a field that will make the robot rotate vertical is fully decomposed on the two horizontal coil pairs.

• Put the clamp around the current input of the coil pair to measure. The clamp needs to be far from the magnetic setup (at least one meter) to prevent perturbations from the magnetic field on the measurement.

• Make different measures by sweeping the frequency from 20Hz to 200Hz.

• Repeat this operation on the other coil pairs.

APPENDIX C. MAGNETIC SETUP TUNING PROTOCOL

• Calculate and apply a linear correction for the magnetic field to be the same on every coils pairs for a given frequency.

• Redo the measure of the three coil pairs to check the correction.

C.2. MEASUREMENT PROBE CHARACTERISTICS

179

Measurement probe characteristics

Gauss meter

The gauss meter is used to directly measure the magnetic field intensity at the center of the coils. For now we use the embedded instrument screen to read the magnetic field value. It only allows to measure a constant field. The following shows an extract of the manual displaying the characterization of this probe. The full manual is available online from Hirst company website http://www.hirst-magnetics.com. Our model is the GM04 and uses a transversal probe.

Current clamp

The ampere metric clamp measures an alternative current in a wire by measuring the associated magnetic field. The complete information on this measurement tool can be found online at http://www.aemc.com. The following shows an extract from the technical data sheet presenting the characteristics of the current clamp.

Appendix D

Control software user manual Program description

Control is a program that serves three mean purposes:

• Provide the interface between the user and the settings of the magnetic field that controls the robot.

• Display and record video feedbacks.

• Track the position of the robot for a closed-loop control and measurement.

The program is now running on Ubuntu, it is written in C++, an export to windows should be possible.

How to launch the program

First the driver of the DAC card (analog output for the coils controller) needs to be set and the setting file specific to a setup need to be loaded. In some case, an error with the DAC driver happens and the video screen does not launch. In this case one needs to close the program by pressing ctrl+C in the terminal and try to launch the software again. Roll is the rotation used to make the propulsion. The user can define the rotation frequency. The yaw angle can be changed to move the X,Y directions of the robot. The pitch angle is used to switch from rolling to spintop and swimming.

RTS control

When the program is launched two windows will appear: one to display the video and a blank one call "keyboard input". To control the robot one must first click on the "keyboard input" windows. Figure D.2 displays the mapping of the keyboard key. For an easy control an advice is to use the left hand for the control of the roll and the yaw (displayed in red) as this one is made to control the robot from a subjective point (Z: forward, s:backward, q:turn left, d: turn right). The right hand can be used to change the pitch and the frequency with the key.

Experimentally and for the current design the primary magnetization axis of the robot is always in the same direction. So if the pitch is positive a forward motion will make the robot move by spintop (corkscrew force will be in the direction of the gravity) and a backward motion moves by swimming (corkscrew force will be in the direction opposite to the gravity). This result could be inverted with other robot/coils design but it would probably stay the same among a similar robot field under the same setup.

Video

The output of the camera is always saved when the program is running. By default the video is stored in the program directory with the name "default.mpeg". If a file with this name already exists when the software is launched (from a previous control software use) this file will be erased. To save the video in another folder the key "r" should be pressed in the window "keyboard input". Then the name of the video file should be entered in the terminal. If this name corresponds to an existing file, the old file will be erased.

Tracking of the robot

An online tracking of the robot can be performed. For this the robot needs to be well-contrasted (black shape of the robot surrounded by white). To start the tracking, click anywhere with the D.6. CLOSED-LOOP CONTROL 183 mouse on the video screen, the video should freeze on the last image. Then click again on the robot (or any black region you want to track). The tracking region will be surrounded by red.

During the tracking the position and orientation of the robot as well as the yaw, pitch, roll angles, the rotation frequency and other various parameters are saved in ".scv" file inside the program directory every 100 ms. In addition the "n" key of the keyboard can be used to enter a integer commentary inside this file. The "m" key is a marker key and adds a marker (1 if pressed, 0 if not pressed) inside the csv file. The "m" key is useful to make speed characterizations. By pressing it on the starting point of the record and releasing it at the end point, the speed of the trajectory in a line can be easily computed. An automatic analysis from the ".scv" file is therefore easy to make with Python or Matlab.

Sometimes when the contrast is not optimal the tracking fails. In good cases this results in returning in normal mode. In bad cases the program may crash. In this case, video and tracking recorded are still saved, however, one will maybe need to open the video with the software "vlc" and "save as" to ensure a smooth reading of the video with other softwares.

Closed-loop control

A closed-loop control is possible with the software for spintop motion. For this the tracking should be already running and a command file need to be put in the program directory. Its name should be "command.csv" And the format is: The closed-loop will start with the coordinate X=0, Y=0 of the command file placed at the current robot position. At the end of the command file the command position will be the last point. If there is no valid command file, the command position will be the current robot position.

Fine-tuning of the software

Parameters such as the sensibility of roll and yaw angles, PID controller for closed-loop, global power of the field command, tuning for the three different coils, offset of the coils command and name of the command file can be changed without any prior knowledge of the C++ code structure or language. For this locate the configuration file (it should be in the same folder as the one containing the program folder) and change the parameters.

If one needs to change other parameters or remap some keys, one needs to edit the source code and recompile the project. For this one needs to open the code project with "QT" software (.pro file) then go to main.cpp and adjust the parameters. Then one needs to click on "build" to recompile the project.

Installation of the program on a new machine

The hardware requirement is a computer with a S-626 dac and FireWire Port for the camera. In the source code, follow the indications in "howto install.txt". This protocol guarantees the installation from a fresh ubuntu installation, therefore we suggest starting from a fresh installation on the computer.

Appendix E Focus Image Analysis Code Protocol

The image analysis is used to detect when the RTS crosses the focal plane. In practice it computes the evolution of a focus indicator depending on time. When the focus reaches the maximum it means that the RTS is on the focal plane. Two Python codes (focus detector.py and open.py) and one script (mp4tocurve) are used for the image analysis. In practice "focus detector.py" is controlled by the script and does not need to be launched by the user. Here is the protocol to perform this analysis from an experimental video.

• Place "focus detector.py" "open.py", "focus detector.py" and mp4tocurve in a folder with the video to analyze.

• Open the video with winff software To install the software if needed, type: "sudo apt-get install libvacodec54 winff" in a terminal. Moreover one probably need to download MP4 preset (https://storage.googleapis.com/google-code-archive-downloads/v2/ code.google.com/winff/presets-libavcodec54_v3.wff) and to add it to winff (file/import preset).

• In crop setting, crop the video of 162 pixels on up and down and 242 pixels on left and right. These values corresponds to the dimension of a red square which is displayed by the control software on the screen by pressing the key "n". The size of this square can be adapted in the parameters of the code (main.cpp) and is just here to visually check during the experiment that the RTS is centered. If these cropping parameters are smaller, the calculation will be quicker and more precise, however, it will be harder to keep the RTS in this virtual square during the experiment. If the RTS image is cropped, it will produce high frequencies on the image and the analysis will be impossible.

• Save the cropped video in mp4 format in the same directory.

• Type in a terminal: "bash mp4tocurve <name of your video>.mp4". This will generate the curve and save it in csv,pdf and Python formats. For the python part of this script to display the curve you will need to install python and matplotlib (sudo apt-get install python python-matplotlib

• Type in the terminal (in the directory position): "python open.py <name of your video>". This is for automatic detection of the maximum, the script will guide you through the setting of different thresholds with time. The value under this threshold will be considered as 0. The goal is to eliminate any local maximum. This assumes that one has performed one ascending and then one descending vertical drop step (marked as up and down) for each frequency.

• Open <name of your video> max.csv to assess the value of the automatically detected maximum.

mp4tocurve.bash #s a v e c u r v e i n pdf format """ p l o t f i g u r e """ p r i n t ( f i g n a m e ) p l t . s a v e f i g ( f i g n a m e +" . """ smoothing """ p l t . p l o t ( t [ 0 : l e n ( c u t s 2 ) ] , c u t s 2 , l a b e l= ' smooth =0.8 ' ) p l t . p l o t ( t [ 0 : l e n ( c u t s 3 ) ] , c u t s 3 , l a b e l= ' smooth =0.9 ' ) p l t . p l o t ( t [ 0 : l e n ( c u t s 1 ) ] , c u t s 1 , l a b e l= ' smooth =0.95 ' ) p l t . l e g e n d ( ( ' smooth =0.8 ' , ' smooth =0.9 ' , ' smooth =0.95 ' ) )

""" c s v s t o r i n g """ #S1 n1=find max ( c u t s 1 ) max1=e x t r a c t a r r a y ( np . a s a r r a y ( t ) , n1 ) data1 =[ e x t r a c t e v e n ( max1 ) , e x t r a c t o d d ( max1 ) ] #S2 n2=find max ( c u t s 2 ) max2=e x t r a c t a r r a y ( np . a s a r r a y ( t ) , n2 ) data2 =[ e x t r a c t e v e n ( max2 ) , e x t r a c t o d d ( max2 ) ] #S3 n3=find max ( c u t s 3 ) max3=e x t r a c t a r r a y ( np . a s a r r a y ( t ) , n3 )

y means t h a t your c u t o f f i s t o h i g h f o r t h i s smoothing " ] ]

E.4. OPEN.PY Appendix F

3D Lithography Volume Simulation Protocol

To get an estimation of the RTS resist volume and metal volume the 3D lithography process is simulated with Python script. The protocol to make this estimation is the following:

• First the dimension of the voxel needs to be estimated. This is explained in Chapter 4.2.3.

In the following the voxel is assumed to be ellipsoidal.

• Edit the first part of "nanoscribe simu.py" to simulate the path of the desired structure. The path is described as a list of three elements which correspond to the x,y,z coordinates of points. This will simulate the trajectory by a partial straight line passing by these points. This mimics the way how the control program of the "nanoscribe" machine works. To add a new point at coordinate (x,y,z), enter the line "path.append(x,y,z)". To move to another location without connecting the point (i.e. to move the pencil up), enter the command "path.append(-1,-1,-1)" and then the desired point. The program displays the path when it is launched. In the following code example the path of the RTS with an helical pitch of 4µm is encoded.

• In a terminal launch the program by typing: python nanoscribe simu.py <mesh size in micron><voxel height><voxel width> Typical values of the mesh size are between 0.1 and 0.01. First the path is displayed. This window needs to be closed to continue. When this program stops it gives the volume of the structure in microns and saves the matrix with the simulated structure with name: d=<mesh size in micron>vz=<voxel height>.pickle

• Type in a terminal: python PVD simu d=<mesh size in micron>vz=<voxel height>.pickle <metallization angle><mesh size in micron> When this program stops it gives the average area exposed to the metallization and displays a curve of this area evolution with the angle. As the structure rotates quickly in the PVD machine, it is a good estimation to consider the average exposed area and it can be multiply by the deposition height to get the metal volume.

nanoscribe simu.py

""" -------------------------------------Path c r e a t i o n --------------------------- p r i n t ( graph [ i ] ) i=i +1; p r i n t ( d p s i ) # uncomment t o d i s p l a y p r o j e c t i o n a t e a c h s t e p """ i f round ( i / 1 ) == ( i / 1 ) : p l t . f i g u r e ( i ) p l t . imshow ( p r o j e c t i o n , cmap=cm . B l u e s ) p l t . show ( ) ; """ p r i n t ( np . a v e r a g e ( graph ) ) p l t . f i g u r e ( 2 ) ; p l t . p l o t ( d p s i , graph ) ; p l t . show ( ) ; Appendix G Micro-pipette fabrication and integration inside a microfluidic chip

Micro-pipette fabrication

For fabricating micro-pipettes with various sizes and profiles, 1mm diameter pipettes are elongated with a heating process. As the experiments with the RTS inside micro-pipettes are still at a prospective step, a simple pulling machine was built to produce them. On this machine one pipette is hold by two sliding parts and is heated on its center. Then the user can manually pull the sliding part on the opposite direction to elongate the pipette which results in the reduction of its diameter. This technique allows the production of micro-pipettes with diameters below 10µm. However due to this manual actuation, reproducibility is not guaranteed and relies on the user's skills.

A picture of the setup is presented below:

Integration protocol

To integrate the micro-pipette for vertical drop tests inside the microfluidic chip, the following protocol is applied:

• The micro-pipette is fabricated with the pulling machine.

• The micro-pipette is placed on the bottom of a Petri dish.

• PDMS is poured on the Petri dish and cured at 70 • C for 24 hours. PDMS must be poured quickly to ensure that air is trapped inside the micro-pipette.

• The solidified PDMS is cut around the micro-pipette. Then slices under 1mm of PDMS containing the micro-pipette are cut perpendicular to the micro-pipette direction. This cutting is realized with a razor blade.

• One slice (its quality can be checked with a microscope) is bonded to the glass bottom of the microfluidic chip. Clean side view is possible by imaging through the face that was situated at the bottom of the Petri dish. Indeed it is the only part optically clean as it was not manually cut.

Appendix H Propulsion Matrix Parameter Calculation Sheet Protocol

The experimental protocol to characterize the RTS is developed in Chapter 4.4.1 and the calculus principle to obtain the coefficient a and b of the propulsion matrix in Chapter 4.2.2. Here we recapitulate the full protocol to get from the experiment to the identification of the coefficient a and b . The protocol is the following:

• Follow the experimental protocol explained in Chapter 4.2.2. The temperature, the series of tested frequencies, the experimental videos for 0Hz test and the experimental video for the series of tested frequency must be recorded. For 0Hz drop tests, it is simpler to make one video for each test as the position of the RTS in the chamber needs to be changed to detect an eventual parasite flow. We recall here that a small constant magnetic field (in addition to the residual offset of the coils) can help to maintain the RTS vertical. For this press "f" during the drop test and adjust the direction of the coils offset with the numerical pad key.

• Apply the protocol for image analysis explained in Appendix E for the video at 0Hz and the frequency series.

• Open the calculus sheet (see the image in the next page)

• Copy-past the automatically detected maximum from the video recording the frequency series. Be sure to fill the corresponding frequency for each test.

• From the focus analysis of the video at 0Hz fill the bottom left part of the calculation sheet. Check that the standard deviation is below 0.3µm m to guarantee that there is no parasite flow.

• Fill in the input in the characterization box. Normally the literature section is constant.

For a new RTS design one has to update the RTS resist and metal volume by the protocol in Appendix F. One has to fill the temperature of the experiment and the speed at 0Hz. The speed curve slope will be updated automatically from the data one enters in the left boxes.

• One can read a and b from the result section and their associated measurement error.

Important Note:

• The correction from the liquid refractive index is made automatically, therefore the distance on the left boxes should be the distance from which the position platform is moved. If the liquid is changed, you need to update the corresponding box.

• In the following example another correction is applied to counterbalance a speed problem in the video. This problem is now fixed in the new program version therefore be sure that the "corr camera time" is equal to 1.

• The sheet gives the values of a and b such that F = ν(a V +b ω), with ν the fluid viscosity, V the RTS speed and ω the RTS rotation.

Appendix I

Bead Characteristics

© 2013 Polysciences, Inc. Rev. #11 05. 16.2013 Should any of our materials fail to perform to our specifications, we will be pleased to provide replacements or return the purchase price. We solicit your inquiries concerning all needs for life sciences work. The information given in this bulletin is to the best of our knowledge accurate, but no warranty is expressed or implied. It is the user's responsibility to determine the suitability for their own use of the products described herein, and since conditions of use are beyond our control, we disclaim all liability with respect to the use of any material supplied by us. Nothing contained herein shall be construed as a recommendation to use any product or to practice any process in violation of any law or any government regulation.

TECHNICAL DATA SHEET 238

Page 1 of 4

Numerical Simulation Code Protocol

To simulate the position of the RTS in the section of a microchannel we perform numerical simulations with finite elements. For this simulation we assume the following:

• The RTS can be represented as a infinite cylinder is an infinite straight channel. Therefore a 2D model is possible.

• The misalignment of the propulsion force can be represented as a force orthogonal to the cylinder axes. We believe that this is valid for a small misalignment angle.

First a map of drag force applied on the RTS depending on its position in the channel is simulated. For this we use FreeFem++ [START_REF] Hecht | New development in freefem+[END_REF] to simulate the flow in the 2D section of the channel. This software solves the Stokes equation (ν∆u = --→ gradp) with an extra term that does not change the final value but forces the stability of the scheme in certain cases. The formulation of the weak form of the Stokes equation in FreeFem++ language was taken from the FreeFem++ manual.

Then this map is used to simulate the trajectory of the RTS as the inertia of the RTS is negligible and therefore the force is directly proportional to its speed. If one wants the simulation to be given pertinent speed, one needs to measure the lateral drag coefficient of the object to link the force to the speed. Otherwise the trajectory will be correct but not the speed amplitude.

Here is the protocol to perform simulations:

• Perform lateral drop test on the RTS to get the lateral drag coefficient.

• Open force.edp with a text editor.

• Adjust the parameters for the simulation. If one changes the mesh resolution, the line 60 can be uncommented to display the mesh.

• In a terminal type: FreeFem++ force.edp. You can install FreeFem++ on linux by typing: sudo apt-get install FreeFem++ For other systems please refer to the FreeFem++ web page.

• When the simulation is finished open trajectory.py with a text editor.

• Edit the parameters to match the ones of the simulation. One also has to fill in the time step, the number of simulation points, and the lateral drag coefficient. One also can choose to apply a lateral force.

• Run the simulation by typing: python trajectory.py.

force.edp // Width o f t h e s q u a r e c h a n n e l // mesh r e s o l u t i o n [START_REF] Terry | A Gas Chromatographic Air Analyzer Fabricated[END_REF] ) ) < P0 [ 0 ] * 0 . 0 3 + 0 . 1 e -6) : p r i n t ( " b r e a k " ) f =1/(k * s t e p ) b r e a k """ Post p r o c e s s i n g """ atX=np . a r r a y ( tX ) atY=np . a r r a y ( tY ) a t i m e=np . a r r a y ( t i m e ) a d i s t= np . s q r t ( ( atX-P0 [ 0 ] ) * ( atX-P0 [ 0 ] ) + ( atY-P0 [START_REF] Terry | A Gas Chromatographic Air Analyzer Fabricated[END_REF] ) * ( atY-P0 [START_REF] Terry | A Gas Chromatographic Air Analyzer Fabricated[END_REF] ) ) #d i s t a n c e from t h e s t a r t i n g p o i n t """ P l o t """ p l t . f i g u r e ( 1 ) p l t . p l o t ( P0 [ 0 ] , P0 [START_REF] Terry | A Gas Chromatographic Air Analyzer Fabricated[END_REF] , ' bo ' ) p l t . p l o t ( tX , tY ) p l t . show ( ) p l t . f i g u r e ( 2 ) #p r i n t ( a t i m e . s i z e ) p r i n t ( P0 [ 0 ] ) p l t . p l o t ( atime , a d i s t ) r e t u r n ( f ) """----Lauch s i m u l a t i o n ----""" #p l o t c h a n n e l boundary xb=[-e / 2 , e / 2 , e /2 , -e /2 , -e / 2 ] yb = [ 0 , 0 , e , e , 0 ] p l t . p l o t ( xb , yb ) #t r a j e c t o r y s i m u l a t i o n simu ( P0 , n b i t e r , s t e p , g * m, X, Y, FX, FY, a )

Appendix K

Two Liquids Chip Protocol Principle

In order to avoid the estimation of the RTS mass as well as to be able of measuring the weight of an arbitrary object by only knowing its volume, we first try to perform drop tests in two different liquids with different viscosity and density. Unfortunately this measure was not precise enough as we could not succeed in using liquid with important viscosity differences. Indeed we did not succeed in using the robot in an isopropyl alcohol and water mixture below 60 % of isopropyl alcohol. Moreover the non-repeatability of the RTS characterization leads in the no guaranty to get the microrobot in the same magnetic configuration during the two liquid tests.

However we think that this process could be used for future developments. For example, it could serve for the study of the bio-compatibility of the RTS with a particular fluid as the comparison between a characterization in this fluid and in a reference fluid of the same microrobot could be used.

Protocol

The main challenge here is to be sure that the RTS environment evolves always towards higher alcohol concentration. Indeed otherwise there is a formation of microbubbles that permanently stuck the RTS to the surface. Liquid 1 refers to a mixture of isopropyl alcohol (60 %) and alcohol (40 %). Liquid 2 refers to pure isopropyl alcohol.

Output

• Close the valve 2.

• Connect the fluid inputs: input 1 with liquid 1, input 2 with liquid 2, (and output to a fluid trash).

• Insert the RTS fabrication substrate in the open chamber.

• Inject liquid 1 until the open chamber is filled. The goal of the chamber 1 slope is to avoid bubbles as the microchannel connecting to the open chamber is used as an input.

• Detach the RTS with the tip and close the open chamber with a glass slide.

• Integrate the RTS into the small microchannel pocket in the chamber 1 in front of the drop test chamber 1.

APPENDIX K. TWO LIQUIDS CHIP PROTOCOL

• Close the valve 1 (you will need two screw holders for the two valves)

• Increase the pressure in the chamber from 1 to 500 mbar through input 1. This is to fill the drop test chamber (it usually takes around 10 minutes).

• Characterize the RTS

• Move the RTS back to the microchannel pocket.

• Inject fluid 2 in the chamber 2.

• Close the output.

• Connect the input 1 to the fluid trash (it will become the output).

• Put a 30 mbar pressure in the chamber 2.

• Open the valve 2 (and remove the screw holder), thanks to the previous step the liquid 2 should flow in the liquid 1. At this step one will probably have to remove the chip from the magnetic setup to open the valve 2. One should put it back to control the RTS.

• Increase the pressure to 100 mbar for 1 minute to flush all the remaining liquid 1 in the chamber 1. You can control the RTS and move it at the bottom of the microchannel pocket periodically to avoid losing it in the flow.

• Close all fluid connections inputs and outputs.

• Move the RTS in the microchanel pocket of the chamber 2

• Close valve 2, open input 2, close output.

• Increase the pressure in the chamber 2 to 500 mbar through input 2. This is to fill the drop test chamber 2.

• Close input 2.

• Move the RTS in the drop test chamber 2 and characterize it.