Ecole Sigle

Doctorale

Renée El

Melhem Bât

Pascal Blaise

R Gourdon

M Stéphane

ÉLECTROTECHNIQUE E E A Électronique

M Gérard Scorletti
email: gerard.scorletti@ec-lyon.fr

M Philippe
email: philippe.normand@univ-lyon1.fr

Mme Sylvie

Jean-Yves Buffière
email: jean-yves.buffiere@insa-lyon.fr

Stéphanie Cauvin

M Jocelyn Bonjour

Véronique Guichard

J Y Toussaint

M Christian Montes

Finally, I would like to thank my wife, Ma de los Angeles Alamilla Daniel

Desde que era un niño siempre soñé con la oportunidad de volverme un científico. Gracias a mis padres aquella oportunidad se hizo realidad. Agradezco su apoyo incondicional, su amor y sus consejos a través estos años, sin ellos esto no habría sido posible.

También agradezco a mi director de Tesis, Dr. Arnaud Leleve, en primera estancia por haberme aceptado, y también por sus consejos y ayuda para que este proyecto saliera adelante. Agradezco también a mis otros dos directores, Damian Eberard y Minh Tu Pham por su ayuda durante mi estancia, especialmente durante los últimos meses para asegurar la entrega de un gran trabajo.

Agradezco también a la gente del laboratorio, en especial a Paolo Massioni, Sylvie Sesmat,Federico Bribiesca Argomedo y Vicent Lechappe, por su amistad durante estos tres años.

Agradezco a CONACyT y al pueblo mexicano por haberme otorgado mi beca y permitirme convertirme en un doctor. Espero que el fruto de mis estudios pueda ayudar a la superación de mi país y ayude a la humanidad.

Finalmente quisiera agradecer a mi esposa, Ma de los Angeles Alamilla Daniel, quien estuvo conmigo en los momentos más claros y oscuros de estos últimos tres años, quien limpiaba mis lágrimas y celebraba mis triunfos. Sin sus palabras de apoyo y consuelo, quizás nunca hubiera sido capaz de ser lo que hoy soy. Cumplimos un sueño más, pero aún nos faltan mucho por recorrer, aún estamos empezando.

English

Ever since I was a child, I always dreamed of the opportunity to become a scientist. Thanks to my parents that opportunity came true. I appreciate their unconditional support, their love, and their advice through these years, without them this would not have been possible. I also thank my thesis director, Dr. Arnaud Leleve, for have accepted me, and also for his advice and help to get this project done. I also thank my other two directors, Damian Eberard and Minh Tu Pham for their help during my stay, especially during the last months to ensure the quality of this thesis.

I want to thank the people at the laboratory Ampère, especially to Paolo Massioni, Sylvie Sesmat, Federico Bribiesca Argomedo, and Vicent Lechappe, for their friendship during these three years.

I want to thank CONACyT and my compatriots for granted me a scholarship which allowed me to become a doctor. I hope that the fruit of my studies can help to develop my country and help humanity.

Définition du problème

La formation des étudiants en médecine est un long processus qui nécessite de nombreuses heures de pratique et d'étude afin d'assurer l'acquisition d'un savoir et d'une dextérité indispensables. Pour maîtriser la palpation, l'injection de produits, la chirurgie et tout autre processus qui implique une interaction directe avec le patient, les étudiants ont besoin de pratiquer de nombreuses fois. Cependant, il n'est pas recommandé de le faire sur des patients pour des raisons éthiques car ceux-ci pourraient être blessés ou simplement en souffrir [START_REF] Beal | The effectiveness of medical simulation in teaching medical students critical care medicine[END_REF]).

Pour cette raison, il est encore aujourd'hui crucial que ces étudiants améliorent leur compétences manuelles sans toucher un patient. Les étudiants en médecine utilisent traditionnellement des simulateur d'entraînement qui les aident à acquérir de l'expérience en leur fournissant des sensations pseudo-réalistes simulant le comportement et les réactions mécaniques du corps humain. Certains simulateurs, utilisés depuis des siècles, sont réalisés en bois, cuir, métal et même à base d'organes voire même de cadavres humains. Par exemple, en obstétrique, le "Phantom" a été développé au 18e sicèle en France par les obstétriciens Grégoire et fils. Ce premier simulateur était constitué d'un vrai pelvis humain et d'un cadavre de bébé afin de reproduire le processus d'accouchement [START_REF] Owen | Early use of simulation in medical education[END_REF]).

De nos jours, les étudiants en médecine ont la possibilité de s'entraîner sur plusieurs types de chirurgie sur des corps morts ou presque. Cependant, l'usage de cadavres entraîne de nombreuses difficultés [START_REF] Berger | Ethics of practicing medical procedures on newly dead and nearly dead patients[END_REF]):

• les cadavres n'ont plus de réaction biologique, ce qui empêche notamment de déterminer s'ils sont blessés par des gestes inappropriés ;

• il est nécessaire d'obtenir le consentement d'une personne ou de sa famille pour pouvoir utiliser son corps post-mortem ;

• un équipement spécifique et onéreux est indispensable pour empêcher sa décomposition naturelle • les cadavres sont à usage limité car les tissus sont altérés définitivement et ne peuvent pas être restaurés.

Depuis les années 60, les simulateurs « mannequins » sont progressivement apparus. Par exemple, Resusci-Anne est une mannequin de formation pratique pour la réanimation cardiopulmonaire. Mais celui-ci ne s'est pas diffusé du fait de son coût élevé [START_REF] Fritz | Review of mannequin-based high-fidelity simulation in emergency medicine[END_REF]). Des recherches ont été réalisées sur la restitution des signes vitaux humains pendant les sessions de formation. L'Université de Miami a créé le célèbre mannequin Harvey, utilisé pour former à l'examen en cardiologie. Il fut le premier être couramment utilisé dans l'ère des simulateurs d'apprentissage de type mannequin [START_REF] Kunkler | The role of medical simulation: an overview[END_REF]).

L'usage de mannequins (Figure 1-1) repose sur une représentation du comportement des patients plus réaliste que celui observable avec les cadavres. En effet, il est alors possible de générer arbitrairement des événements critiques pendant une opération. Un exemple est le mannequin CASE [START_REF] Cooper | A brief history of the development of mannequin simulators for clinical education and training[END_REF]) développé en 1987. Il a été utilisé pour l'entraînement à l'anesthésie et simulait des signes vitaux du patient grâce à des instruments virtuels sur ordinateur.

Le mannequin était manipulé par les formateurs1 pour créer des situations dans lesquelles la vie du patient était en danger afin que les étudiants apprennent à prendre les bonnes décisions.

Plus récemment, les étudiants en médecine ont eu accès à des simulateurs mannequins plus avancés et plus réalistes leur permettant de s'entraîner sur des techniques plus complexes comme en endoscopie [START_REF] Deutsch | High-fidelity patient simulation mannequins to facilitate aerodigestive endoscopy training[END_REF]). Ces simulateurs utilisent désormais une combinaison de systèmes mécaniques, électroniques et logiciels afin de synthétiser une réponse réaliste du corps d'un patient pendant une opération. Il est désormais possible de créer des scénarios rares (très difficile avec des cadavres) et plus besoin de s'approvisionner en organes ou cadavres [START_REF] Fritz | Review of mannequin-based high-fidelity simulation in emergency medicine[END_REF]). Cependant, leur morphologie figée limite la variété des cas d'étude pour la formation. Par exemple, ils ne peuvent pas servir pour s'entraîner à la chirurgie car les apprenants ne peuvent pas modifier/couper/suturer leurs organes. Cependant, ces simulateurs n'offrent pas de retour d'effort, ce qui limite le réalisme de l'opération [START_REF] Neumann | Virtual reality vitrectomy simulator[END_REF] et [START_REF] Tsai | Virtual reality orthopedic surgery simulator[END_REF]). Des simulateurs plus récents implémentent des interfaces haptiques (voir détails en section 2.2)) qui permettent aux utilisateurs de manipuler un outil virtuel pour opérer un patient tout aussi virtuel. Simultanément, ils peuvent sentir les efforts d'interaction entre leur outil et les organes du patient, ce qui produit un réalisme proche d'une opération réelle.

Un exemple de simulateur haptique en formation médicale est le Lapsim R ○(voir Figure 1-2) développé par SurgicalScience. Ce simulateur est utilisé pour former les étudiants en médecine à la chirurgie laparoscopique. Les utilisateurs interagissent avec un monde virtuel affiché à l'écran en manipulant deux interfaces haptiques reproduisant un retour d'effort

Un autre exemple est le Immersive Touch (Figure 1-3), un simulateur développé par l'Université de l'Illinois, qui utilise un miroir transparent pour projeter des figures en 3D dans l'espace et fournir un retour haptique. L'utilisateur doit porter des lunettes spécifiques afin de transmettre au simulateur la position et l'orientation de sa tête afin d'ajuster la perspective stéréoscopique de l'image. Cette méthode de rendu permet à l'utilisateur de bouger ses mains dans un environnement virtuel, ce qui est indispensable pour situer des repères importants [START_REF] Cristian | Design of the ImmersiveTouchTM: a High-Performance Haptic Augmented Virtual Reality System[END_REF]).

Les simulateurs haptiques ont des avantages sur les simulateurs informatiques classsiques, comme l'usage d'environnements virtuels dans lesquels les étudiants peuvent s'entraîner sur différentes morphologies de patients et sur des cas variés. D'autre part, ils peuvent répéter plusieurs fois cet apprentissage sans toucher un patient et sans risque de pénurie de pièce d'usure [START_REF] Sutherland | An augmented reality haptic training simulator for spinal needle procedures[END_REF]). Pour cette raison, l'usage des simulateurs haptiques est devenu le nouveau paradigme dans le processus de formation médicale [START_REF] Jones | Telemedicine Systems[END_REF]). Cependant, un inconvénient significatif est le coût d'usage de ce type de simulateur qui peut monter jusqu'à $1 million de dollars [START_REF] Zevin | Surgical simulation in 2013: Why is it still not the standard in surgical training[END_REF]).

Le problème de la formation pratique non supervisée

Bien que les simulateurs permettent aux étudiants de s'autoformer, ils ne sont pas la panacée. En effet, il est encore aujourd'hui nécessaire d'être guidé par un expert dont les trajectoires d'outils et les commentaires sont bien plus formateurs que de longues répétitions sans guide intelligent [START_REF] Schout | Validation and implementation of surgical simulators: A critical review of present, past, and future[END_REF]). Cette façon de former, dans laquelle le formateur tient les mains de l'apprenant qui opère peut s'appeler de la formation pratique guidée ou supervisée. Hors simulateur c'est possible et même traditionnel. Sur un simulateur, c'est aussi envisageable bien que plus rare. L'inconvénient majeur de cette forme d'apprentissage est que l'apprenant ne peut pas doser ses gestes car le retour d'effort de l'outil est partagé entre les deux protagonistes. Pourtant, cet apprentissage des efforts à fournir est indispensable dans la formation des médecins et ne se fait que « sur le tas » aujourd'hui.

Il est donc indispensable de proposer des simulateurs haptiques offrant la possibilité de transmettre du formateur à l'apprenant ces gestes dans toute leurs dimensions : cinématique et dynamique. Une étude bibliographique récente a montré que la vaste majorité des simulateurs disponibles sur étagère ne 6 proposent pas de deuxième interface pour le formateur afin de l'intégrer dans la simulation. Certains modèles sont équipés de deux interfaces haptiques mais pour un usage à deux mains par le même utilisateur [START_REF] Escobar-Castillejos | A Review of Simulators with Haptic Devices for Medical Training[END_REF]).

Certaines recherches ont cherché à combler ce manque de support pour un apprentissage supervisé sur simulateur haptique. Les résultats de ces recherches sont décrits en section 2.4.5 mais cependant ils ne répondent pas à l'ensemble des exigences qu'un tel simulateur doit remplir ; exigences précisées dans la section suivante.

Cas d'utilisation principal et exigences

Le cas d'utilisation suivant aide à déterminer les principales exigences du système étudié. Supposons, en premier lieu, que le formateur (un chirurgien expérimenté) cherche à montrer les trajectoires à réaliser avec son outil chirurgical afin de réaliser une tâche impliquant successivement des mouvements libres et des contacts entre son outil et son patient. Cela implique un retour haptique réaliste pour qu'il puisse doser ses efforts, comme dans un contexte de téléopération bilatérale. Le formateur prend la main sur le simulateur (il devient leader et l'apprenant follower) afin de réaliser une démonstration. Il a alors un retour haptique complet provenant de l'esclave, comme s'il manipulait directement ses outils. Pendant cette démonstration, l'interface haptique de l'apprenant suit la trajectoire de celle du leader. S'il vient à en dévier, il ressent immédiatement un effort compliant qui le ramène sur la trajectoire imposée. Pendant les phases d'interaction entre l'outil et son environnement, une interface graphique affichée sur un moniteur guide l'apprenant pour qu'il place son interface dans la même position que celle du leader afin de ressentir les mêmes sensations haptiques. Ensuite, le fonctionnement peut être inversé afin que l'apprenant guide l'esclave et que le formateur l'évalue: il s'agit alors du mode évaluation.

Objectives of the thesis

Les objectifs du Groupe de Travail Robotique du laboratoire Ampère sont de développer un simulateur de formation pratique à deux utilisateurs (dual-user) capable de former les apprenants sur des trajectoires et des interactions outil-environnement. Dans ce projet, un premier travail a été réalisé par M.

Contributions

Pour atteindre ces objectifs, nous avons réalisé un état de l'art (présenté en section 2.4. Enfin, nous terminons ce mémoire avec une conclusion couvrant l'ensemble de ces travaux et nous proposons des perspectives pour la poursuite de ce projet de simulateur haptique pour la formation pratique supervisée.

Chapter 2

État de l'art

Introduction

Les humains mémorisent assez précisément la position de leurs membres : c'est ce qui s'appelle la kinesthésie [START_REF] Feygin | Haptic Guidance: Experimental Evaluation of a Haptic Training Method for a Perceptual Motor Skill[END_REF]). Ce mot dérive du grec kinein, « mettre en mouvement » et aisthesis, « perception », ce qui peut s'interpréter comme une perception du mouvement. La kinesthésie est l'agglomération de trois sous-sens : la position et l'orientation, le mouvement et l'effort [START_REF] Rosker | Kinaesthesia and Methods for its Assessment: Literature Review[END_REF]).

Grâce à ce sens, les humains obtiennent une connaissance cognitive du point de vue psychomoteur et apprennent à réaliser des gestes et former des postures afin de réaliser des tâches données [START_REF] Xu | From psychomotor to motorpsycho: learning through gestures with body sensory technologies[END_REF]). Un exemple de cette approche est l'apprentissage d'un instrument de musique. En effet, les musiciens apprennent à lire les partitions et comment l'assemblage de plusieurs sons réalise une mélodie et une harmonie agréables à l'oreille. Ils acquièrent la compétence nécessaire pour reproduire cela principalement par répétition du geste [START_REF] Galvao | Kinaesthesia and Instrumental Music Instruction: Some Implications[END_REF]), en plus de l'acquisition des fondamentaux théoriques. Grâce à la kinesthésie, il est possible de former des apprenants, en complément des canaux visuels et auditifs plus classiques. Il a été démontré que l'apprentissage du geste est même plus efficace quand il s'agit de gestes précis et complexes [START_REF] Panait | The Role of Haptic Feedback in Laparoscopic Simulation Training[END_REF]).

Les interfaces haptiques

Classification des interfaces haptiques

Les interfaces haptiques sont utilisées pour des tâches industrielles, en recherche, et même dans la vie courante. La multiplicité des domaines applicatifs rend difficile leur classification. Ainsi, il est

Avantages et inconvénients

L'intérêt de chaque configuration dépend de la tâche envisagée. Cependant des limites communes sont à prendre en compte :

• ce type de matériel est coûteux ;

• l'effort généré est limité en amplitude et hétérogène en direction;

• limited bandwidth for the data transmission;

• la bande passante pour la génération et la transmission de signaux d'efforts est généralement trop limitée. En effet, pour un signal haptique, la bande passante doit atteindre au moins 1 Khz [START_REF] Tavakoli | High-fidelity bilateral teleoperation systems and the effect of multimodal haptics[END_REF]), ce qui limite des applications nécessitant des environnements virtuels complexes et donc coûteux en temps de calcul.

Simulateurs pour l'apprentissage pratique dans le domaine médical

Configurations multilatérales pour les architectures de contrôle

Pour plus de clarté concernant ces architecture de contrôle pour simulateurs haptiques, voici les principes fondamentaux de la téléopération qui les sous-tend.

La téléopération consiste à contrôler à distance depuis une interface « maître » un système (l'esclave) en échangeant des données via un médium de communication [START_REF] Cui | A review of teleoperation system control[END_REF]). Le schéma de téléopération unilatérale, le plus simple qui existe, consiste à transmettre les ordres de l'utilisateur vers le système à contrôler, sans retour d'information. Ce manque de retour serait problématique, c'est pourquoi les architectures de téléopération sont plutôt bilatérales, ce qui autorise un suivi en position et en effort [START_REF] Niemeyer | Stable Adaptive Teleoperation[END_REF]).

Une architecture de simulation haptique comporte cinq éléments : l'utilisateur (humain), le dispositif maître, le contrôleur, l'esclave et l'environnement. L'esclave peut être un vrai robot ou un logiciel simulant l'outil que l'utilisateur est sensé manipuler ; dans ce cas l'environnement est également virtuel [START_REF] Secchi | Control of Interactive Robotic Interfaces A Port-Hamiltonian Approach[END_REF]). La figure 2

Mode de guidage partagé

Dans ce mode, 0 < α < 1, l'apprenant et le formateur partagent l'autorité sur le système proportionnellement à la valeur de α. Plus α tend vers 0, plus l'apprenant prend de l'autorité sur l'esclave aux dépends du formateur. Par exemple, pour α = 0.3, l'esclave se déplacera à une position correspondant à la moyenne pondérée des positions des maître avec une pondération de 70 % pour l'apprenant et 30 % pour le formateur.

Mode évaluation

Dans ce mode, symétrique du mode démonstration, α = 0 et l'apprenant pilote entièrement l'esclave pendant que le formateur observe passivement les gestes de l'apprenant. Ce mode est utile pour que le formateur puisse évaluer les performances de l'apprenant.

Autorité adaptative

Le formateur peut à tout moment changer la valeur de α pendant la session de simulation. Cependant ceci peut être assez contraignant lorsque, en mode évaluation, il doit se concentrer sur les gestes de l'apprenant.

En effet, si ce dernier réalise un geste inapproprié, il est indispensable que le formateur puisse prendre la main instantanément et corriger le geste, s'il le désire, sans perdre du temps à modifier α. Afin de rendre ce type d'évolution de α plus facile, un mécanisme d'autorité adaptative peut être mis en place. La valeur de α définissant l'autorité de chaque utilisateur peut alors dépendre des performances de l'apprenant (autrement dit de l'écart de position entre l'apprenant et le formateur)

pour redonner le contrôle au formateur le cas échéant.

Une fois l'apprenant revenu sur la trajectoire corrigée du formateur, celui-ci reprend automatiquement la main.

Une première fonction d'autorité adaptative a été proposée dans [START_REF] Shahbazi | A dual-user teleoperated system with virtual fixtures for robotic surgical training[END_REF]). D'autres auteurs ont proposé d'autres approches [START_REF] Huang | Auxiliary asymmetric dual-user shared control method for teleoperation[END_REF]) et (Liu et al. [2015]). Toutes font appel à l'écart de position/orientation entre les interfaces haptiques de l'apprenant et du formateur.

Conclusion de cette étude

Les interfaces haptiques commencent à être utilisées par les simulateurs informatiques en vue de la formation pratique des médecins. Ils permettent aux apprenants d'apprendre des gestes médicaux avec un rendu kinesthésique de plus en plus réaliste, sans toucher un patient.

Toutefois, les simulateurs du commerce ne proposent d'interface que pour l'apprenant ; le formateur reste en dehors de la simulation avec la seule possibilité de guider les mains de l'apprenant guidant les interfaces haptiques. Ce mode de formation aide à transmettre une trajectoire mais ne permet en aucun cas de montrer directement les efforts à exercer. Seule l'intégration du formateur dans la simulation, via ses propres interfaces haptiques peut permettre cette transmission via le canal kinesthésique, pour peu que le contrôleur du simulateur soit conçu pour, ce qui n'a pas été constaté lors de cette recherche bibliographique.

Ainsi, le simulateur « idéal » remplissant l'ensemble des exigences précisées dans ce document n'existe pas encore. Nous avons donc tenté de nous en approcher via les contributions détaillées dans la suite de ce rapport.

Chapter 3

Résumé des contributions

Problem definition

The training of medical students is a long process that requires several hours of practice and study to ensure the acquisition of knowledge and dexterity. To master the palpation, injection, surgeries, or any other processes that involve direct interaction with the patient, students need to practice many times.

However, medical students can't practice with patients, due to the ethical problem that it entails, such as injuring or permanently damaging the patient [START_REF] Beal | The effectiveness of medical simulation in teaching medical students critical care medicine[END_REF]). For this reason, there is still a crucial need for medical students to improve their manual skills without touching a real patient.

Medical students have been using training simulators, which help them acquire the necessary experience by providing pseudo-realistic sensations of the behavior and reactions of the human body.

Some simulators are based on wood, leather, metal, or corpses and have been used for centuries.

An example is the midwifery simulator "Phantom" developed in the 18th century in France by the obstetricians Gregoire and son. This early obstetrician simulator used a real human pelvis with the corpse of an infant to replicate the delivering child process [START_REF] Owen | Early use of simulation in medical education[END_REF]).

Nowadays, medical students can practice several surgeries using corpses; however, the use of cadavers involves several problems [START_REF] Berger | Ethics of practicing medical procedures on newly dead and nearly dead patients[END_REF]):

• Corpses have no biological reaction, so medical students cannot determine if they are injuring them.

• It is necessary to have the consent of the patient or the family to harvest and operate the cadaveric organs, which complicates their acquisition for training purposes.

• It requires equipment to preserve them from rooting.

• Corpses are disposable, as the tissues are permanently altered and cannot be restored.

Besides corpses have been used for training simulations, over time, mannequins-based simulators appeared in the early 1960s. An example is Resusci-Anne, a training mannequin for practicing cardiopulmonary resuscitation that was not widespread due to its high cost [START_REF] Fritz | Review of mannequin-based high-fidelity simulation in emergency medicine[END_REF]). After that, researches began to focus on the rendering of the human body's vital signs for training sessions.

The University of Miami created the famous Harvey mannequin, which was used to train cardiology examination and electrocardiography, beginning the era of mannequin-based training simulators [START_REF] Kunkler | The role of medical simulation: an overview[END_REF]).

The use of mannequins (Figure 1-1) leans a representation of the patients' behavior more realistic than with corpses, as it is now possible to the recreate critical events during the operation. One example is the mannequin named CASE [START_REF] Cooper | A brief history of the development of mannequin simulators for clinical education and training[END_REF]), developed in early 1987, was used for anesthesia training and allowed to simulate the patient vitals using virtual instruments in a computer system. The mannequin is manipulated by the trainers who create situations where the life of the patient is in danger, so students can make decisions and learn from them. In more recent years, medical students have had access to more advanced and realistic simulators based on mannequins which recreate several vitals of the patient and even allow them to practice sophisticated methods like endoscopy [START_REF] Deutsch | High-fidelity patient simulation mannequins to facilitate aerodigestive endoscopy training[END_REF]). These simulators now use a combination of mechanisms, electronic systems, and software algorithms to recreate the response of the patient during the operation. The use of mannequins provides several advantages over the corpses like uncommon scenarios that can be created, and there is no shortage of supplies [START_REF] Fritz | Review of mannequin-based high-fidelity simulation in emergency medicine[END_REF]). However, as they are based on a fixed mechanism, the mannequins cannot be modified to offer more variety of training. For example, they cannot provide surgery training, where the organs of the patients must be modified.

Thanks to the technological advances, a new generation of training simulators solves some of the aforementioned problems. The first computer-based simulators proposed virtual environments where students could interact with the patient's organs. For this, the simulator uses biomechanical mathematical models of the human body to simulate its behavior. However these simulators do not offer force reaction feedback, so the students cannot get a realistic immersion in the operation [START_REF] Neumann | Virtual reality vitrectomy simulator[END_REF] and [START_REF] Tsai | Virtual reality orthopedic surgery simulator[END_REF]).

These simulators provide advantages over the classical ones like the use of virtual environments where students can practice with several kinds of bodies that vary in shape and weight; students can repeat the procedure several times in the same virtual environment without getting short of supplies [START_REF] Sutherland | An augmented reality haptic training simulator for spinal needle procedures[END_REF]). For this reason, the use of computed simulators has become the new paradigm in the process of teaching medical students [START_REF] Jones | Telemedicine Systems[END_REF]). However, one significant drawback is the cost of the use of these simulators which can rise to $1,000,000 [START_REF] Zevin | Surgical simulation in 2013: Why is it still not the standard in surgical training[END_REF]).

More recent computed simulators implement haptic devices (detailed in section 2.2) that allow them to manipulate a virtual tool to operate the virtual model. At the same time, they receive force feedback from the operation. The models used in these simulators tend to behave like the real-life counterparts in matters of deformation and force feedback, which provides the student an experience close to a real human operation.

An example of a haptic simulator used in medical training is the Lapsim R ○ (Figure 1-2a) developed by SurgicalScience. This simulator is used to train medical students for laparoscopic surgeries. The users interact with a virtual world displayed on the screen and manipulate two haptic devices to input their hand motions into the virtual environment while they receive force feedback at the same time.

Another example is Immersive Touch (Figure 1-2b), a training system developed by the University of Illinois, which utilizes a transparent mirror to project 3D models in space and haptic devices to provide force feedback. The user must wear head-tracking glasses to register her/his position and orientation to adjust the stereoscopic perspective of the projected model. This method of rendering the scene allows the student to move her/his head around the virtual environment which provided

The problem of non-guided training

Although medical simulators should allow students to self-teach, they could develop bad techniques.

Because of this, it is still required the guidance of an expert whose motion feedback and commentaries lead them since their first sessions to improve their learning [START_REF] Schout | Validation and implementation of surgical simulators: A critical review of present, past, and future[END_REF]). This approach, where a trainer can manipulate and correct the student movements, is called guided training. In a guided training session, the trainees' hands are conveyed by the trainer during the instruction. In reallife applications, this is made by putting the hands of the trainer over the ones of the trainee. However, this is very impractical for gesture training with computer-based haptic simulators. As the trainer holds the trainee's hands, it is not possible to determine which user is manipulating the slave, and how much force each user perceives from the environment. This last property is a very crucial factor in real-life operations where the patient integrity can be affected.

Because of this, it is necessary that each user has access to a haptic device when they perform the training. Based on a bibliographical review, most commercial simulators do not include a second haptic console that can be used by the trainer during the teaching process. Some commercial simulators focus on the instruction of double-handled operations, but they do not provide an option of guided training mode, as the virtual tools in the environment are completely independent and the only interaction between them is when a collision occurs [START_REF] Escobar-Castillejos | A Review of Simulators with Haptic Devices for Medical Training[END_REF]).

Some researchers have tried to cope with this lack of dual-user manipulation functions for guided training systems. Their results are shown in section 2.4.5 where I explain why they still not fulfill guided training and expectations when dealing with force levels.

Main use case and main requirements

The following typical use case helps determine the main requirements of the system. Suppose, at first, that the trainer (an experienced surgeon) aims at demonstrating the right trajectories of her/his surgical tool, which involves performing tasks featuring free motions and some tool-environment contacts.

This implies that she/he requires realistic force feedback to dose her/his force, as in a bilateral teleoperation context. The trainer manually sets the compliance of the system to become leader (the trainee becomes follower): it is a demonstration mode. She/he then gets full-force feedback from the slave to perform the task as if she/he were handling the real instruments. Meanwhile, the trainee's device follows the trajectory of the leader one. If the trainee deviates from this reference trajectory when the system is in free motion, the compliance of the device brings her/him back to the right position. In case of interaction between the tool and its environment, the trainee can also feel in her/his hands the right level of effort to provide to the tool, using a display which guides her/his to set her/his device at the right position with the right feedback force. Afterward, the functioning can be inverted by reversing the compliance so that the trainee manipulates and the trainer follows and evaluates trainee's motions and applied forces: it is an evaluation mode.

Also, the simulator is not limited to only two users. An extended system with m-trainee in parallel teaching is achievable. A trainer can then teach several trainees at the same time (Figure 1-3b), instead of one by one (Figure 1-3a). Furthermore, a student can present her/his skills to several evaluators and get quantitative feedback from the system, and qualitative feedback from the evaluators. This concept offers a more efficient and less consuming teaching time, as students spend more time practicing with the teacher than waiting for her/his turn on the machine. (R3) Adaptive leadership: The simulator must be able to adapt the user leadership between the trainer and the selected trainee, based on the performance of the last one.

(R4) Trainee leader selection: The trainer can also select the leadering trainee, who is the student that will control the slave.

(R5) Position tracking: The system applies a correctional force when one of the following users deviates from the leader trajectory in order to keep her/him on it.

(R6) Force tracking: The slave directly interacts with the environment and gets force responses from it. These force responses are sent to all the users, no matter the training case or the leader trainee selected.

(R7) Compatibility: The simulator must allow the use of any haptic devices with any degrees of freedom (DoF), no matter their kinematic configuration.

(R8) Stability: The simulator must be stable at any moment, regardless the user's motions or slave interactions with the environment. From these 8 requirements, we deduce that a control architecture that connects several haptic devices with a slave must be developed for the accomplishment of the multi-trainee simulator.

Objectives of the thesis

The objectives of the Robotics Working Group of Ampere lab are to design a dual-user haptic training system able to provide guided force and motion hands-on training. In this project, a first architecture has been introduced by Fei Liu between 2013 and 2016 during his Ph.D., the Energy Shared Control (ESC) (Liu et al. [2015]).

ESC utilizes Intrinsically Passive Controllers (IPC) (details in section 3.2) for compliant control, it is composed of a passive interconnection of passive components to ensure its passivity and therefore its stability (more details about passivity in appendix C). Experiments show good transparency and the effectiveness of guided motion and force hands-on training with 1-trainee in a 1-Dof system.

The main advantages of ESC and requirements it already fulfills:

• It allows to work in three different training cases (R2).

• It provides an adaptive dominance function (AAA) based on the performance of the trainee (R3).

• It is able to transmit the dosing force from the trainer to the trainee when making the same motions (R5).

• The force feedback of the master devices is a function of the slave interaction with the environment and not an amalgam of signals from other masters and the slave (R6).

• As it is based on a Time Domain Passivity Control (TDPC, details in appendix C) global stability is ensured all time (R8).

The main disadvantages of the ESC architecture are:

Disadvantages

• It has been tested only in 1-DoF.

• The AAA depends on four variables that are difficult to tune by trainers.

Based on the disadvantages of ESC, my PhD objectives are the following:

Objectives (O1) To extend the ESC architecture into any degrees of freedom (R7) (O2) To extend the system to a multi-trainee approach, that allows adding more haptic devices without redesigning it (R1), and provide a leader trainee selection mechanism (R4) (O3) To propose an enhanced AAA function with an easier tuning process for the trainer that preserves (R3).

(O4) To ensure that the extended ESC architecture preserves its position and force tracking (R5 and R6).

(O5) To permit using haptic devices with different kinematics than slave robots (R7).

(O6) To guarantee that the extended ESC architecture preserves stability (R8).

Contributions

To achieve these objectives, we carried out a state-of-the-art survey (presented in section 2.4.5), which led us to determine the disadvantages of each architecture found in the literature and helped us determine that the extension and improvement of the ESC architecture was the correct approach to achieve a multi-trainee simulator.

First, we extended the ESC architecture to work in n-DoF. As this architecture was only tested in 1-DoF, this did not provide a way to develop a fully operational simulator. The expansion of this architecture is shown in section III-1 and led to a publication in Automatica in 2019 [START_REF] Liu | An Energy-Based Approach for n-dof Passive Dual-user Haptic Training Systems[END_REF]).

We also experimentally validated that architecture can work with devices with different kinematics.

For this, we tested it with three haptic devices, two identical for the masters and one with different kinematics for the slave.

The original Adaptive Authority Adjusting (AAA) function proposed with the ESC architecture (Liu et al. [2015]) could permit the trainer to get back authority over the slave when the trainee is performing badly. We propose a new adaptive function that only uses one parameter gain and a profile.

Document Outline

This thesis document is organized as follows:

In chapter II we introduce haptic devices, how they work, and a classification of them. Then we introduce the actual state of the art of computer-based simulators that use haptic devices for medical training, and the architectures that are used to develop them. Also, we explain why these architectures were not chosen for our application and why we opted for a previously proposed one corresponding to the different cases proposed for training.

In section III-1 first, we introduce the initial ESC architecture with its controller. We also explain how it works, and its fundamentals. We then introduce its expansion and validation to n-DoF according to two approaches in Articular and Cartesian spaces.

In section III-4 we introduce how we enhanced the Adaptative Authority-Adjusting function that allows changing the dominance of the trainer and the trainee in real-time, initially proposed in Liu [2016]. We explain how this new version provides a simpler way to use for the trainer. We then detailed the evaluation study of the benefits of this function and discuss the obtained results.

In chapter III-5 we expand the architecture presented in previous chapters into a m trainee system and we expose the experimental results.

Finally, in part IV, we present our conclusion about this thesis work and future directions for the improvement of this training system.

Chapter 2

State of art 2.1 Introduction

Humans can remember quite accurately the position of their extremities; this is called Kinesthesia [START_REF] Feygin | Haptic Guidance: Experimental Evaluation of a Haptic Training Method for a Perceptual Motor Skill[END_REF]). Kinesthesia comes from the Greek kinein, "to set in motion", and aisthesis, "perception" which is interpreted as the perception of motion. Kinesthesia is a conglomeration of three different sub-senses: orientation and position, motion, and force [START_REF] Rosker | Kinaesthesia and Methods for its Assessment: Literature Review[END_REF]).

Using kinesthesia, humans can get cognitive knowledge from a motorpsycho approach and learn to perform gestures or postures that serve for a particular task [START_REF] Xu | From psychomotor to motorpsycho: learning through gestures with body sensory technologies[END_REF]). One example of this approach is learning how to play an instrument. Musicians learn how to read music sheets and how every sound conjoint together to form a pleasant melody, but only through repetition, they master the ability to reproduce the music [START_REF] Galvao | Kinaesthesia and Instrumental Music Instruction: Some Implications[END_REF]). Using kinesthesia, humans can have focused kinesthetic training, added to a visual or auditory one, and therefore get more significant learning, especially for learning precise gestures [START_REF] Panait | The Role of Haptic Feedback in Laparoscopic Simulation Training[END_REF]).

Considering this, the technological advances in virtual reality, haptic devices, and augmented reality have helped to the development of haptic simulators where a student can interact with a virtual environment via a joystick, glove, or any input device to get force feedback of her/his actions. These simulators are used in several fields like aeronautics, engineering, and any other field of study where manual gestures are applied. Their use for training is becoming widespread.

Haptic devices

A haptic device is a system that intends to replicate the sensation of feeling or touching a virtual object.

For instance, these devices are used for the creation of virtual worlds where vision, hearing, and touch are replicated to provide a more immersive experience (Figure 2-1). The interaction between haptic devices and the user is a closed-loop process that begins with the motion input of the user on the haptic device. The haptic device senses its new position and sends it to the virtual world. In the virtual world, the cursor or virtual tool updates its position and, depending on if there is or not an interaction against a virtual object, force feedback is calculated as well the aftermaths of the collision like deformation, displacement, or sectioning. The updated virtual world is rendered and displayed on the screen. The user gets the visual feedback, and at the same time, the force feedback is commanded to the haptic device, which in turn exerts it to the user. For better comprehension, figure 2-2 shows a diagram of this process.

Haptics device classification

Haptic devices are used in industrial tasks, research assignments, and daily life gadgets. Because of this, there are multiple ways of categorizing. The first form of classification is based on their use: Consumer or Industrial [START_REF] Sreelakshmi | Haptic Technology: A comprehensive review on its applications and future prospects[END_REF]).

The first category covers low-cost haptic devices added to daily use devices like smartphones, joysticks, and steering wheels. They work by using motors with augmented inertia like the one presented in Figure 2-3. This one is used to alert or give a vague sensation of a collision, for example when something occurs on the screen, like a notification from an application or the explosion in a videogame. The second category is the industrial haptic devices that include a wide range of commercial or designed devices. These devices are used for complex tasks like scientific applications, virtual sculpture, training simulators. There is a wide variety of industrial haptic devices on the market. Most of them have a kinematic chain configuration (Figure 2-4a) although there are also parallel mechanism systems (Figure 2-4b), all of them providing up to 6-DoF of motion.

The industrial haptic devices are also classified by their use and feeling objective [START_REF] Culbertson | Haptics: The Present and Future of Artificial Touch Sensation[END_REF]).

Graspable systems: Haptic devices that allow giving the sensation of pushing or pulling an object.

These systems can also be used for deformation and dissection sensation. These devices are normally grounded and have a staff or holder, which is called a tool or pen and used by the user to activate it and get the force feedback from the virtual object (Figure 2-5a).

Weareble systems: Haptic devices that allow giving the sensation of grabbing objects. These systems Touchable systems: Haptic devices that allow giving the sensation of exploring a surface. Albeit the graspable devices also allow giving this sensation by using the tool, touchable systems achieve this by interacting directly with the cutaneous nerves that the human skin has (Figure 2-5c).

Advantages and disavantages

The advantages of each configuration depend on the specific task, but common limitations are:

• costly investment

• limited force and unequal in all directions

• limited bandwidth for the data transmission

54

• the haptic signal must be rendered at least at 1 Kilohertz [START_REF] Tavakoli | High-fidelity bilateral teleoperation systems and the effect of multimodal haptics[END_REF]), which could limit the simulation loop for very complex virtual environments.

Medical haptic training simulators

As medicine is a practical area, many procedures use the touch sensitivity of the doctor. Endoscopy simulators: used to teach medical students how to perform minimally invasive surgery like neurosurgery. These simulators teach medical students how to safely manipulate the instruments and how much force they must apply to the patients, as these are high-risk procedures for the patient.

One example of these simulators is NeuroTouch R ○ (Figure 2-9) which is a simulator presented by [START_REF] Delorme | NeuroTouch: A physics-based virtual simulator for cranial microneurosurgery training[END_REF])

Laparoscopy simulators: used to teach laparoscopy procedures to medical students. The simulator must be able to represent cutting forces, deformation, and sectioning. One example of this simulator is the Lapsim R ○ (Figure 2-10) which is a commercial simulator introduced first by [START_REF] Woodrum | Construct validity of the LapSim laparoscopic surgical simulator[END_REF]). It uses a specifically made haptic devices to give direction and orientation to the user

Simulator control architectures

Although some simulators use two haptic devices at the same time, the virtual tools are detached, which means that the motion of each device is individual and does not affect the others unless a collision occurs. This configuration does not allow guided training. To achieve it, two or more haptic devices must be interconnected using a communication layer and control laws that ensure the position and force tracking from the trainer device to the student. With the use of such control architectures, it is possible to implement a guided haptic simulator.

Multilateral configurations for control architectures

For a better understanding of the control architectures for haptic simulators, we need to study the more basic connection scheme: Teleoperation.

57

Teleoperation means operating a system remotely by interchanging data via another system [START_REF] Cui | A review of teleoperation system control[END_REF]). The basic configuration of teleoperation allows a user to manipulate a device with the information being sent one-way forward. In this case, the user never gets any feedback from the environment. To solve this, it is necessary to implement a bilateral teleoperation scheme, where

Master and Slave devices can perform position and force tracking [START_REF] Niemeyer | Stable Adaptive Teleoperation[END_REF]).

For haptic simulators, the slave device, which can be real or virtual, represents the tool that the user will handle in a real task. In a basic haptic simulation scheme, there are only five elements: The user or human operator, the Master device, the slave device, the controller, and the remote environment [START_REF] Secchi | Control of Interactive Robotic Interfaces A Port-Hamiltonian Approach[END_REF]). Figure 2-11 shows the haptic simulation scheme

Dual user scheme

A typical approach to implement a guided training simulator is the use of the Dual-user scheme, which is a case of a Multi-Master/Single Slave configuration.

In this scheme, two users, manipulate a haptic device identified respectively Master 1 and Master 2. A Slave device interacts directly with the environment, which can be real or virtual, and is interconnected with each Master device (Figure 2-16). In the use of multilateral architecture, problems of dominance surge as the slave tries to follow all the master devices at the same time. Because of this, it is necessary to establish a mechanism that allows all the devices to share dominance over the slave. [START_REF] Khademian | A four-channel multilateral shared control architecture for dual-user teleoperation systems[END_REF]) proposed the use of a variable named α for solving the dominance problems in the dual-user scheme. α establishes the dominance of each master device over the slave. In a training context, three possible cases are for setting the value of dominance (Figure 2-17).

Demonstration mode

In this mode, α = 1 and the trainer has all the dominance over the slave, and the trainee only receives haptic feedback from the slave. The trainer can teach the trainee how to perform different gestures, and how to properly dose force without being disturbed by trainee's movements. The trainer can also be a virtual one, which in this case, can be a saved trajectory for the virtual tool on the Master device.

Guidance mode

In this mode, 0 < α < 1, trainer and trainee share the dominance of the system. Both master devices receive haptic feedback from the slave, and both devices input their relative dominance. How much dominance has each device is set by α. As α → 1 the dominance opts to the trainer. On the other hand, as α → 0, the dominance opts to the trainee. An example of this is when α = 0.3, which means that the trainee has 70% of the dominance while the trainer has only 30% of it.

Evaluation mode

In this mode, symmetrical to demonstration mode, α = 0, and the trainee now has all the dominance over the slave. The trainer only receives haptic feedback from the slave but cannot input his motion.

This mode is used for the trainee to present its advances to the trainer. The trainee can perform the trajectory without any perturbation from the involuntary movements of the trainer.

Adaptive dominance

The trainer can change the value of α during the process. However, this process can be tedious as she/he needs to adjust the amount of dominance and concentrate on the task at the same time.

To make the change of dominance an easy task, an adaptive dominance can be used as well.

The dominance is then, a function that changes the value of α from 0 to 1, indirectly depending on the trainee. If the trainee performs the task according to the trainer's movements, the function will grant him/her more dominance. On the contrary, if he is moving away from the trainer's position, the function will return the dominance to the trainer so he can correct him in real-time.

A first adaptive dominance function was presented by [START_REF] Shahbazi | A dual-user teleoperated system with virtual fixtures for robotic surgical training[END_REF]) along with their dual-user architecture. Other authors as [START_REF] Huang | Auxiliary asymmetric dual-user shared control method for teleoperation[END_REF]) and (Liu et al. [2015]) have presented different approaches for this function. Each one is based on the position error between the trainee and the trainer devices.

Bibliographical study of control architectures for haptic simulators

Several control architectures have been proposed for guided training simulators. As they are based on MM/SS and dual-user system, we present a study on the more relevant architectures found in the literature and provide which requirement(s) they do not fulfill for the desired simulator.

1. [START_REF] Katsura | A realization of multilateral force feedback control for cooperative motion[END_REF]) proposed a multilateral force feedback control for cooperation tasks.

Their solution is dedicated to systems that do not share the same kinematics (for instance, one translation for master 1, two translations for master 2 and 3 translations for the slave). The authors used an acceleration control with disturbance observers and spatial transformations to facilitate the cooperation between two master users. This solution is interesting, but our goal is that trainees reproduce the same gestures as the trainers (Does not fulfill R5).

2. [START_REF] Moghimi | Haptic-enabled Collaborative Training with Generalized Force and Position Mappings[END_REF]) developed an architecture for cooperation in virtual environments. This architecture works in a dual-user scheme and uses an adaptive controller with filters for the force and position. The architecture can work with impedance and admittance haptic devices. The authors prove their stability with a Lyapunov function and made experimental test but only with 2-DoF robots. The authors addressed that the architecture will be tested for training purposes.

So, for a change of devices, it is necessary to recalculate the control law (Does not fulfill R1 and R7).

3. [START_REF] Shahbazi | A novel shared structure for dual user systems with unknown time-delay utilizing adaptive impedance control[END_REF]) presented an architecture for dual-user systems with different kinematics. They used a decentralized, shared adaptive controller to overcome the uncertainties on the robot's dynamics and to cope with the uncertain delays in the communication line. This solution works for cooperative use but is limited for training purposes as when the operator #1 has the lead on the slave, the controller does not ensure that the operator #2 gets the same force feedback (Does not fulfill R1, R5, and R6).

4. [START_REF] Li | Trilateral Teleoperation of Adaptive Fuzzy Force / Motion Control for Nonlinear Teleoperators[END_REF]) presented a novel architecture that uses an adaptive fuzzy control for motion/force synchronization. The control was created to ensure stability regardless of the delays, the uncertainties of the dynamics/kinematics of the devices and the disturbances. In this architecture, the force and position tracking are two different objectives that are reached by one device at the time. This means that while one master devices perform only position tracking, and the second one only force tracking. This architecture is not usable for guided training, as both users do not share the same position and haptic feedback, which prevents that the trainer can correct the trainee in real-time (Does not fulfill R1 and R6).

5. [START_REF] Khademian | A Framework for Unconditional Stability Analysis of Multimaster/Multislave Teleoperation Systems[END_REF]) studied the transparency with two users and three degree-of-freedom on planar devices. They enhanced the control to guarantee the stability of this system against uncertainties in the environment and the user's dynamics, with the help of Llewellyn's unconditional stability criterion. An experimental user study was carried out to assess the effectiveness of the proposed architecture in terms of transparency in a training context.

However, their studies with planar robots are not validated to work with devices where gravity affects directly the haptic devices. This could be solved by adding low-level gravity compensation control laws. However, the architecture interconnects directly both masters, without any treatment of dominance, invalidating the Demonstration and Evaluation modes (Does not fulfill R1 and R2).

6. [START_REF] Shahbazi | A dual-user teleoperated system with virtual fixtures for robotic surgical training[END_REF]) proposed a dual-user architecture in conjunction with the use of virtual fixtures to teach Minimal Invasive Surgery (MIS) to medical students. The authors utilize an impedance control, and the system uses an adaptive dominance factor law. An online evaluation of the trainee performance determines the dominance factor. However as the system uses virtual fixtures to create a path that the trainee must follow, this does not ensure force feedback from the slave to the masters, as the system focuses in path tracking rather than force tool feedback, which it is not desirable for our goal (Does not fulfill R1 and R6).

7. [START_REF] Shahbazi | An expertise-oriented training framework for robotics-assisted surgery[END_REF]) introduced an architecture that works with fuzzy controls for training purposes. Authors made this architecture to work with four different levels of trainees: Beginner, Intermediate, Advanced, and Skilled. This architecture focuses on changing the feedback of the trainee based on her/his experience. The more skilled the student is, the more haptic feedback from the slave she/he receives instead of the trainer. As this architecture focuses on Demonstration mode, it does not allow the trainer to correct the trainee in real-time like Guidance or Adaptive mode, so it does not work for our objectives (Does not fulfill R1 and R2).

8. [START_REF] Shahbazi | Novel Cooperative Teleoperation Framework: Multi-Master/Single-Slave System[END_REF]) also introduced a MM/SS teleoperated framework for cooperative task.

The passivity of the system is investigated, taking into account time-varying communication delays (but with the assumption that they are all equal, which is not restricting as, in training applications, users are at the same site). A control is developed to provide haptic feedback to every user. Nevertheless, the experiments show that when a user (such as the trainer) has the full control on the slave, the other users are not guided by this user and they get haptic feedback whatever their device's position. This behavior may not be efficient for the training as the trainees will not be able to synchronize position and force in their gesture learning (Does not fulfill R1, R5 and R6). 11. [START_REF] Zakerimanesh | Dual-user nonlinear teleoperation subjected to varying time delay and bounded inputs[END_REF])proposes an expansion to the dual-user scheme: a nonlinear Proportional plus Damping (nP+D) controller, previously proposed for SM/SS configurations. This control strategy considers the saturation of the motors and depends on two dominance factors.

These dominance factors are α, which determines the supremacy of the trainer over the trainee, and β that determines the supremacy of each user over the slave. Both dominance factors provide weight gains over the proportional-damping part of the control, which calculates the torque signal in function of the dominance, position error, and performance of the trainee. They proved the stability of this new architecture and simulated it with a 3-DoF planar robot, but still not with a robot affected by gravity (Does not fulfill R1 and R7).

12. [START_REF] Panzirsch | Haptic intention augmentation for cooperative teleoperation[END_REF]) developed a dual user bilateral architecture for cooperative tasks, where two users must complete complicated labors using remote slave systems. The architecture proposed by the authors has the property to replicate the sensation of movement from each partner.

As an example, the authors perform the task of loading a box. In a real-life situation, two humans can feel the movement of their respective partners when they are loading the box. Thanks to this, it is possible to synchronize the forces and motions without any other feedback more than the kinesthetic feeling of their body. This architecture tries to imitate this kinesthetic feeling using haptic devices and slaves in remote environments. However, the cooperation task is not well suited for the training approach studied in this thesis, as no leader gives the path to follow and the expected input force into the slave (Does not fulfill R1, R2, R5, and R6). Most of the architectures do not offer position and force tracking, or a multi-trainee approach, as they are designed to work only with one trainer and one trainee at the same time.

Conclusion

Haptic Chapter 3

Expanding to n-DoF (eESC architecture)

1-DoF ESC architecture

The ESC architecture embeds three Intrinsically Passive Controls (IPC) to provide compliance to the user haptic interfaces and to ensure that the interfaces with users (on masters' side) and the environment (on the slave's side) remain independently passive.

The ESC architecture utilizes an impedance-admittance controller configuration. This arbitrary choice of causality provides better transparency in practice, as explained in section 3.2.

θs .

D m1 :      θr1 T s1 T s f 1      =      0 α 1 -α -α 0 0 α -1 0 0           T r1 θs1 θs f 1      D m2 :      θr2 T s2 T s f 2      =      0 1 -α α α -1 0 0 -α 0 0           T r2 θs2 θs f 2      D s :      θs1 θs2 T rs      =      0 0 β 1 0 0 1 -β 2 β 1 1 -β 2 0           T s1 T s2 θrs      (3.1)
β 1 =    α, α = 1, 0 1, 0 < α < 1 β 2 =    α, α = 1, 0 0, 0 < α < 1 (3.2)
The advantage of this approach is to provide a model linking passive blocks together in a passive manner, which results in a global passive system. The IPC controllers feature several parameters to tune their compliance to provide transparency without compromising the overall passivity. They do not introduce any steady-state error on (Articular velocities and torques), Each master IPC provides the interconnection part with an "estimation" of the torque provided by the corresponding master device.

This torque reflects, in steady-state, the user's hand interaction force, and gravity, friction, and inertia effects. The slave IPC provides an estimation of the position of the slave. During manipulations, in steady-state, the input torque T rs indirectly reflects the interaction force between the slave and the environment, added with gravity, friction and inertia effects. This architecture does not rely on a force sensor to measure the forces; the only forces used are the ones calculated by the inner model of each IPC. This architecture was designed with three haptic devices that were kinematically identical and with very close motions. In practice, the disturbances are nearly the same for the three of them, so that, they offset one another and the leading user only feels the tool-environment interaction forces (T r1 ≈ T rs ⇒ T h1 ≈ T e in practice). To get the real force feedback, it is possible to install a costly force sensor on each device effector or provide a force estimator and update the IPC model to guarantee its passivity.

By default, the D m1,m2,s interconnection has an important limitation in demonstration (α = 1) and evaluation (α = 0) modes: the following user does not get any feedback from the slave, for energy balancing reasons. A solution, proposed by Liu et al. [2015], consists of adding two Modulated Flow Sources (MFS) providing the necessary complementary energy to the following device. To ensure the global passivity preservation that these additional sources of energy could compromise, a Time Domain Passivity Observer (TDPO) measures the energy E p (t) injected by the two MFS into the system:

E p (t) = t 0 [(α -1)T r1 (τ) -αT r2 (τ)] T θrs (τ)dτ (3.3)
A solution to preserve the system passivity (and therefore stability) consists in ensuring that E p (t) ≤ 0. The outputs of the MFS are accordingly modulated (3.4), acting as a Switched Time Domain Passivity Controller:

θs f 1 (t) = θs f 2 (t) =      θrs (t), if E p (t) ≤ 0 0 otherwise (3.4)
In practice, with a standard passive environment (free or static "walls"), no passivity loss was observed so far by the authors.

The Intrinsically Passive Control

To better understand how the ESC architecture achieves the position and force tracking, we need to introduce the Intrinsically Passive Controller (IPC) propose in [START_REF] Stramigioli | Creating Artificial Damping By Means of Damping Injection[END_REF]). This control uses the concept of passivity to bring global stability to the system (more details in Appendix IV-C).

There exist two configurations for this controller: with impedance and admittance causality.

And for admittance ẍmc

= f h -f mi -ẋm b mi M (3.6)
The dynamic of the force exerted by f mc and f mi are based in Hooke law and shown in equation 3.7

f mc = k mc (x m -x d ) f mi = k mi (x d -x e ) (3.7)
The force f mc is returned to the Master device. The force f mi is the commanded force and applied in the slave side in order. In the case of the impedance IPC, in a teleoperation scheme where position/force tracking is the objective to achieve, k mc = k mi . In case we do not respect this equality restriction, the controller would compute the desired force with a scale factor of

n f = k mc k mi (3.8)
This is not desirable for our case, as n f must be equal to 1 to preserve the transparency of the system by exerting the same force from the environment onto the master device.

Impedance-Admittance IPC

By using two IPC controllers, it is possible to achieve a bilateral teleoperation system. It exists four configurations for this: Impedance-Impedance, Admittance-Admittance, Impedance-Admittance, and

Admittance-Impedance (Hashtrudi-Zaad and Salcudean [2001]). The Impedance-Admittance IPC is the one used in the ESC architecture and is the union of both controllers presented in Figure 3

M mm ẍu = f u -k mc (x u -x m1 ) M 1 ẍm1 = -k mc (x m1 -x u ) -k mi1 (x m1 -x m2 ) -b mi1 ẋm1 M 2 ẍm2 = -k mi1 (x m2 -x m1 ) -k mi2 (x m2 -x e ) -b mi2 ẋm2 M ms ẍe = -k mi2 (x e -x m2 ) -f e (3.9)
As the impedance control reads the position of the device and the admittance of the force/torque, both signals are incompatible. Because of this, position x e , from the impedance control, changes to

x c , and it is now considered as the connection port. With this, the force f mi from the impedance IPC is equal to the input force f u from the admittance IPC, allowing to preserve the transparency and the interchange of energy. This point can also be used to implement a communication layer for remote teleoperation as well or application of the dominance.

Transparency and stability of the IPC Transparency

The objective of any bilateral teleoperation is to give the user the sensation of interacting directly with the final environment, regardless of the number of devices and communication layers implied. This important characteristic is named transparency and specifies the fidelity of the haptic feedback that the user gets from the teleoperator.

For impedance devices, between the interaction of the user, haptic devices, and environment, it exists a mechanical impedance Z that relates the force F and velocity X • s of the system (Raju et al.

[1989]).

Z = F X • s (3.10)
The user moves her/his master device, which commands the slave device, and this last interacts with the environment. With this in mind, we defined a teleoperator as a black box that consists of the master-controller-slave system described in Figure 345.

So the impedance coupling of the user with the environment can be described as a hybrid matrix

 F h -X e • s   =   h 11 h 12 h 21 h 22     X u • s F e   (3.11)
Where h 11 is the unconstrained movement impedance and gives the equivalent of inertia and damping that the user feels when the system is in free motion. h 12 is the backward force gain and the force tracking in contact. h 21 is the forward velocity gain and the position tracking during free motion. And h 22 is the slave output admittance and the position tracking during contact [START_REF] Aliaga | Experimental Quantitative Comparison of Different Control Architectures for Master-Slave Teleoperation[END_REF]).

The velocity of the environment is always negative as must enter into a port according to the two-port convention. A teleoperator that offers full transparency must fulfill the conditions of (3.12)

F h = F e and X d • s = X e • s ∴ Z u = Z e (3.12)
So the total force applied by the user is:

F h = h 11 • X h • s + h 12 F e (3.13)
And the velocity of the slave is:

-

X e • s = h 21 • X u • s + h 22 f e (3.14)
Analyzing (3.11) and (3.12), the perfect transparency, without scaling forces or positions, can be deduced as:

  F h -X e • s   =   0 1 -1 0     X h • s F e   (3.15)

IPC's transparency

To determine the ESC's IPC transparency, we first determined its hybrid matrix. Based on the framework presented by [START_REF] Hannaford | A Design Framework for Teleoperators with Kinesthetic Feedback[END_REF], we use the declared model in (3.9) from the Impedance-Admittance IPC and apply the Laplace transform with initial conditions equal to zero.

M mm X u • s 2 = F h -k mc (X u -X m1 ) M 1 X m1 • s 2 = -k mc (X m1 -X u ) -k mi1 (X m1 -X m2 ) -B mi1 X m1 • s M 2 X m2 • s 2 = -k mi1 (X m2 -X m1 ) -k mi2 (X m2 -X e ) -B mi2 X m2 • s M ms X e • s 2 = -k mi2 (X e -X m2 ) -F e (3.16)
From this, we declare the mechanical impedances (Z) of the system and its gains (C), through the connection channels between master and slave device as

Z 1 = M mm • s Z 4 = M ms • s C 3 = k mi1 s Z 2 = M 1 • s C 1 = k mc s C 4 = k mi1 + k mi2 + B mi2 • s s Z 3 = M 2 • s C 2 = k mc + k mi1 + B mi1 • s s C 5 = k mi2 s
So the model of (3.16) becomes

X h Z 1 • s = F h -C 1 X mm • s +C 1 X 1 • s (3.17) X 1 Z 2 • s = C 1 X mm • s -C 2 X 1 • s +C 3 X 2 • s (3.18) X 2 Z 3 • s = C 3 X 1 • -C 4 X 2 • s +C 5 X ms • s (3.19) X e Z 4 • S = C 5 X 2 • s -C 5 X ms • s -F e (3.20)
And the new diagram that describes the two-channel connection between the master and the slave device is shown in Figure 3-6, where the IPC1 is the Impedance IPC used by the Master 1 or Master 2, and the IPC2 is the Admittance IPC used by the slave device.

+ - -- + -- - -- - -- - + -
= C 1 Z t2 ẋmm +C 3 C 5 F e Z t3 (3.22) With Z t2 = -Z 3 Z t1 -C 4 Z t1 +C 2 5 and Z t3 = Z 2 Z t2 +C 2 3 Z t1 +C 2 Z t2
. Now, substituting (3.22) into (3.17) and isolating for F h we get

F h = (C 2 1 Z t2 -Z 1 Z t3 -C 1 Z t3 ) Z t3 ẋmm + C 1 C 3 C 5 Z t3 F e (3.
= -C 1 C 3 C 5 C 2 5 Z t4 -Z 4 Z t5 -C 5 Z t5 ẋmm + Z t5 C 2 5 Z t4 -Z 4 Z t5 -C 5 Z t5 F e (3.25) With Z t5 = Z 3 Z t4 +C 4 Z t4 -C 2 3 .
So with (3.23) and (3.25), we determine the hybrid matrix as

h 11 = (C 2 1 Z t2 -Z 1 Z t3 -C 1 Z t3 ) Z t3 h 21 = -C 1 C 3 C 5 C 2 5 Z t4 -Z 4 Z t5 -C 5 Z t5 h 12 = C 1 C 3 C 5 Z t3 h 22 = Z t5 C 2 5 Z t4 -Z 4 Z t5 -C 5 Z t5 (3.26)
For a complete expansion of the hybrid matrix, refer to Appendix B. The transparency of the system depends on the parameters of the IPC and by simple inspection, it is possible to determine that the system does not meet the condition established in (3.15) for full transparency. However, it is possible to determine if the architecture is transparent for different inputs in low frequency (LF) and high frequency (HF). We evaluate s → 0 for LF and s → ∞ for HF. The results of the evaluation are visible in Table 3 From the analysis in LF, we can observe that h 12 , h 21 and h 22 behave ideally respecting the full transparency condition given by (3.15). This means that the position and force tracking in free motion and contact are met without any added force. In the case of h 11 , due to the non-zero value of the dampers is not possible that h 11 → 0, which means that the user always feels the damping of the architecture even in very smooth movements. As the damping factors cannot have negative values, one clear solution is to set B mi1 = B mi2 = 0, but it is important to remark that with B mi1 , B mi2 → 0, the passivity of the system becomes compromised, and therefore the stability. From this, the damping factors should mitigate the input ẋu in low frequencies. To get a reduction, we know that the gain must be below zero decibels (dB). So we consider that B mi1 + B mi2 < 1 (as 20 log(1) = 0), so the input speed of the ẋu of the user is mitigated, allowing to approach the system as close as possible to the desired full transparency.

In HF, h 11 indicates that the user will always feel the inertia of the haptic device in free motion.

h 12 , h 21 → 0, so the added force for force tracking during contact and position tracking during free motion is mitigated, which is desirable. h 22 indicates that the position tracking during contact adds the inertia of the slave device.

To illustrate these observations, we drew the Bode diagram (Figure 3 h 11 : For B mi1 + B mi2 ≤ 1, the inertia felt by the user is mitigated in frequencies lower than 100rad/s, which is desirable for a transparent system. After this, it exists a change in the phase of the output force, which is more abrupt for lower damping factors. From this point, the inertia is amplified in higher frequencies, and the values of the dampers are irrelevant, as it is shown how the output has a slope of gains independently of the parameters used. This indicates that the user feels the inertia of the mass, augmented by the speed she/he applies to the tool.

h 12 : For frequencies lower than 100rad/s there is no gain or nor mitigation of the force tracking. This indicates that the output that the user feels is the same that the one given by the environment.

After this point, force tracking is mitigated, which is translated to the user as a reduction in the force felt from the environment.

h 21 : This one as a similar behavior as h 12 , explained by the fact that their values are the same with just a change of sign. This indicates that the position tracking in free motion is achieved in frequencies lower than 100rad/s. After this point, the position tracking is mitigated if the user applies inputs with higher frequency.

h 22 : The position tracking during contact is the only element of the hybrid matrix that behaves as desired with low and high frequencies. The position tracking is only amplified around 100rad/s, which indicates the beginning of amplification for h 11 , reduction for h 12 and h 21 and the loss of transparency from the environment.

The final assumption from this analysis is that ESC is transparent in lower frequencies, and at higher frequencies (around 100rad/s for the test parameters) the transparency is lost. This does not represent a problem, as for guided-training purposes, the trainer does not effectuate sudden or quick movements while the trainee is learning how to do the task.

Finally, we tested ESC vs two other architectures to see how well the performance of this was. The two architectures selected are Position-Error-Based (PEB) and Direct-Force-Reflection (DFR) from [START_REF] Tavakoli | Haptics For Teleoperated Surgical Robotic Systems[END_REF]. PEB was chosen for its similitude to ESC of being a two-channel architecture and both only read the position of the user. DFR was chosen for being a simpler architecture and incorporate a force sensor, which could improve transparency. The hybrid matrix of PEB is given by

H =   Z 1 +C m Z 4 Z ts C m Z ts -C s Z ts 1 Z ts   (3.27)
Where C m = (k mc + B mi1 s)/s, C s = (k mi2 + B mi2 s)/s, Z tm = Z m +C m and Z ts = Z s +C s . For DFR, the hybrid matrix is set as h 11 : PEB and DFR mitigate the inertia felt by the user better than ESC, with a similar behavior between the first two. However, in higher frequencies, the amplification of the inertia is the same for three architectures.

H =   Z m 1 -C s Z ts 1 Z ts   ( 3
h 12 : DFR is the best in force tracking, as the frequency of the input does not change the value of the force exerted by the environment. This is because DFR has a force sensor attached. Between PEB and ESC, this latter behaves worst, as it mitigates the force tracking sooner as PEB.

h 21 : Once again ESC mitigates the position tracking in free motion before PEB and DFR. Between these last two architectures, the behavior is similar and there is no noticeable difference between them.

h 22 : For position tracking during contact, PEB and DFR do not amplify the signal, while ESC only around 100rad/s as it is explained in the previous analysis.

As the results show, ESC has the worst transparency compared with PEB and DFR. The addition of a force sensor can increase the transparency of the system; however, the majority of the haptic devices lack one. A force sensor can be placed at the end of the tool of the haptic devices, but it must be instrumented and adapted to the simulation software, which can increase the cost of the simulator.

Once ESC is demonstrated to be transparent (in low frequencies), we proceed to explain the process to expand it into n-Dof.

3.3 From 1-DoF to n-DoF

Problem

To create a functional simulator, the aforementioned 1-DoF ESC architecture must be expanded to n-DoF. The principal problem with the expansion of the system is to ensure its stability all the time.

The architecture has been tested in 1-DoF, in a planar configuration without gravity. The IPC controller must be able to maintain the system's stability, regardless of the position of the links. The two principal problems with the expansion of ESC to n-Dof is the non-linearity that occur because of the addition of more degrees of freedom. Also, the gravity term complicates the model, as a continuous force/torque must be applied on each link moving direction in the vertical direction. Another difficulty of this expansion is to find the correct parameters for the IPC controllers that can ensure an accurate position/force tracking avoiding side-effects like shattering and loss of transparency. The only method proposed to tune the IPC parameters was by trial and error.

Assumptions and proposal

IPC has been demonstrated working with Multi-Input Multi-Output systems. [START_REF] Arcara | Intrinsically passive control in bilateral teleoperation mimo systems[END_REF] presents simulation results of a planar robot using IPC in parallel for control. In their experimentation, a 3-Dof robot is used for teleoperation. Their results have shown that interconnecting several IPC controllers in parallel Cartesian position and orientation purposes, bilateral teleoperation is reachable.

Based on this, it is assumed that the compliance of the IPC controller absorbs the disturbances (nonlinearities such as frictions, Coriolis forces), and also that every device has the same kinematics and very close so positions and orientations that the gravity applied on each device is the same. By expanding the ESC architecture independently for each joint (Figure 3-9 for articular and Figure 3-10) a n-DoF dual user scheme, named (eESC) can be achieved. It permits connecting devices with the same kinematics. In a second approach, we duplicated the ESC for each Cartesian axis (positions and rotations). θ (1,2,3) .

θ (1,2,3) .

T h2 T 1 θ 1 . T 1 θ r1 .
T r1 θ r2 .

T r2 θ s1 .

T s1 θ s2 .

T r2 θ rs .

T rs -T e θ (1,2,3) . As the ESC architecture is based on the TDPC approach [START_REF] Franken | Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency[END_REF]), the passivity of every link is achieved independently. Therefore every source of energy inside each device is passivated. For each degree of freedom, the dynamic effects produced by the motions, are seen as external input torques and transmitted as is to the communication side (Authority Sharing Mechanism -ASM).

So, the IPC controls must be tuned to get a desirable behavior. This expanded ESC architecture is named eESC. To determine the eESC reliability and precision, a series of experimental tests were performed.

Simulation

We first simulated the system by expanding the architecture into three DoF: θ 1 ,θ 2 and θ 3 for Articular (aESC), and x,y and z for Cartesian (cESC) expansion. The main advantage that Cartesian expansion offers versus the Articular one is the ability to work with devices that do not share the same kinematic configuration. This means that a haptic master device designed for human interaction can be used with a robotic manipulator on the slave side, as long as both systems have a common Cartesian workspace.

Simulation setup

The models used for Master 2 and the Slave are based on the dynamic model of the Geomagic 3D Touch (Appendix A.1). The model only considers 3 actuated DoF, which implies controlling only of the translations of the devices, so not orientations are considered with this setup. In this case, the system is set in Demonstration mode, so Master 1 is the leader device, which inputs the desired position, and therefore, it is represented by a trajectory generator, as no dynamic model is required for this. The simulation is timed from 0s to 10s and the trajectory is set as a circular path with a radius r = 10cm defined by

x = r * sin(t) y = r * sin(t) z = r * cos(t) (3.29)
For the Articular approach, we used the inverse kinematics of the Geomagic Touch 3D (Appendix A.1.2) to establish the desired Articular positions and the direct kinematics transform (Appendix A.1.1) to compare the performed path between both approaches (Articular vs Cartesian). shows the diagram of the simulation.

The Cartesian expansion requires higher gains than the Articular expansion to get a good performance. We opted to use the same numerical value for the gains on both devices. The values of the virtual spring stiffness and masses were set empirically as there is no method to obtain them. In the case of the damper determination, as the IPC resembles a mass-spring-damper system, we assume that it is desirable to have it as a critically damped system, as an underdamped setting involves free vibrations of the mass (which leads into chattering), and an overdamped setting leads to slow reactions [START_REF] Ogata | System Dynamics[END_REF]).

To determine the damping factor of the master IPCs, first, we needed to determine the total stiffness

k t = 1 1 k 1 + 1 k 2 + . . . + 1 k n (3.30)
as k mc = k mi to provide bilateral transparency, the total stiffness is

k t = k mc 2 = k mi 2 (3.31)
In the case of the slave IPC, it only exists one spring, therefore k t = k mi . Then the damping coefficient for a critically damped system is given by

B mi = 2 M * k t (3.32)
With this, Table 3.2 shows the IPC parameters obtained employing simulation. These gains have been obtained empirically through several iterations to get perfect tracking (negligible error) in both approaches. The parameters used for the Articular and Cartesian space are the same and correspond to the minimum of them that allow to get an underdamped reaction in the case of the Cartesian approach, as the following simulation shows.

Simulation results

From the results, we determined that the Articular approach performs a perfect tracking of the trajectory. There are no noticeable deviations or overshoots during the task, as it is seen in Figure 3-12.

In the case of the Cartesian approach, the Master 2 device has overshoot problems during the beginning of the trajectory. Once the system has established, the architecture follows the position in with the same level of performance that the Articular, as it is seen in Figure 3-13. For a better appreciation, Figure 3-14 shows the position tracking for the Articular approach, and Figure 3-15 the error in the Cartesian space. In this case, the Articular architecture can reach the desired position without any undesired behavior in a smooth and fast way. For the Cartesian approach, Figure 3-16 shows that the system suffers from overshooting at the beginning of the task, mainly in the axis Y due to the gravity term. Once the system is stabilized, the tracking of the trajectory is perfect as it is with the Articular. Unlike with the Articular Approach, with the Cartesian approach, the position tracking shows an initial transient mode during around a tenth of a second. This is the only drawback of this approach.

It may be due to errors obtained during the first computations of the Lagrange matrix. The three devices are connected to one computer with two screens in duplicate configuration. The slave is set close to the testing bench, which represents the environment and consists in a 3D printed model disc with three possible paths: a plain one, a guided one and one with peaks that are used to get the sensation of touching a rough pattern (Figure 3-18).

For the Master 1 and Master 2 devices, both are located close to a screen of the computer. A wall is set between each device to avoid the users can directly see their partner device or the slave. A webcam pointing to the slave provides visual feedback for each user. The screens show the streaming video

User interface

During the test, the trainer tries to keep the same position in each axis, but as soon he corrects in one axis, the others get misaligned. Because of this, we designed a new user interface to correct this problem.

Simulink is a very flexible tool that allows modifying the architecture and control scheme but does not provide the tools to create a user-friendly interface. For this reason, we create a new user interface using the Chai3D framework and Visual Studio 2017 as the compiler.

The Chai3D framework is an open-source framework, written in C++, developed for the creation of 3D virtual environments for haptic devices [START_REF] Conti | The CHAI libraries[END_REF]). Chai3D provides all the functions, libraries, and tools needed to connect with several haptic devices, including the Geomagic Touch 3D.

This framework also provides a set of functions for the manipulation of virtual objects as well as the calculation of collisions, deformation, and forces. Ideally, Chai3D is only used to create these virtual environments, lacking the tools offered by other frameworks to develop control schemes.

Instead of translating the ESC architecture and the IPC control into C++ language for being used with the Chai3D framework, we opted to create memory zone location in the RAM that allows Simulink and the developed user interface to share data. By implementing the boost libraries into the Chai3D framework (Boost [9 02]), we create the memory zone. This memory zone is managed by the operative system (Windows 10 in this case) and allows that both processes run in parallel. As the tests are with real environments, it is not necessary to get force calculation from them, and thus the user interface works as a visualization of the actual position of both devices. To better understand this, Figure 3-21 shows the new framework connected with the use of the new user interface. The user interface consists of two spheres, blue for Master 1 and green for Master 2, two force bars and an isometric plane with texture. The spheres provide an intuitive way for the users to locate their device respecting her/his partner, in a 3D Cartesian environment. A gray line links both spheres to help determine how far is each from the other. To give a perception of depth, the spheres are displayed over an isometric plane with a brick-wall texture. Once the slave interacts with the environment, the follower user needs to exert the same effort onto his device. To help them apply the same force, on both sides, two side-bars are colored according to the force exerted by each device.

Determining control parameters

As established in section 3.3.3, the only parameter that must be determined for the IPC controllers is the damping factor B mi1,mi2 . We propose here a method to determine the stiffness of the IPC controllers, based on the reaction of the haptic device.

In this method, masses M 1 > 0 and M 2 > 0. [START_REF] Stramigioli | Creating Artificial Damping By Means of Damping Injection[END_REF] also states that for better performance, the virtual mass in an IPC must be lesser than the one of the devices to be controlled. In our tests, we observed that both masses must be between 0.001 and 0.01 kg to reduce the chattering problem and accords with the parameters of our haptic devices (detailed in Appendix A.1). In the case of Master and Slave devices having the same kinematics, we propose to use M 1 = M 2 . If these are not set as suggested, the system remains stable due to its passive nature. However, the difference between both masses can change the momentum generated by them, leading to a change of the selected springs, dampers, and different establishment time of the haptic device.

The stiffness of the springs can be set by determining the minimum reaction force/torque (R f ). R f is the minimum input signal that is necessary to take it off from the stand position. To acquire it, we made an experimental test by injecting a ramp signal of force/torque as an input in the haptic device.

By plotting the position and the input signal, it is possible to determine R f by observing at which value of the ramp signal the system starts to move. Figure 3-23 shows the determination of R f in the axis X with a Geomagic R ○ 3D touch. As one can observe the relation between the position and the exerted force is not linear, with the presence of a threshold that increases the steady-state error of the system.

To ensure the proper position tracking of the IPC controllers, we determined the minimum force at which the system reacts to reduce this gap as short as possible. From our test, the reaction force is R f = 0.54N as the system starts to actuate when a force of around 0.5N is injected. Also, the system has a non-linear behavior, especially noted from t > 4s, but this result is neglected as it has been supposed in section 3.3.3 IPC controller is robust enough to compensate it. Although R f > 0.5N indicates that the system requires at least this force to be actuated.

This implies that the haptic device can not exert forces lesser than this. R f only defines the necessary force required to set off the system from the static repose. Once the system is in motion, it is possible to render forces lesser than it. With R f it is then possible to get the value of k mc /k mi with

k mc = k mi = R f ∆ r (3.33)
Where ∆ r is the minimum error allowed before the system can be actuated, this value is in meter/radian, and it is directly inverse proportional to the value of the springs. The lower ∆ r is, the more accurate the controller is, but this can produce chattering effects. From our tests the value that performs the best is 1x10 -4 < ∆ r < 5x10 -4 m/rad. In the case of the admittance control for the slave, k mi2 can be equal to their Master counterpart k mi1 as long as the Slave device shares the same kinematic configuration. If this is not possible, a proper R f must be determined.

Types of experiments

To validate the hypothesis that the eESC architecture can perform position and force tracking, two experiments were done in a training proposes context, with the Articular and Cartesian approaches.

The experiments performed in this thesis are categorized into two types: Free motion and Wall Contact.

In Free Motion, the slave device can move freely in the workspace without interacting with the environment. This test is made to evaluate the position tracking of the slave and the follower master according to the leader device. During the test, the follower device attempts to move away from the trajectory given by the leader (a circle in this case). The architecture responds by injecting a correctional force/torque into the lead device until it returns to the desired position. The haptic forces the user gets from the slave are the ones created by the inertia of the slave, which are considered negligible, and in the case of the lead device, the correctional torque.

In Wall Contact, the slave device works in free motion during a few seconds. The leader device takes the slave into a collision with an established wall or environment that can be soft or hard. This test is made to validate the torque/force tracking of the slave to the master devices. The forces/torques that the master devices exert on the user's hand must be equal to the one that the slave is exerting to the wall, assuming the slave or the master has not reached their force/torque saturation point. For the follower devices, if it is overpassing the position of the leader, the architecture will exert more force/torque to correct with the leader. From this point, it is not possible to distinguish the difference between the environment force feedback and the correctional force. It is required to use the human interface to compare the force exerted by the slave and the correctional one.

To get a better analysis of the results of both tests, we compute the Root Mean Square (RMS)

error for the position and force error signals (Appendix A.2). The computation of RMS values helps us quantify the tracking performance between the follower device and the leader devices. This RMS error can be computed for position tracking in Cartesian space, Articular space, and to analyze the force and torque tracking.

Articular expansion

Free Motion for eESC architecture

In this first experiment, the system worked in Demonstration mode (α = 1) at first and changed it to evaluation (α = 0) at t ≈11.5 s.

To show that the device of the following user leads him on the track of the leader, each user performed a gesture to take his device away from the prescribed trajectory (the trainee in demonstration stage a and then the trainer during the assessment stage b in .

Figure 3-24 depicts the global trajectory performed by the users in free motion. This plot shows that, out of the two attempts to take the device away, the three trajectories follow close trajectories. The results are presented in Articular and Cartesian approaches. Although the control is in the Articular approach, the Cartesian position of the system can be obtained directly by the Phantorque library or by using the direct kinematic presented in Appendix A.1.1. The RMS error value of the tracking error (computed from the positions expressed in the Cartesian space) between the Master 1 and slave devices during demonstration mode was 8.2 mm (and 6 mm between the Master 2 and the slave during demonstration mode). This level of precision is to be taken into account when choosing training applications. It can suffice for first hands-on training but may not be precise enough for more accurate training tasks. To enhance precision, it is suggested to use more precise haptic devices, which could, in turn, allow to raise the gains of the IPC and enhances the precision of the whole system. This can be explained by the weight of the arm, which disturbs the IPC controller. A weight compensation approach should be envisaged to raise the precision of this joint control.

Besides, it is logical that the follower user position does not overlap with the two others as this user is led by their device to follow the slave trajectory. According to the resistance she/he brings (the stiffness of the hand), the follower position is shifted from the reference trajectory.

Figure 3-26 shows the exchanged torques T r1,2,s for the three actuated joints. The three plots show a proper torque tracking for the three joints. As the motion is performed in free motion, these torques should be close to zero if neglecting the aforementioned disturbances.

Indeed, in demonstration mode, the master 1 (resp. master 2) and slave torques overlap.

Moreover, one can observe the torque generated by the devices to bring back the following user to the reference trajectory at marks a and b .

Also, the sudden change of α results in a small sudden change of T 1 and T 2 , but in practice, it is hardly perceived by users. It has not any adverse effect on energy levels (see Figure 3-28), which remain negative.

Wall contact for eESC architecture

On wall contact for eESC, the dominance factor α is kept to 1, corresponding to the demonstration mode where the trainer (with master 1) shows an interaction to the trainee (with master 2). The trajectory is visible in Figure 3-29.

The trainer leads his device to apply the slave effector on a solid surface (for the force exerted by the haptic device), to show the behavior of the system in contact with a hard organ, like a bone, that it may encounter in a medical context.

Once in contact, he asks the trainee to come in the same position to be able to feel the same interaction force. This can be very useful in a training context to learn how to dose forces to apply.

To better understand this experiment, it is necessary to understand how the force tracking works in teleoperation systems. First, when the slave contacts the wall, the leader user applies some effort on the leader device, which positions its device beyond the position of the surface and permits him to get haptic feedback from the slave. This phenomenon depends on the stiffness of the surface, the power of the haptic device, and the controllers' gains. The more they are elevated, the less the leader master device will go beyond the real surface position, and the transparency will be better. This limitation is due to a compromise between stability and transparency met in every teleoperation system.

θ (rad) 1 θ (rad) 2 Time (s) θ (rad)
The positions of the masters are virtually beyond the surface (around 4 cm) while the slave effector stopped in contact, which corresponds to stiffness of 250 N/m. As long as the trainer pushes his own device "inside the piece" the force feedback increases accordingly. In this plot, the slave force overlaps the Master 1 feedback force.

In steady-state, the devices being immobile and as users move along the horizontal x axis, there is no torque disturbance in this direction. In the case of vertical interactions, both torque plots would be shifted together to compensate for the gravity (when touching a surface from bottom).

Despite the aforementioned disturbing positioning, the force tracking error is 0.35 N RMS, corresponding to 3.5% of the magnitude of the forces.

When the trainer decides that this corresponds to the right level of force to apply in a training context, he stops his motion and asks the trainee to join him at the same location, which the latter does at t ≈ 13 s.

The follower aligns his device at the same location as the trainer's (error of 2 mm RMS in x direction when t > 13 s) only by way of the video feedback and the real-time plots displayed on his monitor. He then feels force feedback which is very close to the interaction force (error of 0.2 N RMS (2%) when t> 13 s) as far as we can estimate it.

Figure 3-31 shows that MSF energy levels are not influenced by the contacts.

Cartesian expansion Experimental setup for Cartesian expansion

For the experimental validation of the architecture in the Cartesian expansion, we implemented two identical Geomagic Touch 3D TM and one Virtuose TM 6D (Fig. 3-32) as the slave device. Table 3.5

shows the characteristics of the Virtuose device.

The control and architecture were implemented using Matlab 2016a. For the communication with Geomagic Touch 3D the library, we use our modified Phantorque library, and for the case of the Virtuose, the Virtuose Matlab library (Virtuose Mex) developed by Alamilla [START_REF] Daniel | A new method to render virtual walls for haptic systems[END_REF]. As the Haption Virtuose device does not have a torque/force sensor, the measured effort is obtained directly 103 Three experiments were proposed to validate the architecture: Position tracking, Position tracking with eAAA, and Force Tracking. In this case, we are using a two master device, so the multi-trainee eESC architecture works in a dual-user approach.

Y X Z θ 1 θ 2 θ 3 θ 4 θ 5 θ 6

Free motion

This test evaluates if the follower devices can follow the trajectory proposed by the leader. The test consists of a trajectory in free motion given by the leader device. In the first half of the test, α = 1 which means the system is running in demonstration mode and the trainee will try to oppose the trainer in a determined time. The architecture responds by exerting a feedback force to correct the position of the guided device. Then the dominance is turned by the trainer to α = 0, and the system works in evaluation mode, and as it was made with the first half, the process is repeated but now with the roles changed.

- At t = 26, the change of dominance occurs (α = 1) and the system works in evaluation mode.

From 26 < t < 29 and 38 < t < 41 the RMS errors between M2-M1 are 0.31mm and 0.35mm. In the case of M2-S, the RMS is 0.26mm and 1.35mm. As it is shown in the experiment, the average error is less than 2.5mm, which can be considered good in a surgery performed by a human being.

Wall contact

Once position tracking is validated, the system must be able to perform force tracking as well. For this, a contact test was performed using three axial walls (once for each axis). For this test, the system works in demonstration mode. The trainer exerts a force on the wall while the slave and trainee remain at the edge. After a few seconds, the trainee tries to match the trainer's position. As soon the trainer reaches it he/she can feel the same interaction force as the trainer. Figure 3-38 shows the position,

Discussion

For the Free-motion test, the results have shown that the eESC is able the achieve a full hands-on training system. The resulting precision level can be considered as a drawback (lowest error of 6 mm) when practicing precise incisions. Despite this, its use as an introductory simulator can be beneficial, as the trainees can get used to the process, the forces, and the implied methods in the task. Then when students dominate it, they could try a more accurate simulator to improve their performance. Also, the torque plots show that the eESC offers a minimal force that is activated during the motion. This torque is exerted by the system as a result of the IPC's inner dynamic. We called this a parasite torque, that although it is felt by the users, it does not disturb the movement and interaction as the force and frequency of the torque is almost negligible.

For the wall contact test, the system is limited by the balance between transparency and stability that comes with every TDPC system. The trainee must have the same position as the trainer to get the exact amount of torque feedback.

It is validated that eESC architecture can work in Cartesian expansion to provide a haptic simulator able to work with devices of any kinematic configuration. The system can perform trajectory tracking.

For the contact case, the system can also perform force tracking when both master devices share the same position. With this system, it is now possible to create simulators that could use a haptic device with different kinematic configurations. An optimal configuration for a training simulator would be with all the users manipulating the same kind of haptic devices, and a slave device more adapted for the training task.

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Chapter 4

Enhanced AAA

AAA for ESC

Although the dominance factor α can be changed by the trainer during the training task, it is also desirable that the system can adapt the dominance of the system between trainer and trainee based on how well performs the second one. The ESC architecture comes with an inner Adaptive Authority Adjusting (AAA) function proposed by Liu et al. [2015] as well. The proposed AAA uses three functions, Adaptative Virtual Boundary, Virtual Boundary Torque and the Adaptive Control Authority, that allow the architecture to determine the best value of α.

Adaptive Virtual Boundary

This function is in charge of determining the region where the trainee can move. It is almost impossible that trainer and trainee share the same position at the same time (as factors like the precision of position sensors and involuntary movements made this an arduous task) it must exist a boundary zone where the user can move freely without disturbing the dominance.

To establish the boundary, first, it is deduced the maximum allowed distance B using equation 4.1 [START_REF] Shahbazi | A dual-user teleoperated system with virtual fixtures for robotic surgical training[END_REF]).

B = B 0 -k b • ln(α a + ε) (4.1)
where B 0 is the maximum allowed distance and α a is the Adaptive dominance factor. The use of the ln(• ) function allows the function to have a non-linear and smooth boundary. k b is a parameter, and ε is a minimal value that avoids zero cases for the logarithmic function. Equation 4.2 set the error between Master 1 and Master 2.

d θ m (t) = (θ m1 (t) -θ m2 (t)) 2 (4.2)
Where θ m1 (t) is the position of the Master 1 and θ m2 (t) is the position of the master 2. With the error between devices and the maximum allowed distance, it is possible the calculate the Virtual Boundary Torque.

Virtual Boundary Torque

This function is used when the trainee moves beyond the boundary, it will exert a virtual torque into the Adaptive Dominance factor in order to correct the trainee position. The torque is modeled by using the Hooke law as follows:

T v =    0, d θ m ≤ B -k v (θ m1 -θ m2 ) d θ m ≥ B (4.3)
Where k v is a virtual stiffness, and equation 4.3 evaluates wherever the AAA function injects the virtual torque, only if the position error does not overpass the maximum allowed distance the virtual torque remains zero.

Once the virtual torque is calculated, we can establish the adaptive dominance factor.

Adaptive Dominance Factor

This last function is the one in charge of changing the global dominance of the system. It is based on a Gaussian function of the Virtual Boundary Torque T v . The dominance is determined as follows:

α a = 1 -e - T 2 v 2•(T 0 ) 2 (4.4)
Where T 0 is a task parameter, given by the trainer based on the complexity of the selected training, the range of α a is from 0 to 1.

Issue with current AAA

The principal limitation of the AAA is the tuning process of four parameters (B 0 , T 0 , k v and k b ), which can result in a complicated process for the trainer. B 0 is used to establish the maximum distance allowed for the trainer to the trainee; this distance must be determined according to the experience of the trainee and the performed task. T 0 is a variable tied to the type of training. k v and k b are variables that must be set to get the desired behavior of the boundary and the virtual torque. Out of these four parameters, the trainer specifies B 0 and T 0 based on the type of training, the remaining ones are set, based on the configuration of the environment and devices. Because of this, the tuning process can be challenging for the trainer depending on the selected task and used haptic devices.

Proposed eAAA

The training of medical students is varied due to the numerous surgeries that doctors must realize with expertise. Previous adaptive dominance factors [START_REF] Shahbazi | A dual-user teleoperated system with virtual fixtures for robotic surgical training[END_REF], [START_REF] Liu | Dual-user Haptic Training System[END_REF]) base the change of the dominance on the analysis of the path generated by the trainer during the training session and applies a virtual fixture to limit the trainee movements. However, some training tasks can require a higher level of precision, or a novice student needs more freedom to start familiarizing herself/himself with the task.

To solve this, we need a new AAA function that can work by using only the maximum error, which is the error that indicates the system when a trainee has deviated enough from the desired position and gives the trainer the total dominance of the system. For the proposed function, we choose to implement geometric profiles that change the dominance in real-time. These profiles allow linear and non-linear behaviors for the dominance and are in function of the error determined by the euclidean norm (||e(t)||).

The profile selection is made by the trainer before the training session begins and is based on the difficulty of the task and the experience of the trainee. The only parameter that the trainer needs to provide for the profiles is the e max , which is the maximum allowed error between Master 1 and Master 2. This maximum error limits how much the trainee can be far from the trainer before α = 1.

The first four proposed profiles are a line, a concave, a convex, and a Bézier function, all of them shown in Figure 4-1.

Using the profiles in the calculus of an adjustable α value allows delivering a soft change during the training task, as long as e < e max . As the trainee directs the task, the dominance is adjusted, given more dominance to the trainer if it is necessary so he can apply corrections in real-time to the trainee's movements. On the other hand, when |e| ≥ e max , it is assumed that the error between Master 1 and Master 2 is big enough to allow the trainer to get the total dominance over the system to apply correctional movements.

More profiles can be implemented as well, but we consider that the concave, linear and convex profiles are enough for novice, intermediate and expert trainees, with the one dedicated case of the Bézier curve for daily practice.

Line profile

To determine the line profile shown in Figure 4-1a, the system first set the slope m as m = 1 e max (4.5) Then the dominance α is set as

α(e) =     
m * e(t) if e(t) < e max 1 otherwise (4.6) As the dominance between the trainer and the trainee changes directly proportional to the error among them, this profile can be used for intermediate trainees, where the minimal change of the trajectory is reflected as an opposition force exerted by the trainer, indicating them that they need to correct the trajectory.

Concave curve profile

To determine the concave curve profile from Figure 4-1b, the same slope from equation (4.5) is used.

Then, the dominance of α can be set as

α(e) =      (m * e(t)) 2 if e(t) < e max 1 otherwise (4.7)
In this profile, the dominance changes at a slower rate than the linear profile, which brings to the trainee more freedom of movement during the training before they can feel the correctional force. This profile can be used for novice trainees, introducing them to the simulator and the training task.

Convex curve profile

The convex profile of Figure 4-1c, first we determine the slope of a tangential function as

m t = tan (1)
e max (4.8) Then, the dominance α can be set as

α(e) =     
arctan(e(t) * m t (t)) if e(t) < e max 1 otherwise (4.9)

The convex slope reacts faster than all the profiles. This profile can be used for an expert trainee, where the movement is very restrictive due to the sudden increase of torque.

Bézier curve profile

The Bézier curve profile of Figure 4-1d is a particular case selected because it is a junction of the three previously proposed profiles. The Bézier one begins acting like a concave curve, followed by a linear profile and finishes with a convex curve. This enables us to provide as more freedom to move for small position errors, a more corrective force for an intermediary error, and a very restrictive correctional force for a higher error. We assume that this profile can be used for continuous training and practice,

where the trainees are familiarized with the task but do not have enough experience to face a linear or convex curve profile.

This Bézier curve was proposed by [START_REF] Beltran-Carbajal | Advances in Vibration Engineering and Structural Dynamics[END_REF], and it is used to give motors a soft change of velocity when they are controlled. This tenth-order polynomial curve is used because of the non-changing zone presented at the beginning and the end of the curve, allowing to give the trainee and the trainer an offset zone where both can move without disturbing the actual status of the dominance. This characteristic is very crucial since as mentioned before, it is a challenging task that trainers and trainees share the same position at the same time especially when our haptic devices have a nominal resolution of 55µm. Also, the polynomial allows generating a continuous curve during all the segments until e(t) = e max .

The dominance changes using the Bézier profile according to

α =     
b z e(t) < e max

Experimental validation

Using the eAAA algorithm, experimental validations to test the change of dominance were performed.

The purpose is to prove that the system's dominance is changed according to the student's performance, based on the selected profile without any stability issue.

Correctional force validation

First, we wanted to check that the proposed profiles offer different changes of dominance and a correctional force behavior under the same scenario. To prove this, we used our Slave device from the core setup of section 3.4 and the eESC architecture in the Cartesian approach.

For this experiment only, we implemented a perfect trainer and trainee, as it is impossible to replicate the same trajectory in both haptic devices with human users. These two perfect users are calculated values of trajectories introduced directly to the eESC architecture as a position value. The trajectory is set as

x(n t ) = r * sin(n t ) y(n t ) = r * cos(n t ) z(n t ) = r * sin( n t 2 )

(4.13) With n t = 2 * π * t t t (4.14)
Where t t > 0 and is the total time of the experiment and r the radius of the trajectory. The trajectory is a sloped circle used, so all the system axes are actuated during the test. The parameters of the experiment are t t = 25s, e max = 1cm and r = 6cm. This experiment was repeated four times with the same parameters by only changing the used profile. In the beginning, the perfect trainer and the trainee follow the same trajectory, but during 5 < t < 15s the perfect trainee deviates from the trajectory by a 10% of the trainer's position. Figure 4-2 shows the described trajectory.

When a deviation occurs, the correctional force is injected into the Master 2 device as an effort to correct the position. One can observe that the convex curve profile reacts faster than the others in the change of the dominance, followed by the linear, Bézier and the concave curve profiles. However, the correctional force F for the Bézier curve raises in a more consistent way which provides the trainee in a smooth and continuous increase of the correctional force. In the case of the concave Curve profile, which reacts the slowest, the correctional force also changes more abruptly, so the trainee can feel this like a more sudden change of the correctional force. In the case of the convex curve and Line profiles, both increase the correctional force in a more continuous change than the convex curve but in a more authoritative way than the Bézier curve.

Free motion

We tested the eAAA with real users. We chose the Bézier curve profile due to the smooth change of dominance and correctional force it offers. We set e max = 3mm, and used the core setup of section 3.4 and the eESC in Cartesian approach. The experiment was performed in free motion show the resulting position tracking and correctional force.

Master 2 was the leader (α = 0) at the beginning. The trajectory was performed by the trainee until t = 7s when the Master 1 started to correct the trainee's trajectory voluntarily. As the position between both users changed progressively, the dominance of the system did as well, resulting in the 120 remained so until the trainee corrected the position of her/his device, to equal the trainer's one as of t = 17s. Then the system returned the entire dominance to the trainee, and the trajectory ended.

Fig. 4-4 shows the positions of the devices. From 0 < t < 9 and 18 < t < 24, the RMS errors are 1.66mm and 1.75mm for M1-M2, in the case of M2-S the RMS are 1.86mm and 2.42mm for M2-S.

As the position difference between trainer and trainee for these two periods of time is negligible, the dominance does not change significantly α → 0.

When 9 < t < 18 the trainee deviated from the trainer's position. As the position of Master 2 differed from Master 1, the value of α raised to 1. As the dominance changed the system exerted a correctional force (in the three axes) on the trainee's device, as visible in Fig. 45.

Adaptive dominance validation

Albeit the proposed AAA methods are introduced to improve the trainee learning by adapting the dominance based on their performance, there is still no method or study that proves this hypothesis.

Furthermore, there is no way to test and compare the different existing AAA methods. Because of this, it is necessary to establish a test bench to analyze the advances of the trainee using an AAA method vs a just training.

Exercise selection

To validate the improvements of an AAA method vs just training, we proposed a series of real exercises that were performed by test subjects. Two different groups were made and instructed to replicate the same exercises, with the only difference of how they were instructed to do it. The exercises consist of real tasks rather than virtual ones, which made them easy to perform. The principal drawback of the attempts is the lower repeatability, as users cannot repeat the process the same way, which complicates the analysis of data.

To choose the exercises implemented in the study, we first brainstormed possible options that could be performed by the trainee following the instructions of the trainer. The exercise must fulfill two principal characteristics to be considered: the exercise must provide useful force feedback to the user, so she/he can feel like she/he interacts directly with the environment. The exercise must give the sensation to trainees that they are actually modifying the environment and not just touching it. Based on these considerations, eight exercises were proposed:

Surgical game: based on the popular board game, Operation, the trainee tries to recover a piece of plastic, representing and organ, by using a gripper in the slave device in the fastest way possible.

The trainee must avoid touching the edges of a hole containing an organ.

Tie a knot: the trainee tries to complete a knot using the slave's tool in the less time possible.

Dictate Dimensions: the trainer receives instructions to draw a 3D object.

Cutting task: the trainee cut an object following the instructions of the trainer.

Following a path: the trainee must guide a hook from point A to B, following the profile of the winding metal path. The hook must not touch the path, or a sound alarm will be activated.

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Building a Jenga: based on the popular board game, Jenga, the trainee must move bricks from a blocky tower, avoiding collapsing it.

Writing: the trainee tries to write non-Latin characters instructed by the trainer. The trainee must replicate the trainer's character as close as possible.

Stiching: the trainee must follow a given pattern from the trainer in the fastest way possible.

To choose the best-suited exercise for the study we quantitative qualified them by analyzing each exercise regarding the general constraints of the simulator like general feasibility and motion capabilities. Table 4.1 shows the score for general constraints and feasibility, table 4.2 for the motion capabilities and interaction responses. The score of both tables is summarized in Table 4.3.

General constraint General feasibility Exercise

Slave's Workspace Environment <3N Force Total Performable Expert availability Total Surgical game

1 1 1 3 1 -1 0 Tieing a knot 1 -1 1 1 1 1 2 Dictating dimensions 1 1 1 3 1 -1 0 Cutting task 1 1 -1 1 1 -1 0 Following a path 1 1 1 3 1 -1 0 Building Jenga 1 1 1 3 1 -1 0 Writing 1 1 -1 1 1 1 2 Stitching 1 0 1 2 1 1 2
Table 4.1 -General Constraint and General Feasibility criteria for proposed exercises For General constraints, the criteria are slave's workspace, which determines if the exercise can be done inside the physical limitations of the slave. The environment determines if the exercise interacts directly with an object that can be modified or displaced to get haptic force feedback. "<3N Force" determines if the exercise is suitable for a maximum force of 3N, which is the top force that the Slave can offer. For general feasibility, the criteria is "Performable" which indicates if the exercise can be done with the current setup, and expert availability, which determines if a user who is considered an expert in the exercise, can be used to work as the trainer.

In the case of Motion and Interaction, the two criteria are "Quantifiable", which means if the metrics of the exercise can be measured, and "Improves" which determines if the user can improve directly from the exercise.

From the analysis of table 4.3, the best score exercises are "Writing and Stitching". However, after an analysis of the setup from section 3. that was simpler to fit better with the slave's workspace and actuators' limitations. Table 4.4 shows the criteria of "General constraints" and "General feasibility" for the new set of exercises. The exercises are not explained as the previous ones because of their simpler nature and self-explanatory names.

General constraint General feasibility Exercise

Slave's Workspace Environment <3N Force Total Performable Expert availability Total Push an object (certain distance)

1 1 1 3 1 -1 0 Pull a spring (certain distance) 1 1 1 3 1 -1 0 Pick up something to a point 1 1 1 3 1 -1 0 Scratch an object 1 1 1 3 1 -1 0
Table 4.4 -General Constraint and General Feasibility criteria for proposed exercises: Second wave Table 4.5 shows the criteria of Motion and Interaction for the second wave of the proposed exercises.

Finally table 4.6 shows the final score for the exercises proposed in the second wave.

The best scored exercises were "Push an object" and "Pull a spring". To simplify the analysis of data and discussion of the results, the push exercise is focused in the localization of the slave's tool in the environment, while the pull exercise focuses on the replication of the force feedback from the

Validation

Test bench setup First, we established to use the base core test bench of section 3.4. In this case, each participant is a trainee, and the teacher is one of our associates that gives the participants all the necessary instructions and explains how to perform. Due to the simpler nature of the exercises, an expert trainer is not required for both exercises. A wall divides the trainee and the trainer spaces to avoid direct interaction.

The trainer has direct visual feedback of the slave while the trainee receives it from a stream of video on their screen. The slave interacts with two elements, a block that is used to evaluate the push, and a spring to evaluate the pull. Figure 4-6 shows the configuration of the setup used.

The push exercise's objective is to guide the block over a slope until a certain distance to evaluate the dexterity of a trainee during the location in the Cartesian space. The trainer guided the trainee into pushing the block over the slope and stopped at a marked landmark. When the block is returned to the original position, the trainer gives the dominance to the trainee. The trainee must replicate the exercise by stopping as close as possible of the landmark.

The pull exercise's objective is to instruct the trainee on how to pull a spring until a certain distance and angle to evaluate the dexterity and kinesthetic memory of the trainee. The trainer taught the trainee how to pull the spring until a specified landmark and then asked him to replicate the exercise as close For the test, 18 subjects were contacted by one of our associates. The subjects consist of a varied group from different nationalities, ethnicity, and languages (although the test was directed in English).

They were divided into two different groups for comparison. Group 1 (AAA group) and Group 2 (Lead group). Group 1 served to validate if the AAA function improves the trainee performance and learning.

We used the eAAA with a Bézier profile. The process consisted of apprenticeships (demonstration mode), practiced with the trainer (guidance mode) and then evaluated (evaluation mode). For Group 2, the group who was used to compare results vs Group 1, and their process was taught (demonstration mode) and then evaluated (evaluation mode).

All participants were cited to the Laboratory Ampère with a lapse of 30 minutes between participants, of which 15 minutes were for performing the exercises, with 5 minutes to respond to a survey (Appendix D) and 5 minutes to attend unexpected problems that could occur during the test. Participants were introduced to the test bench and the haptic devices. They were explained about how the simulator works and the final proposal of the study. Also, they were indicated how to use the user interface to compare the same position and force. Depending on the group, participants, performed the exercise in the following way.

For Group 1:

• The trainer carried out the push and pull exercise three times in demonstration mode.

• The trainer changed the dominance to guided mode

• The trainer replicated the exercise three more times and was corrected by the Trainer if necessary.

• The trainer changed the dominance to evaluation mode

• The trainee performed three times more the exercises, but without the intervention of the Trainer For Group 2:

• The trainer carried out the push and pull exercise 3 times in demonstration mode.

• The trainer changed the dominance to evaluation mode

• The trainee performed six times more the exercises, but without the intervention of the Trainer It should be noticed that for evaluation mode, for both groups, the user interfaces disabled the force indicators and the position of the Master devices. This is to prevent trainees from replicating the force based on the indications from the screen rather than on their own kinesthetic memory.

Results

For recorded data, we use the position values provided by OpenHaptics and the calculated force of the IPC controls, because of this, the computation force from the IPCs can rise over 3N, which is the saturation force of the Geomagic Touch.

With the recorded data from the tests, we determine the difference between trainee and the landmark (∆ d ), for the push exercise, and the force and angle applied in the pull exercise. Table 4.7

summarizes the position and force difference for push and pull in Group 1 and 2. It should be noted that participants 10 and 16 were eliminated because of inconsistency in their results, specifically in the θ f . The survey and the answers of the participants are detailed in Appendix D.

Group 1 Push

Pull Group 2 Push Pull Participant ∆ d (mm) F(N) θ f ∘ Participant ∆ d (mm) F(N) θ f ∘ 1
For the push exercise, the results of ∆ d for group 1 and 2, show only a variation of 4% between them, which (considering the low accuracy that trainees have due to their inexperience with haptic systems and the performed task) can be considered as negligible. So, from these tests, we conclude that by the moment there is no significant improvement using an AAA method.

In the case of the pull exercise, we see a variation of 268% for Group 1 and 228% for Group 2 in the force exerted. It appears that Group 2 has better performance overall. However, due to the high deviation from the desired force of 1N, the results for the two groups do not permit us to conclude that the eAAA improves the learning of the trainee. Finally, for the θ f , the variation is 21% for Group 1 and 23% for Group 2. The slight difference of 2% between both Groups also does not allow us to conclude an improvement or drawback of using an AAA method.

Results and discussion

The Bézier curve offers a starting point to prove the eAAA, but it can not establish that the function is the optimal one. More test needs to be made, where the Bézier polynomial is compared versus other functions to determine a more qualitative value.

We still have to test these four profiles with real trainees to determine which of those perform better in different approaches of dexterity. Unfortunately, we still can not determine if eAAA performs better than the other methods proposed in the bibliography [START_REF] Shahbazi | A dual-user teleoperated system with virtual fixtures for robotic surgical training[END_REF] and Liu et al. [2015]) as the parameters of those changes the behavior of the dominance. This can be solved by making a series of experiments with trainers and trainees, where the evolution of several test groups are analyzed to determine which method and profile for our case allows the student to improve faster.

We tried to validate the learning improvement brought by eAAA. Unfortunately, our tests do not offer conclusive results, as the variations between both test groups are almost insignificant. We consider that due to the low number of repetitions and the lack of time, trainees do not adapt and get used to the task. As remarked by [START_REF] Vaughan | A review of virtual reality based training simulators for orthopaedic surgery[END_REF], in a medical procedure like epidural insertion, it is required at least eighty repetitions to consider the trainee an experienced student. Although the task does not require so much training in our test, it provides a starting point of how much training is needed to notice a difference in learning improvements. For future work and correct validation, two long-term study groups are required to corroborate the potential improvements and drawbacks of using an AAA.

Our proposed testbed for validation of the AAA function must be improved to include more sophisticated tasks to get significant results about learning improvement, as the push and pull experiments only provide simple actions that are easy to master. For more complicated tasks, we need to provide wrist force feedback to the system. By changing the haptic device into a 6 actuated DoF, like the Virtuose 6D Desktop, and implementing the eESC architecture onto all the joints.

For a more faithful validation of eAAA and the ESC architecture, experiments including a test group should be performed on a real surgical hands-on training to be able to determine which one is the best between single-user, dual-user, and manual training.

Chapter 5

Expanding eESC to m -1 trainees

Problem

Based on the literature review from section 2.4.5, we determined that none of the proposed architecture allows several trainees to be instructed by one trainer at the same time. By making a simulator that can perform this, it is possible to reduce the time that takes every trainee to get instructed in Demonstration mode. This also allows students to present their advances to several trainers at the same time (in evaluation mode) and get feedback from all of them. The main problem with a multi-trainee architecture is to find a correct configuration that enables this.

The difficulty of adapting eESC to a multi-trainee approach is the proposal of a new set of MIMO 1 nodes that ensures the stability and transparency of the system.

Expansion

In a dual-user scheme, it is supposed that all the devices are linked to each other, but as it is stated in section 3.1, ESC only connects Master devices with the Slave. Leaving the Slave device as an intermediary point between Master 1 and Master 2 has the drawback of a potential accumulative error between them, but this also opens the possibility of expanding the architecture to more users.

Expanding the eESC architecture to an m -1 trainee system allows for the development of new simulators that support several trainees, receiving the same guidance at the same time. The main perspective is to provide one device for one trainer (Master 1) and m -1 devices for the m -1 trainees 1 Multiple Input Multiple Output 131 is the preservation of the transparency matrix presented in Eq. (3.11). To achieve this, the matrix must be skew-symmetric while adding the m input forces and output velocities from the master devices.

The expansion of node D s is set as:

           θs1 θs2 . . . θsn T rs            =            0 0 • • • 0 β 1 0 0 • • • 0 1 -β 2 . . . . . . . . . . . . . . . 0 0 • • • 0 1 -β 2 -β 1 β 2 -1 • • • β 2 -1 0                       T s1 T s2 . . . T sm θrs            (5.1)
where D s remains a skew-symmetric matrix and thus preserving the transparency property shown in section 3.2.2. θs1...n are the angular velocity outputs from the Slave towards all master IPC respectively, T s1...n are the torques transmitted by each master IPC to the slave IPC, and T rs is the torque transmitted, to the slave IPC, taking into account the dominance factor.

In the new architecture dealing with m -1 trainees devices, the factor α cannot establish the dominance for all the trainee devices at once. As α indicates the grade of interaction which coexists between the trainer and the trainees, we have to consider it as the global dominance factor. It is desirable that only one trainee, the active trainee, interacts at the same time with the trainer and the slave in evaluation and guidance mode, to avoid possible interposition input problems. The remaining trainee devices can only receive haptic feedback from the Slave.

The selection of the active trainee is manually established in real-time by the trainer. To provide this option a new trainee selection mechanism has been introduced in conjunction with α:

∆ ∈ [2, m].
This discrete variable establishes which of the trainee devices interacts with the Slave and the trainer. ∆ has been split in (m -1) boolean variables δ i whose value is Kronocker delta provided by Eq.

(5.2), in order to integrate them in each D mi node (initially D m2 in the initial dual-user architecture), with i ∈ [2, m].

δ i =      1 ∆ = i 0 otherwise (5.2)
When δ i = 0 the i master device receives haptic feedback, and it is positioned according to the slave device, whatever value of α. When δ i = 1, i the master device has a dominance established by With D s set, new D m2 to D mn nodes must be created in parallel. Equation 5.3 shows the skewsymmetric matrices established for the D mi nodes.

     θri T si T s f i      =      0 f s1 f s2 -f s1 0 0 -f s2 0 0           T ri θsi θsfi      (5.3)
where θ s f i is the angular velocity injected by the MFS2 i into the trainee IPC i, T s f i is the torque provided by the trainee IPC i to the MFS i, and θ ri is the angular velocity transmitted to the trainee IPC i, affected by the dominance computation on θ si and θ s f i . f s1 and f s2 are used to simplify the matrix notation, and their values are set by equations 5.4 and 5.5

f s1 = (1 -α)δ n (5.4) f s2 = 1 + δ i (α -1) (5.5)
Each input/output of torque and angular velocity is applied consecutively in the expanded matrix D s of equation 5.1.

The passivity (and so its stability) of the whole system is derived from the original architecture where a Time-Domain Passivity Observer monitored the energy generated by all the MFS in order to avoid any extra energy injection which may compromise the passivity and destabilize the system. Equation 5.6 shows how the energy generated by each MSF E pi is computed.

E pi (t) = t 0 αδ i T ri θrs dt (5.6)
The passivity observer uses E pi in equation 5.7 to determine the real-time value of θs f i , to ensure the preservation of passivity and the haptic feedback as long as the passivity is not compromised.

θs f i =      θ rs (t) if E pi (t) ≤ 0 0 otherwise (5.7)
5.3 Experimental results

New setup

To validate the extension of eESC into a multi-trainee approach, experiments were performed. For this, it was necessary to add more haptic devices into the core test bench, but as we only have access to three real devices, one virtual haptic device based on the model shown in the appendix A.1.4 was created, and it is used as the Master 1 device.

Indeed, the user who is manipulating (for whom δ i = 1) operates the Slave which follows her/his gestures. The Slave feeds back the interaction force between its tip and its environment. The other user devices reproduce the slave motion to guide these users. When a slave-environment interaction takes place, the follower users are asked to move their device to the same position as the leader device in order to feel the same force feedback and learn how to dose this force in a particular training context.

Note that in all the plots, the notation (v) next to the device name represents the use of the virtual device.

Free motion

This experiment was performed to validate the position tracking between all devices, in free motion, and whatever value of the dominance factor α and the trainee selector ∆. All the follower devices must follow the leader's path, which is the one who has major dominance. For this experiment, we put the system in evaluation mode (α = 0). During the task, the value of ∆ is changed from 1 to 2 to verify that the change of dominance between trainee devices does not compromise the tracking task.

The chosen trajectory was a helical path performed by the trainee as consistent as possible, which allows us to demonstrate the position tracking in all the degrees of freedom. To evaluate the performance of the position tracking, the RMS tracking errors between the Cartesian positions of the devices were computed. Table 5.1 shows these values when M2 and M3 are the respective leaders. This table clearly shows that the RMS errors between the leader device and the other devices are smaller than between other devices. For instance, the error between M2 and Slave (when M2 is the leader for t ≤ 5 s) is smaller than the one between M2 and the Slave (S) when it is a follower (t > 5 s).

The position tracking errors between the slave and follower devices depend on the reaction of the users which may voluntarily resist the guidance of their device and artificially raise this error. 4.5 3.5 The Cartesian RMS errors between each leader and the Slave are around 4 mm. With this kind of off-the-shelf low bracket haptic device, we estimate that this is a good result.

Force tracking

Once position tracking has been validated, we checked that the force tracking was accurate. This test was performed similarly to the one in section 3.5.3, with ∆ changing from 1 to 2 during the task to prove the torque tracking of all devices. In the beginning, ∆ = 1 and Master 2 controls the Slave which collides with a surface located at x = 9cm. At this moment, every follower device is guided up to the position of the wall. In order to feel the same force feedback as the leader user, follower users are asked to position their device in the same position as the leader master (displayed to each follower on

Conclusion

The inherited configuration of the original ESC architecture, allows eESC to be expanded into a multi trainee approach without compromising the passivity of the system. With this architecture, it is possible to perform parallel training (in demonstration mode) between the medical students, as a trainer could teach m trainees, where the only limit is the number of available haptic devices. The trainer must determine the trainee that shares the dominance with him, while the rest only gets haptic feedback.

This system can also be implemented in evaluation mode, where a student can perform a test to several medical evaluators and get qualitative feedback from them.

In the case of the guidance mode, the trainer can also establish with which trainee he/she wants to share the dominance. For example, during a session, the trainer can correct the trainee in real-time and

give the other trainees a caution of what to avoid before committing the mistake. On the other hand, the trainees can train with their classmates, under the supervision of the trainer. Yet, it is not proved that this configuration is effective in terms of training efficiency. More tests in this matter could help determine this.

The use of computed based simulators for medical training is a recent paradigm for teaching complicate procedures. They present advantages over classical methods like mannequins and corpses due to its ability to repeat a process several times without getting short in supplies and the ability to get precise information about the performance of trainees for objective assessment purposes. Nowadays, there are several simulators on the market, but the vast majority do not provide a dual-user approach.

With a dual-user approach, students can directly interact with the expert, or trainer, and with the environment. The trainer can lead the trainee and show her/him how to perform the task while the latter receives haptic feedback in addition to the trainer's commentaries and suggestions. The architectures exposed in section 2.4.5 do not satisfy the requirements, so we improved the ESC architecture introduced by Fei Liu during his Ph.D.

The first modification to the ESC architecture was the expansion into an n-DoF architecture. The expansion was performed by duplicating ESC for each degree of freedom. We proposed a new method to calculate the IPC controller based on experimental results.

The transparency analysis of Chapter 3 demonstrates that the Impedance-Admittance IPC control used in ESC is not fully transparent in low frequency. The control always exerts a sensation of inertia on the user action, however, it is possible to reduce this inertia by selecting a lower damping factor, but with the cost of stability. The experimental results prove that the architecture can perform position and force tracking, and the in Cartesian space verification shows that the system can overcome the limitation of using kinematically identical haptic devices.

The original ESC architecture utilizes a dominance factor α to determine the dominance of the slave according to the trainer and the trainee. This dominance allows the three possible scenarios of training: Demonstration, Guidance, and Evaluation. This dominance factor can also be used with an Adaptive Authority Adjusting method that provides a change of dominance in real-time according to the trainee's performance. Although ESC provides an AAA function, it uses four different parameters, which complicates the tuning process for the trainer. To solve this, we proposed a new method based on four profiles. The proposed profiles (Linear, Concave, Convex, and Bézier) allow a smooth change of the dominance according to the performance of the trainee. The profiles and its parameter e max can be easily parameterized in real-time by the trainer. Unfortunately, our user feedback tests do not offer conclusive results to consider that the eAAA improves trainee learning. However, our test bench can be implemented for future work with long-term test subjects to validate this hypothesis.

The eESC architecture was expanded to work with multiple users at the same time. This allows m trainees to interact directly with one trainer. The dominance was upgraded by introducing a selection trainee (∆) variable. The connection nodes of the architecture have been reworked to allow easy expansion to n master devices. Our test with two real trainees, one virtual trainee, and one trainer show that the system can perform position tracking and force tracking in all the devices. This new architecture opens the way to implementing parallel teaching, where a single trainer instructs m trainees in real-time.

The expanded ESC architecture can also be used for other training areas as control of manipulators used in dangerous environments like explosives, nuclear or biological environments, hazardous material manipulation, manual arts, etc.

Resuming from and retaking from the objectives and use requirements we developed an architecture that can:

• be operated by m trainees at the same time (R1 and O2)

• provide several training modes which vary the dominance between trainer and trainees (R2, R3 and O3). And also allows the trainer to select a trainee leader (R4)

• be used with different haptic devices, regardless of its kinematic configuration in n-DoF (R5, R7, O1, and O5)

• offer position and force tracking while ensuring the systems' stability (R5, R6, R8, O4, and

O6)

For future work, we propose the following objectives:

• To enable teleoperation with the eESC architecture. By allowing the architecture to work in a remote training approach, the trainee can practice in any place regardless of the localization of the trainer. This also gives the possibility of training with costly medical equipment, like assisted-surgery robots, that can not be displaced from its location. With a remote training approach, students can use this equipment from their university. To achieve this several Time-Varying delay techniques like the Smith predictor [START_REF] Uddin | Annual Reviews in Control Predictive control approaches for bilateral teleoperation R[END_REF]), Adaptative-control under delay [START_REF] Ching | Internet-Based Bilateral Teleoperation Based on Wave Variable With Adaptive Predictor and Direct Drift Control[END_REF]) or scattering variables [START_REF] Stramigioli | Geometric scattering in robotic telemanipulation[END_REF]). A study comparative between these methods must be made to determine which one has better performances in training sessions.

• To validate the didactic interest of the dual user training system. For this, it is needed a more detailed study with long-term training sessions and more significant and real tasks, whose difficulty can be changed for evaluated trainee improvement. Also, this study can provide information about how immersive the simulator is, and how well the acquired skills are extrapolated into a real event. This also requires a change of the haptic devices, because of the limitations of the Geomagic Touch 3D, tasks that require the use of mechanical wrist can not be implemented.

As it is necessary to prove that the architecture improves the trainee skills in complex tasks, the study must be a long-term one and continuously evaluate the students progress in comparison with students using classical approaches and other simulators.

• To reduce the felt inertia to the user. Based on the transparent study, to reduce the felt inertia added by the damping factor, it is required to propose a modification to the Impedance-Admittance IPC without compromising the passivity of the system. This can be done by recalculating eESC architecture and by finding a mathematical approach that allows to reduce the damping effect without compromising the passivity, or by adding in parallel a component that mitigates the inertia during low-frequency.

Part IV Appendix 147

The Jacobian is as a 6×n matrix where n is the number of Dof that the manipulator has it is set as:

J = J v J w (A.7)
Where J v and J w are 3 x n matrix, denoting the linear and angular velocity of the end effector respectively.

The Jacobian matrix for a Geomagic 3D touch is determined as:

J(θ ) =              
l 1 -l 1 sin(θ 1 )sin(θ 2 ) sin(θ 2 )sin(l 2 + l 2 sin(θ 2 )) 0 l 1 cos(θ 2 ) l 1 (cos(θ 1 )cos(θ 2 ))

0 -l 1 cos(θ 1 )sin(θ 2 ) cos(θ 1 )(l 2 + l 1 sin(θ 2 )) 0 0 -cos(θ 2 )

1 0 0 0 0 sin(θ 1 )               (A.8)
And the linear velocity of the system is given by:

     ẋ ẏ ż      = [J v ]      θ1 θ2 θ3      (A.9)
To determine the desired torque applied to the actuators given desired force in the end-effector, we use:

τ = J T v × F (A.10)
where τ is the 3 x 1 vector torque applied to the manipulator actuators and F is the 3×1 vector force. By isolating F we could also get the force that is applied by the end effector : .11) This last expression determines the forces applied by the Geomagic Touch without the need of a torque sensor. However the use of this expression is limited by the capacity of the actuators. If the haptic device gets saturated, this force signal will further to increase, even if in reality such force is not applied it.

F = J -1 v T × τ (A

A.1.4 Lagrangian formulation

The Lagrangian formulation can be used to get the dynamic model of the Geomagic Touch 3d. The Lagrangian formulation is:

d dt ∂ L ∂ θi - ∂ L ∂ θ i = τ i i = 1,

C.1.2 Passivity observer

A passivity observer is a function which helps determine if a system remains passive or not during its operation. The passivity observer can be instrumented by reading the forces and velocities of the system, which can be approximated or sensed. Equation C.1 defines the passivity observer.

E obsv (n) = n Σ k=1 [ f 1 (k)v 1 (k) + ... + f M (k)v M (k)] (C.1)
So, in the passivity observer if E obsv ≥ 0 for every time n, the system is dissipating energy, thus the system is passive. On the other hand, if E obsv < 0 this means that the system is active, and therefore generating energy. Depuis les débuts de la médecine, les étudiants en médecine s'entraînent sur des simulateurs (animaux, cadavres, mannequins) afin d'acquérir puis enrichir leurs compétences médicales, dont notamment celles nécessitant des gestes précis. C'est un moyen de faire des erreurs sans blesser de patient. Pourtant, ces simulateurs manquent souvent de réalisme, s'usent et finissent par coûter cher sur le long terme. Depuis plusieurs décennies, les technologies de simulation informatique ont enrichi le panel des simulateurs médicaux, et aujourd'hui les technologies haptiques offrent désormais un réalisme encore accru. Cependant, ces simulateurs haptiques n'intègrent pas le formateur dans la simulation, ce qui empêche de former les apprenant sur des gestes impliquant à la fois des trajectoires et des interactions outil/environnement où les efforts doivent être subtilement dosés et donc maîtrisés. Dans les travaux de recherche récents, des architectures dual-user (à deux utilisateurs) de simulateurs dédiés à la formation au geste ont été proposés ces dernières années, mais l'étude bibliographique proposée dans ce document démontre qu'aucun d'entre eux n'a été conçu dans ce sens : un retour haptique est proposé à l'apprenant mais le formateur n'a pas la possibilité de montrer simultanément la position des outils et les efforts à appliquer dessus. Récemment M. Fei Liu a conçu une solution à ce besoin (l'architecture dual-user ESC -Energy Shared Control), fondée sur une approche énergétique garantissant la passivité et donc la stabilité du), utilisable avec un dispositif esclave réel ou virtuel, et intégrant un mécanisme d'autorité adaptative (Adaptive Authority Adjustment -AAA) permettant au formateur de reprendre la main instantanément à partir du moment où l'apprenant dévie de la trajectoire désirée par le formateur. Cependant, cette solution se limitait à un seul degré de liberté et ce mécanisme d'autorité adaptative nécessitait de régler laborieusement trois paramètres peu intuitifs. Les solutions proposées dans ce mémoire poursuivent donc les travaux de M. Liu en améliorant l'architecture ESC afin de l'étendre à des dispositifs à plusieurs degrés de liberté, ayant potentiellement des cinématiques différentes (surtout le dispositif esclave par rapport aux dispositifs maîtres) et à plusieurs apprenants simultanés. Une amélioration de la fonction AAA est proposée ainsi que des profils d'utilisation dépendant du niveau de l'apprenant. Une première série de retours d'usage a été réalisée afin de déterminer l'intérêt pédagogique de cette fonction. Les résultats ne permettant pas de conclure, des préconisations sont proposées pour une deuxième série.

MOTS-CLÉS

1

 1 Problem definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 The problem of non-guided training . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Main use case and main requirements . . . . . . . . . . . . . . . . . . . . . 1.2 Objectives of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Document Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 State of art 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Haptic devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Haptics device classification . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Advantages and disavantages . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Medical haptic training simulators . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Simulator control architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Multilateral configurations for control architectures . . . . . . . . . . . . . . 2.4.2 Dual user scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Dominance sharing in a training context . . . . . . . . . . . . . . . . . . . . 2.4.4 Adaptive dominance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.5 Bibliographical study of control architectures for haptic simulators . . . . . . 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III Contributions 3 Expanding to n-DoF (eESC architecture) 3.1 1-DoF ESC architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Intrinsically Passive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Impedance-Admittance IPC . . . . . . . . . . . . . . . . . . . . . . . . . . ii List of Tables2.1 MM/SS architectures comparison table . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 MM/SS architectures comparison table . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Analysis of the hybrid matrix in Low and High Frequency . . . . . . . . . . . . . . 3.2 IPCs' parameters for simulation validation: Cartesian vs Articular . . . . . . . . . .3.3 Geomagic 3D Touch specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 IPCs' parameters for Articular approach . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Haptic Device's specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 IPCs' parameters for Cartesian approach . . . . . . . . . . . . . . . . . . . . . . . . 4.1 General Constraint and General Feasibility criteria for proposed exercises . . . . . . 4.2 Motion and Interaction criteria for proposed exercises . . . . . . . . . . . . . . . . . 4.3 Final score for proposed exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 General Constraint and General Feasibility criteria for proposed exercises: Second wave125 4.5 Motion and Interaction criteria for proposed exercises: Second Wave . . . . . . . . . 4.6 Final score for proposed exercises: Second Wave . . . . . . . . . . . . . . . . . . . 4.7 Push and Pull results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 RMS error in free motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D.1 Participants' answers to the survey . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1 - 1 -

 11 Figure 1-1 -Simulateurs type mannequins

Figure 1 - 2 -

 12 Figure 1-2 -Simulateur haptique pour la laparoscopie :Lapsim(SurgicalScience)

Figure 1 - 3 -

 13 Figure 1-3 -Simulateur haptique en réalité augmentée : Immersive touch (University of Illinois, USA)

DFigure 1 - 4 -Figure 1 - 5 -

 1415 Figure 1-4 -Simulateurs mono et multi apprenants

Fei

  Liu entre 2013 et 2016 dans le cadre de son doctorat, qui a mené à la conception de l'architecture Energy Shared Control (ESC). ESC utilise des contrôleurs de type Intrinsically Passive Controllers (IPC) (détaillés en section 3.2) pour le contrôle compliant des interfaces et du robot. Elle est composée d'interconnexions passives afin d'assurer la passivité de l'ensemble et donc sa stabilité (des détails sur cet aspect sont disponibles en annexe C). Des expérimentations ont montré une bonne transparence en terme de suivi en position et en efforts lors des interactions, sur une architecture à un seul degré de liberté. Les principaux avantages d'ESC et les exigences auxquelles il répond sont : Advantages • ESC intègre le réglage dynamique de la dominance entre les utilisateurs permettant de travailler dans les modes démonstration/évaluation ainsi que de la faire évoluer de manière adaptative (R2) ; • ESC propose une fonction de dominance adaptative (Adaptive Authority Adjusting AAA) ajustant la dominance entre l'apprenant et le formateur en fonction des performances de l'apprenant (R3) ; • Il transmet les efforts mesurés entre l'outil et son environnement aux utilisateurs (leader ainsi que follower(s) pour peu qu'il(s) positionne(nt) adéquatement son/leur interface haptique) (R5) ; • L'effort reproduit par les interfaces haptiques des utilisateurs est simplement et précisément celui d'interaction entre l'outil et son environnement (R6) ; • Intégrant un contrôleur de passitivité (Time Domain Passivity Control (TDPC), dont les détails sont fournis en annexe C), sa stabilité est garantie (R8). Les principaux inconvénients d'ESC sont: Disadvantages • ESC n'a été validé expérimentalement que pour un seul degré de liberté ; • La fonction AAA dépend de quatre variables difficiles à paramétrer par le formateur en fonction du niveau d'expertise de l'apprenant et de la précision désirée de la tâche. En tenant compte de ces inconvénients, les objectifs de mon doctorat sont : Objectives (O1) Étendre ESC à n degrés de liberté (ddl) (R7) ; (O2) Étendre le système à plusieurs apprenants sans remettre en cause l'architecture actuelle (R1), et fournir un mécanisme de sélection par le formateur de l'apprenant leader (R4) ; (O3) Améliorer la fonction AAA afin qu'elle soit plus facile d'utilisation (R3) ; (O4) S'assurer que la version étendue d'ESC conserve ses performances en terme de suivi de trajectoire et d'efforts (R5 et R6) ; (O5) Permettre l'usage d'interfaces et robots ayant des cinématiques différentes (R7) ; (O6) Garantir que la version étendue d'ESC préserve ses propriétés de stabilité (R8).

  Une interface haptique (ou dispositif haptique) est un système visant à reproduire la sensation de toucher d'un objet virtuel ou distant. Par exemple, ces dispositifs sont utilisés pour l'immersion dans des mondes virtuels impliquant la vision (généralement stéréoscopique), l'ouïe et le toucher (Figure 2-1).

Figure 2 - 1 -

 21 Figure 2-1 -Simulateur immersif pour apprendre les techniques d'arthroplastie du genou 1

Figure 2 - 2 -

 22 Figure 2-2 -Processus d'interactions entre l'utilisateur et un monde virtuel dans un simulateur

Figure 2 - 3 - 3 Figure 2 - 4 -

 23324 Figure 2-3 -Manette haptique pour jeux vidéo

Figure 2 - 5 -

 25 Figure 2-5 -Exemples d'interfaces haptiques pour chaque catégorie de rendu haptique

  Figure 2-6 -Suturehap: stitching simulator

Figure 2 -Figure 2 -

 22 Figure 2-7 -Simulateur de palpation

  -11 illustre ce schéma où ẋm et ẋs sont respectivement les vitesses du maître et de l'esclave. F h et F e sont les forces exercées par l'utilisateur sur le maître et l'environnement sur l'esclave. De plus, F c1 et F c2 sont les signaux de contrôle envoyés par le contrôleur au maître et à l'esclave.

Figure 2 -Figure 2 -Figure 2 -Figure 2 -

 2222 Figure 2-11 -Bilateral teleoperation scheme

Introduction

  l'espace cartésien(3 translations et 3 rotations). Les premières expérimentations ont mis en relief que le paramétrage optimal en terme de compromis stabilité/transparence des contrôleurs IPC diffère entre approche articulaire et cartésienne. Nous avons donc déterminé méthodiquement tous les paramètres des 3 contrôleurs IPC en tenant compte de l'amortissement désiré des mouvements afin d'éviter des trajectoires oscillantes ou trop amorties. Nous avons simulé les deux architectures d'après une trajectoire circulaire de référence dans l'espace cartésien afin de confirmer nos choix. Ceux-ci mènent à un suivi en position tout à fait acceptable avec l'approche articulaire et présentant des transitoires légèrement oscillants au début de la simulation puis un régime permanent stable et tout aussi acceptable pour l'approche cartésienne. Nous avons ensuite mis en place un banc d'essai utilisant 3 interface haptiques Geomagic 3D Touch interconnectées via un PC faisant tourner Matlab Simulink en temps réel. La bibliothèque de fonctions OpenHaptics a été enrichie afin de pouvoir communiquer simultanément avec les 3 interfaces. Un environnement d'interaction spécifique a été fabriqué en impression 3D afin de reproduire des trajectoire circulaires en relief permettant de mettre en valeur les propriétés de suivi en position et en effort (cf. figure3-17, page 91). La figure3-18, page 92, illustre l'organisation spatiale de ce banc et l'environnement proposé à chaque utilisateur. L'architecture informatique est synthétisée en figure 3-19, page 92. Une interface utilisateur 3D a été programmée grâce aux bibliothèques de fonction Chai3D afin d'aider l'utilisateur follower à se placer à la même position que le leader pour ressentir les bons efforts d'interaction (figure 3-21, page 94). Une méthodologie de réglage optimal des paramètres expérimentaux des contrôleurs IPC est proposée et appliquée. Les validations expérimentales ont consisté à réaliser des sessions incluant : • des passages entre modes de démonstration et évaluation afin de démontrer qu'un changement abrupt d'autorité n'induit pas d'instabilité ; • des trajectoires en régime libre afin de tester la qualité du suivi en position des différents dispositifs et le retour haptique qui ramène l'utilisateur follower sur la trajectoire du leader ; • des phases d'interaction outil/environnement afin d'évaluer la qualité du retour en effort du leader par rapport à l'effort outil/environnement et du follower quand il positionne adéquatement son interface haptique ; • des essais avec l'architecture articulaire et cartésienne (dans ce cas avec un dispositif esclave de type Virtuose 6-Desktop d'Haption). L'ensemble de ces tests expérimentaux montrent des performances acceptables étant donné que les interface haptiques utilisées sont plutôt de bas de gamme : erreur moyenne en position de 2, 5mm et erreur en effort sous le seuil de précision (moins d'1 N). Il est à noter que la mesure des efforts est réalisée d'après les données transmises par la bibliothèque de fonctions OpenHaptics, d'après une estimation fondée sur la consommations des moteurs de chaque articulation. Des essais avec de réels capteurs d'effort est à envisager pour une validation encore plus probante. Le chapitre 4 détaille les améliorations apportées à la fonction d'adaptation automatique de l'autorité entre utilisateurs. Nous rappelons le principe exposé par M. Fei LIU et nous avons proposé une nouvelle fonction pour déterminer α en fonction de la distance entre les interfaces des deux protagonistes. Quatre profils ont été proposés, sélectionnables par le formateur, afin d'offrir à l'apprenant plus ou moins de liberté d'action en mode évaluation. Cette évolution a été testée expérimentalement en régime libre et en interaction avec l'approche articulaire. Afin de valider l'intérêt de cette fonction du point de vue pédagogique, un retour d'usage a été mis en place. Des exercices concrets amenant à faire apprendre aux apprenants des trajectoires et des efforts ont été proposés et testés par 18 utilisateurs novices (seulement neuf d'entre eux avaient accès à cette fonction). Les conclusions de cette première étude n'ont malheureusement pas permis de déterminer de plus-value à cette fonction. Une discussion approfondie précise les facteurs ayant pu polluer les résultats expérimentaux afin de proposer un nouveau protocole expérimental pour une prochaine étude d'usage. La contribution suivante, détaillée au chapitre 5, a consisté à étendre le nombre d'apprenants pouvant utiliser simultanément le simulateur. Cette extension ouvre la voie à des démonstrations réalisées pour un public plus large avec les mêmes propriétés de formation aux trajectoires et aux efforts qu'en mono-apprenant. L'approche théorique est détaillée et implique d'ajouter un nouveau paramètre δ afin de sélectionner l'apprenant leader en mode évaluation. Les autres apprenants sont alors followers et peuvent suivre simultanément (et éventuellement évaluer) leur collègue toujours sur les mêmes critères de performance trajectoire/efforts. Le formateur a toujours les mêmes outils qu'en mono-apprenant : la possibilité d'évaluer la performance de l'apprenant sélectionné et de pouvoir corriger sa trajectoire (AAA). Des expérimentations ont validé cette approche. Faute d'un nombre suffisant d'interfaces haptiques, nous avons du simuler en logiciel l'une d'entre elles. Cependant, cela nous a permis de montrer qu'une réaction idéale d'un utilisateur mène à de très bonnes performances du système (en terme de positionnement précis par rapport au leader et donc de retour d'effort précis). Ce document s'achève par une conclusion synthétisant l'ensemble de ces contributions, leurs performances et leurs limites. Nous rappelons quels objectifs initiaux ont été remplis et nous proposons deux pistes d'améliorations pour la suite de ce projet. This work is introduced in a medical context as this one is particularly illustrative. Yet, it can apply to any other hands-on training context where the training of gestures including trajectories and interaction forces is necessary.

Figure 1 - 1 -

 11 Figure 1-1 -Mannequin based simulators

Figure 1 - 2 -

 12 Figure 1-2 -Commercial simulators

Fig 1 . 5 Figure 1 - 3 -

 1513 Fig 1.5 synthetizes this main use scenario with a Use Case Diagram following the SysML standard. This scenario leads to the following requirements for a training simulator enabling efficient motion and force haptic training. Based on the Case Diagram the requirements to fulfill are:

Figure 1 - 4 -

 14 Figure 1-4 -Guided training simulator: Case Diagram

  This new AAA function adapts the dominance based on the performance of the trainee compared in real-time to one of the trainers, for each task. We also carry out experimental tests with 20 subjects to determine if the AAA function improves training efficiency. . Finally, once the new architecture was able to work in 3-DoF (Articular and Cartesian space) and had a newly implemented AAA function, we decided to expand it into an m-trainee architecture. This expansion has the property to preserve the stability and transparency of the original ESC. This work has been presented at IROS 2019 conference[START_REF] Rodriguez | A multi-trainee architecture for haptic hands-on training[END_REF]).

Figure 2 - 1 -

 21 Figure 2-1 -FundammentalVR immersive simulator for Knee Arthroplasty 1

Figure 2 - 2 -

 22 Figure 2-2 -Haptic environment diagram

Figure 2 - 3 -

 23 Figure 2-3 -Videogame controller with force feedback motors

3 Figure 2 - 4 -

 324 Figure 2-4 -Serial and parallel mechanism haptic devices

Figure 2 - 5 -

 25 Figure 2-5 -Haptic Devices Classification

  Haptic training simulators are developed to aid medical students to practice procedures and repeat an endless amount of time without being short of supplies, unlike the one-time-use training solutions like corpses. There is a wide variety of medical simulators that cover various medicine areas (Escobar-Castillejos et al.[2016]). Some examples of these haptic simulators and their use are:Stitching simulators: used to teach the medical students how to stitch skin for healing wounds.It uses two 6-DoF haptic devices to guide a virtual needle and scissor. The haptic devices allow positioning and rotating the tool in the Cartesian space. This simulator uses finite element meshes to calculate the force feedback sent to the student. An example of these simulators is the Suturehap (Figure2-6) presented in[START_REF] Escobar-Castillejos | A Review of Simulators with Haptic Devices for Medical Training[END_REF]).

Figure 2 -

 2 Figure 2-6 -Suturehap: stitching simulator

Figure 2 -

 2 Figure 2-7 -Palpation simulator

Figure 2 -

 2 Figure 2-9 -NeuroTouch simulator: Endoscopy simulator

Figure 2 -

 2 Figure 2-10 -Lapsim R ○: Laparoscopy simulator

Figure 2 -Figure 2 -Figure 2 -Figure 2 -

 2222 Figure 2-11 -Haptic simulation architecture

Figure 2 -

 2 Figure 2-16 -Dual-user system

Figure 2 -

 2 Figure 2-17 -Dominance sharing training cases

  9.[START_REF] Shamaei | Design and evaluation of a trilateral sharedcontrol architecture for teleoperated training robots[END_REF]) developed a trilateral architecture for training purposes. They propose two dominance factors as an extension of the one introduced by[START_REF] Shahbazi | An expertise-oriented training framework for robotics-assisted surgery[END_REF]), but with fuzzy controllers (α and β , to establish Demonstration and Evaluation mode). The implementation of two dominance factor allow the system to separate and give priority of the force feedback from the environment and the trainer are applying to the trainee. The architecture requires six forces, and velocities as desired values. And, as it is remarked, the lack of the third mode, guidance or adaptative mode avoids that the architecture can be used for correct the trainee's movements in real-time (Does not fulfill R1 and R2).10.[START_REF] Huang | Auxiliary asymmetric dual-user shared control method for teleoperation[END_REF]) introduced an architecture that splits the dominance factor into three different ones, to enable a shared control of the slave with one user protecting the gestures of the second one. They took the opportunity of these two new variables to provide some adaptive behavior to help users in their tasks. They provided experimental results including two different master devices (a Phantom Omni, and an Omega (2-DOF)). Nevertheless, this architecture carries out the drawbacks of Shahbazi's solution (lack of obvious and efficient force training capability) (Does not fulfill R1, R2).

  of the architectures mentioned above work in a trilateral or dual-user scheme and have been tested for 1-DoF or more, but in planar robots, which does not fully illustrate the feasibility in 3D of haptic devices. Also, the use of trilateral architectures limits the requirement R1, due to the dif-ficulty of expanding the number of implied devices without a deeper redesign of the controllers and architecture structure.

  devices are used in computer-based simulators for medical training. They allow students to get kinesthesia training and aim at training on surgeries without touching a real patient while getting the same feeling.The current commercial simulators offer only one trainee consoles. Although they accomplish their objective, they lack a console that allows a trainer to monitor and correct the trainee movements in real-time.Researchers have proposed control architectures that allow a trainer and a trainee to interact directly during a training session. Some of these architectures allow position/force tracking and calculate the dominance of the slave device based on the trainee's performance. However, they have not been fully developed to work with n-DoF devices to allow several trainees to be instructed at the same time. With this in mind, we choose to expand the previously proposed ESC architecture into an n-DoF multi-trainee architecture.

Figure 3 - 1 -

 31 Figure 3-1 -ESC architecture dual-user haptic system for one dof

Figure 3 - 2 -Figure 3 - 3 -

 3233 Figure 3-2 -Impedance IPC controller for the master

-2 and 3 - 3 .

 33 Its diagram is shown in

Figure 3 - 4 -

 34 Figure 3-4 -Impedance-Admitance IPC for ESC

Figure 3 - 5 -

 35 Figure 3-5 -Teleoperator scheme

Figure 3 - 5 ( 3

 353 Figure 3-6 -ESC's IPC transparency diagram

Figure 3 - 7 -Figure 3 -

 373 Figure 3-7 -Bode diagram for the ESC hybrid matrix with different dampers

Figure 3 - 8 -

 38 Figure 3-8 -Comparison between differents architectures

Figure 3

 3 Figure 3-9 -Multiple DoF Articular eESC architecture

Figure 3 -

 3 Figure 3-10 -Multiple DoF Cartesian eESC architecture

Figure 3 -

 3 Figure 3-11 -Simulation diagram: Cartesian vs Articular approaches

Figure 3 -

 3 Figure 3-12 -Expansion n-DoF: simulated Articular approach trajectory

Figure 3 -

 3 Figure 3-14 -Expansion to n-DoF (Cartesian approach): simulated Articular position

Figure 3 -Figure 3 - 3 . 4 Figure 3 -

 33343 Figure 3-15 -Expansion to n-DoF (Cartesian approach): simulated position error

Figure 3 -

 3 Figure 3-18 -3D printed environment

Figure 3 -

 3 Figure 3-19 -Setup organization

Figure 3 -Figure 3 -

 33  shows the connection framework for a better comprehension of the communication between the ESC architecture and the haptic devices. In this case, the only shared values are the1 An executable file that Matlab uses to perform the process with high priority in the Operative System environment

Figure 3 -

 3 Figure 3-21 -Framework layer hierarchy with the new user interface

  Figure 3-22 shows a screenshot of the resulting user interface.

Figure 3 -

 3 Figure 3-22 -Chai3D user interface

Figure 3 -

 3 Figure 3-23 -Determining R f in X axis with a Geomagic 3D Touch

Figure 3 -

 3 Figure 3-25 shows the Articular positions of the three actuated joints. The error of all the trajectory between Master 1-Master 2 (M1-M2), Master 1-Slave (M1-S), and Master 2-Slave (Slave) are shown in Figure 3-27. One can observe that the precision is the best for θ 1 (tracking error of 17.10 -3 rad RMS between Master 1 and slave when t < 5 s) and the worst for θ 2 (55.10 -3 rad RMS).

Figure 3 -

 3 Figure 3-24 -Expansion n-DoF: trajectory in free motion

Figure 3 -Figure 3 -Figure 3 -

 333 Figure 3-25 -Expansion to n-DoF: Articular positions in free motion

Figure 3 -Figure 3 -

 33 Figure 3-30 shows the position of the effectors along the x axis in Cartesian space and the resulting

ForceFigure 3 -

 3 Figure 3-30 -Expansion to n-DoF: Position and force along Cartesian x in wall contact

Figure 3 -

 3 Figure 3-31 -Expansion to n-DoF: Energy E p in wall contact

Figure 3

 3 Figure 3-32 -Haption Virtuose 6-Desktop

Figure 3 -

 3 Figure 3-33 -Framework connection for Haption Virtuose slave

Figure 3 -Figure 3 -Figure 3 -Figure 3 -

 3333 Figure 3-34 -Expansion to n-DoF (Cartesian approach): Trajectory in free motion

Figure 3 -Figure 3 -Figure 3 -Figure 3 -Figure 3 -

 33333 Figure 3-40 the position errors, Figure 3-39 the force plots and Figure 3-41 the forces errors. The test is divided into three sections ( a ○, b ○, c ○) where the device interacts with a "wall" each time set at different position and orientation. In section a ○ the test is performed on a wall X= 50mm. At 17 < t < 19s the trainee applies a force on his device to reach trainer's position. The RMS errors in this section are 0.1mm for position and 0.02N for force. In the section b ○ the test is performed into

  Figure 4-1 -eAAA default profiles

Figure 4 -

 4 Figure 4-2 -Validation trajectory

Figure 4 - 3 -

 43 Figure 4-3 -Forces and dominance change for various profiles

Figure 4 - 5 -

 45 Figure 4-4 -AAA position tracking test: positions

Figure 4 -

 4 Figure 4-6 -AAA validation setup

  Figure 4-7 -Environment interaction object

Figure 5 -

 5 Figure 5-2 illustrates how the new hierarchy of dominance works.

  Figure 5-2 -Dominance hierarchy

Figure 5 Figure 5 - 3 -

 553 Figure 5-3 -Expansion m-trainee: Trajectory in free motion

Figure 5 - 4 -

 54 Figure 5-4 -Expansion m-trainee: Position with α = 0 in free motion

Figure 5 - 5 -Figure 5 - 6 -Figure 5 Figure 5 - 8 -

 5556558 Figure 5-5 -Expansion m-trainee: Position errors with α = 0 in free motion

1

 1 Figure C-2 -M-port network

  : Haptique, Simulateur, Apprentissage supervisé, Dual-user, Passivité, Étude comparative Laboratoire (s) de recherche : AMPERE -Laboratoire AMPERE (UMR5005) Directeur de thèse : Minh tu PHAM Co-directeur de thèse : Arnaud LELEVÉ Président de jury : Composition du jury : Pierre Vieyres (Rapporteur), Emmanuel Promayon (Rapporteur), Véronique Perdereau, Minh Tu Pham, Damien Ebérard, Arnaud Lelevé

  Nous avons ensuite commencé par étendre ESC à n degrés de liberté, car avec un seul ddl, il n'était pas possible d'en faire un simulateur utile pour l'apprentissage du geste. Cette extension est détaillée au chapitre 3 et a mené à publication dans la revue Robotica en 2019[START_REF] Liu | An Energy-Based Approach for n-dof Passive Dual-user Haptic Training Systems[END_REF]).

	Nous avons montré que cette architecture peut fonctionner également avec des interfaces maîtres et
	robot esclave à cinématiques différentes. Nous avons validé expérimentalement cette proposition avec
	3 degrés de liberté (position dans l'espace). This work has been submitted for presentation at ICRA
	2020 conference.

5), qui nous a permis de déterminer les avantages et inconvénients des solutions présentes dans la littérature sci-11 entifique. Nous avons pu en conclure que les objectifs d'extension et amélioration d'ESC étaient cohérents vis à vis de l'existant. La fonction Adaptive Authority Adjusting (AAA) proposée initialement par Fei Liu dans (Liu et al. [2015]) a pour objectif de modifier dynamiquement le niveau de dominance de chaque utilisateur en fonction des performances de l'apprenant. Nous avons proposé une nouvelle fonction pour cela, qui ne fait appel qu'à deux paramètres numériques et le choix d'un profil d'utilisation dépendant de la tâche à réaliser et de l'expertise de l'apprenant. Nous avons réalisé une validation expérimentale avec une dizaines d'utilisateurs afin de déterminer si cette fonction aide à l'apprentissage du geste en terme de trajectoires et d'efforts d'interaction. Nous avons ensuite étendu l'architecture ainsi obtenue à m apprenants simultanés en maintenant les propriétés de stabilité et transparence de l'architecture ESC initiale. Ce travail a été présenté lors de la conférence IROS 2019 (Licona Rodriguez et al. [2019]). 1.4 Document Outline Ce document est organisé comme suit : Au chapitre 2, nous introduisons les interfaces haptiques, comment elles fonctionnent, et nous en proposons une classification. Ensuite, nous réalisons un état de l'art sur les simulateurs informatiques pour la formation pratique en médecine, faisant appel à des interfaces haptiques. Nous étudions leurs architectures et précisons pourquoi celles-ci ne remplissent pas toutes les exigences listées précédemment. Au chapitre 3, nous rappelons l'architecture ESC développée par Fei LIU afin d'en proposer deux méthodes d'extension en terme de nombre de degrés de liberté (approche articulaire et cartésienne). Au chapitre 4, nous rappelons le principe de fonctionnement de la fonction AAA pour adapter dynamiquement la dominance entre formateur et apprenant(s) et nous détaillons les améliorations apportées afin qu'elle soit plus ergonomique et efficace. Nous détaillons également les retours d'usage réalisés sur cette fonction et discutons des résultats obtenus et des perspectives envisageables.

Au chapitre 5, nous détaillons l'approche utilisée pour étendre le simulateur en terme de nombre d'apprenants simultanés. Nous présentons ensuite les résultats expérimentaux validant cette approche.

Table 2 .

 2

1 sums up the characteristics of all the aforementioned architectures. The table is ordered by year and we use the authors' names as identification as some architectures do not have a proper name. The DoF column indicates the number of degrees of freedom that have has been tested or proposed by the authors; in case the authors do no mentioned it, this is considered as an n-DoF architecture. We recall the important advantages and disadvantages of each architecture. The column "Training purpose" defines if the architecture has been used or can be used for training purposes compliant with our use case.

Table 2 .

 2 1 -MM/SS architectures comparison table

	No. Authors	DoF Advantages	Disavantages	Training
						purpose
				Solution dedicated to
					Trainees do not
	1	(Katsura et al. [2007])	n	systems that do not	reproduce the same
				share the same
					gestures as trainers
				kinematics at all

Table 3 .

 3 .1.

	Parameter LF (s → 0) HF (s → ∞)
	h 11	B mi1 + B mi2	M mm s
	h 12	1	1/s 6 → 0
	h 21	-1	-1/s 6 → 0
	h 22	0	M ms /s 6 → 0

1 -Analysis of the hybrid matrix in Low and High Frequency

Table 3 .

 3

			2 -IPCs' parameters for simulation validation: Cartesian vs Articular
	Impedance (Master IPC)				Admittance (Slave IPC)
	Parameter	H H θ 1	H H H H x H H θ 2	H H H H y H H H H H H θ 3 z Parameter	H H H H H θ 1 H x H θ 2 H H H H H y H θ 3 H H H H H z
	M 1 kg	0.01	0.01	0.01	M 2	0.01	0.01	0.01
	k mc (N/m)	2000	2000	2000	k mi2	2000	2000	2000
	k mi1 (N/m)	2000	2000	200	B mi2	8.94	8.94	8.94
	B mi1 (Ns/m)	6.32	6.32	6.32

Table 3 . 3

 33

	-Geomagic 3D Touch specifications
	Haptic Device	Geomagic 3D Touch
	Degrees of freedom	6
	Actuated Dof	3
	Workspace (mm)	160x120x70
	Nominal position resolution	55µm
	Max. Normal Force	3N
	Force/Torque sensors	No
	Communication protocol	Ethernet
	API Software	Openhaptics

Table 3

 3

	Impedance (Master IPC)		Admittance (Slave IPC)
	Parameter	θ 1	θ 2	θ 3	Parameter	θ 1	θ 2	θ 3
	M 1 (kg) k mc ( Nm rad ) k mi ( Nm rad ) B mi ( Nms rad )	0.002 0.002 0.002 20 40 15 20 40 15 0.4 0.56 0.34	M 2 ( kg m 2 ) k s ( Nm rad ) B mi ( Nms rad )	0.002 0.002 0.002 20 40 15 0.4 0.56 0.34

.4 and are used in all the experiments of part II, unless the contrary is indicated.

Table 3 . 4

 34

-IPCs' parameters for Articular approach

  = e r (t) 5 [r 1r 2 * e r (t) + r 3 * e r (t) 2r 4 * e r (t) 3 + r 5 * e r (t) 4r 6 * e r (t) 5 ]With r 1 , r 2 , r 3 , r 4 , r 5 , r 6 as constants with values of 252, 1050, 1800, 1575, 700 and 126 respectively.

			(4.10)
	1 otherwise
	Where b z is
	b z (4.11)
	And e r is
	e r (t) =	e(t) e max	(4.12)

Table 4 .

 4 4, the lack of an actuated wrist in the master and slave devices limits both activities. Starting from the previous analysis, we proposed a second wave of exercises, 3 -Final score for proposed exercises

		Motion (position)		Interaction (Force)
	Exercise	Quantifiable Improves Total Quantifiable Improves Total
	Surgical game	1	1	2	1	-1	0
	Tieing a knot	-1	-1	-2	1	1	2
	Dictating dimensions	1	1	2	-1	-1	-2
	Cutting task	1	1	2	1	1	2
	Following a path	1	1	2	-1	-1	-2
	Building Jenga	-1	-1	-2	1	-1	0
	Writing	1	1	2	1	1	2
	Stitching	1	1	2	1	1	2
	Table 4.2 -Motion and Interaction criteria for proposed exercises
		Exercise	Final Score
		Surgical game	5
		Tieing a knot	3
		Dictating dimensions	3
		Cutting task	5
		Following a path	3
		Building Jenga	1
		Writing		7
		Stitching	8

Table 4 .

 4

		Motion (position)		Interaction (Force)
	Exercise	Quantifiable Improves Total Quantifiable Improves Total
	Push an object (certain distance)	1	1	2	1	1	2
	Pull a spring (certain distance)	1	1	2	1	1	2
	Pick up something to a point	1	1	2	-1	-1	-2
	Scratch an object	-1	-1	-2	1	1	2
	Table 4.5 -Motion and Interaction criteria for proposed exercises: Second Wave
		Exercise		Final Score
	Push an object (certain distance)	4
	Pull a spring (certain distance)	4
	Pick up something to a point	0
		Scratch an object		0

6 -Final score for proposed exercises: Second Wave environment.

Table 5 .

 5

		1 -RMS error in free motion
	Error [mm] M2 Leader (t <5 s) M3 Leader (t ≥5 s)
	M2-M1(v)	2.7	4.9
	M2-M3	2.5	5.1
	M2-S	4.2	5.1
	M3-M1(v)	3.5	1.4
	M3-S

Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2020LYSEI018/these.pdf © [A.R.Licona Rodriguez, [2020], INSA Lyon, tous droits réservés

Afin d'alléger l'écriture pour mieux me centrer sur le fond, je n'utiliserai pas d'écriture inclusive dans le texte français de ce document. Il va de soi que chaque acteur/trice dans le texte peut aussi bien être du genre féminin comme masculin.

The Verge. Consulté April

21, 2020 URL: https://www.theverge.com/2018/8/14/17670304/virtual-reality-surgerytraining-haptic-feedback-fundamentalvr

The Verge. Consulted April

21, 2020 URL: https://www.theverge.com/2018/8/14/17670304/virtual-reality-surgerytraining-haptic-feedback-fundamentalvr

Modulated Flow Sources. Introduced here in order to provide, on the one hand, force feedback and guidance to users for which α > 0, and on the other hand, to guarantee the passivity of the system, seeLiu et al. [2015]

Acknowledgments

Español Acknowledgments

The ESC architecture interconnects the haptic systems, and the controllers using Multiple-Input-Multiple-Output (MIMO) nodes D m1 for Master 1, D m2 for Master 2 and D s for the Slave. During the expansion of the ESC architecture, the node D m1 remains unaltered, as it is intended that Master 1 will always be the device used by the trainer. The node D s serves as a union point between the implicated devices and the Slave, this connects directly to D m1 and D m2 . Expanding the node D s allows us to use it as a union point between the trainees' devices and the Slave. For this, first, it is necessary to modify the node D m2 and duplicate it in parallel with their corresponding IPC controller. It is also necessary to update D m2 and D s in a way that allows the introduction of the m -1 complementary devices. Figure 5-1 shows the expansion of the ESC architecture, augmenting the number of nodes.

The nodes D m2 to D mm are identical and allow the connections between each trainee device and their corresponding IPC controller to the node D s (eq. 3.1).

Each trainee device is identified from Master 2 to Master m, and each trainee device works in parallel to the others. As D s is the node that interconnects all the IPC controllers and establishes the dominance factor of the system, it is necessary to update it to be used with m -1 new devices. D s reuses the factors β 1 and β 2 introduced in Eq. (3.2) in order to avoid the appearance of α 2 terms in the relations between angular velocities and torques of devices. The principal restriction of the expansion Appendix A

Mathematical models A.1 Geomagic Touch 3D

The following mathematical models for the Geomagic Touch 3D ( The forward kinematic model of a manipulator is the relation between the end effector Cartesian position and the joint angles of the links. The Forward direct kinematics of the Geomagic 3D Touch is identical to the Phantom Omni (which is a previous version) presented by [START_REF] Jarillo-Silva | PHAN-ToM OMNI haptic device: Kinematic and manipulability[END_REF] and are set as:

x =sin(θ 1 )(l 1 cos(θ 2 ) + l 2 sin(θ 3 ))

A.1.2 Inverse kinematics

The inverse kinematics is used to obtain the angular configuration of a serial-link robot (θ 1 ...θ n ) in function of the cartesian variables (x,y and z). For the Geomagic Touch the inverse kinematics is set by equations A.2, A.3 and A.4

Where

A.1.3 Jacobian matrix

The coordinates Jacobian matrix of a manipulator robot is the function that helps relate the velocity the cartesian with the joint velocities [START_REF] Spong | Robot Dynamics and Control[END_REF]). It is used to commute the Cartesian velocity of the end-effector, to plan the trajectories and to transform the actuator torques into the force exerted by the end effector in Cartesian coordinates.

it. The RMS function is used to represent an enhanced the average of the error between two devices (which can be Master 1, Master 2, or the slave) for all the performed trajectories. This value helps determinate how close are both devices during a task.

To compute the RMS, first we need to get the difference of position of each sample during a test.

The difference of position is given by:

Where △P is the position error between the first device and the second device. x 1,2 ,y 1,2 ,z 1,2 are the position components for each device. These components are expressed in the Cartesian space but can be also expressed in the angular space (θ 1 ,θ 2 ,θ 3 ).

Once the position error is determined, we evaluate all the position samples for all the trajectory. By using eq. A.17 with the values of each iteration, we get the value of RMS.

Where ε is the RMS error and k t is the total number of samples of the trajectory. As ε represents a difference of position between both devices, it is always desirable that ε → 0, as this means both systems are as close as possible, following the same trajectory.

Appendix B

Hybrid matrix of Impedance-Admittance

IPC

Expanding the hybrid matrix of eq.( 3.26) in section 3.2.2, we get

Where

Where

Where

Appendix C

Time Domain Passivity Control (TDPC)

A standard method used to offer stability in a bilateral teleoperation system is the use of a Time Domain Passivity Control (TDPC). These methods are based on the passivity approach, which offers stability to the system as long as the conditions are met.

C.1 Passivity

The passivity approach focuses on the quantity of energy exchanged between a system and its environment. The advantages of the passivity, listed by [START_REF] Hannaford | Time-domain passivity control of haptic interfaces[END_REF], are:

• The system is passive if the energy that flows in the inputs always exceeds the one flowing in the outputs . That means a system must dissipate more energy than it receives.

• It allows subdividing the system into individual system blocks, or subsystems. If all the blocks are passive, and their interconnections are passive, the global system is passive as well.

• It is valid for linear and non-linear systems

• There is evidences in the bibliography that prove the human intervention is passive as well.

To define passivity, it is necessary to consider a system H, as shown in Figure C-1 with input

Then the passivity is defined by [START_REF] Van Der Schaft | L2 -Gain and Passivity Techniques in Nonlinear Control[END_REF] as: The system H with states x is passive from input u ∈ U and output y ∈ Y if there exists a semidefinite function S : R p → R + called storage function such that

For all input signals u : [0, τ] → R p with initial states x 0 ∈ R p and τ ∈ R + . It is said also that:

The input is strictly passive if there exists δ u > 0 such that

Moreover, the output is also strictly passive if there exists a scalar δ y > 0 such that S(x(τ)) -S(x 0 ) ≤ τ 0 (y T (t)u(t)δ u y(t) 2 )dt For all the input signals u

Where S is the total energy of the system, the term y T (t)u(t) is the power supplied to the system at time t. The integral term τ 0 y T (t)u(t) is the energy supplied to the system during the time interval [0, τ].

C.1.1 Passivity for an M-port network

To prove passivity in an M-port network (a system with multiple inputs and outputs) first, we establish the system, as shown in Figure C-2, with the convention of forces and velocities. We declare storage energy as E and initially is equal to 0 at t = 0.

The definition of passivity for the M-port network given is:

Appendix D

Survey AAA validation

The following questions were asked to the participants of section 4.4 to evaluate their qualitative response to the haptic system. In the case of question 4 to 7, the Group 2 participants were instructed to no answered it as this mode was not implicated in their test.