Hanna Bismuth

Laurent Aussel
email: aussel@imm.cnrs.frezraty@imm.cnrs.fr

Benjamin Ezraty

La teigne Galleria mellonella pour les études hôte-pathogène

choix dans certaines études de pathogénicité d'agents infectieux et pour l'identification de moyens de traitement plus efficaces. Cette synthèse présente ce modèle alternatif et décrit ses nombreuses possibilités d'utilisation.

« Les études expérimentales sur les animaux ont toujours été indispensables pour mettre au point des méthodes de prévention et de limitation des maladies humaines et animales ».

Cette phrase extraite de la charte de Bruxelles de 2015 dresse un constat laconique : la recherche scientifique est contrainte d'utiliser des modèles animaux pour progresser. Leur utilisation à des fins scientifiques n'est pas nouvelle et accompagne de nombreuses découvertes en médecine, notamment avec Hippocrate dès le V e siècle avant J-C. Celui que l'on considère comme « le père de la médecine » fut l'un des premiers à décrire l'anatomie et la physiologie par des observations de dissections animales [1]. Actuellement, 75 à 100 millions de vertébrés sont utilisés chaque année pour la recherche médicale et fondamentale [START_REF] Baumans | Science-based assessment of animal welfare: laboratory animals[END_REF]. Mais depuis la fin des années 1940, des voix s'élèvent pour dénoncer l'utilisation abusive d'animaux en laboratoire. Ratifié en 2010, le traité d'Amsterdam pour la protection des animaux stipule que tout projet de recherche doit faire l'objet d'une autorisation et place au centre de la démarche le principe des trois « R » : Remplacer, Réduire, Raffiner [START_REF] Richmond | The 3Rs-Past, present and future[END_REF][START_REF] Veissier | Expérimentation animale: biologie, éthique, réglementation[END_REF]. La législation n'est pas la seule contrainte liée à l'expérimentation animale puisque l'utilisation de modèles animaux en laboratoire nécessite un investissement temporel et financier important. En effet, de l'élevage à l'entretien en passant par le traitement, le coût de revient d'une expérimentation animale peut atteindre plusieurs milliers d'euros et nécessiter plusieurs semaines de manipulations.

Face à ces problématiques, la communauté scientifique s'attache à trouver des alternatives à l'utilisation de vertébrés.

Parmi les modèles « alternatifs », un nouvel organisme suscite un intérêt croissant : Galleria mellonella ou fausse teigne de la ruche (Figure 1A,B). Ce lépidoptère de la famille des Pyralidae est, au stade larvaire, un nuisible pour les abeilles car il se nourrit de cire et de pollen. En laboratoire, il combine plusieurs avantages pratiques, dont une reproduction rapide et peu coûteuse car la ponte d'un papillon peut atteindre un millier d'oeufs qui deviendront, en quelques jours, autant de larves suffisamment grandes pour être manipulées au bout de quatre semaines. Il est actuellement admis que les insectes ne possèdent pas de nocicepteurs et ne ressentent pas la douleur [START_REF] Eisemann | Do insects feel pain? -A biological view[END_REF] ; les chenilles ne sont ainsi pas soumises aux réglementations appliquées aux vertébrés [START_REF] Hardin-Pouzet | Organismes-modèles et réglementation de la recherche animale[END_REF] (M/S : voir 32). G. mellonella peut être obtenue auprès de revendeurs d'appâts de pêche, d'entreprises spécialisées dans la production de lignées (True larvae) ou de certains laboratoires publics (INRA, université) ayant leur propre élevage.

Depuis près de vingt ans, le modèle G. mellonella tend à coloniser les laboratoires de biologie, particulièrement ceux de microbiologie. L'utilisation de ce modèle pour l'étude des interactions hôte-pathogène est en effet de plus en plus fréquente dans le contexte de l'émergence de souches bactériennes résistantes aux antibiotiques. L'Organisation mondiale de la santé (OMS) a publié une première liste « d'agents pathogènes prioritaires », énumérant les douze familles de bactéries les plus menaçantes pour la santé humaine [START_REF] Tacconelli | Global priority list of antibiotic-resistant bacteria to guide research, discovery, and development of new antibiotics[END_REF]. Il est donc nécessaire de déployer de nouveaux outils afin de faire progresser les connaissances liées aux processus et aux mécanismes responsables du pouvoir infectieux de ces pathogènes.

Titre niveau 1

La teigne, un modèle pour la microbiologie

Les larves de G. mellonella peuvent atteindre 3 cm de longueur au dernier stade larvaire, stade généralement utilisé pour les infections. Le corps est segmenté en 12 métamères et constitué de 3 paires de pattes à l'avant et 4 paires de ventouses appelées « proleg », au centre (Figure 1A). Plusieurs études ont révélé des similitudes entre le système immunitaire inné de G. mellonella et celui des mammifères [START_REF] Sheehan | Innate humoral immune defences in mammals and insects: The same, with differences?[END_REF]. Chez l'insecte, la première barrière face aux infections est l'enveloppe externe appelée cuticule. Dès qu'un agent infectieux (bactérie, champignon ou virus) traverse cette paroi, il rencontre deux types de réponse immunitaire : la réponse cellulaire et la réponse humorale [START_REF] Kavanagh | Exploiting the potential of insects for in vivo pathogenicity testing of microbial pathogens[END_REF][START_REF] Tsai | Galleria mellonella infection models for the study of bacterial diseases and for antimicrobial drug testing[END_REF]. Dans l'hémocoel, l'équivalent du sang des mammifères, le microorganisme est reconnu par des cellules appelées hémocytes, dont six types existent chez G. melonella : les plasmocytes, les granulocytes, les sphérulocytes, les coagulocytes, les adipohémocytes et les oenocytoïdes . Trois mécanismes interviennent dans l'immunité cellulaire : la nodulation, l'encapsulation et la phagocytose [START_REF] Pereira | Recent Advances in the Use of Galleria mellonella Model to Study Immune Responses against Human Pathogens[END_REF]. La réponse humorale est déclenchée simultanément. Comme chez les mammifères, les TLR (Toll-like receptor), recepteurs de l'immunité innée exprimés par les cellules dans l'hémolymphe, reconnaissent l'élément étranger et sont à l'origine de la production de peptides antimicrobiens (PAM), des petites molécules capables d'agir sur une grande diversité de microorganismes. Le mécanisme de l'immunité de la larve le plus visible est la production de mélanine. Contrairement à l'homme, chez qui la mélanine aide à protéger les cellules des radiations ultra-violettes et pigmente les cheveux ou la peau, elle est, chez la larve, le résultat d'un processus de défense contre les pathogènes. En effet, lors d'une infection, une tyrosinase est convertie en sa forme active, la phénoloxidase, qui déclenche une cascade de réponses avec, comme étape finale, la production de mélanine. Cette cascade fait partie du système de coagulation de la larve qui est commun à la plupart des insectes et correspond, chez les mammifères, à la cascade du complément permettant la coagulation. Ce mécanisme de mélanisation présente un avantage majeur pour l'expérimentateur : il lui permet de suivre, à l'oeil nu, la progression de l'infection en fonction de l'évolution de la couleur que prend la chenille (Figure 1C). Les larves sont, en outre, capables de vivre à des températures comprises entre 5°C et 45°C, ce qui permet des incubations à la température de croissance du microorganisme étudié et/ou à la température du corps humain.

Cependant, comme tous modèles, l'utilisation de G. mellonella présente des limites. Cet organisme n'est en effet pas l'hôte naturel des germes qui sont étudiés et qui lui sont injectés et l'environnement que rencontrent ces pathogènes diffère de celui au sein duquel ils prolifèrent habituellement. La durée de vie de la larve est aussi un facteur limitant. Après 15 à 20 jours, les larves initient le processus de métamorphose en papillon, ce qui ne permet d'étudier que les stades précoces de l'infection : dans la plupart des études, les analyses sont réalisées après 1 à 6 jours d'infection.

Titre niveau 1 Méthodes d'infection et technique

Deux voies peuvent être utilisées pour l'infection des teignes : l'ingestion ou l'injection. Dans le premier cas, une solution contenant l'agent microbien est introduite dans le tube digestif de l'insecte par voie orale. Le microorganisme ainsi administré se retrouve dans l'intestin avec le bol alimentaire. Chez la larve, le microbiote intestinal est séparé du bol alimentaire par une matrice péritrophique qui protége l'épithélium intestinal des contaminations chimiques et bactériennes [START_REF] Lehane | Peritrophic matrix structure and function[END_REF]. La seconde technique, plus largement utilisée, consiste à Pour cela, quelques microlitres d'hémolymphe sont prélevés après incision de la cuticule de la teigne et retro-cultivés sur milieu gélosé. Il est ainsi possible d'avoir une indication de la survie de l'agent infectieux dans l'hémolymphe de la larve. Ces techniques et leurs étapes sont parfaitement décrites dans deux vidéos disponibles sur internet, facilitant l'accès à ces manipulations pour un utilisateur néophyte [START_REF] Ramarao | The insect Galleria mellonella as a powerful infection model to investigate bacterial pathogenesis[END_REF][START_REF] Harding | Use of Galleria mellonella as a Model Organism to Study Legionella pneumophila Infection[END_REF].

Titre niveau 1

Pathogénie et études des facteurs de virulence

Lorsqu'on étudie une bactérie pathogène, il est important de connaître son pouvoir infectieux, c'est-à-dire sa capacité à provoquer une maladie. Le pouvoir pathogène d'un microorganisme est corrélé à sa virulence, définie comme sa capacité de se multiplier dans l'hôte. La virulence repose, entre autres, sur des facteurs appelés facteurs de virulence qui peuvent être des toxines sécrétées par le pathogène ou des protéines qui sont essentielles à sa survie et à sa croissance dans l'hôte.

Très récemment, G. mellonella a été utilisée pour tester la pathogénicité des bactéries à Gram-négatif (BGN) présentes dans le fromage traditionnel français [START_REF] Imran | Safety assessment of Gram-negative bacteria associated with traditional French cheeses[END_REF]. Ces tests étaient jusqu'à présent effectués sur des mammifères modèles et la facilité d'utilisation de la teigne a séduit les chercheurs. Dans cette étude, des larves de Galleria ont été infectées avec l'une des 20 bactéries à Gram-négatif retrouvées dans le fromage ou avec des souches de bactéries non pathogènes. En comparant la mortalité des larves pendant 10 à 15 jours, la dose létale 50 (LD50) 1 de chaque souche de bactéries a été déterminée. Sur les 20 souches testées, 13 ont présenté une LD50 similaire à celle des souches contrôle (soit 10 7 à 10 8 1 C'est-à-dire la quantité de bactéries nécessaires pour provoquer la mort de 50 % des larves. bactéries par ml), 5 une LD50 intermédiaire (10 6 ) et 2 se sont révélées être plus virulentes, 10 5 de ces bactéries tuant 50 % des larves. Chez l'homme, ces résultats pourraient être sensiblement différents en raison des interactions que peuvent établir les bactéries avec les microorganismes qui composent le microbiote et de l'existence d'un système immunitaire plus évolué que celui de l'insecte, modulant la virulence de ces bactéries. Cet exemple illustre toutefois l'exploitation possible de la teigne comme modèle permettant un criblage rapide et l'indentification de bactéries potentiellement pathogènes au sein d'une population complexe. Il ne se substitue cependant pas à des vérifications qui seront réalisées ensuite sur les hôtes naturels des germes examinés.

La caractérisation des gènes responsables de la production des facteurs de virulence est un autre domaine dans lequel les larves peuvent montrer leur utilité. Des chercheurs de l'université de Milan [START_REF] Raneri | Pseudomonas aeruginosa mutants defective in glucose uptake have pleiotropic phenotype and altered virulence in non-mammal infection models[END_REF] ont ainsi utilisé G. mellonella pour étudier le rôle des systèmes d'import de glucose dans la virulence de la bactérie Pseudomonas aeruginosa. En montrant une diminution de la mortalité des larves infectées par des souches de bactéries n'exprimant plus les gènes codant le système d'import de glucose, ils ont ainsi montré le rôle essentiel de ce système dans la virulence de Pseudomonas lors de l'infection chez G. mellonella.

Ces deux études illustrent donc la facilité d'utilisation de la teigne et la possibilité de réaliser des cribles à « haut débit » pour estimer la pathogénicité de germes et caractériser les gènes impliqués dans le processus infectieux de nombreux pathogènes (Tableau I). G. mellonella contribue également au développement de nouvelles molécules thérapeutiques afin de lutter contre les bactéries résistantes aux antibiotiques, un problème de santé publique particulièrement préoccupant.

Titre niveau 1 Identification de molécules antimicrobiennes

L'utilisation d'antibiotiques est fréquente en santé humaine ainsi qu'en agriculture. Elle constitue la base d'un problème dont les institutions se sont saisies il y a une dizaine d'année. Plusieurs cas de maladies, habituellement curables, sont en effet devenus problématiques dès lors qu'aucun antibiotique n'est plus en mesure de les traiter. Ainsi, la communauté scientifique s'attache à trouver de nouveaux traitements antimicrobiens. Dans ce domaine, Galleria s'impose comme un outil de choix. Récemment, des chercheurs de l'European Molecular Biology Laboratory de Heidelberg et de la Goethe University de Francfort (Allemagne), en collaboration avec une équipe du laboratoire de chimie bactérienne de Marseille [START_REF] Brochado | Species-specific activity of antibacterial drug combinations[END_REF] ont entrepris une étude « à haut débit » afin d'identifier de possibles effets synergiques entre les antibiotiques et différents types de molécules. En réalisant dans un premier temps des tests de sensibilité des bactéries en milieux de culture, il a pu être montré que la combinaison de la spectinomycine (un antibiotique proche de la famille des aminoglycosides) et de la vanilline (un additif alimentaire) permettait d'augmenter l'action antimicrobienne de l'antibiotique. Cette combinaison a ensuite été testée in vivo, en utilisant la teigne. Trois espèces de bactéries pathogènes (Escherichia coli, Salmonella enterica et Pseudomonas aeruginosa) ont été indépendamment injectées dans l'hémolymphe de l'insecte. Une heure après infection, les larves ont été traitées soit avec la spectinomycine seule, soit avec la combinaison spectinomycine-vanilline. L'analyse des taux de survie des larves infectées a révélé des taux de survies nettement supérieurs pour les larves traitées par la combinaison que ceux obtenus avec les larves traitées avec le seul antibiotique. L'utilisation de G. mellonella a donc permis de confirmer l'amplification de l'efficacité du traitement antibiotique par la présence de la vanilline.

La combinaison de plusieurs molécules antimicrobiennes est une piste prometteuse dans la lutte contre les microorganismes résistants. Ces effets ont également été démontrés chez d'autres organismes pathogènes tels que la levure Candida albicans. Ce champignon commensal peut former des biofilms à la surface des cathéters et d'autres matériels médicaux, et être à l'origine d'infections récidivantes chez les patients immunodéprimés.

Majoritairement traitées par le Fluoconazole (un antifongique de la famille des azolés), de plus en plus de souches de C. albicans résistantes à cet antifongique sont apparues ces dernières années. Récemment, un effet synergique a été obtenu chez la teigne en combinant le Fluoconazole au Licofelone (un inhibiteur de la synthèse de prostaglandine E2) pour traiter l'infection par la levure [START_REF] Liu | Synergistic Antifungal Effect of Fluconazole Combined with Licofelone against Resistant Candida albicans[END_REF].

Titre niveau 1

Conclusion

Au vu de ses similitudes avec le système immunitaire des mammifères, de sa facilité d'utilisation, de son faible coût et de sa sensibilité, le modèle Galleria mellonella permet d'étudier la pathogénicité et la virulence d'un large spectre d'agents pathogènes et d'effectuer des tests rapides de criblage de nouveaux agents antimicrobiens. Plusieurs techniques peuvent êtres utilisées pour suivre l'infection et détecter les pathogènes chez la larve, comme la microscopie à fluorescence en utilisant des bactéries marquées à la GFP (green fluorescent protein) [START_REF] Barnoy | The Galleria mellonella larvae as an in vivo model for evaluation of Shigella virulence[END_REF] , ou la bioluminescence avec des bactéries exprimant la luciférase [START_REF] Delarze | Adaptation of a Gaussia princeps Luciferase reporter system in Candida albicans for in vivo detection in the Galleria mellonella infection model[END_REF] (Figure 3). Son utilisation n'est pas exclusive aux traitements antibiotiques ou antifongiques. Elle permet également des études reposant sur l'utilisation de phages qui ont montré leur intérêt comme antidote contre les infections bactériennes. G. mellonella a ainsi été utilisée pour évaluer l'efficacité d'un bactériophage contre la bactérie pathogène opportuniste Escherichia coli [START_REF] Manohar | Isolation, characterization and in vivo efficacy of Escherichia phage myPSH1131[END_REF].

Dernièrement, le séquençage du génome de G. mellonella a été réalisé, ouvrant la voie aux études d'homologie entre les gènes de l'insecte et ceux de l'homme ou d'autres mammifères [START_REF] Lange | Genome Sequence of Galleria mellonella (Greater Wax Moth)[END_REF]. La pathogénicité d'une large gamme d'agents bactériens et fongiques (Streptococcus pneumoniae, Staphylococcus aureus, Listeria monocytogenes, Pseudomonas aeruginosa, Escherichia coli, Legionella pneumophila, Bacillus cereus, Candida albicans, etc.) peut être étudiée via ce lépidoptère [START_REF] Champion | Galleria mellonella as a model host for microbiological and toxin research[END_REF]. L'étude de la réponse immunitaire de l'insecte luimême peut également permettre des découvertes. En mai 2018, le mécanisme d'action d'un inhibiteur de la Pseudomonas elastase (PE), un facteur de virulence de Pseudomonas aeruginosa, a été élucidé [START_REF] Eisenhardt | The therapeutic potential of the insect metalloproteinase inhibitor against infections caused by Pseudomonas aeruginosa[END_REF]. Cet inhibiteur n'est autre qu'une métalloprotéinase qui a été en fait découverte chez… G. mellonella. Ce lépidoptère nous prouve une nouvelle fois ses capacités prometteuses dans un domaine où la lutte contre les bactéries pathogènes est un enjeu majeur.

Liens d'intérêt

Les auteurs déclarent n'avoir aucun lien d'intérêt concernant les données publiées dans cet article.

Summary The greater wax moth, Galleria Mellonella to study host-pathogen interactions

The massive use of antibiotics in health and agriculture led to the emergence of pathogenic microorganisms resistant to frequently used treatments. In 2017, World Health Organization (WHO) published its first ever list of antibiotic-resistant "priority pathogens", a catalogue of twelve families of bacteria that pose the greatest threat to human health. In this context, a new model for the study of host-pathogen interactions is becoming increasingly popular: the greater wax moth, Galleria mellonella. This butterfly larvae, sometimes considered as a new "laboratory rat", has many practical advantages and is an important host in the study of some steps in the pathogenicity of infectious agents and the identification of new treatments. This review presents this alternative model and describes its possible applications.

Légende des figures

  injecter à l'aide d'une aiguille, quelques microlitres d'une solution concentrée d'agent infectieux au niveau du « proleg » gauche du dernier métamère (Figure 1D), le microorganisme se retrouvant alors dans l'hémolymphe qui constitue un environnement stérile. Deux méthodes d'injection sont possibles. Soit la larve est immobilisée entre les doigts du manipulateur, ou entre deux éponges (Figure 1D) (ce qui permet de protéger les doigts du manipulateur [12]), et l'injection est réalisée à l'aide d'un pousse-seringue automatique. La programmation de cet appareil permet de contrôler la dose injectée dans chaque larve. Soit la larve est immobilisée sur un support en plastique et l'injection est réalisée manuellement à l'aide d'une seringue Hamilton. Les larves infectées sont ensuite incubées dans des boites de Pétri à la température désirée et le taux de mortalité des teignes est évalué au cours du temps. Afin de réduire l'effet de l'hétérogénéité entre individus, 15 à 30 larves sont utilisées par expérience.La courbe de survie (Figure2), élaborée en rapportant le nombre de larves mortes par rapport au nombre initial de larves en fonction du temps, est corrélée à la virulence du pathogène étudié ou à l'efficacité d'un traitement antibiotique. Quelques jours suffisent pour établir une telle courbe de survie avec G. mellonella et plusieurs souches bactériennes ou fongiques peuvent être testées en parallèle. Il est également possible de déterminer la quantité de bactéries ou de champignons présents dans l'hémolymphe au cours du temps.

Figure 1 .

 1 Figure 1. A. Photographie d'une larve de Galleria mellonella. B. Évolution du nombre de publications mentionnant Galleria mellonella sur la période 1998-2018. C. Schéma représentant les différents stades de mélanisation d'une larve. D. Photographie de l'injection d'une larve : l'aiguille est insérée à l'intérieur du « proleg » gauche.

Figure 2 .

 2 Figure 2. A. Représentation théorique de la mélanisation de Galleria mellonella infectées dans différentes conditions. (B) Courbe de survie théorique de G. mellonella infectée dans différentes conditions.

Figure 3 .

 3 Figure 3. Galleria Mellonella : avantages, applications et paramètres analysés.


J E Crois

/ Pense

/ Trouve

/ Estime

/ Considère Que

Laurent Gosselin

INTRODUCTION 1

French expressions of personal opinion, like je crois que 'I believe', je pense que 'I think', je trouve que 'I find', je considère que 'I consider', and j'estime que 'I reckon', have been studied extensively from different points of view -as parentheticals from a syntactic perspective [START_REF] Blanche-Benveniste | Constructions verbales "en incise" et rection faible des verbes[END_REF][START_REF] Apothéloz | La rection dite "faible" : grammaticalisation ou différentiel de grammaticité[END_REF][START_REF] Blanche-Benveniste | Un nouveau regard sur les verbes "faibles[END_REF]Avanzi and Glikman 2009;[START_REF] Haßler | Étude comparée de l'usage parenthétique des verbes épistémiques dans trois langues romanes[END_REF][START_REF] Schneider | Parenthetical Verbs[END_REF], as metarepresentational prefixes in a pragmatic and cognitive framework [START_REF] Récanati | Les énoncés performatifs : contribution à la pragmatique[END_REF][START_REF] Récanati | Oratio obliqua, oratio recta: an essay on metarepresentation[END_REF], as conventional implicatures from a pragmatic point of view [START_REF] Jayez | Parentheticals as conventional implicatures[END_REF], as evidential markers [START_REF] Dendale | A semantic description of French lexical evidential markers and the classification of evidentials[END_REF], or as epistemic operators from a logical perspective [START_REF] Martin | Langage et croyance[END_REF][START_REF] Martin | CROIRE QUE p / PENSER QUE p[END_REF]) -while je trouve que was analysed by [START_REF] Ducrot | Les mots du discours[END_REF] as a marker of prédication originelle 'original predication'.

These expressions have the particularity of indicating that the judgement that they introduce falls within the personal opinion of the speaker (for a discussion of this notion, see [START_REF] Tuchais | Comment dire ce que « je » pense en japonais et en français. Etude contrastive de l'expression de l'opinion personnelle[END_REF]. As such, they belong to the general category of expressions with modal values, specifically markers of individual subjectivity (referring to the subjectivity of the speaker, see [START_REF] Martin | Langage et croyance[END_REF][START_REF] Borillo | Les "Adverbes d'opinion forte" selon moi, à mes yeux[END_REF]). This class includes not only propositional attitude verbs (croire, trouver estimer ...), in the first person and present tense, but also prepositional phrases (selon moi, à mon avis, à mes yeux, pour moi 'in my opinion', and so on; see [START_REF] Borillo | Les "Adverbes d'opinion forte" selon moi, à mes yeux[END_REF][START_REF] Coltier | La modalisation du discours de soi: éléments de description sémantique des expressions pour moi, selon moi et à mon avis[END_REF]). These expressions are generally (see [START_REF] Haillet | Présentation. In Procédés de modalisation: l'atténuation[END_REF] 3) regarded as expressing epistemic modalities that apply to a propositional content (as part of the modus / dictum opposition according to Bally, 1932) and as discourse markers of mitigation. This attenuative value is due to a general principle explained by Borillo (2004: 31):

Pour le locuteur, signaler le point de vue subjectif du propos qu'il énonce est une manière d'en affaiblir la portée. Il manifeste ainsi une certaine prudence, soit par rapport à la vérité de ce qu'il avance, soit par rapport aux jugements évaluatifs qu'il introduit dans son discours.

[For the speaker, to indicate the subjective character of what he states is a way to weaken it. He thus manifests some caution, either with respect to the truth of what he says, or in relation to evaluative judgements he issues in his speech.] The purpose of this article is to challenge the "unitary view" of the semantic and discursive role of verbal expressions of personal opinion. We want to show 1) that the expressions studied each have a specific meaning and therefore are not always substitutable for one another, 2) that though they all indicate the speaker's personal opinion, they do not systematically operate an attenuative modalization, and 3) that, contrary to what their syntactic similarity suggests, not all of them express an epistemic modality that applies to the propositional content (as it is generally admitted; see Thompson and Mulac 1991: 313;Boone 1996: 48;Apothéloz 2003: 252;Haßler 2014: 6).

The analyses are carried out in the framework of the Modular Theory of Modalities [START_REF] Gosselin | Les modalités en français (Chronos studies 1)[END_REF]), which will be discussed here informally. We will successively present the theoretical perspective (Section 2), the semantics of je crois que and the mechanism that leads to the attenuation effect (Section 3), the semantics of je trouve que (Section 4), that of je considère / estime que (Section 5), and finally that of je pense que (Section 6). The conclusion will summarize the differences by means of a table.

MODALITY IN A WIDE SENSE

We classically distinguish judgements of reality from value judgements. A judgement of reality states what the case is (it describes a situation), while a value judgement consists of speaking well or ill of an individual or situation. A judgement of reality can be objective, in the sense that it is presented as true regardless of the subjective point of view of the speaker (ex. 1), or subjective, i.e. depending on the speaker's point of view (ex. 2).

( The judgement expressed by ( 2) is subjective since it assumes a norm of evaluation, which remains implicit, and depends on the speaker.

A value judgement cannot be objective, but depends either on the subjectivity of individuals (e.g. 3) or on a system of conventions (moral, ideology, religion, etc.) These phenomena can be analysed in modal terms, provided that it is recognized, following Brunot (1922: 541) and Bally (1965, § 47), that the lexical constituents of the dictum can themselves express modalities (taken in a wide sense). In this case, Gosselin (2010: 102-114;[START_REF] Gosselin | De l'opposition modus/dictum à la distinction entre modalités extrinsèques et modalités intrinsèques[END_REF] speaks of intrinsic modalities (i.e. internal to the dictum). In this framework, we will say that (1) illustrates an alethic modality attached to the predicate of the sentence, (2) illustrates an epistemic one, (3) illustrates an appreciative one, and (4) illustrates an axiological one. The alethic modality corresponds to a judgement of reality presented as objective, epistemic modality to a judgement of reality made in a subjective assessment, appreciative modality to a value judgement about the (un)desirable character of an object or a situation, and axiological modality to a value judgement about the (blame) worthiness of an individual or situation.

These intrinsic modalities may be marked linguistically, as in the examples above, in which they are associated with tokens, or inferred on the basis of background knowledge. For example, statement (2) may have, in some contexts, a positive appreciative value (thus becoming a value judgement in addition to being a judgement of reality). Pragmatically inferred modalities have the specificity of being avoidable in some contexts (unlike linguistically marked modalities).

Intrinsic modalities can be embedded by extrinsic modalities (i.e. belonging to the modus), as in the statement

(5) Je crois que Paul est honnête 'I believe Paul is honest'.

Here an extrinsic epistemic modality, expressed by je crois que, applies to an intrinsic axiological modality associated with the predicate in the complement clause (honnête).

JE CROIS QUE AND THE LOGIC OF CONVICTION

The expression je crois que 'I believe' expresses an extrinsic epistemic modality, which is compatible with all sorts of modalities, intrinsically associated with the predicates: alethic (7a), epistemic (7b), appreciative (7c), or axiological ones (7d) 3 : The role of this expression (je crois que) is to introduce the judgements as belonging to the individual subjective opinion of the speaker (her belief). It has long been observed (see Benveniste 1966: 264;[START_REF] Borillo | Deux aspects de la modalisation assertive: croire et savoir[END_REF]Vet 1994) that this expression plays the role of mitigator of an assertion (as a rhetoric-pragmatic function). We will try to explain this effect.

Imagine that you are in your office, and you are asked on the phone if your colleague is there. If you answer (8) Je crois qu'elle est ici 'I believe she's here', your interviewer will think that you are not sure. One might assume that this is because croire que p expresses a relatively low degree of belief, but this explanation is not satisfactory. Indeed in this case, statement (9), ( 9) Pierre croit que sa collègue est ici 'Peter believes his colleague is here', should imply that Peter is not sure of it. But it is false. This statement is compatible with the assumption that Peter is convinced that his colleague is here. In fact, croire is a verb that only indicates that the speaker of the utterance does not presuppose the content of the completive. Moreover, what is remarkable and at first sight paradoxical is that even if the speaker uses expressions that literally mean certainty, it is understood that she is not absolutely sure of what she says:

(10) Je suis certaine / sûre / convaincue / persuadée qu'elle est là 'I am confident she is here'.

These phenomena can be explained in the light of the logic of conviction [START_REF] Lenzen | Epistemic Logic[END_REF]. Lenzen (2004: 973) posits that if a subject is convinced that p, if she is really certain of it, she believes that she knows that p.

Principle of conviction: "C (a,p) → B(a,K(a,p))"

a: person; C: "is convinced"; B: "believes"; K: "knows".

It follows that "knowledge and conviction are subjectively indiscriminable in the sense that person a cannot tell apart whether she is 'only' convinced that p or whether she really knows that p" (Lenzen 2004: 973).

On the other hand, among epistemic verbs, a distinction is classically made between factive verbs (which presuppose the truth of the propositional contents of the complement clause) and non-factive verbs (which do not presuppose the truth of this content, see [START_REF] Karttunen | Presuppositions of Compound Sentences[END_REF][START_REF] Kreutz | Une typologie des prédicats factifs[END_REF][START_REF] Korzen | Factivité, semi-factivité et assertion: le cas des verbes savoir, ignorer, oublier et cacher[END_REF]. Savoir que 'know', se douter que 'suspect', and ignorer que 'ignore' belong to the first class and croire que 'believe' and être certain(e) / sûr(e) /persuadé(e) que 'be confident' to the second.

From all this follows that the speaker who is convinced that p will assert je sais que p 'I know that p', or even simply p (p and je sais que p being equipollent; see [START_REF] Gosselin | Sémantique des jugements épistémiques: degré de croyance et prise en charge[END_REF]. Therefore, if a speaker uses non-factive epistemic expressions, like je crois / suis certain(e) / persuadé(e) / convaincu(e) que 'I believe / am sure / persuaded / convinced that', it triggers an implicature from the utterance. The interpreter will think that if the speaker has used not just p or je sais que p, it is because she does not believe that she knows that p and therefore she is not really convinced that p, hence the systematic mitigation effect, which may seem contradictory to what the statement says literally (as in the example 10). As Martin notes (1987: 57), it is "impossible de dire sans mauvaise foi Je crois qu'il est à la maison si je sais pertinemment qu'il y est" ['impossible to say without bad faith I believe he is at home if I know for a fact that he is'].

This very regular inferential mechanism helps to explain why the degree of belief indicated by non-factive belief expressions is not weakened when belief is attributed to a third party (ex. 9): as belief is not attributed to the speaker of the utterance, the inferential mechanism grounded on the principle of conviction does not apply, and there is no implicature.

This inferential mechanism helps also probably to explain the origin of the weakening of epistemic adverbs (which refer to the belief of the speaker): sans doute 'probably' (lit. 'without any doubt'), certainement 'certainly', and sûrement 'surely', which do not involve certainty, in contemporary French. We may assume that in the diachronic evolution of the meaning of these expressions, the implicature, systematically associated with the principle of conviction, has been conventionalized.

JE TROUVE QUE AS AN INDICATOR OF INDIVIDUAL SUBJECTIVITY

As [START_REF] Ducrot | Les mots du discours[END_REF] and Blanche- [START_REF] Blanche-Benveniste | Un nouveau regard sur les verbes "faibles[END_REF] observe, je trouve que 'I find' is not compatible with all sorts of predicates in a complement clause (unlike the expressions studied in the previous section). In terms of intrinsic modalities, we can say that this expression is not compatible with intrinsic alethic modalities, while it combines with epistemic, appreciative, and axiological ones: Moreover, in discourse, je trouve que does not systematically express mitigation of the assertion. Tuchais (2014: 106) observes that, by presenting a judgment as a personal opinion, the speaker may mitigate her position or, conversely, cause other points of view to stand out and thus affirm that she is taking a very strong position. It depends on the situation of speech. One can even say that if a speaker chooses to indicate explicitly that she opposes the common opinion (e.g. moi, personellement, je trouve que 'I, personally, I find that'), it is a way of strengthening her position, claiming her refusal to follow the common opinion.

At the semantic level this expression only serves to clarify the nature of the subjectivity intrinsically associated with the predicate by restricting it to the individual subjectivity of the speaker. By default, an intrinsically subjective predicate refers to the collective subjectivity, to common opinion: by stating that ce pain est bon 'this bread is good', the speaker presents her judgement as referring to a collective subjective evaluation. However, by adding je trouve que, she indicates that the subjectivity is not collective but individual, related to the person of the speaker (it is her personal opinion).

Therefore, we will consider that je trouve que does not introduce an additional modality (in addition to the intrinsic subjective modality of the predicate), but serves to make clear the (individual) nature of the subjectivity of the predicate. The predicative lexeme and the phrase je trouve que together contribute to building the expression of individual subjectivity. Thus je trouve que is fundamentally different from epistemic modal expressions (je crois / suis certain(e) / persuadé(e) que). It is because je trouve que does not trigger the construction of an extrinsic epistemic modality, like je crois que, but specifies the intrinsic subjective modality of the complement clause's predicate, that this expression imposes restrictions on predicates. It is not compatible with alethic ones, because they are objective. This is also why it does not systematically serve as an assertion's mitigator: the mechanism founded on the principle of conviction, described in relation to epistemic modalities, does not apply. We conclude with an example that illustrates the respective operations of these two types of expressions of personal opinion: Statement (12a) expresses an individual belief of the speaker concerning a collective subjective evaluation. The inferential mechanism presented in Section 2 leads to a rhetoric-pragmatic effect of mitigation. This mitigated judgement may correspond to two distinct situations (at least):

-The speaker has not tasted the soup and expresses a personal opinion about the probability that the soup is good (since she knows the cook, the ingredients of the soup, what is said about it, etc.); -She tasted the soup, but does not consider herself able to deliver a collective subjective evaluation of the soup's flavour, for example, either because she is sick and unable to appreciate it or because this soup belongs to some exotic cuisine for which she does not know the evaluation criteria.

The same does not apply to je trouve que (12b), which is only used to restrict the judgement to the speaker's individual subjectivity regarding the appreciative evaluation expressed by the predicate (bonne), which otherwise would refer, by default, to the collective subjectivity, to common opinion. According to the state of opinion of the participants in the conversation, this restriction concerning the nature of the subjectivity may correspond to its attenuation (the speaker indicates that she does not seek to impose her personal appreciative evaluation) or, conversely, to its strengthening (she signals, in this way, that she opposes her personal opinion to the common opinion).

J'ESTIME / CONSIDÈRE QUE: SUBJECTIVITY AND VARIABILITY OF JUDGEMENTS

The expressions j'estime / considère que 'I reckon / consider' are similar to je trouve que: they do not signal an extrinsic epistemic modality, but specify the nature of an intrinsic subjective modality (associated with the predicate). Consequently, they do not necessarily mitigate the assertion, and they are compatible with epistemic, axiological, and appreciative predicates but with much more difficulty with alethic ones:

(13) a. ??J'estime / ?? Considère que cette table est They differ, however, from je trouve que relative to the type of restriction made on the subjectivity of the predicate.

The opposition between subjective and objective judgments is based, according to the Kantian tradition, on the "variability in the validity of judgements" between subjects. If a judgement is true for any subject, whatever she may be when she is endowed with reason, it is considered objective. It is subjective in the opposite case, when its validity varies between subjects. However, this dimension of "variability" has two characteristics that are relevant to our study. On the one hand, there are degrees of variability. For example, to say that an axiological judgement (such as 4) refers to a system of conventions implies that it is stable and shared within this system, which itself depends on the variability of ethics and ideologies. In other words, the axiological variability of judgements corresponds to an intermediate degree between objectivity of alethic (i.e. objective) judgements and unstable individual subjectivity. On the other hand, variability may concern not only subjects but also temporality, because a subject can change his mind or, on the contrary, remain steady in his convictions. And there are also different degrees of temporal variability of judgements: axiological judgements correspond to an intermediate degree of temporal variability, between alethic judgements and appreciative judgements (which are unstable).

Consider Conversely, je considère / estime que, unlike je trouve que, are compatible with some alethic predicates that express a categorization along a continuum (15), or an approximate categorization (17), and are thus on the border between (objective) alethic and (subjective) epistemic predicates. In a situation of crachin 'drizzle' in Normandy, (15a) sounds more natural than (15b):

(15) a. Je considère / estime qu'il pleut 'I consider / reckon it's raining' b. ? Je trouve qu'il pleut 'I find it's raining'.

Similarly, Tuchais (2014: 324) From all this, it follows that je trouve que marks a higher degree of variability of the judgement than je considère / estime que. This is why je considère / estime que are more appropriate for the expression of axiological judgements (based on convention systems, which are relatively stable), while je trouve que is more appropriate for appreciative judgements bound to particular time positions, as the contrast between (18a) and (18b) shows:

(18) a.

Je considère / estime / ? trouve qu'il est coupable 'I consider / reckon / find that he is guilty' b. Je trouve / ? considère / ? estime que la soupe est brûlante 'I find / consider / reckon that the soup is hot'.

It is remarkable that trouver becomes acceptable in (18a) in the case of moral culpability, whereas it is excluded in the case of legal guilt. Morality is more akin to collective subjectivity, while legal guilt rests on a system of stable and codified conventions.

As for the difference between je considère and j'estime, considérer que refers to a judgement that can be voluntary and subject to a decision, which is not the case for the expressions j'estime / trouve que any more than for je crois / pense que. J'ai décidé de considérer / ?* estimer / ?* trouver qu'il était responsable de cette situation 'I decided to consider / reckon / find that he was responsible for this situation'.

THE DUAL FUNCTION OF JE PENSE QUE

Just like je crois que, je pense que 'I think' is compatible with all types of predicates (respectively alethic, epistemic, axiological, and With alethic predicates, this expression has a value very close to je crois que 'I believe'. It expresses an epistemic modality, which has a systematic effect of mitigation of the assertion in discourse. In the situation described in Section 3, in which the speaker is asked if her colleague is here, the answer (21) Je pense qu'elle est ici 'I think she is here' has, at first glance, effects similar to je crois qu'elle est ici. However, there are differences between croire 'believe' and penser 'think' in this construction (see [START_REF] Martin | CROIRE QUE p / PENSER QUE p[END_REF][START_REF] Dendale | A semantic description of French lexical evidential markers and the classification of evidentials[END_REF]. A judgement expressed by croire cannot be the subject of a decision (unlike considérer, see above), but it may be subject to a desire which is not possible with penser:

(22) Je veux bien croire / ?* penser qu'il ne m'a pas reconnu 'I want to believe / think that he did not recognize me'.

In this respect, croire functions like considérer, while penser is akin to trouver, estimer:

(23) Je veux bien croire / considérer / ?* penser / ?* trouver / ?? estimer qu'elle est belle 'I want to believe / consider / find / reckon she is beautiful'.

Moreover, the judgement denoted by je crois que must be based on knowledge about the situation, which gives positive reasons for belief, while the judgement expressed by je pense que may rely only on general knowledge and the absence of arguments against it. For example, if the speaker has not seen someone for a long time, she will use (24a) instead of (24b). The latter utterance would imply that the speaker has grounds, based on her knowledge of recent facts, to believe that her interlocutor remembers her:

(24) a.

Je pense que vous vous souvenez de moi 'I think you remember me' b. Je crois que vous vous souvenez de moi 'I believe you remember me'.

Consequently, even in the situation described above (in which the speaker is interviewed about the presence of her colleague), the two answers, je crois / pense qu'elle est ici, do not have exactly the same value. The first (with je crois que) assumes that the speaker has positive reasons to believe in her colleague's presence -that is, for example, the result of an abduction (see [START_REF] Desclés | La notion d'abduction et le verbe devoir "épistémique[END_REF] based on the observation of the presence of her car in the car park -while the second (with je pense que) may be grounded either on positive reasons or on a simple lack of information that would oppose the judgement: as this colleague is usually here and if the speaker has no reason to think otherwise, she says that she thinks (pense) she is here.

However, the main specificity of je pense que is that this expression works in a way comparable to je crois que when combined with an alethic predicate, but may also work like je trouve / considère / estime que when combined with an axiological one. Thus, in the statement (25) Je pense que cette décision est juste 'I think this decision is right', the expression "je pense que", in its most plausible interpretation, does not express an epistemic modality, but simply refers the axiological assessment to the speaker's personal opinion, without any effect of mitigation. In that case, penser que becomes almost synonymous with trouver que, considérer que, and estimer que.

With epistemic and appreciative intrinsic modalities (and also, to a lesser extent, with some axiological ones), two interpretations may appear, sometimes leading to ambiguity. For example, the utterances (26) a.

Je pense que ce champ est assez vaste 'I think that this field is quite extensive' b. Je pense que ce pain est bon 'I think that bread is good' can be interpreted either as expressions of belief (with a mitigation effect) in a judgement assigned to collective subjectivity (penser and croire are quasi-synonyms) or as a marker of individual subjectivity, not introducing any mitigation of the assertion. This second interpretation appears more clearly if we consider (26a) and (26b) as responses to the question Qu'en penses-tu? 'What's your opinion?'. Je pense que becomes almost synonymous with j'estime / considère que or mon avis personnel est que 'my personal opinion is that'. In other words, the speaker of (26b) either may not have tasted the bread and expresses a belief about its taste quality (with a mitigation effect) or may have tasted it and gives her personal opinion (with no mitigation effect). We can summarize this analysis with a schema:

CONCLUSION

The syntactic similarity of expressions of personal opinion is misleading. They are likely to play two distinct roles: either they trigger the construction of an extrinsic epistemic modality (compatible with all sorts of predicates in the complement clause) or they specify the nature of the subjective modality intrinsically associated with the predicate (excluding in the same time objective ones). Je crois / suis certain(e) / persuadé(e) ... que belong to the first case and je trouve / considère / estime que to the second one. The peculiarity of je considère / estime que versus je trouve que is the fact that these terms are able to transform some alethic approximate categorization judgements into subjective judgments (e.g. 15-17). The expression je pense que may, depending on the context (and in particular on the modality intrinsically associated with the predicate), fulfill either of these two roles: sometimes it expresses extrinsic epistemic modality (in the manner of je crois que) and sometimes it restricts the inherent subjectivity of the predicate to the personal opinion of the speaker.

It is only when they express an extrinsic epistemic modality that these expressions systematically have a mitigating effect on the speaker's commitment. This effect results from a discourse implicature triggered on the basis of a principle of the logic of conviction [START_REF] Lenzen | Epistemic Logic[END_REF]) saying that a subject who is really convinced that p "believes she knows that p". Accordingly, if the speaker does not use the factive epistemic modality je sais que p or does not simply say p, but uses a non-factive epistemic

(

  12) a. Je crois que cette soupe est bonne 'I believe the soup is good' b. Je trouve que cette soupe est bonne 'I find this soup is good'.

Figure 1

 1 Figure1

  provides the example:

		'I consider / reckon it is square'
	but with much more difficulty,
	(17) b. ? Je trouve qu'elle est carrée
		'I find it is square'.
	(16)	Ma chambre, je considère que je l'ai payée (Cl. Mauriac, La marquise sortit à cinq
		heures)
		'My room, I consider that I paid for it'.
	In this example, it is possible to replace considérer with estimer, but much less naturally
	with trouver.
	Even more clearly, regarding a table measuring 65 cm by 68 cm, one can say, by
	approximation,
	(17) a. Je considère / estime qu'elle est carrée

I am grateful to Gerda Haßler and an anonymous reviewer for their helpful comments and suggestions.

This distinction corresponds to the opposition between appreciations and judgements[START_REF] Martin | The language of evaluation[END_REF]

[35][36], and also to the distinction between judgements referring to personal norms and judgements referring to a system of social norms(Asher, Benamara and Mathieu 2009: 283).

In order to control rigorously the interaction between modalities, we have constructed examples and we judge their acceptability by introspection. A study based on corpora would be more convincing, but it would have required a far longer discussion.

modality (je crois / pense / suis certain(e) / sûr(e) / convaincu(e) ... que p), the interpreter will infer that, the speaker is, in fact, not really convinced that p.

Within these two subclasses of expressions of personal opinion, every expression has characteristics of its own, as the possibility of referring to a judgement which may result from a desire or decision, or, for epistemic modality, the requirement or not for positive reasons to believe that p.

Table 1 summarizes the main modal characteristics of these different expressions. Finally, let us note also that the contrasts observed concerning the use of these expressions of personal opinion make possible the use of such phrases as tests to identify the intrinsic modal value of predicates (the compatibility test with je trouve que can be used to isolate alethic predicates).


Nicolas Tremblay
email: nicolas.tremblay.31@ulaval.ca

Kaveh Kamali
email: kaveh.kamali.1@ens.etsmtl.ca

Philippe Cardou
email: pcardou@gmc.ulaval.ca

Christian Desrosiers
email: christian.desrosiers@etsmtl.ca

Marc Gouttefarde
email: marc.gouttefarde@lirmm.fr

J.-D Otis

Eye-on-Hand Calibration Method for Cable-Driven Parallel Robots

Keywords: Cable-driven parallel robot, parameter identification, experimental testing, vision-based calibration

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

Cable-driven parallel robots (CDPRs) are a type of parallel robots where rigid links are replaced by cables, known for their advantageous payload to weight ratio which allows for higher dynamic capabilities, potentially larger translational workspace, portability and reconfigurability. In order to fully benefit from these capabilities, the CDPR geometric parameters have to be determined accurately, which can prove to be difficult on a medium to large scale. Indeed, a poor knowledge of these parameters inevitably degrades the positioning accuracy of the end effector.

Excluding conceptually simple but impractical direct measurement of the geometry, some techniques have been developed for the Gough-Stewart platform calibration, but also apply to CDPRs. A popular and straightforward method uses measurements of the end effector pose in order to minimise inverse kinematic residuals [START_REF] Zhuang | Calibration of Stewart platforms and other parallel manipulators by minimizing inverse kinematic residuals[END_REF]. The required measurements are often obtained using external sensors, such as a redundant leg [START_REF] Patel | Calibration of a hexapod machine tool using a redundant leg[END_REF], a theodolite [START_REF] Zhuang | Kinematic calibration of a Stewart platform using pose measurements obtained by a single theodolite. Intelligent Robots and Systems 95[END_REF] or a camera [START_REF] Renaud | Vision-based kinematic calibration of a H4 parallel mechanism[END_REF]. The calibration can also be performed by imposing additional kinematics constraints to render the internal sensors redundant [START_REF] Khalil | Self calibration of Stewart-Gough parallel robots without extra sensors[END_REF].

Methods were proposed specifically for calibrating fully-constrained CDPRs, without the need for external sensors [START_REF] Dit Sandretto | Calibration of a fullyconstrained parallel cable-driven robot[END_REF][START_REF] Fortin-Côté | An admittance control scheme for haptic interfaces based on cable-driven parallel mechanisms[END_REF][START_REF] Lau | Initial Length and Pose Calibration for Cable-Driven Parallel Robots with Relative Length Feedback[END_REF]. The use of force sensors, allowing for simultaneous stiffness identification, is also addressed in [START_REF] Miermeister | Auto Calibration Method for Cable-Driven Parallel Robots Using Force Sensors[END_REF]. A few different calibration algorithms are also tested experimentally in [START_REF] Dit Sandretto | Calibration of a fullyconstrained parallel cable-driven robot[END_REF]. However, because they rely on measurement redundancy, these methods algorithms cannot be applied to cable-suspended CDPRs. Without proper initial estimation of the solution to the geometric identification problem, the calculation time for a large number of calibration poses can also be considerable and the accuracy of the solution cannot be guaranteed.

An alternative to these self-calibration methods consists in resorting to external sensors to measure directly the end effector pose. Over the large workspace of CDPRs, one could use traditional surveying sensors such as theodolites or total stations but their use is time-consuming. This problem can be resolved by resorting to automated measurement devices such as laser trackers [START_REF] Izard | A Reconfigurable Robot for Cable-Driven Parallel Robotic Research and Industrial Scenario Proofing[END_REF] or motion capture systems, which can be used to perform different measurements either to directly measure the geometry or to establish the robot posture. However, while these solutions currently seem to prevail within academia, the cost of such systems may be of the same order of magnitude as that of the CDPR itself. Hence, there is a true incentive to find an inexpensive methodology for the calibration of CDPRs.

It is well known that a calibrated camera can be used to estimate the position and orientation of a size-known object expressed in its own reference frame and vice versa. Eye-on-hand, or eye-in-hand calibration is performed using a moving camera, often attached to the robot end effector and a fixed target. This method is used in particular to calibrate serial robots [START_REF] Lenz | Calibrating a Cartesian robot with eye-on-hand configuration independent of eye-to-hand relationship[END_REF]. In the case of a CDPR, one advantage of this method is that only one camera is needed to perform a calibration over a large workspace. Moreover, the placement of the camera is simple and space efficient, considering that the camera on the end effector can move across the whole workspace. This avoids having to position one or more fixed cameras in such a way that it is possible to accurately track targets fixed on the end effector. Considering those potential benefits, the present paper outlines a new approach to CDPR calibration using this technique.

In section 2, the calibration process and the generation of a list of poses used to gather data is addressed. Then, in section 3, a control scheme for reaching the calibration poses is described. Finally, experiments are presented and the results are discussed in section 4.

Calibration

The goal of the calibration process is to identify the geometry of a given CDPR. In the current case, we work under the hypothesis of massless and inextensible cables. Fig. 1 shows the general geometric model of a CDPR driven by m cables. We assume that the cable lengths are measured using relative encoders, so that the total length of the i th cable is expressed as ρ i = ∆ρ i + ρ i,0 , where ρ i,0 is the cable length when the robot controller is first powered on after a reconfiguration. The geometric loop-closure equation, for a given pose X = {p, Q} takes the form:

(∆ρ i + ρ i,0 ) 2 = (p + Qb i -a i ) T (p + Qb i -a i ), (1)
where p and Q are respectively the position vector and orientation matrix of the end effector. In the case of a CDPR, the unknown parameters are usually the position of the cable output points and the initial cable lengths, namely a i and ρ i0 . A full calibration would include an identification of the end effector attachment points b i but since the latter is generally small, we consider that these parameters can be established beforehand using conventional measuring techniques. Regardless of the value of m, if a spatial mechanism is considered, the constraint n ≥ 4 must be satisfied in order to avoid underdetermination of the system, where n is the number of calibration poses. The residual of the loop-closure equation, for each measurement j, is written

u i,j = ||p j + Q j b i -a i || 2 2 -(∆ρ i,j + ρ i,0 ) 2 . ( 2
)
where ∆ρ i,j is directly obtained from the relative encoders and p j and Q j are provided by an external sensor. The calibration problem is then written as a nonlinear least squares optimisation, namely minimise ai,ρi,0

m i=1 n j=1 u 2 i,j (3)
when considering all cables i = 1, ..., m. The next section provides details concerning the external measurements for every calibration pose.

Eye-on-Hand Calibration

In the work reported in this paper, this external sensor is an embedded camera, which must provide enough data to estimate the end effector pose (p j , Q j ). The detection of fiduciary markers is the chosen approach because it is simple and it allows for fast processing and reliable positioning.

As the end effector is intended to cover a large workspace, the use of a single marker would result in poor positioning accuracy and would be limited to only a small part of the workspace. This problem could be solved by using an array of different markers of known relative poses but the manufacturing of such objects would be impractical or prone to errors. Instead, we choose to spread uniquely identified markers throughout the robot workspace, without prior knowledge of their relative pose. The existing ArUco C++ library [START_REF] Garrido-Jurado | Generation of fiducial marker dictionaries using Mixed Integer Linear Programming[END_REF][START_REF] Romero-Ramirez | Speeded up detection of squared fiducial markers[END_REF] can be used for marker generation and detection and the corresponding marker mapper [START_REF] Muñoz-Salinas | Mapping and localization from planar markers[END_REF] tool can easily be adapted, which makes it well suited for the current application. This library allows for localisation and mapping of the markers. The resulting map can then be used to estimate the camera pose. In such a case, the markers can be removed after the calibration is completed.

The end effector pose can be obtained from the measured camera pose through the rigid transformations p ce and Q ce , namely,

p = p mw + Q mw p cm + Q mw Q cm p ce , (4a)
Q = Q mw Q cm Q T ce , (4b)
where p cm and Q cm are obtained using the camera pose reconstructed by the marker mapper. If p mw and Q mw are not known beforehand, it is possible to choose O w such as it is coincident with O m , which leads to p mw = 0 and Q mw = 1 3×3 , thus eliminating any possibility of measurement errors between the two reference frames. The constant values p ce and Q ce must be determined prior to calibration. These can be obtained by observing a marker with the end effector camera and comparing the resulting p cm and Q cm measurements to the measured position and orientation of the end effector with respect to the marker reference frame. For fully-constrained CDPRs, this transformation can also be estimated alongside the calibration by simply adding the parameters p ce and Q ce to the decision variables of the optimisation problem of Eq. 3.

Generation of a List of Reachable Calibration Poses

In order to perform an autonomous calibration, it is essential to generate a pool of poses X j = {p j , Q j }, which can be reached from an initial pose X 0 = {p 0 , Q 0 }, located inside the workspace. To be feasible, the trajectory must be included within the wrench-feasible workspace and free of collision between cables. The proposed method works by projecting X r , a pose randomly generated inside a 6-dof box, towards X 0 , on the workspace of the robot.

However, in order to find reachable poses, an initial estimation of the parameters to calibrate is needed. In the context of this paper, the latter is obtained using a simple measuring tape, but other viable and affordable solutions are available, such as ultra-wideband positioning systems and inclinometers.

Let us define the trajectory between X 0 and X r as a straight-line motion of point p 0 combined with a constant angular velocity of the end effector. Such a motion is parameterised as

p(λ) = p 0 + λ(p r -p 0 ), (5a) Q(λ) = Q t (λ)Q 0 , (5b)
where 0 ≤ λ ≤ 1 and

Q t (λ) = ee T + cos(λφ)(1 3×3 -ee T ) + sin λφE (6)
is the rotation undergone by the end effector along its trajectory from its attitude at λ = 0 to that at λ. We use

E = cpm(e), where cpm(x) ≡ ∂(x × y) ∂y (7)
so that e and φ respectively represent the rotation axis and the rotation angle. Upon solving Eq. (5b) for Q t (λ) and setting λ = 1, we obtain

Q t (1) = Q r Q T 0 . (8)
Those axis and angle values can be then found first by defining vect(Q t (1)) ≡ 1 2   q t32 -q t23 q t13 -q t31 q t21 -q t12   and tr(Q t (1)) ≡ q t11 + q t22 + q t33 (9)

and then using the properties

tr(Q t (1)) = 1 + 2 cos φ, (10a) vect
(Q t (1)) = sin φe. ( 10b
)
For the purpose of satisfying the wrench-feasible criterion, we aim to find the maximum λ = λ s value that can be reached without any constraint violation. This can be ensured first by defining the cable direction for each cable

c i (λ s ) = a i -p(λ s ) -Q(λ s )b i ||a i -p(λ s ) -Q(λ s )b i || (11)
and constructing the end effector pose-dependant wrench matrix

W(λ s ) = c 1 (λ s ) • • • c m (λ s ) Q(λ s )b 1 × c 1 (λ s ) • • • Q(λ s )b m × c m (λ s ) . ( 12
)
By imposing bounds over the cable tensions in the cables t min ≤ t i ≤ t max and the static equilibrium constraints, we then formulate the problem as follows maximise λ s subject to t min ≤ t ≤ t max , W(λ s )t + w e = 0,

0 ≤ λ s ≤ 1 ( 13
)
where t is the array of cable tensions and w e is the wrench applied on the end effector by its environment.

A similar approach is used for considering the cable-cable interferences. Let ζ(p k1 , p k2 , p l1 , p l2 ) be a function computing the distance between two line segments defined by their four end-points p k1 , p k2 , p l1 and p l2 , as presented in [START_REF] Meziane | Cable interference control in physical interaction for cable-driven parallel mechanisms[END_REF]. The cables k and l are therefore represented by the line segments p k2 -p k1 and p l2 -p l1 . These points can then be rewritten as functions of the geometry and of the trajectories described in Eqs. (5a) and (5b):

p k1 = a k , (14a) p k2 = p(λ k,l ) + Q(λ k,l )b k , (14b) p l1 = a l , (14c)
p l2 = p(λ k,l ) + Q(λ k,l )b l . (14d)
A collision between two real cables occurs when ζ(p k1 , p k2 , p l1 , p l2 ) < , where is the diameter of the cables. For the sake of simplicity, we consider cables of a negligible diameter, i.e., = 0. The roots of the function are then found using minimise

λ k,l ζ(p k1 , p k2 , p l1 , p l2 ) subject to 0 ≤ λ k,l ≤ 1 (15)
for the m 2 (m -1) possible pairs of cables, i.e., for k, l ∈ {1, ..., m}, k < l. If no root is found, then λ k,l = 1. Ultimately, when considering simultaneously wrench feasibility and the possibility of interference between any cable pair, the maximum point that can be reached on the trajectory is obtained as:

λ = µ min{λ s , λ k,l } (16)
where 0 ≤ µ ≤ 1 is a factor introduced to account for discrepancies between the initial estimate of the robot geometry and its true geometry. It can be adjusted according to the level of trust in the initial approximation of the parameters, a high value representing confidence, and a low one, uncertainty. The resulting pose X can finally be obtained using Eqs. (5a) and (5b). Since the optimisations ( 13) and ( 15) both starts from X 0 , known to be located within the workspace of the robot, a feasible solution is always found, the worst case scenario being that X j = X 0 , i.e., λ = 0.

Once the list of poses and their associated trajectories is generated, the focus can shift to the problem of tracking them with the robot.

Control

In order to move the end effector to the computed calibration poses before the robot is fully calibrated, a control scheme capable of dealing with errors in the initial estimate of the geometric parameters is necessary. Thus, control is achieved by a simple low-level velocity controller, inspired by [START_REF] Fortin-Côté | An admittance control scheme for haptic interfaces based on cable-driven parallel mechanisms[END_REF], driven by a Cartesian position controller. The block diagram of the control algorithm is presented in Fig. 2. To ensure valid cable measurements, this controller purpose is to keep the cables thaught, while trying to reach the desired pose. The controller C p generates trajectories with trapezoidal speed profiles ṗ and ω in order to reach the desired Cartesian position p and orientation Q. The matrix J = -W T is then used to transform the desired Cartesian and angular speeds into articular speeds. A set of feasible cable tensions τ e is generated from w e using quadratic programming. The algorithm is concretely implemented using a C program generated with CVXGEN [START_REF] Mattingley | CVXGEN: A code generator for embedded convex optimization[END_REF]. The gain K τ is derived from the geometry of the winches and used to link the desired cable tension to the motor torque, while K v is the gain of the low-level proportional speed controller. It should be noted than K τ could be replaced by a closed loop tension controller. To address undesirable speed variation issues caused by the cogging ripple of the permanent magnets motors used in section 4, a cogging compensation block was introduced in the model. Even though this addition produced satisfying results, it will not be discussed in detail in this paper. The controlled motor torque is then given by the sum of the cogging compensation torque t c , the torque t τ needed to achieve the desired set of tensions and the torque t v generated by the low-level proportional speed controller. A saturation is placed on t v to prevent any excessive unwinding of the cables that could be caused by modeling errors, since the mechanism that will next be presented for validation is backdrivable.

Experiment

To test the performance of the proposed method, a validation is carried out on an existing CDPR. The setup consists of eight winches, each mounted on a motorised linear axis, allowing it to be easily reconfigured. The winches were designed to operate in industrial-like conditions and to withstand a large payload. They are driven by Parker MPP0923D motors coupled to 4:1 gearboxes. The size of the gantry is approximately 5 m × 4 m × 3 m and the winches are brought as close as physically possible to the corners of the structure.

The end effector is a 0.2 m, × 0.2 m × 0.6 m prism. The cables are made of 5 mm Dyneema SK75 synthetic rope. As can be seen in Fig. 3, they are attached to the end effector in a way that allows the control of its orientation. A self-contained vision module consisting of a 1.3 megapixel Basler ace acA1300-30gm camera, a battery and a Raspberry Pi computer is located inside the latter. The camera is oriented towards the markers, placed on the ground for practical reasons. For generality's sake, the markers are not considered to be located on a common plane. One marker is chosen as the reference for the whole map.

For the measurements, the ground truth is provided by a Faro X130 laser scanner with a ranging error of ± 2 mm (at 1σ).

Trials and results

At first, the camera is calibrated using the Aruco calibration board, laminated on a flat plastic surface, resulting in a mean reprojection error is 0.51 pixels. Then, three different lists of random calibration poses (A, B and C) are generated using µ = 0.8 and a length of n = 100 samples. The practical choice of O w coincident with O m is made. Data is then gathered in the form of relative cable length and pictures of the marker map are taken using the camera. Once the robot covered all calibration poses, the marker map geometry is established. Fig. 4 shows an example of the reconstructed camera poses and markers locations. Using the reconstructed camera poses, the calibration is performed by solving Eq.( 3) using the trust-region-reflective algorithm provided by the lsqnonlin MATLAB function. The resulting geometric parameters are then updated, and the accuracy is tested for ten witness poses, shown in Fig. 5.

A second calibration, for comparison purposes, is performed again but excluding the camera data, i.e., using only cable measurements. The second method, described in [START_REF] Fortin-Côté | An admittance control scheme for haptic interfaces based on cable-driven parallel mechanisms[END_REF][START_REF] Lau | Initial Length and Pose Calibration for Cable-Driven Parallel Robots with Relative Length Feedback[END_REF], relies exclusively on the motor encoders of fully constrained CDPR architecture and as stated above, it can only be applied to robots with more cables than degrees of freedom. Without an external reference, the mechanism geometry is unconstrained. To resolve this indeterminacy and to ensure consistancy, six components of the a i vectors are prescribed from the values obtained in the previous step. The end effector pose previously computed using the camera is also provided to the optimisation algorithm as an initial estimation of the solution to avoid convergence to a different local minimum. Upon completion of the calibration, the accuracy is tested for the same ten witness poses.

The error is determined by the difference between the forward kinematics problem (FK) result and an external measurement between the end effector and the reference marker, provided by the laser scanner. The optimisation convergence is expressed by r, which is defined as the fourth root of the residual of Eq. ( 3), divided by the number of calibration poses n.

Table 1 presents the compiled performance results. The pose is measured relative to the marker map (R.t. marker) used for calibration. To ensure proper comparison between the two calibration methods, and to prevent any bias caused by the camera from degrading the accuracy over the entire workspace, the pose is also measured relative to the first pose (R.t. 1 st pose). It should be noted that according to the ground truth measurements, errors in both position and orientation do not seem to be predominant in one particular direction. Additionally, for each of the 10 validation poses of the eye-on-hand calibrations, a snapshot of the marker map is taken using the camera. The resulting images can be compared to the previously established marker map geometry for the purpose of validating the camera pose reconstruction. Because the pose of the camera cannot be directly picked up, we measured instead the end effector pose. Table 2 summarises the errors obtained using the laser scanner data as a reference while Table 3 presents the discrepancy between the poses obtained with the camera measurements alone, and those obtained through the cable lengths, after calibration. In the following section, relationships between these data and the calibration results will be discussed.

Discussion

From the results of Table 1, it appears that the proposed eye-on-hand calibration method did improve the accuracy of the robot relative to the first pose, but this improvement is only statistically significant for some data sets. It can also be seen by looking at the data set C that, when compared to the calibration method using only measurement redundancy, the use of the camera can prevent excessive divergence of the geometric parameters. Upon one-way analysis of variance using a significance level of 0.05, the positioning accuracy was improved only for the dataset C, while the orientation accuracy was improved for all datasets. It can be observed from Table 3 that the FK solution is generally consistent with the reconstructed camera pose, especially in the case of the mean position error of data sets A and B. However, Table 2 shows that the same camera pose estimation is subject to errors in an order of magnitude similar to those measured after calibration, both in orientation and in translation. This suggests that the precision of the camera pose reconstruction is limiting the accuracy of the calibration. Improving the resolution and calibration of the vision system could therefore lead to improvements in calibration and thus in positioning accuracy.

Conclusion

This paper presents an investigation into the use of an eye-on-hand calibration method, for determining the geometric parameters of CDPRs. To this end, a list of reachable poses was generated based on an estimate of the CDPR geometry. A control scheme was adapted to allow the end effector to reach each of these poses. Finally, the method was experimentally validated on a medium sized fully constrained CDPR. While the worst relative mean position and orientation errors measured were respectively of 30.5 mm and 1.6 • , the results suggest that the positioning accuracy of the calibrated CDPR could be increased by improving the accuracy of the reconstruction of the camera pose.

Fig. 1 .

 1 Fig. 1. Cable robot geometric model for eye-on-hand calibration

Fig. 2 .

 2 Fig. 2. Control scheme used to perform the calibration

Fig. 3 .Fig. 4 .Fig. 5 .

 345 Fig. 3. Experimental setup: on the left, an overall view of the gantry and markers located on the ground. On the right, the end effector and the embedded vision system

Table 1 .

 1 Calibration results

	Data set		r (mm) Position error (mm) Orientation error (deg)
				R.t. marker R.t. 1 st pose R.t. marker R.t. 1 st pose
				Mean Std Mean Std Mean Std Mean Std
	Proposed	A 12.9	60.9 8.1 25.8 7.8	2.1	0.8	1.3	0.9
	method	B 14.1	64.5 14.0 27.4 8.2	2.3	0.5	1.3	0.7
	(with camera)	C 15.6	59.5 17.2 30.5 11.1 2.9	0.6	1.6	1.2
	Cable lengths only [2, 6]	A B C	3.8 4.2 4.0	278.3 22.0 28.6 11.2 4.6 268.2 24.0 28.7 16.0 3.2 984.5 25.6 110.1 32.1 7.6	1.8 1.2 4.4	2.9 2.7 5.7	2.0 1.0 1.1

Table 2 .

 2 Camera pose errors, relative to ground-truth

	Data set	Position error (mm) Orientation error (deg)
		Mean	Std	Mean	Std
	A	59.2	9.1	1.8	0.4
	B	61.5	12.4	1.9	0.4
	C	30.8	9.6	1.5	0.4

Table 3 .

 3 Camera pose inconsistencies, relative to FK solution

	Data set	Position error (mm) Orientation error (deg)
		Mean	Std	Mean	Std
	A	8.4	4.2	1.3	0.4
	B	8.2	3.5	1.2	0.5
	C	32.2	10.3	2.3	0.5

Acknowledgments

This work is financially supported by the Fonds de recherche du Québec -Nature et technologies (FRQNT), under the grant number 2016-PR-188869.