Guillaume Vailland

Fabien Grzeskowiak

Louise Devigne

Yoren Gaf- Fary

Bastien Fraudet

Emilie Leblong

Florian Nouviale

François Pasteau

Ronan Le Breton

Sylvain Guégan

Valérie Gouranton

Bruno Arnaldi

Yoren Gaffary

Valérie Gouran- Ton

Marie Babel

Sylvain Guegan

Expérience

Fabio Morbidi

Stefan Catalin

Bastien Teodorescu

Emilie Fraudet

Tom Leblong

Marie Carlson

Guillaume Babel

Sarah Caron

François Del- Mas

Guillaume Pasteau

National conference with proceedings JCJC 2019

Je commencerais par remercier le Jury d'avoir accepté de lire ce manuscrit et d'assister à ma soutenance de thèse. Je vous suis également reconnaissant pour vos travaux qui m'ont permis de réaliser cette thèse.

Je voudrais remercier mes deux encadrantes, Marie et Valérie car vous avez été d'un grand soutien indéfectible durant ces 3 années.

Vient le tour de tous mes collègues et personnes que j'ai pu rencontrer grâce à cette aventure, je pense notamment aux équipes Hybrid et Rainbow et plus spécifiquement à mes collègues du projet ADAPT. J'ai apprécié tous nos moments passés ensemble qui ont rendu cette thèse très confortable et agréable. J'aimerais remercier profondément toute ma famille et plus spécifiquement mes parents, ma soeur et mon frère de m'avoir toujours soutenu dans ce que j'ai entrepris, de m'avoir toujours écouté et conseillé.

Ensuite je voudrais remercier tous ceux que je nomme "Amis", il y en a bien trop pour que je les nomme tous. Vous m'avez permis de m'évader, vous m'avez fait rire, vous m'avez écouté et pour ça je vous en suis éternellement reconnaissant. C'est un peu votre thèse à vous également, car sans détente et sans vous je n'aurais pas pu avancer clairement dans mes recherches. Cézo, Le Collectif, La Cochouais, Les Mansaouls, Kiràly, Ysifa, vous faites partie de moi.

Je terminerai par quelques mentions spéciales à commencer par une mention pour toi, Claire, car sans toi je n'aurais probablement pas commencé cette aventure. Tu as accompagné mes pensées durant ces 3 années et même si l'on s'est éloigné tu comptes énormément pour moi. Je te souhaite de trouver ton bonheur car tu le mérites autant que tu es passionnante. Ma seconde mention s'adresse à Hugo, mon ami, co-bureau puis coloc'. Notre relation est magnifique, pleine de couleur, de relief et de profondeur. Merci de m'avoir écouté et épaulé pendant ce voyage. J'espère que celui que tu prépares sera tout aussi épanouissant.

Cette thèse a été motivée par la volonté de développer des solutions innovantes liées aux fauteuils roulants électriques pour permettre aux personnes en situation de handicap de retrouver leur mobilité. En effet, de nombreux handicaps entraînent une perte de mobilité qui peut se traduire par une perte de confiance en soi, limitant ainsi grandement les interactions et les activités sociales. Les fauteuils roulants électriques sont l'une des solutions les plus populaires pour maintenir ou retrouver un certain degré de mobilité. Grâce à une prise de conscience sociétale accompagnée de progrès technologiques, les innovations autour des fauteuils roulants électriques se sont multipliées ces dernières années. Les objectifs de cette thèse sont d'abord de comprendre les enjeux et le contexte social liés au handicap et plus particulièrement aux fauteuils roulants électriques, puis de proposer des solutions innovantes pour améliorer et simplifier la navigation des fauteuils roulants électriques dans des contextes complexes.

Après ce chapitre introductif présentant le contexte social, les motivations et les objectifs de la thèse, le chapitre 1 explore l'état de l'art des fauteuils roulants électriques classiques et des fauteuils roulants électriques intelligents, en exposant les objectifs, les résultats et les défauts des innovations récentes. Ensuite, le chapitre 2 passe en revue la littérature relative à la réalité virtuelle (RV) et plus particulièrement à la simulation et aux simulateurs de fauteuils roulants électriques. La navigation en fauteuil roulant électrique est le résultat des compétences du conducteur combinées à l'"intelligence" du fauteuil. Ainsi, cette thèse présente des solutions pour améliorer les deux respectivement dans les chapitres 3 et 4. Enfin, le chapitre 5 souligne comment cette thèse constitue un pas de plus vers la conception de solutions de fauteuils roulants électriques intelligents.

Mobilité et enjeux

Selon l'Organisation mondiale de la santé, environ 785 millions de personnes vivent avec un handicap, ce qui représente près de 10% de la population mondiale. Parmi elles, entre 110 et 190 millions de personnes ont des difficultés importantes, comme l'incapacité de marcher ou d'effectuer des activités sociales ou d'auto-soins [START_REF] Organization | Guidelines on the provision of manual wheelchairs in less resourced settings[END_REF]]. Bien que ce nombre soit susceptible d'augmenter en raison du vieillissement de la population mondiale, la question du handicap et en particulier de la perte de mobilité ne concerne pas uniquement les personnes âgées. En effet, en 2001, 32% des 145000 participants à l'étude présentée dans [START_REF] Iezzoni | Mobility difficulties are not only a problem of old age[END_REF]] ont déclaré que leurs principales difficultés de mobilité avaient commencé avant la cinquantaine. La figure A.2 du rapport annuel 2015 sur les statistiques du handicap [START_REF] Kraus | Disability Statistics Annual Report[END_REF]] montre que la majorité des civils américains en situation de handicap ont entre 18 et 64 ans.

La perte de mobilité représente un enjeu médical et social majeur puisque de multiples études ont révélé un lien direct entre elle et la diminution de l'emploi, la réduction du salaire, les faibles interactions sociales, les activités limitées et la faible indépendance [START_REF] Smith | A review of factors influencing participation in social and community activities for wheelchair users[END_REF][START_REF] Salter | Impact of loss of mobility on instrumental activities of daily living and socioeconomic status in patients with MS[END_REF][START_REF] Finlayson | Experiencing the loss of mobility: Perspectives of older adults with MS[END_REF]. En outre, les activités limitées et l'isolement social ont un impact négatif sur la santé mentale, ce qui peut parfois conduire à une faible estime de soi et à la dépression à long terme, comme cela a été observé lors des confinements dus à la pandémie de COVID-19 [START_REF] Usher | Life in the pandemic: Social isolation and mental health[END_REF]. Par conséquent, la mobilité réduite et ses conséquences, en particulier l'isolement social, doivent être considérées comme des facteurs de risque importants pour une morbidité et une mortalité générales plutôt que comme une condition particulière [J. T. Cacioppo and S. Cacioppo 2014]. Ainsi, le maintien ou la récupération de la mobilité semble être une problématique de premier plan pour toutes les personnes en situation de handicap, qui représentent une part importante et croissante de la population mondiale. Au fil des ans, de nombreux dispositifs d'aide à la mobilité aux objectifs et aux champs d'application variés ont été développés, de la canne ordinaire à l'exosquelette complet. L'un des dispositifs d'assistance les plus connus et les plus utilisés est le fauteuil roulant [START_REF] Fomiatti | A systematic review of the impact of powered mobility devices on older adults' activity engagement[END_REF]]. Alors que les cannes et les déambulateurs visent à compenser les pertes de mobilité mineures, les fauteuils roulants permettent aux personnes ayant des handicaps les empêchant de marcher de manière autonome de parcourir éventuellement de longues distances par elles-mêmes [Richard C Simpson, LoPresti, and R. A. Cooper 2008]. Cependant, l'utilisation régulière de fauteuils roulants manuels entraîne fréquemment des blessures et des douleurs : les utilisateurs doivent se propulser non seulement eux-mêmes, mais aussi le fauteuil roulant lui-même et ce qu'ils portent en même temps [START_REF] Ott | Evaluation of rolling resistance in manual wheelchair wheels and casters using drum-based testing[END_REF]]. Ainsi, dans l'étude [START_REF] Ramirez | But, I Don't Want/Need a Power Wheelchair" Toward Accessible Power Assistance for Manual Wheelchairs[END_REF], 12 utilisateurs de fauteuils roulants manuels s'accordent à dire qu'ils en souffrent quotidiennement, en particulier sur de longues distances, indépendamment du relief de la surface sur laquelle ils se déplacent et de la force de leurs bras. En fonction de la force de l'utilisateur, le moindre obstacle comme un simple trou ou une légère pente représente un plus grand défi pour les utilisateurs de fauteuil roulant manuel que pour les utilisateurs de fauteuil roulant électrique. Par conséquent, les fauteuils roulants électriques, qui sont des fauteuils à propulsion électrique, sont préférés pour réaliser des déplacements plus longs car ils sont plus confortables et moins blessants. En outre, plusieurs études comme [START_REF] Martins | Psychosocial Impact of Assistive Technologies for Mobility and Their Implications for Active Ageing[END_REF]] et [START_REF] Fomiatti | A systematic review of the impact of powered mobility devices on older adults' activity engagement[END_REF] suggèrent que les fauteuils roulants électriques sont aussi efficaces que les fauteuils roulants manuels pour aider les personnes à mobilité réduite et qu'ils ont un impact positif plus important que les autres dispositifs d'aide à la mobilité.

Les impacts et l'efficacité du fauteuil roulant en termes d'aide à la mobilité sont difficiles à évaluer car la plupart des méthodes d'évaluation sont basées sur des données subjectives. En 2007, les auteurs de [START_REF] Pettersson | The value of an outdoor powered wheelchair with regard to the quality of life of persons with stroke: A follow-up study[END_REF] ont mené une étude de suivi auprès de 32 utilisateurs agés de fauteuil roulant électrique en se basant sur les questionnaires EuroQo1-5D et PIADS pour évaluer l'impact psychologique et global de l'utilisation d'un fauteuil roulant électrique. Ils ont révélé une influence positive significative de l'utilisation d'un fauteuil roulant électrique sur la qualité de vie en ce qui concerne les critères de performance tels que la compétence, l'indépendance et la capacité, mais aussi les critères psychologiques tels que l'estime de soi, le bien-être et le bonheur. Ces résultats ont été confirmés par des études plus récentes auprès de diverses populations. En 2016, le fauteuil roulant électrique a été qualifié de facilitateur par les 35 jeunes utilisateurs interrogés dans [START_REF] Salatino | An observational study of powered wheelchair provision in Italy[END_REF]]. Les auteurs de [START_REF] Labbé | Mobility and participation among ageing powered wheelchair users: Using a lifecourse approach[END_REF]] en 2018 sont arrivés aux mêmes conclusions à partir d'une étude de suivi de l'acquisition d'un fauteuil roulant électrique sur 2 ans auprès de 19 participants. Ils ont noté un impact psychologique positif, notamment sur l'estime de soi. Cependant, ils ont également souligné des problèmes concernant l'accessibilité et l'utilisabilité du fauteuil roulant électrique. En effet, selon la littérature, la majorité des personnes qui ont besoin d'un fauteuil roulant n'y ont même pas accès en raison du prix, de leur géolocalisation ou de leur incapacité à le conduire. En 2015, l'Organisation mondiale de la santé estimait que 65 à 75 millions de personnes avaient besoin d'un fauteuil roulant mais que seulement 5 à 15% d'entre elles en disposaient [Organization 2015;[START_REF] Organization | Guidelines on the provision of manual wheelchairs in less resourced settings[END_REF]. Un fauteuil roulant électrique est un appareil coûteux, difficile à acquérir et surtout à conduire. Ainsi, au-delà de l'efficacité, les avis sur les fauteuils roulants électriques sont mitigés [START_REF] Salatino | An observational study of powered wheelchair provision in Italy[END_REF][START_REF] Torkia | Power wheelchair driving challenges in the community: A users' perspective[END_REF]].

Fauteuil roulant électrique et défis

Au-delà des questions financières et géographiques, la conduite d'un fauteuil roulant électrique tel qu'il est conçu aujourd'hui est une tâche terriblement difficile qui requiert de bonnes capacités visuo-spatiales et cognitives [START_REF] Massengale | Effect of visual perception, visual function, cognition, and personality on power wheelchair use in adults[END_REF][START_REF] Fehr | Adequacy of power wheelchair control interfaces for persons with severe disabilities: A clinical survey[END_REF].

Conduire un fauteuil roulant électrique en toute sécurité requiert un niveau d'expertise encore plus élevé, en particulier pour les personnes ayant des handicaps complexes [START_REF] Hardy | Powered wheelchair mobility: An occupational performance evaluation perspective[END_REF]]. Ainsi, les personnes présentant des déficiences cognitives et visuo-spatiales doivent s'exercer à la conduite par le biais de programmes de formation pour être autorisées à conduire un fauteuil roulant électrique [START_REF] Anstey | Cognitive, sensory and physical factors enabling driving safety in older adults[END_REF]. En effet, les thérapeutes doivent s'assurer que l'aide à la mobilité motorisée qu'ils vont prescrire à l'utilisateur sera utilisée en toute sécurité dans la vie quotidienne. [START_REF] Mortenson | Prescribers' Experiences With Powered Mobility Prescription Among Older Adults[END_REF]. Si l'évaluation ou la formation n'aboutit pas, les thérapeutes peuvent décider d'empêcher la prescription d'un fauteuil roulant électrique à un patient pour des raisons de sécurité.

Le sentiment général des utilisateurs est que les fauteuils roulants électriques sont difficiles à utiliser [START_REF] Labbé | Mobility and participation among ageing powered wheelchair users: Using a lifecourse approach[END_REF][START_REF] Torkia | Power wheelchair driving challenges in the community: A users' perspective[END_REF]. Parfois, c'est le résultat de fauteuils roulants électriques mal conçus ou non adaptés au handicap de l'utilisateur, rendant son utilisation presque impossible ou non pertinente [START_REF] Ramirez | But, I Don't Want/Need a Power Wheelchair" Toward Accessible Power Assistance for Manual Wheelchairs[END_REF][START_REF] Rice | A systematic review of risk factors associated with accidental falls, outcome measures and interventions to manage fall risk in non-ambulatory adults[END_REF]. Parfois, l'environnement n'est pas adapté aux fauteuils roulants et notamment les environnements extérieurs et publics qui n'intègrent pas systématiquement les utilisateurs de fauteuils roulants dans leur processus de conception [START_REF] Salatino | An observational study of powered wheelchair provision in Italy[END_REF][START_REF] Bromley | City centre accessibility for wheelchair users: The consumer perspective and the planning implications[END_REF]. Enfin, parfois, les utilisateurs sont mal suivis par les thérapeutes ou mal formés ce qui entraîne des accidents mais aussi des renoncements [START_REF] Salatino | An observational study of powered wheelchair provision in Italy[END_REF]. Selon les auteurs de [START_REF] Edwards | A survey of adult power wheelchair and scooter users[END_REF], 21% des utilisateurs de fauteuil roulant électrique ont eu un accident au cours de la première année. Non seulement les accidents sont dangereux pour les utilisateurs et leurs proches, mais ils peuvent aussi facilement endommager le fauteuil roulant électrique lui-même, ce qui peut entraîner des frais supplémentaires coûteux [START_REF] Salatino | An observational study of powered wheelchair provision in Italy[END_REF]. En outre, un accident a un impact négatif sur l'estime de soi car il représente un échec et/ou une source d'embarras et de honte pour certains utilisateurs [START_REF] Pettersson | The value of an outdoor powered wheelchair with regard to the quality of life of persons with stroke: A follow-up study[END_REF]. Le simple fait d'attirer l'attention à cause d'une chute ou d'un accessoire est une situation désagréable pour de nombreux usagers qui ont le sentiment d'être perçus à travers leur handicap plutôt que comme une personne à part entière [START_REF] Labbé | Mobility and participation among ageing powered wheelchair users: Using a lifecourse approach[END_REF]]. Enfin, même si les utilisateurs n'ont pas d'accident, la peur d'en avoir un, de blesser quelqu'un ou de perdre le contrôle est constante et altère l'expérience de navigation [START_REF] Torkia | Power wheelchair driving challenges in the community: A users' perspective[END_REF]. Pour éviter ces accidents, la solution la plus simple serait de rendre la formation et les évaluations plus strictes [START_REF] Bigras | A scoping review of powered wheelchair driving tasks and performance-based outcomes[END_REF]. Cependant, cette idée réduirait une accessibilité aux fauteuils roulants électriques déjà faible. Ainsi, d'autres solutions doivent être trouvées pour simplifier et sécuriser la conduite, en d'autres termes, pour améliorer la navigation en fauteuil roulant électrique.

Motivations

Une façon d'améliorer la navigation en fauteuil roulant électrique est d'améliorer le fauteuil lui-même. Au fil des ans, un grand nombre d'outils et d'innovations liés aux fauteuils roulants électriques ont été proposés. En particulier, des fauteuils roulants électriques intelligents ont vu le jour, comme le détaille le chapitre 1. De plus, les progrès continus de la technologie et de l'informatique, visibles à travers l'amélioration de la puissance des machines, la réduction du temps de réponse et l'émergence de l'intelligence artificielle, nous permettent de repenser chaque solution récente [START_REF] Haddad | Deep Learning Architecture to Assist with Steering a Powered Wheelchair[END_REF]. Malheureusement, il semble que les fauteuils roulants électriques actuellement disponibles soient encore imparfaits; ni totalement adaptés ni facilement adaptables à chaque utilisateur et à chaque déficience. En général, le développement même des nouvelles technologies d'assistance est à peine centré sur l'utilisateur : le fauteuil roulant électrique semble toujours être considéré comme un robot mobile avec un siège monté dessus plutôt que comme un dispositif de mouvement complet avec un conducteur [START_REF] Leaman | A comprehensive review of smart wheelchairs: Past, present and future[END_REF]. Par exemple, ce n'est qu'au cours de la dernière décennie qu'un projet a concentré ses recherches sur le confort de l'assise et la répartition de la masse lorsque le fauteuil roulant électrique est incliné [START_REF] Kanki | An evaluation of physical strains while driving an electric wheelchair[END_REF]. L'inclusion des utilisateurs de fauteuils roulants électriques fait défaut dans tous les domaines, de l'urbanisme, qui est généralement très mal conçu pour le passage d'un fauteuil roulant, à la conception des objets de la vie quotidienne [START_REF] Torkia | Power wheelchair driving challenges in the community: A users' perspective[END_REF]. Concernant les fauteuils roulants électriques intelligents, lorsque les utilisateurs sont interrogés, beaucoup reprochent aux systèmes semiautonomes ou autonomes de ne pas les inclure dans la boucle du processus de décision, de ne pas les informer du processus en cours [START_REF] Leaman | A comprehensive review of smart wheelchairs: Past, present and future[END_REF]. Ce manque de sensibilisation peut conduire à un sentiment de perte de contrôle et n'aide pas à développer l'estime de soi [START_REF] Ramirez | But, I Don't Want/Need a Power Wheelchair" Toward Accessible Power Assistance for Manual Wheelchairs[END_REF]. À ce titre, certaines recherches récentes suggèrent de recentrer les développements liés aux fauteuils roulants électriques sur l'utilisateur [Erdogan and Argall 2017b].

Une autre façon d'améliorer la navigation en fauteuil roulant électrique est d'améliorer les compétences du conducteur. Les programmes classiques de formation en situation, encore utilisés aujourd'hui, apparaissent impersonnels, trop courts et parfois inefficaces [START_REF] Salatino | An observational study of powered wheelchair provision in Italy[END_REF]. En effet, selon les capacités de la personne et le type de son handicap, le processus d'apprentissage peut prendre plus ou moins de temps et nécessiter plus ou moins d'attention de la part des thérapeutes [START_REF] Harrison | The role of virtual reality technology in the assessment and training of inexperienced powered wheelchair users[END_REF][START_REF] Cromby | The potentials of virtual environments in the education and training of people with learning disabilities[END_REF]. De plus, ces programmes d'entraînement peuvent être coûteux et parfois irréalisables compte tenu de la situation à simuler.

Ainsi, les situations d'entraînement simples sont privilégiées, comme les espaces confinés, avec peu de danger et des manoeuvres spécifiques, alors que les utilisateurs devraient être formés pour faire face à des situations complexes également. Depuis quelques années, de nouvelles méthodes de formation ont été explorées, basées sur les nouvelles technologies telles que la réalité virtuelle (RV). La RV fait référence à un domaine de l'informatique consistant à simuler des environnements virtuels (EV). Parmi ses multiples avantages présentés au chapitre 2, la RV permet de simuler n'importe quelle situation de manière sûre, contrôlée et reproductible. En tant que telle, la simulation basée sur la RV apparaît comme un excellent outil pour une formation plus spécifique. En outre, les simulateurs basés sur la RV ont déjà fait leurs preuves dans d'autres domaines tels que l'aviation ou la chirurgie [START_REF] Basdogan | VR-based Simulators for Training in Minimally Invasive Surgery[END_REF][START_REF] Hays | Flight Simulator Training Effectiveness : A Meta-Analysis[END_REF]. Cependant, plusieurs défis détaillés dans le chapitre 2 restent à résoudre afin d'adapter au mieux cette technologie prometteuse au champ clinique et social que représentent les fauteuils roulants électriques. • améliorer les compétences des conducteurs grâce à des formations innovantes;

Contributions

• améliorer l'intelligence des fauteuils roulants électriques grâce à des algorithmes innovants.

Le premier axe est abordé dans le chapitre 3 qui présente un simulateur de fauteuil roulant électrique basé sur la réalité virtuelle qui expose les conducteurs à des situations virtuelles complexes et sûres. Le chapitre 4 se concentre sur le deuxième axe par le biais d'un algorithme de planification de trajectoire innovant, permettant de générer de manière autonome des trajectoires adaptées aux utilisateurs et aux fauteuils roulants électriques. Le travail sur ces deux axes a permis de prendre conscience des principaux obstacles au développement de solutions de navigation en fauteuil roulant électrique. Pour être plus précis, il a révélé un manque d'inclusion des utilisateurs de fauteuils roulants électriques dans les processus de développement et de conception. Comme la simulation basée sur la RV peut fournir un moyen sûr pour les utilisateurs d'expérimenter des solutions recréées virtuellement, les simulateurs basés sur la RV pourraient également servir d'outils de test pour accompagner tout développement. Ainsi, sur la base des résultats des autres contributions, le dernier travail présenté dans le chapitre 5 aborde les méthodes et les concepts pour recentrer la conception et le développement de solutions d'assistance innovantes autour des besoins et des attentes des utilisateurs finaux à l'aide de la RV. En particulier, il présente des lignes directrices pour concevoir des simulateurs de fauteuils roulants électriques basés sur la RV comme outils de développement d'assistance. Cette thèse ouvre ainsi la voie à des conceptions intelligentes de solutions innovantes de navigation en fauteuil roulant électrique.

Chapitre 1 : Ce chapitre donne une définition du terme "fauteuil roulant électrique intelligent" à partir de la littérature. En partant de la définition et du fonctionnement d'un fauteuil roulant électrique simple, ce chapitre révèle les besoins qui se cachent derrière les fauteuils roulants électriques intelligents. En particulier, le chapitre se concentre sur les fauteuils roulants électriques à navigation autonome et semi-autonome et détaille leur fonctionnement ainsi que les concepts clés associés. La navigation autonome représente l'avenir de l'aide à la mobilité, avec des solutions de plus en plus innovantes soutenues par des technologies récentes telles que l'intelligence artificielle et la réalité virtuelle (RV).

Chapitre 2 : Ce chapitre définit la RV et détaille ses avantages et ses inconvénients, notamment dans le contexte de la simulation. Il décrit ensuite en détail les concepts qui ont un impact important sur la qualité d'une simulation basée sur la RV, comme le Sentiment de Présence (SdP), la Cinétose ou la Fidélité du simulateur. Ces concepts faisant l'objet d'un vif débat dans la littérature, il est important d'associer leur définition présentée à ce document seulement et à son contenu. Enfin, ce chapitre présente une vue d'ensemble des projets de RV existants appliqués au domaine des fauteuils roulants électriques, tels que les simulateurs ou les outils et méthodes de simulation de fauteuils roulants électriques. De cette façon, il révèle les défauts de la simulation de fauteuils roulants électriques qui doivent être corrigés dans les projets futurs.

Chapitre 3 : Ce chapitre présente la première contribution de la thèse, dédiée à l'amélioration des compétences du conducteur, qui consiste en un Simulateur d'entraînement multisensoriel de fauteuil roulant électrique basé sur la RV. Bien que de nombreux simulateurs de fauteuils roulants électriques existent, peu de projets se sont concentrés sur les concepts clés de la qualité de la simulation RV et les besoins spécifiques des utilisateurs finaux. Ainsi, le simulateur exposé répond aux principales exigences cliniques et se distingue par son rapport efficacité/qualité. En effet, sa plateforme de mouvement originale permet de produire un retour vestibulaire et haptique qui contribue grandement à l'efficacité et au confort de l'expérience de formation RV en améliorant le SdP tout en réduisant la Cinétose. Néanmoins, des améliorations sont prévues car l'évaluation de la qualité de l'expérience du simulateur a révélé son inadaptation actuelle à une utilisation dans des programmes cliniques.

Chapitre 4 : Ce chapitre présente la deuxième contribution de cette thèse, qui vise à faciliter la navigation en fauteuil roulant électrique en améliorant l'" intelligence " du fauteuil grâce à un nouvel algorithme de planification de chemin. Bien qu'inspiré de la littérature, il se distingue des algorithmes similaires par sa simplicité et son contexte ciblé puisqu'il est basé sur des courbes de Bézier cubiques et spécifiquement adressé aux fauteuils roulants électriques. La conception et le développement d'un algorithme pour fauteuil roulant électrique intelligent nous ont permis de nous confronter aux problèmes et aux défis du processus de développement. En particulier, cela nous a permis de réaliser le rôle clé de la compréhension du contexte cible pour pouvoir développer un outil utile et significatif.

Chapitre 5 : Enfin, ce chapitre suit directement les perspectives révélées dans les chapitres précédents ainsi que leurs résultats. Tout d'abord, ce chapitre présente un nouveau modèle conceptuel de Fidélité du simulateur qui aide à la conception d'un Simulateur d'assistance au développement basé sur la RV. Ensuite, il présente une version révisée du simulateur de fauteuil roulant électrique afin de l'utiliser dans tous les processus de conception et de développement de solutions de fauteuil roulant électrique intelligent en tant qu'outil d'assistance principal. Ainsi, les processus de conception et de développement de solutions liées aux fauteuils roulants électriques peuvent être plus facilement testés et recentrés sur les attentes et les besoins de l'utilisateur final.

Conclusion :

Cette thèse est le journal de bord d'un voyage à travers un sujet complexe à fort impact social, dans lequel les questions sont nombreuses et de nombreuses voies inexplorées. Elle témoigne notamment d'une prise de conscience quant aux méthodes de développement liées aux fauteuils roulants électriques qui manquent de dimensions humaines et médicales. Ce dernier chapitre résume les étapes clés de ce manuscrit qui ont permis d'indentifier de nouvelles perspectives à explorer dans le futur afin d'atteindre l'objectif final dans lequel je suis impliqué depuis 3 ans : une inclusion parfaite et sûre des utilisateurs de fauteuil roulant électrique dans notre société et nos environnements. This thesis was motivated by the desire to develop innovative solutions related to power wheelchairs to allow people with disabilities to regain mobility. Indeed, many disabilities lead to a loss of mobility that can result in a loss of self-confidence thus greatly limiting social interactions and activities. Power wheelchairs are one of the most popular solutions to maintain or regain mobility. Thanks to a societal awareness accompanied by technological progress, innovations around power wheelchairs have multiplied in recent years. The objectives of this thesis are first to understand the issues and the social context related to disability and more specifically to power wheelchairs, then to propose innovative solutions to enhance and simplify the navigation of power wheelchairs in complex contexts.

Introduction: Power wheelchair and social outcome

After this introductory Chapter presenting the thesis social context, motivations and objectives, the Chapter 1 further explores power wheelchair and smart power wheelchair state of the art, exposing recent innovations objectives, outcomes and flaws. Then, the Chapter 2 reviews the literature regarding Virtual Reality (VR) and especially power wheelchair simulation and simulators. Power wheelchair navigation is the result of the driver's skills combined with power wheelchairs "intelligence". Thus, this thesis presents solutions to enhance both respectively in Chapters 3 and 4. In the end, Chapter 5 highlights how this thesis constitutes one more step towards smart power wheelchair solutions designs.

Mobility issues

According to the World Health Organization, about 785 million people live with a disability which represents nearly 10% of the world population. Among them, between 110 and 190 million people have significant difficulties like the inability to walk or to perform self-care or social activities [START_REF] Organization | Guidelines on the provision of manual wheelchairs in less resourced settings[END_REF]. While this number is likely to grow as the world population is ageing, disability issue and in particular mobility loss is not solely about the elderly. Indeed, in 2001, 32% of the 145000 participants to the study presented in [START_REF] Iezzoni | Mobility difficulties are not only a problem of old age[END_REF] reported that their major mobility difficulties began before their fifties. The Figure 2 from the 2015 disability statistic annual report [START_REF] Kraus | Disability Statistics Annual Report[END_REF] shows that a majority of the US Civilians with disabilities are between 18 and 64 years old.

Mobility loss represents a major medical and social issue as multiple studies revealed a direct link between it and decreased employment, reduced salary, low social interactions, limited activities and low independence [START_REF] Smith | A review of factors influencing participation in social and community activities for wheelchair users[END_REF][START_REF] Salter | Impact of loss of mobility on instrumental activities of daily living and socioeconomic status in patients with MS[END_REF][START_REF] Finlayson | Experiencing the loss of mobility: Perspectives of older adults with MS[END_REF]. In addition, limited activities and social isolation negatively impact mental health leading sometimes to long-term low self-esteem and depression as observed during lock-downs due to the COVID-19 pandemic [START_REF] Usher | Life in the pandemic: Social isolation and mental health[END_REF]. Therefore, reduced mobility and its consequences, in particular social isolation, must be considered as significant risk factors for broad-based morbidity and mortality rather than just a particular condition [J. T. Cacioppo and S. Cacioppo 2014]. Thus, maintaining or regaining mobility appears to be of primary importance for all people with disabilities, which represents an important and growing part of the world population. Over the years, many mobility assistive devices with various objectives and scopes have been developed from the ordinary cane to the complete exoskeleton. One of the most known and commonly used assistive devices is the wheelchair [START_REF] Fomiatti | A systematic review of the impact of powered mobility devices on older adults' activity engagement[END_REF]. While canes and walkers aim to compensate for minor mobility losses, wheelchairs allow people with disabilities preventing them from walking independently to eventually travel long distances by themselves [Richard C Simpson, LoPresti, and R. A. Cooper 2008]. However, regular use of manual wheelchairs frequently leads to injuries and pain: users must propel not only themselves, but also the wheelchair itself and what they are carrying at the same time [Ott et al. 2020] Hence, in [Morgado Ramirez and[START_REF] Ramirez | But, I Don't Want/Need a Power Wheelchair" Toward Accessible Power Assistance for Manual Wheelchairs[END_REF], 12 manual wheelchair users agreed on daily struggle, in particular for long distances, regardless of the smoothness of the surface they were traveling on and the strength of their arms. Depending on user strength, the slightest obstacle like a simple whole or a light slope represents a greater challenge for manual wheelchair users than power wheelchair users. As a consequence, power wheelchairs, which are wheelchairs electrically propelled, are commonly preferred to achieve longer trips as they are more comfortable and less injurious. In addition, several studies like [START_REF] Martins | Psychosocial Impact of Assistive Technologies for Mobility and Their Implications for Active Ageing[END_REF]] and [START_REF] Fomiatti | A systematic review of the impact of powered mobility devices on older adults' activity engagement[END_REF] suggest that power wheelchairs are as efficient as manual wheelchairs to assist people with reduced mobility and that they have a greater positive impact than other mobility assistive devices. The wheelchair's impacts and efficiency in terms of mobility aid is difficult to evaluate because most evaluation methods are based on subjective data. In 2007, authors in [START_REF] Pettersson | The value of an outdoor powered wheelchair with regard to the quality of life of persons with stroke: A follow-up study[END_REF] conducted a follow-up study with 32 senior power wheelchair users based on the EuroQo1-5D and PIADS questionnaires to evaluate the psychological and overall impact of the use of a power wheelchair. They revealed a significant positive influence of the use of a power wheelchair on the quality of life regarding performance criteria such as competence, independence and capability but also regarding psychological criteria like selfesteem, well-being and happiness. Those results were confirmed with more recent studies with various populations. In 2016, power wheelchairs have been qualified as a facilitator by the 35 young users surveyed in [START_REF] Salatino | An observational study of powered wheelchair provision in Italy[END_REF]]. Authors of [START_REF] Labbé | Mobility and participation among ageing powered wheelchair users: Using a lifecourse approach[END_REF] in 2018 have reached the same conclusions from a 2-years power wheelchair acquisition follow-up study with 19 participants. They noted a positive psychological impact, particularly on self-esteem. However, they also pointed out issues regarding power wheelchair accessibility and usability. Indeed, according to the literature, the majority of people who need a wheelchair do not even have access to one because of the price, their geolocation or their inability to drive it. In 2015, the World Health Organization estimated 65 to 75 million people need a wheelchair but that only 5 to 15% of them had one [Organization 2015;[START_REF] Organization | Guidelines on the provision of manual wheelchairs in less resourced settings[END_REF]. A power wheelchair is an expensive device, hard to acquire and especially to drive. Thus, beyond efficiency, power wheelchairs are perceived as a mixed blessing [START_REF] Salatino | An observational study of powered wheelchair provision in Italy[END_REF][START_REF] Torkia | Power wheelchair driving challenges in the community: A users' perspective[END_REF]].

Power wheelchair challenges

Financial and access issues aside, driving a power wheelchair as they are designed today is a terribly difficult task that requires good visuo-spatial and cognitive abilities [START_REF] Massengale | Effect of visual perception, visual function, cognition, and personality on power wheelchair use in adults[END_REF][START_REF] Fehr | Adequacy of power wheelchair control interfaces for persons with severe disabilities: A clinical survey[END_REF]. Driving a power wheelchair safely requires an even greater level of expertise, in particular for people with complex disabilities [START_REF] Hardy | Powered wheelchair mobility: An occupational performance evaluation perspective[END_REF]]. As such, people with cognitive and visuo-spatial disabilities must practice safe driving through training programs to be allowed to drive a power wheelchair [START_REF] Anstey | Cognitive, sensory and physical factors enabling driving safety in older adults[END_REF]. Indeed, therapists need to ensure that the powered mobility aid that they are to prescribe to the user will be operated safely in daily-life. [START_REF] Mortenson | Prescribers' Experiences With Powered Mobility Prescription Among Older Adults[END_REF]. If assessment or training is unsuccessful, therapists can decide to prevent power wheelchair prescription to a patient for safety reasons. The overall user's feeling is that power wheelchairs are hard to use [START_REF] Labbé | Mobility and participation among ageing powered wheelchair users: Using a lifecourse approach[END_REF][START_REF] Torkia | Power wheelchair driving challenges in the community: A users' perspective[END_REF]. Sometimes, this is the result of power wheelchairs which have been badly designed or which is not adapted to the user's disability, making its use almost impossible or irrelevant [START_REF] Ramirez | But, I Don't Want/Need a Power Wheelchair" Toward Accessible Power Assistance for Manual Wheelchairs[END_REF][START_REF] Rice | A systematic review of risk factors associated with accidental falls, outcome measures and interventions to manage fall risk in non-ambulatory adults[END_REF]. Sometimes the environment is not suitable for wheelchairs and especially outdoor and public environments which not systematically integrate wheelchair users into their design process [START_REF] Salatino | An observational study of powered wheelchair provision in Italy[END_REF][START_REF] Bromley | City centre accessibility for wheelchair users: The consumer perspective and the planning implications[END_REF]. Finally, sometimes, users are poorly followed by therapists or poorly trained which leads to accidents but also to renunciation [START_REF] Salatino | An observational study of powered wheelchair provision in Italy[END_REF]].

According to authors in [START_REF] Edwards | A survey of adult power wheelchair and scooter users[END_REF], 21% of power wheelchair users have had an accident within the first year. Not only are accidents dangerous for users and their relatives, but they can also easily damage the power wheelchair itself, which may result in expensive additional costs [START_REF] Salatino | An observational study of powered wheelchair provision in Italy[END_REF]. Also, an accident has a negative impact on self-esteem as it represents a failure and/or a source of embarrassment and shame for some users [START_REF] Pettersson | The value of an outdoor powered wheelchair with regard to the quality of life of persons with stroke: A follow-up study[END_REF]. The simple fact of attracting attention because of a fall or an accessory is an unpleasant situation for many users who feel that they are perceived through their disability but rather as a whole person [START_REF] Labbé | Mobility and participation among ageing powered wheelchair users: Using a lifecourse approach[END_REF]. Finally, even if users do not have an accident, the fear of having one, of hurting someone or of losing control is constant and alters the navigation experience [START_REF] Torkia | Power wheelchair driving challenges in the community: A users' perspective[END_REF]]. To avoid these accidents, the simplest solution would be to make training and assessments more stringent [START_REF] Bigras | A scoping review of powered wheelchair driving tasks and performance-based outcomes[END_REF]]. However, this idea would reduce an already low power wheelchair accessibility. Thus, other solutions must be found in order to simplify and secure the power wheelchair driving, in other word, to enhance power wheelchair navigation.

Motivations

One way to enhance power wheelchair navigation is to improve the power wheelchair itself. Over the years, a large panel of different tools and innovations related to power wheelchairs were proposed. In particular, smart power wheelchairs have emerged as detailed in the Chapter 1. Moreover, the continuous progress of the technology and of the computer science visible through the machine power enhancement, response time reduction and the emergence of AI, allows us to rethink each recent solution [START_REF] Haddad | Deep Learning Architecture to Assist with Steering a Powered Wheelchair[END_REF]. Unfortunately, it seems that the currently available power wheelchairs are still flawed, neither totally adapted nor easily adaptable to each user and each impairment. In general, the very development of new assistive technologies is barely user-centered: power wheelchair still appears to be considered as a mobile robot with a seat mounted on it rather than a whole motion device with a driver [START_REF] Leaman | A comprehensive review of smart wheelchairs: Past, present and future[END_REF]. For example, it is only in the last decade that a project has focused its research on seating comfort and mass distribution when the power wheelchair is reclined [START_REF] Kanki | An evaluation of physical strains while driving an electric wheelchair[END_REF]. Power wheelchair user inclusion is lacking in all areas, from urban planning, which is generally very poorly designed for the passage of a wheelchair, to everyday life objects design [START_REF] Torkia | Power wheelchair driving challenges in the community: A users' perspective[END_REF]. Regarding smart power wheelchairs, when users are interviewed, many blame semi-autonomous or autonomous systems for not including them in the decision process loop, for not informing them about the ongoing process [START_REF] Leaman | A comprehensive review of smart wheelchairs: Past, present and future[END_REF]. This lack of awareness can lead to a feeling of loss of control and does not help to develop self-esteem [Morgado [START_REF] Ramirez | But, I Don't Want/Need a Power Wheelchair" Toward Accessible Power Assistance for Manual Wheelchairs[END_REF]. As such, some recent research suggests recentering power wheelchair related developments on the user [Erdogan and Argall 2017b].

Another way to improve power wheelchair navigation is to improve driver skills. Classic situational training programs, still used today, appear impersonal, too short and sometimes ineffective [START_REF] Salatino | An observational study of powered wheelchair provision in Italy[END_REF]]. Indeed, depending on the person's abilities and the type of its disability, the learning process may take more or less time and require more or less attention from the therapists [START_REF] Harrison | The role of virtual reality technology in the assessment and training of inexperienced powered wheelchair users[END_REF][START_REF] Cromby | The potentials of virtual environments in the education and training of people with learning disabilities[END_REF]. Moreover, these training programs can be expensive and sometimes unfeasible given the situation to be simulated. Thus, simple training situations are preferred such as confined spaces, with little danger and specific maneuvers, whereas users should be trained to face complex situations as well. For the last few years, new training methods have been explored, based on new technologies such as Virtual Reality (VR). VR refers to a domain of computer science consisting of simulating virtual environments (VE). Among its multiple advantages presented in Chapter 2, VR allows to simulate any situation in a safe, controlled and reproducible way. As such, VR based simulation appears as a great tool for specific training. In addition, VR based simulators have already proven themselves in other fields such as aviation or surgery [START_REF] Basdogan | VR-based Simulators for Training in Minimally Invasive Surgery[END_REF][START_REF] Hays | Flight Simulator Training Effectiveness : A Meta-Analysis[END_REF]]. However, several challenges detailed in Chapter 2 remain to be solved in order to best adapt this promising technology to the clinical and social field that power wheelchairs represent. The work presented in this manuscript has been concentrated around 2 axes as illustrated by the Figure 3: • improve driver skills through innovative training;

Contributions

• improve the intelligence of power wheelchairs through innovative algorithms.

The first axis is addressed in Chapter 3 which presents a virtual reality based power wheelchair simulator that exposes drivers to complex and safe virtual situations. Chapter 4 focuses on the second axis through an innovative path planning algorithm, allowing to autonomously generate user and power wheelchair friendly trajectories. Working on both axis has raised awareness of the major barriers to the development of power wheelchair navigation solutions. To be specific, it has revealed a lack of power wheelchair users inclusion in the development and design processes. As VR based simulation can provide a safe way for users to experience virtually recreated solutions, VR based simulators could also serve as testing tools to accompany any development. Hence, based on VR and other contributions outcomes, the last presented work in Chapter 5 addresses methods and concepts to recenter innovative assistive solutions design and development around end-users needs and expectations. In particular, it presents guidelines to design VR based power wheelchair simulators as assistive development tools. This thesis thus paves the road toward smart designs of innovative power wheelchair navigation solutions.

Chapter 1 : This chapter draws a definition of the term "smart power wheelchair" from the related literature. Starting from the definition and functioning of a simple power wheelchair, this chapters reveal the needs behind smart power wheelchairs. In particular, the chapter focuses on autonomous and semi-autonomous navigating power wheelchairs and details their operation as well as key related concepts. Autonomous navigation represents the future of mobility assistance, with increasingly innovative solutions supported by recent technologies such as artificial intelligence and Virtual Reality (VR).

Chapter 2 : This chapter defines VR and details its advantages and drawbacks, especially applied to a simulation context. It then fully describes concepts strongly impacting a VR based simulation quality like Sense of Presence (SoP), Cybersickness or Simulator Fidelity. As these concepts are hotly debated in the literature, it is important to associate their presented definition to this document and its content. Finally, this chapter presents an overview of the existing VR based projects applied to power wheelchair domain such as simulators or power wheelchair simulation tools and methods. This way, it reveals existing power wheelchair simulation flaws yet to correct in future projects.

Chapter 3 : This chapter presents the first thesis contribution, dedicated to enhancing driver skills, which consists of a VR based power wheelchair multisensory feedback training simulator. Although many power wheelchair simulators exist, few projects focused on VR simulation quality key concepts and end-users specific needs. Hence, the exposed simulator meets primary clinical requirements and is distinguished by its efficiency and quality ratio. Indeed, its original motion platform allows producing vestibular and haptic feedback that greatly contribute to the efficiency and comfort of the VR training experience by improving the SoP while reducing Cybersickness. Nonetheless, enhancements are planned as the simulator quality of experience evaluation revealed its current unsuitability for use in clinical programs.

Chapter 4 : This chapter presents the second contribution of this thesis, aiming to ease power wheelchair navigation through the enhancement of the power wheelchair "intelligence" with a new path planning algorithm. Although this algorithm is inspired by the literature, it differs from similar algorithms by its simplicity and its targeted context as it is based on Cubic Bézier curves and specifically addressed to power wheelchairs. Designing and developing a smart power wheelchair algorithm have allowed us to confront ourselves to development process issues and challenges. In particular, it allowed us to realize the key role of understanding the target context to be able to develop a useful and significant tool.

Chapter 5 : Finally, this chapter directly follows the perspectives revealed in previous chapters as well as their outcomes. First this chapter presents a new Simulator Fidelity concept model that helps in the design of VR based development assistive simulator. Then, it presents a revised version of the power wheelchair simulator to use it throughout all smart power wheelchair solution development and design processes as a primary assistive tool. Thus, power wheelchair related solutions design and development processes can be more easily tested and recentered on end-user expectations and needs.

Conclusion :

This thesis is the logbook of a journey through a complex subject with high social impact, in which the questions are numerous and many paths unexplored. In particular, it witnesses an awareness regarding the power wheelchair related development methods which lack human and medical dimensions. This last chapter summarizes the key steps of this manuscript that led to new perspectives to explore in the future in order to reach the final goal I have been involved in for 3 years: a perfect and safe inclusion of power wheelchair users in our society and our environments.

1

State of the art : Smart Power Wheelchairs

This chapter draws on the literature and various research projects to explore what are smart power wheelchairs, one of the main subjects of this thesis work. Indeed, smart power wheelchairs are a major accessible solution to reduced mobility. However, they refer to a large and complex domain as they are combining robotics, computer science and medical assistance fields. Thus, discovering through the literature how they work, their differences and limitations, is necessary to understand the contributions presented later in the thesis. Section 1.1 defines what a power wheelchair is and how it works. Then, smart power wheelchair definition and related projects are reviewed in Section 1.2. Finally, this chapter concludes on smart power wheelchairs overall impact and current issues.

Power Wheelchair

Regardless of the definition, a smart power wheelchair is first and foremost a power wheelchair. As such, it is important to first detail what makes up a power wheelchair. A power wheelchair consists of a mechanical structure or 'power wheelchair structure' and a driving system or 'control chain'. Both parts are further developed, respectively in Subsection 1.1.1 and in Subsection 1.1.2.

Power wheelchair structure

As stated in the introductory Chapter, one of the main power wheelchair navigation barriers is the power wheelchair structure itself [START_REF] Ramirez | But, I Don't Want/Need a Power Wheelchair" Toward Accessible Power Assistance for Manual Wheelchairs[END_REF][START_REF] Rice | A systematic review of risk factors associated with accidental falls, outcome measures and interventions to manage fall risk in non-ambulatory adults[END_REF]. The power wheelchair structure has a significant impact on the power wheelchair usability and mechanical constraints. Thus, for the past 30 years, many innovations around the structure have been proposed generally concerning main power wheelchair structure parts : the chassis, the power supply system, the steering system or the seating system [START_REF] Leaman | A comprehensive review of smart wheelchairs: Past, present and future[END_REF]. Even though some projects largely deviate from the classic wheelchair structure, such as the walking chair proposed in [START_REF] Wellman | An adaptive mobility system for the disabled[END_REF], the majority are interested in improving the standard structure capabilities to match specific situations or to enhance its overall dynamics. For example, in [START_REF] Quaglia | Wheelchair.q, a mechanical concept for a stair climbing wheelchair[END_REF], authors present a power wheelchair able to climb stairs, a unique yet regularly problematic situation. Another example of specific solution is the Gyrolift project presented in [START_REF] Trénoras | Gyrolift, a new way of verticalisation on mobile personal transporter[END_REF]] and pictured in Figure 1.1. Gyrolift consists of a power wheelchair including a verticalization system that helps users to reach a standing position from a seated one. As opposed to those contextual solutions, some projects propose innovative structures to enhance the overall usability of power wheelchairs. That is the idea behind the "all-terrain" power wheelchair presented in [START_REF] Podobnik | All-terrain wheelchair: Increasing personal mobility with a powered wheel-track hybrid wheelchair[END_REF]] and also illustrated in Figure 1.1. However, because of its dimension, this power wheelchair is unsuitable for indoor environments. Enhancing usability is also the objective of the power wheelchair proposed in [START_REF] Hsu | Mobility assistance design of the intelligent robotic wheelchair[END_REF] which requires much less space to maneuver than a standard power wheelchair as it is based on four motorized wheels. Nevertheless, this feature drastically changes the dynamic model of the power wheelchair and the required control command.

In fact, all those projects result in power wheelchair structure specific designs, dynamics and mechanical constraints which are sometimes much more complex than standards. As such, the proposed power wheelchair structures require numerous skills, expertise, time and money to be implemented, tested and maintained. Other solutions to enhance power wheelchair usability might require fewer resources, such as smart power wheelchairs.

Power wheelchair control chain

The second main part of a power wheelchair is the driving system or control chain which highly depends on the power wheelchair structure. Indeed, the type of commands needed by the steering system, the final power wheelchair motion and the power wheelchair mechanical constraints are determined by the power wheelchair structure and especially its wheels form and its chassis design. As illustrated by the Figure 1.2, the simplified control chain of a standard power wheelchair consists in a 3-steps workflow. The user interface or controller generates and send user control signal to the power module which will translate it into an actual control command compliant with the steering system. Nowadays, power wheelchairs are mainly driven using a classic direct controller which provide direct signal and do not require complex computer solution. The most used direct controller is the 2D joystick controller because it provides an adapted command and a proportional control over both speed and direction [START_REF] Nisbet | Who's intelligent? Wheelchair, driver or both?[END_REF]]. However, even though multiple ergonomic adjustments accessories exist, some disabilities prevent people from using a joystick. Other type of direct controllers exist like head arrays or sip-and-puff [START_REF] Devigne | Solutions robotiques bas coût pour l ' aide à la navigation en fauteuil roulant électrique : vers une contribution dans le champ de la rééducation neurologique To cite this version[END_REF]], but they provide a less precise control and require more complex control command [START_REF] Nisbet | Who's intelligent? Wheelchair, driver or both?[END_REF]]. As such, people with complex disabilities that can not use a joystick are often led to use a smart power wheelchair [START_REF] Nisbet | Who's intelligent? Wheelchair, driver or both?[END_REF]].

Smart power wheelchair

This section discusses the smart power wheelchair definition in Subsection 1.2.1. It then details types of smart power wheelchairs in Subsection 1.2.2 before further exploring the autonomously and semi-autonomously driving smart power wheelchair in Subsection 1.2.3.

Definition

Innovative designs of power wheelchair structures facilitate maneuvers and enhance power wheelchair driving comfort. However, it does not allow people with complex disabilities or driving difficulties to drive a power wheelchair safely or to obtain the right to drive one. In other terms, smart designs of power wheelchair structure expand power wheelchair driving usage rather than its accessibility. As stated in the introductory Chapter, because of their deficiencies or lack of skills, many people are not allowed to drive a power wheelchair, despite the benefits it can bring. The idea behind "smart" power wheelchairs is to compensate those user inabilities by autonomous or semi-autonomous embedded systems in order to broaden accessibility [START_REF] Desai | Advances in smart wheelchair technology[END_REF]. The first smart power wheelchair was presented in 1986 and was able to autonomously drive a user to different places in an office [START_REF] Madarasz | The Design of an Autonomous Vehicle for the Disabled[END_REF]]. Like all other smart power wheelchairs, its control chain was enhanced by smart embedded systems and sensors as illustrated in Figure 1.3. Thus, a smart power wheelchair can be considered as a navigational robot with its structure, its dynamic, its constraints and its embedded system. Definition -A smart power wheelchair consists of a power wheelchair equipped with embedded systems and sensors in order to facilitate its operation and reduce the required workload. Just as users rely on their senses and experience to drive the chair, smart solutions need information about the environment and/or the localization to assist the user in driving. Many sensor types exist, based on different techniques such as Light Detection And Ranging [START_REF] Baltazar | Autonomous wheelchair for patient's transportation on healthcare institutions[END_REF], infrared [START_REF] Leblong | SWADAPT1: assessment of an electric wheelchairdriving robotic module in standardized circuits: a prospective, controlled repeated measure design pilot study[END_REF] or ultrasonic [START_REF] Haddad | Deep Learning Architecture to Assist with Steering a Powered Wheelchair[END_REF]. Each type of sensor has different properties and is better adapted to a certain type of context [START_REF] Devigne | Solutions robotiques bas coût pour l ' aide à la navigation en fauteuil roulant électrique : vers une contribution dans le champ de la rééducation neurologique To cite this version[END_REF]]. Some smart power wheelchairs mix multiple types of sensors to achieve maximum efficiency in different situations and enhanced the system robustness like in [START_REF] Hartman | Design and development of an autonomous robotic wheelchair for medical mobility[END_REF] where authors coupled Laser range finder with RGB vision camera. That way, autonomous systems and smart power wheelchairs are able to evolve into multiple environments and conditions.

Smart power wheelchair categories

Smart power wheelchairs are characterized by their "smart" functionalities which can be categorized in 3 different groups identified by the literature [START_REF] Baltazar | Autonomous wheelchair for patient's transportation on healthcare institutions[END_REF][START_REF] Braga | IntellWheels: Modular development platform for intelligent wheelchairs[END_REF][START_REF] Hu | Head gesture recognition for handsfree control of an intelligent wheelchair[END_REF]] :

• automatic device communication;

• innovative and autonomous user interactions;

• autonomous and semi-autonomous navigation.

The first category includes every project with a power wheelchair communicating with other devices such as smart homes or medical systems. In particular, this category includes network-connected power wheelchair projects such as in [START_REF] Kojima | Fault tolerant calculation method of predicting road condition for network-connected wheelchair[END_REF] and cloud robotic projects like in [START_REF] Ikeda | Cooperative Strategy for a Wheelchair and a Robot to Climb and Descend a Step[END_REF]].

The second category concerns "smart" controllers and user interfaces based on embedded system and sensors to algorithms as opposed to "direct" controllers previously presented in subsection 1.1.2. Latest scientific progress and domains such as artificial intelligence allow rethinking user interactions with the power wheelchair. This way, embedded systems can compensate for users' inabilities allowing them to use a simpler controller like a joystick [START_REF] Nisbet | Who's intelligent? Wheelchair, driver or both?[END_REF]]. Moreover, new controllers can also emerge to broaden power wheelchair driving accessibility [START_REF] Faria | A Survey on Intelligent Wheelchair Prototypes and Simulators[END_REF]. Authors in [START_REF] Dey | Smart wheelchair integrating head gesture navigation[END_REF]] propose an intelligent system able to translate head gestures into command. Voice control also requires complex system commonly relying on machine learning techniques [START_REF] Abed | Design of Voice Controlled Smart Wheelchair[END_REF][START_REF] Kollar | Grounding Verbs of Motion in Natural Language Commands to Robots[END_REF]. A final example is the gaze driving solution used in RoboEYE [START_REF] Maule | RoboEye, an Efficient, Reliable and Safe Semi-Autonomous Gaze Driven Wheelchair for Domestic Use[END_REF]] which depends on new eye-tracking technology. However, those projects are answering very specific needs with very specific solutions unsuitable for many people as they require specific skills.

The last category concerns power wheelchairs including automatic driving systems which makes driving easier, safer and more accessible. This is the largest category of smart power wheelchairs as it regroups most of the related works. It includes many different projects that tries to compensate user's inability to fulfill certain driving steps with embedded systems. Those projects are further reviewed in the following subsection as the thesis contributions are part of this category.

Autonomous and semi-autonomous navigation

Smart power wheelchair automatic driving systems consist in modules varying in terms of service, objective, scope and technology [START_REF] Desai | Advances in smart wheelchair technology[END_REF][START_REF] Leaman | A comprehensive review of smart wheelchairs: Past, present and future[END_REF]. For example, while some embedded systems will assist the user in steering the power wheelchair by correcting its trajectory or providing additional environment information, others will autonomously drive when specific situations occur without the need of user intervention. As an example, in the previously mentioned RoboEYE project [START_REF] Maule | RoboEye, an Efficient, Reliable and Safe Semi-Autonomous Gaze Driven Wheelchair for Domestic Use[END_REF], one proposed control mode is the completely autonomous navigation toward a point of interest selected by the user. Moreover, in [START_REF] Baltazar | Autonomous wheelchair for patient's transportation on healthcare institutions[END_REF], authors present another completely autonomous chain of control with world exploration, path planning and goal decision based on heuristics and power wheelchair structure constraints. Other more specific works focus on improving certain tasks of the control chain or functionalities autonomous systems rely on rather than the complete chain. For example, a new path planning algorithm for unknown environment exploration is proposed in [C. Wang et al. 2019] and authors in [Alonso-Mora, Beardsley, and Siegwart 2018] present a cooperative avoidance collision method. Both solutions address very specific issues and task of the control chain. To this end, recent innovations are used like deep learning on which the path correction algorithm presented in [START_REF] Haddad | Deep Learning Architecture to Assist with Steering a Powered Wheelchair[END_REF] is based. In [Vishnu Karakkat Narayanan 2016], the author investigates the social and comfort aspect of the smart power wheelchair navigation as illustrated in Figure 1.4. Furthermore, many projects attempt to perfect the sensors' data processing to better explore the environment and detect obstacles [START_REF] Devigne | Solutions robotiques bas coût pour l ' aide à la navigation en fauteuil roulant électrique : vers une contribution dans le champ de la rééducation neurologique To cite this version[END_REF][START_REF] Hartman | Design and development of an autonomous robotic wheelchair for medical mobility[END_REF]]. However, complete autonomous control in every environment and under every condition is considered as a myth by researchers [START_REF] Abbink | A topology of shared control systems-finding common ground in diversity[END_REF]. Most of the complete autonomous power wheelchairs are dedicated to specific scenarios and environments leading sometimes to permanent environment modification [START_REF] Leaman | A comprehensive review of smart wheelchairs: Past, present and future[END_REF]. In particular, current solutions mainly focus on avoiding obstacles within indoor environments [START_REF] Baltazar | Autonomous wheelchair for patient's transportation on healthcare institutions[END_REF][START_REF] Devigne | Low complex sensor-based shared control for power wheelchair navigation[END_REF][START_REF] Trautman | Robot navigation in dense human crowds: Statistical models and experimental studies of human-robot cooperation[END_REF] and are not robust and precise enough for more complex situations such as urban environment navigation [Richard C. [START_REF] Simpson | Smart wheelchairs: A literature review[END_REF], social interactions with pedestrians [START_REF] Kruse | Humanaware robot navigation: A survey[END_REF][START_REF] Hansen | Adaptive human aware navigation based on motion pattern analysis[END_REF], and negotiation of ramps, curbs or negative obstacles [START_REF] Devigne | Solutions robotiques bas coût pour l ' aide à la navigation en fauteuil roulant électrique : vers une contribution dans le champ de la rééducation neurologique To cite this version[END_REF][START_REF] Devigne | A shared control solution for safe assisted power wheelchair navigation in an environment consisting of negative obstacles : a proof of concept[END_REF]. In general, outdoor environments are a complex situation as they are too hazardous for completely autonomous smart power wheelchairs. Indeed, autonomous systems cannot innovate and adapt to every situation as an experienced human driver would. Thus, a better smart power wheelchair design should always take into account the experience and skills of the driver when possible in order to overcome those system robustness issues. In other words, as defined earlier, a smart power wheelchair should "compensate" users inabilities but without replacing it. Furthermore, while autonomous power wheelchair control ease workload [START_REF] Onnasch | Human performance consequences of stages and levels of automation: An integrated meta-analysis[END_REF][START_REF] Carlson | Increasing robotic wheelchair safety with collaborative control: Evidence from secondary task experiments[END_REF], it can lead to a user loss of skills as remaining abilities are no longer solicited [START_REF] Zolotas | Head-Mounted Augmented Reality for Explainable Robotic Wheelchair Assistance[END_REF][START_REF] Onnasch | Human performance consequences of stages and levels of automation: An integrated meta-analysis[END_REF]. Plus, doing a task by oneself instead of having it done by a robot has been shown empowering [START_REF] Meyerson | Effect of Empowerment on Employees Performance[END_REF][START_REF] Hurst | Empowering individuals with do-it-yourself assistive technology[END_REF]. Hence, those concerns have led researchers to find other more cooperative methods of power wheelchair control summarized in Table 1.1. Two operating methods that we will call "Guided Control" and "Traded Control" allow moving towards a more cooperative control where a complete autonomous system can solicit the user. Both require a user command acquired through any kind of controller, giving the user the illusion to drive the power wheelchair by itself. The guided control consists of using user controller data to compute its intention and autonomously moving toward it without considering continuous user input signal. RoboEYE, presented in [START_REF] Hsu | Mobility assistance design of the intelligent robotic wheelchair[END_REF], proposes a guided control mode where point-of-interest goals are computed through gaze direction. Author in [Vishnu Karakkat Narayanan 2016] also proposes a semi-autonomous method based on long goal prediction computed from joystick angle. As for the traded control refers to every smart power wheelchair that switches between manual control and complete autonomous control depending on situation. For example, author in [Vishnu Karakkat Narayanan 2016] also proposes a control mode where the power wheelchair autonomously moves away from obstacles when the system judges the situation to be dangerous. Work presented in [START_REF] Hsu | Mobility assistance design of the intelligent robotic wheelchair[END_REF]] takes advantage of both operating methods by offering the possibility to manually override autonomous control through joystick input when the autonomous navigation based on gaze detected goals fails.

• Self-driving power wheelchair Autonomous Control

• On and off switch • Long predefined goal • Self-driving power wheelchair Guided Control

• On and off switch Nevertheless, even though they give the user the impression of driving, traded and guided controls still lack robustness during complete autonomous driving times leading to failures. As a smart power wheelchair goal is only to compensate user's inabilities, its control should rely on every ability the user still have [START_REF] Onnasch | Human performance consequences of stages and levels of automation: An integrated meta-analysis[END_REF][START_REF] Nisbet | Who's intelligent? Wheelchair, driver or both?[END_REF]. This way, a smart power wheelchair would take advantage of both user driver experience and computer based corrections and could be used in unpredictable environments. Mixing user controller data and autonomous decision is called Shared Control and is precisely defined by [START_REF] Abbink | A topology of shared control systems-finding common ground in diversity[END_REF] as "human(s) and robot(s) congruent interaction in a perception-action cycle to perform a dynamic task that either the human or the robot could execute individually under ideal circumstances".

Many types of Shared Control methods exist, and the appropriate one to use highly depends on user controller type, user abilities, needs and preferences [Erdogan and Argall 2017b;Erdogan and Argall 2017a]. The most used method is to linearly blend user command with autonomous decision as done in [START_REF] Haddad | Deep Learning Architecture to Assist with Steering a Powered Wheelchair[END_REF], but other approaches like probabilistic are also promising [START_REF] Ezeh | Probabilistic vs linear blending approaches to shared control for wheelchair driving[END_REF][START_REF] Trautman | Assistive Planning in Complex, Dynamic Environments: A Probabilistic Approach[END_REF]. Using Shared Control, smart power wheelchair are able to correct trajectories in dangerous situations while respecting the driver intentions as much as possible like the autonomous obstacle avoidance system presented in [START_REF] Devigne | Solutions robotiques bas coût pour l ' aide à la navigation en fauteuil roulant électrique : vers une contribution dans le champ de la rééducation neurologique To cite this version[END_REF] or in [Vishnu Karakkat Narayanan 2016]. In this context, not only is the smart power wheelchair navigation possible in more unpredictable situations, but it also stimulates the user and empowers him.

However, smart power wheelchairs can be perceived as frustrating systems. Indeed, multiple studies have reported a lack of autonomous system awareness leading to a feeling of control loss and incomprehension [START_REF] Ramirez | But, I Don't Want/Need a Power Wheelchair" Toward Accessible Power Assistance for Manual Wheelchairs[END_REF][START_REF] Torkia | Power wheelchair driving challenges in the community: A users' perspective[END_REF]. A misunderstanding of the autonomous part or system can easily lead to the user changing behavior and alter its comfort [START_REF] Onnasch | Human performance consequences of stages and levels of automation: An integrated meta-analysis[END_REF][START_REF] Carlson | Increasing robotic wheelchair safety with collaborative control: Evidence from secondary task experiments[END_REF]. In order to address this awareness shortage, researchers have imagined feedback systems to explain decisions in addition to classic user manual or tutorials. For example, in [START_REF] Zolotas | Head-Mounted Augmented Reality for Explainable Robotic Wheelchair Assistance[END_REF], an Augmented Reality system is used to provide information about autonomous system navigation decisions. Also, sometimes, the user is perfectly capable to drive a power wheelchair by itself but struggles gathering information about surroundings. In that case, the purpose of the embedded systems should only be to provide more information about the environment through different modalities such as haptic resistance feedback joystick [START_REF] Devigne | Design of a Haptic Guidance Solution for Assisted Power Wheelchair Navigation[END_REF] or vibrotactile armbands [START_REF] Devigne | Power Wheelchair Navigation Assistance Using Wearable Vibrotactile Haptics[END_REF]]. While being careful not to overstimulate, the latest technologies such as Virtual Reality based systems can be used to provide additional information about the environment as suggested by literature [START_REF] Zolotas | Head-Mounted Augmented Reality for Explainable Robotic Wheelchair Assistance[END_REF][START_REF] Levin | Feedback and virtual environments for motor learning and rehabilitation[END_REF].

Conclusion

In this chapter we have defined what a smart power wheelchair is and designates. Overall, "adding intelligence" to a power wheelchair is seen as one of the main solutions to address power wheelchair accessibility, comfort and usage issues evoked in introductory Chapter. In particular, autonomously navigating smart power wheelchairs allow people with complex disabilities to drive a power wheelchair safely without the need of extensive training. However, new solutions to autonomously manage a control chain step are yet to discover and existing embedded systems and control modes are still to be improved. Indeed, actual solutions are not yet adapted to every disability and context and rarely co-developed in partnership with end users i.e. people with disabilities. Nevertheless, new technologies such as Virtual Reality (VR) based tools allow scientists and therapists to address power wheelchair challenges from a new perspective and sometimes revisit smart power wheelchair solutions and their development.

2

State of the art : Virtual Reality based power wheelchair simulation Previous Chapter 1 mentions Virtual Reality (VR) as an area on which researchers could rely to imagine innovative smart power wheelchair solutions. This chapter investigates existing links between VR and power wheelchair areas in the literature. It first reviews literature in Section 2.1 in order to define VR and related key concepts such as Sense of Presence (SoP), Cybersickness and Simulator Fidelity. Then, it focuses on VR based power wheelchair simulation related work in Section 2.2, especially revealing existing simulators impact, advantages and gaps.

Virtual Reality

VR is a complex area of research that animates many projects, debates and innovations. This section explains VR foundations necessary for a good understanding of the work presented below, even if this field goes far beyond the concepts discussed. Additionally, note that the definitions presented are interpretations of the literature and are only of value to understanding the thesis contributions. After defining VR in Subsection 2.1.1, this section defines each key concept related to VR based simulation; Sense of Presence (SoP) is discussed in Subsection 2.1.2, Cybersickness in Subsection 2.1.3 and Simulator Fidelity in Subsection 2.1.4.

Definition

This subsection first reviews VR origins before presenting main VR related hardware and software tools and investigating VR interests.

Origin

The notion of Virtual Reality (VR) takes root in the 60s with Morton Heilig idea of a "theater experience" involving several senses. In 1962, he presented the Sensorama machine, pictured in Figure 2.1, considered as the first VR simulator and able to project short movies while stimulating multiple senses [START_REF] Heilig | Sensorama Simulator[END_REF]]. In the years that followed, various researchers became interested in this multisensory experience and brought it closer to computer science domain. In particular, in 1965, Ivan Sutherland imagined users tracked by computers interacting with highly realistic virtual worlds [I. [START_REF] Sutherland | Augmented Reality: "The Ultimate Display[END_REF]. The term "Virtual Reality" will come later to designate these digital sensory experiences, popularized by cultural works and various technological advances. Nowadays, VR is defined as "a scientific domain that uses computer science and interaction interfaces in order to simulate, in a virtual environment (VE), the behaviour of 3D entities that are interacting in real time with themselves and with one or more users in pseudonatural immersion via sensorimotor channels" [START_REF] Arnaldi | Virtual reality and augmented reality: Myths and realities[END_REF][START_REF] Arnaldi | Chapitre 1 du volume 1 du traité de la réalité virtuelle[END_REF]. This definition highlights the main objective of VR applications such as simulators; to allow a user to interact through different sensory modalities with VE. According to Bowman, 3 types of interactions exist being navigation, selection and manipulation [START_REF] Bowman | Formalizing the design, evaluation, and application of interaction techniques for immersive virtual environments[END_REF]. It is with the aim of improving these interactions and involving more sensory modalities that many devices and tools have been developed.

Tools

The main sense involved in VR interactions and experience is the sight stimulated through a display interface. The simplest display interface is the screen whose size, quality, field of view (FOV) and curvature vary. However, screen immersion capacity is quickly limited because of reduced depth perception and FOV. Another type of display interfaces called Immersive Rooms (Figure 2.3a), also offers a large FOV, 3D surrounding immersion and depth perception. Direct descendants of the cinema, Immersive Rooms have the particularity to be less isolating than HMD as they are based on more distant screens. Nonetheless, they are more expensive and less convenient to use than HMD and more likely to induce discomforts than screens. In addition, each Immersive Room constrains compatible solutions to strict specifications such as weight and volume limit for simulators. With the technological advances of the last 30 years, many other devices have been designed to stimulate additional senses during virtual experiences [START_REF] Coles | The Role of Haptics in Medical Training[END_REF][START_REF] Sherman | Understanding Virtual Reality : Interface, Application, and Design[END_REF] like Haptic Gloves [N. [START_REF] Cooper | Transfer of training -Virtual reality training with augmented multisensory cues improves user experience during training and task performance in the real world[END_REF]] or olfactive devices [START_REF] Porcherot | Immersive techniques and virtual reality[END_REF]]. Those additional feedback systems are likely to reinforce the virtual experience realism, quality or novelty. Thus, many realistic simulators have been equipped with feedback platforms such as driving simulators [START_REF] Bruck | A Review of Driving Simulation Technology and Applications[END_REF][START_REF] Telpaz | Haptic Seat for Automated Driving: Preparing the Driver to Take Control Effectively[END_REF]. From a broader perspective, the number of VR-based simulators and applications continues to grow with more and more powerful and accessible tools. In particular the use of "Game Engines", software allowing to model, build and animate the 3D VE has become more democratic. The term "Game" is a residual of their popularization which was first done via the video game industry.

Plenty of Game Engines exist, but it is Unity, whose interface can be seen in Figure 2.5, which has been used during this thesis for its many qualities [START_REF] Haas | A History of the Unity Game Engine[END_REF]]. Indeed, in addition from being efficient, Unity benefits for constant updates with additional handy features and for a large and helpful community. Moreover, Unity is compatible with multiple display interfaces including those used during this thesis; the HTC Vive Pro HMD visible in Figure 2.3b [START_REF] Ogdon | HoloLens and VIVE Pro: Virtual Reality Headsets[END_REF]] and the Immersia1 Immersive Room localized in Rennes [START_REF] Gaugne | Immersia, an open immersive infrastructure: doing archaeology in virtual reality[END_REF].

Interest

Nowadays, VR has gone far beyond the realms of entertainment and video games and is making an impact in many areas of research [START_REF] Slater | Enhancing our lives with immersive virtual reality[END_REF][START_REF] Fuchs | Virtual reality: concepts and technologies[END_REF]. Indeed, VR allows building safe, controllable, engaging and reproducible VEs of any nature [START_REF] Schultheis | The application of virtual reality technology in rehabilitation[END_REF]. Within realistic simulators, using VR increases the possibilities to improve simulation realism and immersion inside the VE [START_REF] Slater | Enhancing our lives with immersive virtual reality[END_REF]. Furthermore, VR allows imagining and reproduce any real-life situations regardless of real constraints and dangers. These possibilities make VR a widespread tool to design simulators for entertainment but also for many other purposes especially in the medical field for rehabilitation and training [START_REF] Howard | A meta-analysis and systematic literature review of virtual reality rehabilitation programs[END_REF][START_REF] Coles | The Role of Haptics in Medical Training[END_REF]. In particular, VR-based simulation is a suitable tool for training on very complex tasks with high constraints such as nurse training [START_REF] Bracq | Training situational awareness for scrub nurses: Error recognition in a virtual operating room[END_REF][START_REF] Bracq | Learning procedural skills with a virtual reality simulator: An acceptability study[END_REF] or surgery [START_REF] Basdogan | VR-based Simulators for Training in Minimally Invasive Surgery[END_REF][START_REF] Seymour | Virtual reality training improves operating room performance: results of a randomized, double-blinded study[END_REF]. Indeed, while the costs and constraints necessary to reproduce certain training situations make their realization utopic in real-life, VR offers a simulated alternative. For example, no standard power wheelchair driving training program in real-life includes an urban complex outdoor space since such a scenario is far too dangerous. In addition, a recent study highlighted that VR can increase user excitement and motivation while performing a task in the VE [START_REF] Howard | A meta-analysis and systematic literature review of virtual reality rehabilitation programs[END_REF]]. This is an interesting result for low motivating domains such as wheelchair driving. It has been shown that people with visuo-spatial and cognitive impairments may experience reduced motivation while driving a wheelchair [START_REF] Cawood | Impact of post-stroke impairments on activities and participation as experienced by stroke survivors in a Western Cape setting[END_REF]. Finally, VR and especially VR based simulators are used in a wide variety of contexts, from cosmetic marketing to medical treatment or the automotive industry which is further discussed in Section 2.2 [START_REF] Arlati | Virtual reality-based wheelchair simulators: A scoping review[END_REF][START_REF] Slater | Enhancing our lives with immersive virtual reality[END_REF]. Coupled with innovative sensory stimulation devices, VR based simulators are able to offer highly immersive experiences with a strong Sense of Presence (SoP) [START_REF] Weech | Presence and cybersickness in virtual reality are negatively related: A review[END_REF].

Sense of Presence

This subsection presents the Sense of Presence, its definition, factors and measurements methods.

Definition

Sense of Presence (SoP) refers to the subjective phenomenon designating the impression of existing in a VE, of "being there" in the simulation [START_REF] Slater | A framework for immersive virtual environments (FIVE): Speculations on the role of presence in virtual environments[END_REF]. In other words, "SoP is the perceptual illusion of non mediation, produced by means of the disappearance of the medium from the conscious attention of the subject" [START_REF] Fuchs | Les casques de réalité virtuelle et de jeux vidéo[END_REF]]. Although many works refer to it as "Presence", the use of the word "sense" emphasizes the subjective and individual character of this concept as well as distances it from the concept of "immersion". As distinct from SoP, "immersion is the perceptive, mental or emotional state of a subject when one or more of his senses are isolated from the reality and are only solicited by computer generated signals" [START_REF] Pimentel | de l'autre côté du miroir[END_REF]. Thus, SoP is the user subjective response to a VR experience whereas immersion is more of concrete and objective property of a system [START_REF] Slater | Immersion and the illusion of presence in virtual reality[END_REF]]. Nonetheless, SoP and immersion are closely related as a more immersive system is likely to generate more SoP. SoP is commonly associated with the amount of knowledge transfer from a virtual experience to real life [START_REF] Stevens | The Relationship between Presence and Performance in Virtual Simulation Training[END_REF]. Indeed, the more the SoP, the more likely the user is to behave similarly to a real situation and thus be inspired by their previous virtual experiences to tackle similar real-life experiences. This result is particularly sought in training contexts for better skill transfer [N. [START_REF] Cooper | Transfer of training -Virtual reality training with augmented multisensory cues improves user experience during training and task performance in the real world[END_REF][START_REF] Tarr | Virtual reality in behavioral neuroscience and beyond[END_REF]. As such, SoP represents a key concept of VR based simulation, especially within training contexts [START_REF] Riva | Presence and rehabilitation: Toward second-generation virtual reality applications in neuropsychology[END_REF]. Nevertheless, further researches are needed to fully understand what SoP induces and concerns.

Factors

Apart from immersion and according to the literature, SoP depends on several concepts and criteria such as realism, interaction and incarnation, each impacted by several material and sensory factors [START_REF] Servotte | Virtual Reality Experience: Immersion, Sense of Presence, and Cybersickness[END_REF]. In particular, SoP strongly depends on visual feedback such as the simulated 3D models realism [START_REF] Schuemie | Research on Presence in Virtual Reality: A Survey[END_REF] or the display type and field of view size [START_REF] Alshaer | Immersion factors affecting perception and behaviour in a virtual reality power wheelchair simulator[END_REF]. A more immersive display device is likely to induce more SoP during a VR experiment [Nigel W. [START_REF] John | The Implementation and Validation of a Virtual Environment for Training Powered Wheelchair Manoeuvres[END_REF]. Virtual representation of the user's own body is also likely to induce more SoP [START_REF] Sun | The effect of user's perceived presence and promotion focus onusability for interacting in virtual environments[END_REF]]. In addition, related works have shown that SoP is impacted by other sensory modalities. Authors in [START_REF] Weech | Presence and cybersickness in virtual reality are negatively related: A review[END_REF] prove that SoP increases when multiplying sensory feedback such as vestibular, haptic or auditory feedback. This result has also been observed in the entertainment field, in particular within cinema including additional feedback [Oh, M. Lee, and S. Lee 2011]. Nevertheless, some VR experiment variables impacts on SoP are discussed among the literature such as VE realism or user overall comfort during the simulation [START_REF] Servotte | Virtual Reality Experience: Immersion, Sense of Presence, and Cybersickness[END_REF][START_REF] Melo | Presence and cybersickness in immersive content : Effects of content type , exposure time and gender[END_REF].

Measurements methods

As SoP refers to a subjective phenomenon, it is mainly measured through subjective questionnaires. The most used one is the IGroup Presence Questionnaire presented in [START_REF] Schubert | The sense of presence in virtual environments: A three-component scale measuring spatial presence, involvement, and realness[END_REF]], however multiple questionnaires address SoP such as the 32 items Presence Questionnaire proposed in [START_REF] Witmer | Measuring Presence in Virtual Environments[END_REF] or the Immersion Virtual Environments Questionnaire (IVEQ) presented in [START_REF] Tcha-Tokey | Conception et évaluation de l' expérience utilisateur en environnement virtuel immersif[END_REF][START_REF] Tcha-Tokey | A questionnaire to measure the user experience in immersive virtual environments[END_REF]]. The particularity of the latter is that it addresses several VR experience quality aspects inside a single questionnaire such as immersion, comfort or SoP. Using same measurement methods as literature allows authors to compare and rate their simulated experiments while exploring their limit and drawing improvements guidelines. Indeed, SoP is one of the keys to a good quality virtual experience and especially to an efficient training simulation. Thus, virtual experiences and in particular training simulations, must seek to obtain a high level of SoP while limiting the discomforts that can alter their quality such as Cybersickness. This subsection presents Cybersickness; its definition, origin, factors and measurement methods.

Definition

Cybersickness refers to discomforts that can arise when immersed in a VE and characterized by various symptoms such as nausea, sweating, dizziness, etc. [START_REF] Mchugh | Measuring and Minimizing Cybersickness in Virtual Reality[END_REF][START_REF] Laviola | A Discussion of Cybersickness in Virtual Environments[END_REF]. Cybersickness symptoms are similar to Motion Sickness symptoms which have been categorized in 4 types [START_REF] Nichols | Health and safety implications of virtual reality: A review of empirical evidence[END_REF][START_REF] Gianaros | A questionnaire for the assessment of the multiple dimensions of motion sickness[END_REF]] :

• gastrointestinal (stomach awareness, nausea, vomiting);

• central (fainting, lightheadedness, blurred vision, disorientation, dizziness, sensation of spinning);

• peripheral (sweating, feeling hot);

• sopite (annoyance, drowsiness, tiredness, uneasiness).

As such, most of the literature agreed upon considering Cybersickness as a type of Motion Sickness [Robert S. Kennedy, J. Drexler, and R. C. [START_REF] Kennedy | Research in visually induced motion sickness[END_REF]. However, the way that Cybersickness symptoms and "classic" Motion Sickness symptoms differ in terms of severity, probability and complexity is unclear and disputed [Bockelman and Lingum 2017; Robert S. Kennedy, J. Drexler, and R. C. [START_REF] Kennedy | Research in visually induced motion sickness[END_REF]. Building a complete Cybersickness symptomatology is not an easy task since humans are not equally responding to Cybersickness. Indeed, Cybersickness is likely to manifest itself more severely to some more sensitive people [START_REF] Weech | Presence and cybersickness in virtual reality are negatively related: A review[END_REF]. In addition, Cybersickness symptoms diversity and nature will vary from person to person. Nonetheless, a recent study shows that Cybersickness and "classic" Motion Sickness symptoms and physiological impacts are alike [START_REF] Gavgani | A comparative study of cybersickness during exposure to virtual reality and "classic" motion sickness: Are they different?[END_REF][START_REF] Gavgani | Profiling subjective symptoms and autonomic changes associated with cybersickness[END_REF]]. Literature also distinguishes Cybersickness from Simulator Sickness, generally considered as another type of Motion Sickness which occurs when using a simulator providing other sensory stimuli in addition to visual. Here again, their differences regarding symptoms profile, severity and duration are unclear. In particular, the question remains whether Cybersickness and Simulator Sickness represent separate clinical entities. Studies qualifying Simulator Sickness symptoms as more [Robert S. Kennedy, J. Drexler, and R. C. [START_REF] Kennedy | Research in visually induced motion sickness[END_REF] or less [Stanney, Robert S. Kennedy, and J. M. Drexler 1997] severe than Cybersickness symptoms both exist. Considering a VR based simulator that is, a simulator in-cluding VE immersion, literature seems to use the term "Cybersickness" to designate discomforts symptoms as it occurs when using cyber systems [START_REF] Bockelman | Factors of cybersickness[END_REF]. In that specific case, differentiate Cybersickness and Simulator Sickness would have little clinical interest. As such, in this thesis, we will use the term Cybersickness to designate those Motion-Sickness-like symptoms and discomforts occurring when using a VR based simulator.

Origin theories

Beside to symptomatology similarities, literature tends to explain Cybersickness causes through the same Motion Sickness origin theories [START_REF] Mchugh | Measuring and Minimizing Cybersickness in Virtual Reality[END_REF][START_REF] Rebenitsch | Review on cybersickness in applications and visual displays[END_REF]. The two most prominent ones are the Sensory Conflicts theory [Palmisano, Mursic, and J. Kim 2017;[START_REF] Oman | Motion sickness: A synthesis and evaluation of the sensory conflict theory[END_REF]] and Postural Instability theory [Y. [START_REF] Wang | VR sickness prediction for navigation in immersive virtual environments using a deep long short term memory model[END_REF][START_REF] Riccio | An Ecological Theory of Motion Sickness and Postural Instability[END_REF].

The Sensory Conflicts theory is the predominant explanation and supports the idea that Cybersickness is induced by cognitive mismatches occuring during the VE immersion [LaViola 2000]. For example, the differences between what user sees and feels i.e. the motion visually perceived compared to the actual physical immobility, are well known sources of cognitive mismatches. This theory could explain why some old studies have supported that simulators could generate more severe symptoms when including additional sensory stimuli to visual feedback. Indeed, older sensory stimulation systems with badly synchronized sensory stimuli may have emphasized sensory conflicts rather than reduced them.

The Postural Instability is based on the predicate that humans aim to keep their posture as stable as possible [START_REF] Venkatakrishnan | A Structural Equation Modeling Approach to Understand the Relationship between Control , Cybersickness and Presence in Virtual Reality[END_REF]]. As such, the theory states that Cybersickness comes from a destabilization of this posture. In other words, the theory considers physical displacements to be the source of Cybersickness rather than one symptom. While the theory is promising and makes it easier to explain the negative impact of VR exposure time on Cybersickness, it is lacking recent experimental proofs. A recent study could not find a correlation between postural displacements and Cybersickness [START_REF] Dennison | Cybersickness without the wobble: Experimental results speak against postural instability theory[END_REF]. They did however found that some participants experienced Cybersickness without any postural instability. In addition, people with inactive vestibular system still suffer from Cybersickness [START_REF] Harm | Motion sickness neurophysiology, physiological correlates, and treatment[END_REF]].

A third complementary theory called Poison Theory exists and concerns Cybersickness, Motion Sickness and Simulator Sickness symptomatology similarities and origins [START_REF] Rebenitsch | Review on cybersickness in applications and visual displays[END_REF][START_REF] Laviola | A Discussion of Cybersickness in Virtual Environments[END_REF]. The Poison theory states that due to evolution, the postural instabilities or sensory conflicts is interpreted by the brain as signs of hallucination due to consumption of a toxic substance. Thus, discomforts and in particular gastrointestinal symptoms would represent the user body response to poisoning. Understanding the origin of Cybersickness allows better exploring its factors in order to eliminate or counteract them. However, identifying the hardware-related, content-related and human-related factors and their importance is a complex task that has animated many projects for several years. Authors in [Chang, H. T. Kim, and Yoo 2020] present several Sankey diagrams such as Figure 2.6 which illustrates the variety of content-related factors research. Furthermore, not only Cybersickness factors are numerous, but their importance also depends on the supported theory. In this thesis, we will address Cybersickness through the Sensory Conflicts theory. As such, the most important factors are those related to the sensory system such as visual feedback, exposure time or health condition. In particular regarding visual feedback, a relationship was identified between Cybersickness and the type of display interface used [START_REF] Mchugh | Measuring and Minimizing Cybersickness in Virtual Reality[END_REF]; Rebenitsch and Owen 2016] Indeed, the display interface chosen impacts the Field of View (FOV) [START_REF] Nichols | Health and safety implications of virtual reality: A review of empirical evidence[END_REF], the latency [START_REF] Stauffert | Latency and Cybersickness: Impact, Causes, and Measures. A Review[END_REF], the vection [Palmisano, Mursic, and J. Kim 2017], the "lag" [LaViola 2000] and more other visual feedback aspects, all of which known to impact Cybersickness. Thus, by extension, Cybersickness and SoP seem correlated as SoP is also impacted by such visual factors. Nonetheless, the existence and nature of this correlation are unclear, although suspected negative [START_REF] Weech | Presence and cybersickness in virtual reality are negatively related: A review[END_REF].

Factors

Measurement methods and precautions

Treating Cybersickness is necessary as it can drastically alter the user comfort to the point of making the virtual experience unbearable [START_REF] Gavgani | Effects of visual flow direction on signs and symptoms of cybersickness[END_REF] especially since symptoms can last long after the exposition [Stanney, Robert S. Kennedy, and J. M. Drexler 1997]. In a VR based simulator training context, authors of [START_REF] Weech | Presence and cybersickness in virtual reality are negatively related: A review[END_REF][START_REF] Venkatakrishnan | A Structural Equation Modeling Approach to Understand the Relationship between Control , Cybersickness and Presence in Virtual Reality[END_REF] consider that above a certain level, such discomforts can limit user concentration and propensity to learn. It is therefore imperative for simulators to implement solutions to limit Cybersickness and to be able to detect and measure these discomforts as soon as possible. Some simple precautions concerning the VR experience can limit the Cybersickness like reducing the VR exposure time or the movements planned in the scenario [START_REF] Mchugh | Measuring and Minimizing Cybersickness in Virtual Reality[END_REF]]. Other solutions concerning the simulator very design exist such as adding a motion stimuli correctly aligned with visual feedback, implementing rest frames within the VE or multiplying static virtual reference points [START_REF] Mchugh | Measuring and Minimizing Cybersickness in Virtual Reality[END_REF][START_REF] Laviola | A Discussion of Cybersickness in Virtual Environments[END_REF]. Regarding measurements, a lot of different methods exist but according to a recent review [Chang, H. T. Kim, and Yoo 2020], researchers mainly use subjective measures such as questionnaires. In particular, the Simulator Sickness Questionnaire (SSQ) elaborated by [Robert S [START_REF] Kennedy | Simulator Sickness Questionnaire : An Enhanced Method for Quantifying Simulator Sickness[END_REF] is the mostly used questionnaire paired with the Motion Sickness Susceptibility Questionnaire (MSSQ) presented in [START_REF] Golding | Predicting individual differences in motion sickness susceptibility by questionnaire[END_REF]] to detect more Cybersickness sensitive people before exposition. The use of the Motion Sickness Assessment Questionnaire (MSAQ) [START_REF] Gianaros | A questionnaire for the assessment of the multiple dimensions of motion sickness[END_REF]] is also widely spread while this questionnaire was dedicated to Motion Sickness rather than Cybersickness [START_REF] Bockelman | Factors of cybersickness[END_REF]. Several more precise and specific to Cybersickness were proposed in the recent years [START_REF] Sevinc | Psychometric evaluation of Simulator Sickness Questionnaire and its variants as a measure of cybersickness in consumer virtual environments[END_REF]. The Virtual Reality Sickness Questionnaire (VRSQ) presented in [H. K. [START_REF] Kim | Virtual reality sickness questionnaire (VRSQ): Motion sickness measurement index in a virtual reality environment[END_REF]] is one of those promising new tools that corrects some of the SSQ misconceptions. In the same way as SoP measurements, using same questionnaires as the one used by literature is important in order to be able to compare results. However, unlike SoP, measurement methods based on objective data exist based on physiological response [START_REF] Stauffert | Latency and Cybersickness: Impact, Causes, and Measures. A Review[END_REF]. For example, authors in [START_REF] Gavgani | A comparative study of cybersickness during exposure to virtual reality and "classic" motion sickness: Are they different?[END_REF]] used tonic and phasic forehead skin conductance level. Nevertheless, objective measures require additional systems installed during the VR experiment that can be cumbersome for the user, especially with VR simulator that might already require a complex setup.

Simulator Fidelity

While many projects have discussed VR key-concepts such as SoP and Cybersickness, the concept of fidelity seems to have received less attention in the recent years. In fact the fidelity concept is far from being a consensus in the literature with almost as many definitions as there are simulation projects [START_REF] Tun | Redefining Simulation Fidelity for Healthcare Education[END_REF][START_REF] Liu | Simulation fidelity[END_REF]. In general, fidelity is associated with the notion of realism and similarity of a virtual experience with its real reference situation. However, what does induce and compose fidelity, and what does fidelity impact and involve remain unclear.

The concept of fidelity seems to be an inherent multidimensional property of every simulation contexts more than a subjective concept as explained in [START_REF] Roza | Fidelity considerations for civil aviation distributed simulations[END_REF]. In [START_REF] Liu | Simulation fidelity[END_REF], authors propose a multidimensional model to define fidelity, where each dimension participates in the global simulation degree of fidelity, i.e., in the realistic and replicated character of a real situation. However, this model has limitations since dimensions are not independent of one another. As such, it appears difficult to use this model in certain contexts, notably the medical field. Moreover, the model mixes elements related to the simulator as a tool and elements related to the simulation as a virtual experience contrary to what the authors of [START_REF] Tun | Redefining Simulation Fidelity for Healthcare Education[END_REF] suggests. Indeed, in [START_REF] Tun | Redefining Simulation Fidelity for Healthcare Education[END_REF], authors suggest differentiating the simulator fidelity from the simulation fidelity. From their work and definitions of simulator and simulation, simulator fidelity can be defined as "the simulator propensity to provide a realistic simulation" whereas the simulation fidelity can be defined as "the virtual experience similarity with a real situation including scenario, interactions and user behaviour". As such, a "high" fidelity simulator does not systematically result in a "high" fidelity simulation i.e., a realistic user behavior within a realistic virtual experience.

However, the terminology is often misused in literature. Indeed, simulator fidelity or simulation fidelity are commonly employed to designate other concepts like SoP, or as a guarantee of virtual experience quality, like an efficient skill transfer in the training domain [START_REF] Presado | Learning with High Fidelity Simulation[END_REF]. For example, the simulation fidelity positive impact on the virtual experience quality revealed in some works such as in [START_REF] Presado | Learning with High Fidelity Simulation[END_REF][START_REF] Mcmahan | Exploring the Effects of Higher-Fidelity Display and Interaction for Virtual Reality Games[END_REF]] could be attributed to other causes such as an amplified SoP through realism factor [START_REF] Massoth | High-fidelity is not superior to low-fidelity simulation but leads to overconfidence in medical students[END_REF][START_REF] Tarr | Virtual reality in behavioral neuroscience and beyond[END_REF]. This imposture is probable since it has been shown within training situations that including some unrealistic features enhances SoP and training efficiency while altering fidelity [N. [START_REF] Cooper | Transfer of training -Virtual reality training with augmented multisensory cues improves user experience during training and task performance in the real world[END_REF][START_REF] Alexander | From Gaming to Training: A Review of Studies on Fidelity, Immersion, Presence, and Buy-in and Their Effects on Transfer in PC-Based Simulations and Games[END_REF]. Those ambiguities have led some researchers, as in [START_REF] Hamstra | Reconsidering fidelity in simulation-based training[END_REF], to abandon the term fidelity due to its abusive use, its overly nebulous definition and its imprecise quantification of "low", "mid" or "high". Indeed, regarding simulator fidelity, it is common to speak of "high-fidelity" simulator to underline the high quality of their generated simulation whereas the simulator fidelity level does not seem to have any impact on the virtual experience quality nor efficiency [START_REF] Massoth | High-fidelity is not superior to low-fidelity simulation but leads to overconfidence in medical students[END_REF][START_REF] Norman | The minimal relationship between simulation fidelity and transfer of learning[END_REF]. In particular, within the medical training domain, many examples of non-significant results in performance evaluation between the use of high fidelity simulators and low fidelity simulators exist [START_REF] Levett-Jones | Examining the impact of high and medium fidelity simulation experiences on nursing students' knowledge acquisition[END_REF][START_REF] Kardong-Edgren | Does Simulation Fidelity Improve Student Test Scores?[END_REF]. Nevertheless, while these subjective levels do not provide any indication on a simulator efficiency, they do provide insight into its purpose, operation and scope [START_REF] Beaubien | The use of simulation for training teamwork skills in health care: How low can you go?[END_REF]].

Hence, it seems that fidelity remains a confused notion, first with what it concerns, i.e., the simulation or the simulator. Simulator fidelity appears much more as a concrete and measurable property than simulation fidelity. In addition, simulation fidelity is often confused with other concepts like SoP or immersion especially within specific application contexts such as simulation training. Thus, in this thesis, the term "fidelity" will refer to the simulator fidelity previously defined and used as a qualifier of the simulator and its architecture rather than a qualifier for a virtual experience's aspect : Definition-The simulator fidelity is the intrinsec propensity of a simulator to provide a realistic simulation

Power Wheelchair VR Simulation

Within the power wheelchair domain, numerous VR based simulators projects have emerged, especially for training purposes. This section reviews those projects in order to understand how they have addressed VR key concepts previously exposed. It first explains their interest as a training tool in subsection 2.2.1 before exploring how they addressed SoP (subsection 2.2.2) and Cybersickness (subsection 2.2.3). Then subsection 2.2.4 reviews different application contexts than training.

Training efficiency

Aside some projects with industrial scope like smart urban planning [START_REF] Götzelmann | Towards the inclusion of wheelchair users in smart city planning through virtual reality simulation[END_REF][START_REF] Herrlich | Development of a virtual electric wheelchair -Simulation and assessment of physical fidelity using the unreal engine 3[END_REF] or industrial design tools [START_REF] Braga | IntellWheels: Modular development platform for intelligent wheelchairs[END_REF][START_REF] Sasaki | Simulator for Optimal Wheelchair Design[END_REF], the majority of the existing various fidelity degree power wheelchair simulators aims to provide medical therapy support [START_REF] Arlati | Virtual reality-based wheelchair simulators: A scoping review[END_REF][START_REF] Pithon | Wheelchair simulators: A review[END_REF]]. Indeed, the beneficial effects of training in simulation have been long recognized in many applications and contexts as reported by [START_REF] Slater | Enhancing our lives with immersive virtual reality[END_REF] such as aviation with flight simulators to train pilots [START_REF] Hays | Flight Simulator Training Effectiveness : A Meta-Analysis[END_REF]. Navigational skills acquired thanks to training in simulation have also been demonstrated to positively transfer into real situations for military training [START_REF] Loftin | Training in peacekeeping operations using virtual environments[END_REF]] or more recently for car driving training [START_REF] Hirsch | Pilot Project to Validate the Transfer of Training of Driving Skills Learned on a High Fidelity Driving Simulator to On-Road Driving[END_REF]. In addition, it has been shown that different fidelity degrees have varying educational value depending on training objectives and learners profile [START_REF] Tun | Redefining Simulation Fidelity for Healthcare Education[END_REF].

Within a power wheelchair driving context, VR based simulation allows users to learn in a controlled, repeatable and safe environment and therapists to achieve abilities assessment while reducing time, cost or safety constraints [START_REF] Ogourtsova | Ecological Virtual Reality Evaluation of Neglect Symptoms (EVENS): Effects of Virtual Scene Complexity in the Assessment of Poststroke Unilateral Spatial Neglect[END_REF]. In particular, the use of power wheelchair simulation has been efficient within training and rehabilitation programs [START_REF] Leaman | A comprehensive review of smart wheelchairs: Past, present and future[END_REF][START_REF] Abellard | Electric Wheelchair Navigation Simulators: why, when, how?[END_REF][START_REF] Levin | Feedback and virtual environments for motor learning and rehabilitation[END_REF]. In [START_REF] Morere | ViEW, a wheelchair simulator for driving analysis[END_REF], authors performed an experiment on the ViEW simulator in a rehabilitation center with 12 young patients. Their objective was to evaluate acquired skills through a custom level progression. ViEW simulator, pictured in Figure 2.7, consists of a VE displayed on a computer screen in which the user can control a virtual wheelchair while sitting on a chair. Their results prove the existence of a skill transfer from virtual experience to reality even though the ViEW simulator is only screen based and does not include a motion platform with vestibular or proprioceptive stimuli. Also, authors reported that the use of the ViEW simulator stimulated participant's interest. Moreover, in [START_REF] Rodriguez | Development of a wheelchair simulator for children with multiple disabilities[END_REF]] and [START_REF] Linden | Efficacy of a powered wheelchair simulator for school aged children: A randomized controlled trial[END_REF]], a power wheelchair simulator was tested with children respectively with and without disabilities. The first study discussed simulator impact and accessibility for children while the second proved that a brief amount of time using projector screen is sufficient for young children to improve their wheelchair navigation skills. Similar results with a screen-based simulator are presented in [START_REF] Adelola | Virtual environments for powered wheelchair learner drivers: Case studies[END_REF]. In addition, using the VRSIM-2 simulator, authors in [START_REF] Kamaraj | Interrater Reliability of the Power Mobility Road Test in the Virtual Reality-Based Simulator-2[END_REF] showed that driving assessments made by raters where highly correlated with real-life assessment suggesting that VR based power wheelchair simulators are also useful for driving evaluations. All these studies prove the usefulness of simple and cost-effective screen-based power wheelchair simulator in a training context. However, with such simulators, user head movements and FOV are limited by screen size which might limit learning and reduce its quality. Indeed, these FOV limitations could have a negative impact on visual information taking, in particular for some maneuvers that require the user to look around. In addition, using screen can limit the SoP felt during the virtual experience thus limiting skill transfer and training efficiency.

Addressing Sense of Presence (SoP)

In 2016, a study with the screen-based miWe simulator reported a low SoP experienced and associated it with a lack of motion feedback and depth perception [START_REF] Tao | Powered wheelchair simulator development: Implementing combined navigation-reaching tasks with a 3D hand motion controller[END_REF]. In order to improve user exploration and SoP, authors [START_REF] Niniss | Electric wheelchair simulator for rehabilitation of persons with motor disability[END_REF] present a new version of their simulator including a screen with a larger FOV. With the same idea, various recent researches have proposed more immersive systems with higher fidelity, starting with the use of a VR headset as visual interface to provide depth perception and immersive FOV like in the Simcadrom project [START_REF] Hernandez-Ossa | Virtual Reality Simulator for Electric Powered Wheelchairs using a Joystick[END_REF][START_REF] Hernandez-Ossa | Simulation system of electric-powered wheelchairs for training purposes[END_REF]. Still with the aim of improving SoP and inspired by literature advice and car driving simulators [START_REF] Bruck | A Review of Driving Simulation Technology and Applications[END_REF][START_REF] Telpaz | Haptic Seat for Automated Driving: Preparing the Driver to Take Control Effectively[END_REF], some power wheelchair simulators include systems to stimulate additional sensory modalities. As such, a 6 degree of freedom (DoF) motion platform was integrated in the simulator proposed in [START_REF] Ito | Development of a Powered Wheelchair Driving Simulator for Research and Development Use[END_REF]] in order to provide vibration feedback, thus enhancing its fidelity. For its part, the simulator presented in [START_REF] Niniss | Electric wheelchair simulator for rehabilitation of persons with motor disability[END_REF] is able to provide haptic and vestibular feedback through its 6 DoF stewart platform. That is also the case of the Virtual Fauteuil simulator which is concerned by the same problematics as a power wheelchair simulator even though it simulates a manual wheelchair [START_REF] Pouvrasseau | Discussion about functionalities of the Virtual Fauteuil simulator for wheelchair training environment[END_REF]]. However, these platforms are often complex and not well adapted to user needs. Indeed, people with disabilities require a platform able to adapt to their impairments as a power wheelchair would. Furthermore, a platform with a structure and dimensions too different from those of a standard power wheelchair reduces the possible similarity of motion feedback thus, the maximum SoP generated. The platform included in VRSIM-2 simulator and proposed in [START_REF] Kamaraj | Interrater Reliability of the Power Mobility Road Test in the Virtual Reality-Based Simulator-2[END_REF]] allows people to use their own power wheelchair which maximizes comfort but complicates the system dynamic and the method to generate realistic motion feedback. Thus, the existing solutions to enhance SoP can be improved, especially regarding motion platform and additional sensory stimuli.

Addressing Cybersickness

Enhancing simulator fidelity using immersive systems and multiplying stimulated sensory modalities allows increasing the global SoP generated by the virtual experience, thus, within a training scenario, the effectiveness of the skill transfer. However, more immersive systems are also more likely to induce Cybersickness. For example, authors in [Nigel W. [START_REF] John | The Implementation and Validation of a Virtual Environment for Training Powered Wheelchair Manoeuvres[END_REF]] report an effective skill transfer but also a moderate Cybersickness using HMD. Nonetheless, aside measuring and reporting it, only few VR-based power wheelchair simulator projects propose solutions to Cybersickness, considering it as a VR inexorable discomfort. For example, the VRSIM-2 simulator does not implement any solution to reduce Cybersickness and the related study [START_REF] Kamaraj | Interrater Reliability of the Power Mobility Road Test in the Virtual Reality-Based Simulator-2[END_REF]] just eliminates the users who feel too much discomfort. Within the Simcadrom project presented in [START_REF] Hernandez-Ossa | Simulation system of electric-powered wheelchairs for training purposes[END_REF], researchers have only limited the maximum velocity of the simulated power wheelchair in the expectation of limiting Cybersickness. Unfortunately, this constraint was not sufficient, and they have reported a significant level of Cybersickness that will have to be reduced in the future. Indeed, not only Cybersickness alters training efficiency, but it also prevents more sensitive people to use the simulator thus reducing the simulator based training accessibility. VR based power wheelchair training simulators should implement solutions to maximize their training efficiency, with bigger FOV and/or enhanced SoP, but also user comfort, with adaptable platforms and limited Cybersickness.

Beyond training

While VR simulation appears as a promising training tool [START_REF] Slater | Enhancing our lives with immersive virtual reality[END_REF], VR based simulators of various fidelity degrees have also been beneficial in many other areas of cultural influence, social stakes or economic issues [START_REF] Slater | Enhancing our lives with immersive virtual reality[END_REF][START_REF] Tarr | Virtual reality in behavioral neuroscience and beyond[END_REF]. In particular, within industrial development processes, VR based simulators with more or less fidelity are used at different steps such as design or evaluation [START_REF] Granda | The use of high-fidelity real-time driving simulators for geometric design[END_REF]. For example, in [START_REF] Tiainen | Virtual prototypes reveal more development ideas: comparison between customers' evaluation of virtual and physical prototypes[END_REF], authors explained how they used VR to gather customer feedback in order to fit their needs within a more user-centered product development. In fact, within an industrial context such as car manufacturing, VR simulators appears as a support tool that can be used at every development process step (design, prototyping, production, evaluation, marketing...) especially to involve end-users [START_REF] Bruck | A Review of Driving Simulation Technology and Applications[END_REF][START_REF] Lawson | Future directions for the development of virtual reality within an automotive manufacturer[END_REF].

In the context of power wheelchair, low to high fidelity simulators are sometimes used for other purposes than training or rehabilitation. For example, authors in [START_REF] Zatla | OPCM model application on a 3D simulator for powered wheelchair[END_REF]] have used the ViEW simulator to better understand and analyze power wheelchair driving task. In addition, just like car simulators, VR based power wheelchair simulators of various fidelity degrees are starting to be used within power wheelchair related tools development process. Indeed, low fidelity simulators are used for tuning smart algorithms like obstacle avoidance or path planning [START_REF] Maule | RoboEye, an Efficient, Reliable and Safe Semi-Autonomous Gaze Driven Wheelchair for Domestic Use[END_REF]] whereas higher fidelity simulators are used to design innovative control input [START_REF] Ito | Development of a Powered Wheelchair Driving Simulator for Research and Development Use[END_REF] or recently within urban planning [START_REF] Götzelmann | Towards the inclusion of wheelchair users in smart city planning through virtual reality simulation[END_REF][START_REF] Herrlich | Development of a virtual electric wheelchair -Simulation and assessment of physical fidelity using the unreal engine 3[END_REF]. Finally, some projects use simulators within smart power wheelchair design and development processes in order to better center the solution on end-users needs and expectations [START_REF] Braga | IntellWheels: Modular development platform for intelligent wheelchairs[END_REF][START_REF] Sasaki | Simulator for Optimal Wheelchair Design[END_REF]]. This way, as authors report in [START_REF] Faria | A Survey on Intelligent Wheelchair Prototypes and Simulators[END_REF], power wheelchair simulators could be further used as testing tools in order to better adapt power wheelchair related solutions to each user.

Conclusion

In this chapter we have discussed VR, a wide scientific domain whose impacts and areas of application have increased in recent years. Its popularization has also brought to light the different key concepts necessary for a good quality VR experience like SoP and Cybersickness. Their impacts and factors are still unclear and hotly debated by researchers, but are considered essential within the simulation domain. Within training simulation, SoP is considered as a key to high skill transfer whereas Cybersickness as a main barrier to comfortable VR experience. As such, high-fidelity simulator projects aiming to provide a virtual experience as much realistic as possible should address both concepts. In particular, considering this thesis objectives and power wheelchair clinical requirements, a power wheelchair training simulator should maximize SoP while minimizing Cybersickness, regardless of its fidelity level.

3

High fidelity Virtual Reality based power wheelchair simulator

As underlined in the previous chapters, people with disability may struggle to drive a power wheelchair because of altered perception skills. It has been shown that good visuo-spatial and cognitive abilities are necessary to achieve safe power wheelchair driving [START_REF] Massengale | Effect of visual perception, visual function, cognition, and personality on power wheelchair use in adults[END_REF]. While training and repeated practice through occupational therapy sessions can be satisfactory for some people to master their wheelchair, this conventional training may be insufficient for others [START_REF] Anstey | Cognitive, sensory and physical factors enabling driving safety in older adults[END_REF]]. Some people may need training in specific situations such as driving in urban environments or crowded places. However, such training set-ups raise safety issues and are difficult to carry out. Moreover, a lack of situation-specific training could lead to hazardous driving [Richard C. [START_REF] Simpson | Smart wheelchairs: A literature review[END_REF]. As a consequence, therapists can decide not to prescribe a power wheelchair for safety concerns (e.g. driving behavior is above a subjective risk level) [START_REF] Mortenson | Prescribers' Experiences With Powered Mobility Prescription Among Older Adults[END_REF]. If smart systems such as the ones presented in Chapter 1 can enhance driving performances and accessibility, they still require good driving skills by the user [Leaman and Hung M. La 2017] and thus require training before they can be used in daily life.

In this context, power wheelchair driving simulation can provide an additional training tool. As shown in Chapter 2, VR is one way of simulating ecological situations with daily-life scenarios which are hardly reproducible in a real world. In addition, VR appears to be efficient and largely used in training programs [D. [START_REF] Inman | VR Education and Rehabilitation[END_REF] and rehabilitation [START_REF] Howard | A meta-analysis and systematic literature review of virtual reality rehabilitation programs[END_REF]]. It has also been shown as being safe, easy to use, and contributing to high patient satisfaction [START_REF] Dascal | Virtual Reality and Medical Inpatients: A Systematic Review of Randomized, Controlled Trials[END_REF]. VR could therefore reveal itself a more motivating tool for people with neurological disorders within wheelchair-related training programs.

A recent review on VR-based wheelchair simulators identified 29 wheelchair simulator projects: 20 of them tackle power wheelchair simulation [START_REF] Arlati | Virtual reality-based wheelchair simulators: A scoping review[END_REF]]. This review particularly highlighted the discrepancy among the proposed simulators. On the one hand, they differ in terms of assessment methodology and training programs, as most of the simulators were initially designed for driving training applications. On the other hand, they differ in their designs and configuration setups. For example, as stated in Chapter 2, some of them only use screens as display interface whereas others are based on HDM and immersive rooms. Some higher fidelity level VR-based wheelchair driving simulators try to reach a higher SoP level by providing haptic feedback and/or motion cues in addition to the visual feedback. The major drawback of the majority of these simulators is that they are not compliant with clinical and user requirements and needs. Indeed, while the choice of the visual display should be adapted to user needs, they often rely on a specific visual display technology. Moreover, they do not provide easy user transfer and adapted seating as they do not incorporate wheelchair standard components.

This chapter presents then a high fidelity multisensory power wheelchair simulator (Figure 3.1) designed in close collaboration with clinicians and power wheelchair users. This high fidelity simulator aims to provide realistic wheelchair driving experience for training and skill transfer to real-life situations. The proposed simulator includes a platform providing vestibular and haptic feedback in addition to the common visual and auditory feedback. Its modular design allows to easily interface with any visual display (e.g. HMD, immersive rooms, single screen). It also allows easy integration of add-ons and configuration tuning to match individual user needs.

The Section 3.1 presents the simulator requirements, design and final implementation. Then, Section 3.2 explores the benefit of the additional vestibular feedback that the simulator provide on the virtual experience quality, especially regarding SoP and Cybersickness. Section 3.3 presents the evaluation of the proposed simulator within a clinical context. our design choices have benefited from qualified experts' experience. In particular, computer scientists, like myself, and mechanical scientists worked closely with the clinical staff to better match therapists and wheelchair user needs and constraints. In this team, I actively participated in the software design, in the technical development of the simulator and in the elaboration and analysis of user studies.

This chapter is related to several publications [ICORR2019, JCJC2019, HRI2020, HANDI-CAP2020, MMCC2020, VR2021].

Simulator design and development

This section presents a new VR-based power wheelchair simulator and in particular the requirements it meets (subsection 3.1.1), its design (3.1.2) and its implementation (subsection 3.1.3) before concluding (subsection 3.1.4). It transcribes the work presented in [ICORR2019, JCJC2019].

Simulator requirements

We proposed a high fidelity multisensory power wheelchair simulator design providing visual, auditory, haptic feedback and motion cues. To this aim, in addition to display interface, the presented simulator includes a motion platform stimulating additional sensory modalities. This high fidelity simulator aims to serve wheelchair driving training and clinical rehabilitation purposes. As such, its design, especially regarding the mechanical platform, is subject to constraints deduced from targeted user requirements but also from the VR technology itself. End-user needs were formulated thanks to therapists and patients from the Pôle Saint Hélier Physical Medicine and Rehabilitation center. In particular, regarding targeted user and considering the complexity and plurality of mobility impairments, wide range of control input and of seating adjustments are needed. On one hand, to avoid improperly fitted seating or positioning, the seating should be adjustable and dynamic, allowing for tilt and recline. A wide range of postural supports must be available on the seat based on the specific user needs, disability type, and postural condition. Moreover, the seat should include add-ons such as lateral trunk supports, hip guides, head rest, lateral thigh supports, armrests, and abduction block. A belt should also be used properly to secure participant positioning during simulation. Proper seating also requires footrests. The platform seat width and height must also be compliant to average wheelchair standards. Platform width must not be significantly larger than the seat width, so it can be assimilated as a power wheelchair-like platform by its users. On the other hand, proportional controllers like joysticks are not suitable for everyone and the simulator should be compliant with any other types of controller like discrete controllers (e.g. head array, sip-and-puff) [START_REF] Rodriguez | Development of a wheelchair simulator for children with multiple disabilities[END_REF]]. Moreover, various input adaptations should be available for people with low upper limb strength or grasping difficulties (e.g. T-bar handle, U-bar handle, foam ball).

Regarding VR technology and training requirements, the objective is to provide a virtual driving experience similar to the one obtained with a power wheelchair. In other words, following Chapter 2 suggestions, the simulator should be of high fidelity and implement solutions to enhance SoP and thus the overall training efficiency and quality of the virtual experience.

Therefore, the simulator should include a motion feedback system to accurately reproduce the dynamic behavior of a power wheelchair. Of course, dynamics occurring to accidental events, Figure 3.3 -Power wheelchair simulator proposed in [START_REF] Devigne | Design of an immersive simulator for assisted power wheelchair driving[END_REF].

such as collisions and bumps, must not be fully reproduced by the motion feedback in order to alleviate the risks for users. These particular situations should be addressed through bearable haptic and auditory feedback. In addition, to increase SoP and match real situations, the proposed VE should be as realistic as possible. Furthermore, the simulator should be compliant with multiple display types such as HMDs and immersive rooms to provide more immersive visual feedback and bigger FOV. However, as stated in Chapter 2, more immersive visual system tends to generate more Cybersickness: related discomforts can impair participants and alter the experiment quality and efficiency. In particular, an enhanced VE realism tends to increase Cybersickness severity and likelihood, especially when no vestibular feedback is provided [Chang, H. T. [START_REF] Chang | Virtual Reality Sickness: A Review of Causes and Measurements[END_REF]. Thus, motion feedback should include vestibular cues correctly aligned with the visual stimuli to limit Cybersickness as suggested in [START_REF] Laviola | A Discussion of Cybersickness in Virtual Environments[END_REF]]. Moreover, depending on user susceptibility to Cybersickness, simulator should be compliant with less immersive display types like screens as illustrated in Figure 3.2.

Multisensory design

Following those requirements and based on a previous simulator design made by our research team and presented in [START_REF] Devigne | Design of an immersive simulator for assisted power wheelchair driving[END_REF], we propose a new simulator design which aims to match VR-related constraints by maximizing SoP as well as addressing the Cybersickness issue (Figure 3.1).

The previous simulator pictured in Figure 3.3 consisted of a standard power wheelchair fixed on the Immersia immersive room in Rennes, France. As it directly includes an off-the-shelf power wheelchair, this simulator matched the constraints related to clinical assessment presented in Section 3.1.1. The user was seating on a motionless wheelchair and immersed in the VE through 3D rendering only. Although this first simulator generated a rather good SoP, most of the people who tested it felt Cybersickness.

Inspired by literature and convinced by the theory of sensory conflict to explain the origin of Cybersickness [START_REF] Oman | Motion sickness: A synthesis and evaluation of the sensory conflict theory[END_REF]], we propose a multisensory power wheelchair simulator design with the aim to enhance SoP and to reduce sensory conflicts, hence, Cybersickness.

Motion platform and feedback

Following requirements and suggestions of previous subsection 3.1.1, the simulator includes a motion platform to both enhance SoP and limit Cybersickness. In particular, this motion platform generates motion cues in order to simulate accelerations as well as haptic feedback in order to reproduce interactions with the VE such as bumps, vibrations and collisions. This way, SoP should be reinforced by more realistic sensations and Cybersickness limited by reduced sensory conflicts due to additional feedback synchronized with visual stimuli. In other words, the motion platform simulates the dynamics of a real power wheelchair to get as close as possible to a real experience. Hence, the major kinematics parameters of power wheelchair motion have been identified (Figure 3.4), e.g. the values of accelerations felt by a user (Table 3.1). These values have been experimentally obtained thanks to a set of driving scenarios representing classical indoor and outdoor use cases. In particular, these scenarios included curb and ramp climbing, navigation on rough surfaces, door passing etc. The collected values correspond to a natural and safe navigation of a regular wheelchair user, and serve as reference.

Among the existing wheelchair simulators depicted in Chapter 2, different types of motion platform can be identified, depending on the number of degrees of freedom (DoF) that are used.

x wc direction y wc direction z wc direction Linear accelerations 2 m.s -2 n.a. 15 m.s -2 Angular accelerations 2 rad.s -2 10 rad.s -2 5 rad.s -2

Table 3.1 -Maximum kinematics values of power wheelchair (wc). The simulator motion platform should replicate these features.

In majority, motion platform classically use either 3 DoF or 6 DoF (Stewart platform) [START_REF] Arlati | Virtual reality-based wheelchair simulators: A scoping review[END_REF]]. If 6 DoF motion platforms achieve high frequency performances, 3 DoF motion platforms have been shown to be sufficient for training applications in terms of acceleration rendering. In addition, some 6 DoF motion platforms add a turntable in order to extend rotation capabilities along vertical axis: this design achieves a high level of realism [START_REF] Ito | Development of a Powered Wheelchair Driving Simulator for Research and Development Use[END_REF][START_REF] Niniss | Electric wheelchair simulator for rehabilitation of persons with motor disability[END_REF]. However, 6 DoF motion platforms are expensive, complex and cumbersome. As such, we propose to add a turntable on a 3 DoF simulator, leading to an innovative 4 DoF simulator.

Its kinematic was designed according to areal power wheelchair behaviour [START_REF] Baudry | Taking caster wheel behavior into account in the kinematics of powered wheelchairs[END_REF] in order to meet kinematic requirements stated in section 3.1.1. The Figure 3.5 illustrates the proposed solution, based on a parallel mechanism using 4 linear actuators (3 DoF) and a turntable on the top (4th DoF). This design is a trade-off between the desired range of motion and the compactness. An off-the-shelf SALSA M2 wheelchair seat from Sunrise Medical is then fixed on the turntable, so that user environment does not differ from a commercial power wheelchair (see Figure 3.10): simulation experience is thus compliant with daily life experience. In the same idea, the platform electrical system is an of-the-shelf standard power wheelchair electrical system which allows the use of any kind of off-the-shelf controllers and tools. The whole form factor of the platform is similar to the one of a power wheelchair so that it further increases the SoP. Also, the platform is lightweight in order to be compliant with immersive rooms. For example, the platform needs to be lighter than 100kg/m 2 to match Immersia specifications. This choice will also ease the use and transport.

Virtual Environment

A virtual wheelchair is included in the VE and co-located with the motion platform to enhance the quality of experience (QoE). Indeed, in order to reduce sensory mismatches and Cybersickness, visual feedback must provide adequate and correctly aligned wheelchair motion perception for each 6 DoF matching self-motion sensations suggested by the motion platform. In addition, to enhance SoP, the 3D representation of the wheelchair seat in the VE matches the exact position of the motion platform seat. Furthermore, the complexity of the VE, in terms of feedback modalities and simulated entities, is adapted to user impairments and training programs. For example, as some user may not be able to process too many visual stimuli, proposed VE would represent in these cases a less populated environment. Finally, the VE must be adapted for HMD as well as for immersive rooms in terms of interactions.

Auditory feedback

Auditory feedback is provided to the user in order to increase immersive experience and SoP. This includes not only the virtual sound rendered on speakers for ambient sounds, but also specific sound effects directly coming from the platform itself. In particular, the sound produced by the brakes of the wheelchair is an important auditory cue for the users: this sound is the first feedback perceived by users when a wheelchair starts to move.

Workflow

The main modules required in the power wheelchair simulator workflow are identified in Figure 3.6:

• the Game Engine manages the VE and its display;

• the Physics Engine updates the virtual wheelchair position, velocity and acceleration in the VE. These values are computed from input controller data, previous position, • the Motion Engine then computes the mechanical motion to be applied by the motion platform.

Each module is independent and dedicated to distinct specific tasks. This way, they can be concurrently and independently developed or replaced. The Figure 3.7 illustrates the power wheelchair simulator implemented architecture used during the studies presented thereafter in this document. The presented architecture connects multiple modules based on the Robot Operating System (ROS) library [START_REF] Quigley | ROS: an open-source Robot Operating System[END_REF].

Implementation

Each software module is represented by a node in a ROS network that can send or receive data regardless of its execution environment and programming language. Some modules are ROS nodes whereas others are represented by a specific wrapper node with which they are communicating through low level sockets. This modular design allows each module to independently evolve as long as input and output specifications are fulfilled as well as being concurrently developed. The first module emulates a real standard wheelchair Power Module and translates the signal generated by the controller into standard power wheelchair user command. The represented user controller is a joystick, but the Power Module is compliant with any kind of standard power wheelchair controller. This way the user command can be further processed by the Physics Engine which simulate virtual physics reactions, motions and interactions of the virtual entities. In the architecture presented in Figure 3.7, this module is contained in the Game Engine. Indeed, the Game Engine used is Unity presented in Chapter 2 which includes a Physics Engine module called PhysX among its plugins. In addition to its popularity and helpful community, Unity also has the major advantage of handling visual feedback compatibility with multiple display interfaces and especially screens, the HTC Vive Pro and the Immersive Room Immersia. In order to easily set up and manage the simulator, the Unity module also includes a launch interface referred as Launcher in the Figure . Finally, Unity also has the advantage of handling visual feedback with multiple devices such as screens, multiple HMDs and the immersive room Immersia as pictured in Figure 3.8. However, the use of Unity has required the development of a software bridge module to connect it to the ROS network through sockets as Unity is not directly compatible with ROS.

To perfect their realism appearance, proposed VE are replication of real places known by end-users as real-like VE are likely to increase user trust, comfort and SoP. For now, our simulator includes two VEs that are reproduction of real places. The first one is an outdoor environment; an urban area whose base model has been provided by Rennes Metropole and illustrated in the Figure 3.9. The second one is an indoor scene; a replication of Pôle Saint Hélier experimental room with enough space to add navigation circuits. Then, physic information and processed user command are sent to the Motion Engine which computes the motion feedback, vestibular and haptic, to be applied by the motion platform. In particular, for now, linear accelerations are rendered using pitch, and centrifugal effects using roll and yaw, depending on both linear and angular speeds. Using the "tilt coordination" method [START_REF] Colombet | Motion Cueing: What Is The Impact On The Driver's Behavior?[END_REF]], the Motion Engine generates feedback resulting from user command (vestibular feedback) or from physical response to the VE such as collisions (haptic feedback).

This feedback data is then sent to the Platform Driver which drives the motion platform, and is also sent back to Unity in order to apply visual compensation. The motion platform has been manufactured by CL Corporation1 from the specifications and previously presented design. As visible in Figure 3.10, its volume is similar to a standard power wheelchair.

Conclusion

The section has presented a user-centered design and implementation of a high fidelity multisensory VR based power wheelchair simulator for simulated driving training and clinical rehabilitation. The originality of the simulator relies on the combination of visual, vestibular and haptic feedback provided by an innovative 4 DoF motion platform which reinforces the simulator fidelity. Apart from the mechanical design and manufacturing of the platform, I personally took part in all the simulator software design and development and in the elaboration of every related studies and analysis. Those additional feedback are likely to enhance the quality of the virtual experience. In particular, the vestibular feedback is supposed to enhance SoP and reduce Cybersickness as it limits sensory mismatches between what user feels and sees. In addition, the motion platform is electrically and mechanically similar to a real standard power wheelchair. This way, the motion platform is adaptable with off-the-shelf ergonomic accessories and able to meet any specific clinical requirements. Furthermore, the simulator also propose VEs adapted to the simulation context as well as to the diversity of impairments and needs. However, the simulator safety and usability needs to be validated with able-bodied users before being able to conduct clinical studies with people with disabilities. As such, the next Section 3.2 presents a pilot user study with able-bodied participants investigating the vestibular impact on SoP and Cybersickness.

Evaluation of the Vestibular feedback impact: pilot user study

This section describes a pilot study conducted in order to investigate the contribution of vestibular feedback to SoP and Cybersickness within a multisensory driving experience using Figure 3.11 -The high-fidelity power wheelchair simulator, composed of an HMD for visual immersion, a joystick to control the virtual power wheelchair, and a vestibular feedback platform.

the simulator previously presented. Indeed, literature suggests that reproducing real power wheelchair accelerations and centrifugal effects will enhance SoP while reducing perception discordance and Cybersickness. As such, a pilot user study, aiming to confirm or infer this hypothesis, has been conducted. As a pilot study that enriches expectations for future works, it focuses on the impact of vestibular feedback for able-bodied people. Indeed, conducting a first study as a basis was a necessary step before assessing the same assumptions for people with disabilities.

The first subsection 3.2.1 clarifies the study objectives and hypothesis. Subsection 3.2.2 details the study apparatus. Then subsection 3.2.3 presents the study procedure and method. Finally, subsection 3.2.4 presents results before discussing them in subsection 3.2.5 and concluding in subsection 3.2.6. This section is linked to the following publications [HRI2020, HANDICAP2020, MMCC2020].

Pilot user study objectives and hypothesis

Only able-bodied participants were enrolled in this first experiment, even though the simulator is designed for people with disabilities. Indeed, it is necessary to prove and ensure the simulator safety and viability with able-bodied participants through a preliminary study to get the Research Ethics Committee's approval for enrolling people with disabilities and end-users to assess the Figure 3.12 -Participant point-of-view during trials. The black part in the bottom-right corner corresponds to the arm of a virtual wheelchair, which is spatially co-located with the real joystick and vestibular feedback platform. relevancy of such a simulator in training applications and improving wheelchair driving skills. Moreover, testing a hypothesis in a pilot study with able-bodied people before using clinical patients as subjects is a commonly applied procedure [START_REF] Recio | Use of a virtual reality physical ride-on sailing simulator as a rehabilitation tool for recreational sports and community reintegration: A pilot study[END_REF][START_REF] John | The Implementation and Validation of a Virtual Environment for Training Powered Wheelchair Manoeuvres[END_REF]]. Based on previous works and our own VR experience, we defined our hypothesis as follows:

H1 The addition of vestibular feedback to visual feedback increases SoP for users. In particular, according to the IGroup project consortium [START_REF] Schubert | The sense of presence in virtual environments: A three-component scale measuring spatial presence, involvement, and realness[END_REF]]:

H1-Spa This feedback increases spatial presence for users.

H1-Inv This feedback increases user involvement.

H1-Rea This feedback increases experienced realism for users.

H2

The addition of vestibular feedback to the visual feedback decreases sensory conflicts and thus Cybersickness.

Apparatus

The main device used in this study is the multisensory power wheelchair driving simulator (see Figure 3.11) presented in previous Section 3.1. The simulator was equipped with a standard R-Net joystick as controller and a Salsa M power wheelchair seat.

Regarding feedback for this study, the motion platform was only generating vestibular motion feedback, since this is one of the main innovations of our simulator, and the visual display chosen was an HTC Vive HMD. HMD devices make it possible to immerse users in a VE, obscuring the real world around them. As it covers all the user vision angles, it also enables users to look backward, which is important for reverse driving. In our case, this would also prevent participants from seeing the vestibular feedback platform movements. Besides, HMDs are largely used in the VR field and provide good head tracking as well as a suitable graphic rendering quality for an immersive experience.

Concerning the VE, the replication of a square located in the city of Rennes was used. This square was mainly unfamiliar to participants as our experiment took place in another city. Only one participant knew the real square. Assets were added to this 3D VE to mark out a path that users had to follow in the experiment (see Figure 3.12). As users might not be familiar with power wheelchair driving, the speed limit of the virtual wheelchair was set to 0.86 m.s -1 which corresponds to a common and comfortable navigation speed.

Method

This section details each aspect of the study design regarding the participants (subsection 3.2.3.1), the different conditions (subsection 3.2.3.2), the collected measures (subsection 3.2.3.3), the experimental procedure (subsection 3.2.3.4) and the experimental task (subsection 3.2.3.5).

Participants

A total of 29, unpaid and able-bodied French-speaking participants were enrolled in this experiment. They were all naive to the purpose of the experiment. All of them signed a consent form explaining the running of the experiment to them. They were explained that they could ask to stop the experiment whenever they wanted. In order for the experiment to be reliable, a strict validation policy was applied. This policy will be explained in details in Section 3.2.4. In total, we removed 13 participants. Then, 16 people (average age of 28.6, SD= 12.33, min = 19, max = 60) were kept in the analysis. 13 of them were males, and 3 were females. 14 were right-handed.

On average, the participants had little experience with VR and simulators. However, most of them had an intermediate to high level of experience with video games. Finally, only one participant had an intermediate level of experience with power wheelchair driving.

Experimental conditions

This pilot user study aimed to determine the impact of the vestibular feedback on SoP and Cybersickness during a wheelchair driving task in VR. For this experiment, two experimental conditions were identified:

C V
No vestibular feedback. Participants were only provided with Visual feedback through the HMD.

C M With vestibular feedback. Participants were provided with visual and vestibular Multisensory feedback.

Each participant completed two trials during this experiment, one for each of the two experimental conditions. The order of presentation was counterbalanced across participants (8 participants were presented with C V first, and 8 with C M first).

Measures

In addition to measured completion time and in order to assess the hypothesis and the impact of the platform vestibular feedback on user QoE, participants completed three subjective questionnaires after each experimental condition, all previously validated in French:

• The NASA Task Load Index (NASA-TLX) [START_REF] Hart | NASA-task load index (NASA-TLX); 20 years later[END_REF]]. This questionnaire was used to determine whether the presence of the vestibular would alter the cognitive load of the user.

• The IGroup Presence Questionnaire (IPQ) [START_REF] Schubert | The sense of presence in virtual environments: A three-component scale measuring spatial presence, involvement, and realness[END_REF]]. This questionnaire allows spatial presence, involvement, and experienced realism to be assessed.

• The Immersive Virtual Environments Questionnaire (IVEQ) [START_REF] Tcha-Tokey | Conception et évaluation de l' expérience utilisateur en environnement virtuel immersif[END_REF][START_REF] Tcha-Tokey | A questionnaire to measure the user experience in immersive virtual environments[END_REF]. We used all measures concerning immersion, presence, engagement, and experience effects.

Experimental Procedure

Participants were asked to sit on the wheelchair seat attached to the vestibular feedback platform. First, we asked them to attach a seat belt mounted on the platform as a safety measure. We indicated the presence of a big red button, attached to the side of the platform, and that they could press it to immediately shut down the platform if needed.

They received instructions on the use of the joystick controller to operate the virtual power wheelchair in the VE. They also received instructions on the virtual path they had to follow. This path was indicated to the user in the VE by means of red arrows on the floor. It consisted in linear movements, slight curves, large curves, a stop, a U-turn and finally a reverse driving and parking maneuver. This set of maneuvers was intended to ensure that participants would perceive various visual and vestibular feedback experiences during the driving task in each trial. The participants were informed that they would have to complete this path twice, and that they would be asked to fill in questionnaires after each time they completed it. Participants did not receive any information about the type of feedback they would have for each trial and about the platform itself. Thereafter, they could ask any questions they had.

Participants were equipped with earmuffs to prevent them from hearing the platform moving or not moving during the trial. They were not able to see the platform either moving or not moving during the trial due to the wearing of the HMD to display the VE. They were given time to familiarize themselves with the VE before starting the experiment, and were invited to start the driving task whenever they were ready to. The trial automatically stopped once they reached the end of the path. They were then taken to another room to fulfill the questionnaires assessing user experience in this first trial. This prevented them from seeing the vestibular feedback platform moving when changing the experimental condition. Once they had completed the questionnaires, they performed the second trial. At the end of the second trial, they filled in the same questionnaires again to evaluate their QoE in the second trial. As shown in Figure 3.13, the virtual driving task consists of a sequenced path to be completed inside the virtual scene representing a city square. The path starts at point A and ends at point B, moving over symbols. Each symbol represents a specific instruction as presented in Table 3.2. Note that every symbol should be rolled over. The constructed path includes a lot of actions in order to increase acceleration variations to ensure user involvement during the driving task, but also to ensure that users perceive the vestibular feedback while following the path.

Virtual Driving Task

Results and Analysis

This section presents our validation policy to ensure that our results were unbiased for the analysis. Then, we will present the results obtained through the three questionnaires for the analysis of SoP and Cybersickness, according to the two investigated experimental conditions.

Validation policy

Analyzing subjective user perceptions such as the SoP required the experiment to be unbiased regarding (1) knowledge related to the vestibular feedback provided and (2) perceptive biases that could have occurred during the experiment. We removed two participants from the experiment after they reported having previously observed the vestibular feedback platform while operating during demonstrations. We then removed additional participants according to three identified perceptive biases they experienced during trials. Firstly, three participants experienced visual discomforts (such as lags or bad quality settings). This might have decreased the immersion. Secondly, six participants might have heard surrounding noises (such as human voices coming from people not involved in the study) despite the earmuff. This might have influenced their SoP along with their focus on the virtual driving task.

Finally, two participants decided on their own to achieve the parking maneuver by moving forward against instructions. As such, they did not experience all expected feedback and their data were discarded from analysis.

After selecting the participants for the analysis, we ensured that the duration of trials completed by the participants was sufficient for them to potentially experience SoP and Cybersickness. Participants completed each trial in 119 s on average (SD=28 s). No significant difference was found between the first and second trial, regardless of the experimental condition. The duration of trials was sufficient for participants to potentially experience both SoP and Cybersickness as the exposure time does not affect these two components of VR experience [Melo, Vasconcelosraposo, and Bessa 2018].

Analysis procedure

For each item of the three questionnaires, we compared the intra-subject answers depending on the type of feedback. This section presents only the significant results obtained using a Wilcoxon signed-rank test, related to our hypothesis (see Table 3.3 andFigure

Spatial presence

Concerning the IVEQ, for item 1(fr) / 2(en) "My interactions with the virtual environment seemed natural.", participants reported significantly higher ratings for the C M condition. These results support H1-Spa.

Involvement

Concerning the IPQ, for item INV 3 ("I still paid attention to the real environment."), participants reported significantly lower ratings in the C M condition. For item INV 4 ("I was completely captivated by the virtual world."), participants reported higher ratings in the C M condition.

Concerning the IVEQ, for item 5(fr)/6(en) ("The sense of moving around inside the virtual environment was compelling"), participants reported higher ratings in the C M condition. For item 15(fr)/19(en) ("I became so involved in the virtual environment that it was as if I was inside the game rather than manipulating a gamepad and watching a screen."), participants reported higher ratings in the C M condition. These results support H1-Inv.

Experienced realism

Concerning the IPQ, for item REAL2 ("How much did your experience in the virtual environment seem consistent with your real world experience ?"), participants reported higher ratings in the C M condition. These results support H1-Rea.

All components of SoP (Spatial presence, Involvement and Experienced realism) presented a significant enhancement through the addition of our vestibular feedback. Thus, these results support our global hypothesis H1 concerning SoP.

Cybersickness

Concerning the IVEQ, for item 61(fr)/70(en) ("I suffered from vertigo during my interaction with the virtual environment."), participants reported lower ratings in the C M condition. Besides, one of our participants reported in open feedback that "the simulation without movements was not pleasant and disrupted the brain". These results support H2 concerning Cybersickness.

Concerning the TLX, for item ("How insecure, discouraged, irritated, stressed and annoyed were you?"), participants reported lower ratings in the C M condition. Besides, multiple participants reported in open feedback having preferred the trial with the vestibular feedback. This suggests that our vestibular feedback globally enhanced quality of the VR experience for our participants.

Discussion

This section discusses three aspects of our research: the user study, the simulator and observations on SoP and Cybersickness.

User study

After applying a strict validation policy and despite the number of participants retained for results analysis, enough data were collected and analyzed to obtain significant results. Indeed, the Wilcoxon signed-rank test is a non-parametric test, which implies that no difference between groups could have been established without a consequent effect size. However, a larger set of participants would allow us to investigate the influence of user characteristics (e.g. age, gender, habits, experience) on driving behaviour. Furthermore, this pilot study only involved able-bodied participants, who are not the target population for a wheelchair driving simulator. However, such a study with able-bodied participants constitutes the very first step before assessing our hypothesis with people with disabilities. On the one hand, this is because the relevancy of the simulator modalities provided had to be validated (here, the vestibular feedback). On the other hand, it is mandatory to perform such a preliminary study with able-bodied participants in order to obtain authorizations from the Research Ethics Committee to initiate clinical investigations with people with disabilities. Although the study was not performed with the targeted population, the results remain valid and usable in other projects.

Despite the fact that participants were not acquainted with the city from which the virtual scene had been modelled, the fact that it represents a real world city square contributes to the realism of the environment. Elements used to mark the path for users to follow were inspired by real world objects (barriers and cones), and the arrows were designed to look like tags on the ground. This ensured that the whole environment was as realistic as possible to enhance user SoP. As the path and environment were the same in both conditions, significant differences found for SoP and Cybersickness cannot be explained by their variations. The path was also complex enough to ensure the diversity of vestibular feedback presented to users (e.g. accelerations, brakes, slight and sharp turns, reverse driving). Furthermore, the experiment driving speed was limited (0.86 m.s -1 ) to half the average speed of a real power wheelchair. Indeed, a higher speed would have induced higher accelerations and more stimulate the vestibular system. Thus, we believe that if vestibular stimulation works at low speed, it will work even better at high speed. Plus, the simulator's target audience is mainly first-time power wheelchair users, who are more likely to drive slower than experienced users. However, this scene suffers from a major drawback: the lack of dynamic elements and features. The participants were alone in the scene, while the existing place is usually crowded. The reproduced scene was therefore not entirely ecological. It would be interesting to conduct an experiment with pedestrians and cars to better immerse participants in the VE.

Simulator and vestibular feedback

The power wheelchair simulator benefited from the dual contribution of computer and mechanical scientists to design and build the vestibular feedback platform. It is important to note that this pilot user study only assesses vestibular while the motion platform is also able to simulate haptic and auditory feedback. Indeed, in order to avoid bias and ensure that only the impact of vestibular feedback was evaluated, the haptic feedback was turned off as it was not being evaluated yet. However, once the user is driving at maximum speed, the power wheelchair is no longer subject to accelerations. Thus, the user does not feel any vestibular feedback. This is why the number of actions that induced acceleration variations was maximized during virtual task.

Compared to other types of existing feedback modalities, the main objective of the vestibular feedback is not to give additional information to the user or to help in the navigation [START_REF] Devigne | Design of a Haptic Guidance Solution for Assisted Power Wheelchair Navigation[END_REF]]. The proposed feedback only provides a consistent and realistic wheelchair behavior in order to decrease Cybersickness, increase SoP and thus enhance the VR experience. However, the next presented study includes haptic feedback and provides additional relevant information regarding both the navigation and QoE improvements as haptic feedback concerns reactions to the VE.

SoP and Cybersickness

As seen in Chapter 2, most of the other power wheelchair simulators aim to analyze the issues related to the use of a wheelchair in an urban environment, or to assess training possibilities [START_REF] Pouvrasseau | Discussion about functionalities of the Virtual Fauteuil simulator for wheelchair training environment[END_REF][START_REF] Morere | ViEW, a wheelchair simulator for driving analysis[END_REF]]. To the best of our knowledge, there is no other study investigating the impact of vestibular feedback on SoP and Cybersickness in VR. However, SoP and Cybersickness are key elements in simulator based training. On the one hand, SoP is linked to spatial presence and experienced realism, but also user involvement and motivation, which is known to be an important factor for training [START_REF] Steinmayr | The importance of motivation as a predictor of school achievement[END_REF]. On the other hand, reducing Cybersickness is critical to increase user QoE since most users would not be able to use VR for training purposes due to Cybersickness symptoms.

Conclusion

This section presented a pilot user study with able-bodied participants investigating the impact of the simulator vestibular feedback on SoP and Cybersickness levels of a virtual power wheelchair driving task. In the end, the pilot user study validates not only the positive impact on virtual experience of vestibular feedback but also the safety and usability of the simulator. Thus, the study that followed was able to involve people with disabilities and evaluate the simulator in a clinical context. This clinical evaluation, presented in the next section 3.3, was also the occasion to compare the virtual driving experience to a similar real situation.

Clinical usability evaluation through a clinical user study

Clinical user study objectives and hypotheses

The main objectives of this user study were to compare user performances conditions and to evaluate the QoE provided by our simulator. As authorized by the Research Ethics Committee (Study SIMADAPT1 NCTØ4171973), we enrolled people with neurological degenerative disorders who are used to drive a power wheelchair. In this user study, the participants were asked to navigate and complete 3 different circuits of increasing difficulty within two conditions: in a virtual environment with our simulator and in real conditions with a real power wheelchair. The proposed circuits have been identically designed by clinicians in virtual and real conditions as well as clinically validated [START_REF] Leblong | SWADAPT1: assessment of an electric wheelchairdriving robotic module in standardized circuits: a prospective, controlled repeated measure design pilot study[END_REF]. For each circuit, the participant performance was measured by completion time and the QoE provided by our simulator was assessed using subjective questionnaires on SoP and Cybersickness as well as objective measures regarding user motion and behavior. In order for the simulator to be efficient within contexts of clinical training and rehabilitation, it needs to provide a comfortable user experience similar to a real one. In other words, users should perform the same task similarly in both conditions and should feel high SoP and low Cybersickness levels within the virtual condition using the simulator. As such, the main prior hypothesis for this clinical study only concerned performance and was defined as H In a power wheelchair navigation clinically validated task, regular users perform in the same way in virtual condition using our simulator as if they were in real condition with a real power wheelchair.

Apparatus

In addition to the variant driving task, the clinical study involved a specific setup for each condition, detailed in the following sections.

Driving task

In order to investigate user performances in different situations, the driving task consists in the completion of 3 circuits of increasing difficulty. Each circuit has been designed by clinicians, providing a number of maneuvers and dimensions adapted to its level of difficulty. For example, circuit 1 consists of a short sequence of maneuvers in a wide corridor while circuit 3 includes a ramp and a moving obstacle in its long sequence of maneuvers as well as tighter turns in narrower corridors. These same circuits have already been used in a clinical study presented in [START_REF] Leblong | SWADAPT1: assessment of an electric wheelchairdriving robotic module in standardized circuits: a prospective, controlled repeated measure design pilot study[END_REF] with their structure further detailed. For the sake of this study, the 3 circuits were identically reproduced in VR before being reevaluated and validated by therapists in both conditions real and virtual.

Real condition

In the real condition, circuits were set up in a room at the rehabilitation center that is usually used by clinicians for various training sessions. The circuits are made of light plastic panels that can move easily in case of collision. Participants drove a Quickie Salsa M2 power wheelchair adapted to their specific needs with ergonomic accessories. The power wheelchair was also equipped with various sensors such as accelerometers and two different motion tracking systems i.e. Vicon and ULB allowing to record user head trajectory on the circuit as well as wheelchair trajectory, velocities and accelerations. The completion time was measured using manual chronometers. Participants QoE was assessed using the USE questionnaire with 30 questions grouped into 4 criteria and rated on a seven-point Likert rating scale [START_REF] Lund | Measuring usability with the USE questionnaire[END_REF]]. Figure 3.16 illustrates the setup while one participant is performing circuit 3 in the real condition.

Figure 3.16 -Real setup with Quickie Salsa M2 power wheelchair.

Virtual condition

To complete the task in the virtual condition, participants used the power wheelchair simulator previously presented. In the virtual condition, the platform was equipped with a Quickie Salsa M2 wheelchair seat and joystick, adapted to each participant needs with ergonomic accessories. Participants wore an HTC Vive Pro HMD which was cleaned and disinfected before each session. Regarding the virtual environment, as previously stated, the room hosting the real circuits and the circuits themselves have been identically reproduced from real ones. The software nature of the simulator pipeline allowed us to record data such as user head trajectory and virtual wheelchair trajectory, velocities and accelerations. The QoE provided by our simulator was assessed through subjective questionnaires using the Simulator Sickness Questionnaire (SSQ) [Robert S [START_REF] Kennedy | Simulator Sickness Questionnaire : An Enhanced Method for Quantifying Simulator Sickness[END_REF]] and the IGroup Presence Questionnaire (IPQ) [START_REF] Schubert | The sense of presence in virtual environments: A three-component scale measuring spatial presence, involvement, and realness[END_REF]]. Both questionnaires are commonly used in literature. The IPQ is a 14 items questionnaire rated on a 7-point Likert scale that subjectively measures SoP in terms of involvement, realism and spatial presence. The SSQ aims to evaluate Cybersickness symptoms level with 16 items rated on a scale from 0 to 3 and grouped into 3 main criteria namely nausea, occulomotor and disorientation. Furthermore, we evaluated Cybersickness participant susceptibility using the Motion Sickness Susceptibility Questionnaire (MSSQ) [START_REF] Golding | Predicting individual differences in motion sickness susceptibility by questionnaire[END_REF]]. The MSSQ contains 9 questions rated on a scale of 0 to 3 that tries to detect people who are more likely to experience discomforts during a VR experience. The completion time was also measured using manual chronometers and the participants QoE was also assessed using the USE questionnaire. Figure 3.15 illustrates the virtual setup while one participant is performing circuit 3. The entire study lasted 3 weeks at a rate of 2 days per week with 1 circuit. In total, the 3 different circuits with increasing difficulties have been completed 2 times in both virtual and real conditions. All circuits were reproduced identically in both conditions as shown in Figure 3.18 and Figure 3.19. The condition by which each participant started, between virtual and real, was randomized. As such, half of the participants started with the virtual condition using our simulator and the other half with the real condition using a real power wheelchair. In total, we considered 4 different configurations C v 1 , C v 2 , C r 1 and C r 2 with the condition nature indicated by v for virtual and r for real and the digit to designate the order, either starting condition 1 or second condition 2. Note that every participant will only complete 2 configurations, namely either C v 1 and C r 2 or C r 1 and C v 2 . After each condition, real or virtual, participants filled in the USE Questionnaire. Study procedure is summarized in the Figure 3.17 flowchart. Finally, each condition had its own explanatory procedure, setup and equipment which are detailed in the following sections.

Experimental Procedure

Real condition

In the real condition, the participants were first welcomed by at least 2 clinicians and 2 members of the research team who stayed throughout the session and who initially helped them adapt the power wheelchair seating to their specific needs. After settling comfortably, the participants navigated using the equipped power wheelchair in a room without circuit. Once the participants are accustomed to the equipped power wheelchair control, they were taken to the experimentation room where the task was explained to them. Then, the participants completed the circuit twice with a little break between both passages if needed.

Virtual condition

Before starting the virtual task, the participants had to complete the MSSQ as well as a small checklist to ensure they were in their usual state of fitness. The MSSQ contains 9 questions rated on a scale of 0 to 3 that tries to detect people who are more likely to experience discomforts during a VR experience. Then, clinicians adapted the simulator motion platform seating to the participants needs. Afterwards, the task was explained to them just after a recognition time during which the participants navigate inside the virtual room without circuit in order to get accustomed to the VR setup and to allow clinicians to make the final adjustments. Once ready, participants completed the circuit twice with a little break between each passage if needed. The participants were free to stop the experiment at any time. They were told to report any excessive discomfort and that an emergency stop button attached on the simulator was available at any moment. At all times, the participants were supervised and accompanied by at least two clinicians evaluating driving performances and one member of the research team. The simulator parameters were exactly the same for every participant. During passages, silence was maintained in the room as much as possible to avoid distracting the participant. After both passages were completed, participants completed the subjective SSQ and IPQ questionnaires.

Participants

Conducting a study with people with disabilities is a challenge that is rarely overcome. In total 29 participants were screened by clinicians to take part in this study. According to the inclusion criteria, participants present neurological degenerative disorders, physical characteristics (weight, size) compatible with the use of our simulator, benefit from a powered wheelchair prescription and used it for more than 3 months as their main means of locomotion. Thus, as power wheelchair regular users, they are the best able to complete the navigation task and evaluate our simulator provided QoE. Moreover, all participants were naive or novice to VR.

Results and Analysis

We have selected the most relevant results for each aspect of this study and virtual experience i.e. the performance, the SoP and the Cybersickness. Furthermore, depending on the circuit and passage conditions, some participant data were discarded from final analysis. Thus, only 13 participants data remain for circuit 1, 28 for circuit 2 and 25 for circuit 3. Regarding the small number of participants selected for circuit 1 and its structural simplicity, we decided to exclude it from the study. Indeed, circuit 1 analyzed data, in addition to poorly differentiate participants, are too sparse to lead to significant and interpretable results.

Driving performance in terms of completion time

First, are presented the comparison results of performance in terms of completion time between real and virtual conditions. To avoid any training bias, we decided to sort the data by configurations, depending on its execution order. Indeed, after completing the task in the first condition, participants could have learned the circuit structure and performed accordingly in the second condition. Sorting data by configuration and comparing only firstly and secondly executed conditions together allows us to eliminate any training bias if it exists. Figure 3.20 -Mean circuit completion time for first condition (C r 1 vs C v 1 ) and second condition (C r 2 vs C v 2 ). Each configuration color correspond to procedure flowchart colors in Figure 3.17.

Time (in seconds)

Circuit 2 Circuit 3 C r 1 vs C v 1 T C r 1 < T C v 1 T C r 1 ! < T C v 1
Wilcoxon Rank Sum less test 3.3e-2 5.7e-2 As such, Figure 3.20 shows the circuit mean completion times observed for configurations C v 1 and C r 1 firstly performed and for configurations C v 2 and C r 2 secondly performed. On one hand, the Wilcoxon Rank Sum test (Table 3.4) reveals a significant difference in participant performance according to the nature of the condition they start for circuit 2. Tackling a navigation task through VR for the first time with our simulator seems to be more difficult and leads to higher completion times. Indeed, completion time mean within C v 1 is significantly higher which is visible in Figure 3.20a. However, it exists no result nor interpretation for circuit 3 as data are not sufficient and differentiating enough to obtain significant results. On the other hand, the Kruskal-Wallis test (Table 3.4) statistically proves the significant similarity in mean completion time distribution for both circuits when performing the task in the second condition, whether real or virtual. These results are easily visible in their box plot representation in Figure 3.20b. Parametric tests could not be used as the time distribution in real condition was found to be non-normal using Shapiro-Wilk test. Kruskal-Wallis results show that participants performed similarly under both conditions in terms of completion time thus validating our hypothesis H. In order to evaluate a potential learning bias between the first and second passage in both virtual and real conditions, we performed paired analyses of completion times.

C r 2 vs C v 2 T C r 2 ! ̸ = T C v 2 T C r 2 ! ̸ = T C v 2 Kruskal-
By comparing results, we can visually observe in Figure 3.21 that the second passage P 2 completion times are generally lower than the first passage P 1 ones in the virtual condition C v whereas this completion times difference is less pronounced in the real condition C r . This greater difference for the virtual condition was demonstrated using a Wilcoxon Signed Rank test on paired samples (Table 3.4) and shows a greater learning margin in this condition. This adaptation time and novelty aspect of VR might also explain the small difference in USE Questionnaire scores between both conditions as shown in Figure 3.22.

v (C v 1 ∪ C v 2 ).
Figure 3.22 -USE score means and standard deviations by criterion.

Quality of the virtual experience

Cybersickness

Regarding Cybersickness, SSQ scores have been calculated using the SSQ reference paper guidelines and reported in Table 3.5. Based on the detailed SSQ Total Severity scores, no participant experienced severe Cybersickness and only one has a score above the moderate step value. Although the scores for each criterion are below their respective averages and correspond for the majority, in the worst-case, to discomforts deemed "moderate", the Total Severity score remains high when compared to literature. Authors in [Balk, Bertola, and However, the SSQ scores remain low and are clearly lower than some other power wheelchair VR-based simulator SSQ ones such as in [START_REF] John | The Implementation and Validation of a Virtual Environment for Training Powered Wheelchair Manoeuvres[END_REF]]. Furthermore, it is important to note that the SSQ rating scale is not entirely relevant in studies involving a non-trained population since this scale is based on studies with military personnel. An alternative way of assessing Cybersickness, based on the same questions and answers as the SSQ, has recently been proposed: the Virtual Reality Simulator Questionnaire (VRSQ) [H. K. [START_REF] Kim | Virtual reality sickness questionnaire (VRSQ): Motion sickness measurement index in a virtual reality environment[END_REF]]. After being compared to the SSQ and its variants, this new rating scale proved to be more accurate and more relevant in particular with VR headsets as display interface [START_REF] Sevinc | Psychometric evaluation of Simulator Sickness Questionnaire and its variants as a measure of cybersickness in consumer virtual environments[END_REF]. The VRSQ score scales also have the advantage of being equivalent for each criterion, ranging from 0 to 100. In order to evaluate our simulator more precisely, VRSQ scores are shown in Table 3.6. Note that the change of scale between SSQ and VRSQ does not impact the level of discomfort felt during VR experiences but allows a more precise evaluation of Cybersickness especially when using a VR headset. For example, based on the detailed VRSQ Total Severity scores, 3 participants experienced moderate Cybersickness and no one experienced severe Cybersickness. To further investigate Cybersickness causes, we tried to determine factors influencing SSQ and VRSQ scores among different measures such as power wheelchair and user head accelerations and velocities. Figure 3.23 exposes significant Spearman correlation tests results with a correlation coefficient greater than 0.3. Significant factors are represented on x-axis and criterion on the y-axis. Each disc is colored regarding the positive or negative nature of the correlation and its size varies according to the correlation coefficient value reported inside it. Every correlation value displayed in Figure 3.23 are significant and are consistent with factors identified in the literature [START_REF] Laviola | A Discussion of Cybersickness in Virtual Environments[END_REF][START_REF] Gavgani | Profiling subjective symptoms and autonomic changes associated with cybersickness[END_REF][START_REF] Venkatakrishnan | A Structural Equation Modeling Approach to Understand the Relationship between Control , Cybersickness and Presence in Virtual Reality[END_REF].

Sense of Presence

Finally, IPQ scores have been reported in Figure 3.24 and estimate our simulator performance in terms of SoP for this study. From Figure 3.24, we notice a great score for General Presence and Spatial Presence. Only the Involvement score is slightly under the average. Compared to literature, our simulator presents great IPQ scores, largely higher than the screen based simulator miWe [START_REF] Tao | Powered wheelchair simulator development: Implementing combined navigation-reaching tasks with a 3D hand motion controller[END_REF] but still a little lower than scores reported by the two studies using the Simcadrom simulator [START_REF] Hernandez-Ossa | Simulation system of electric-powered wheelchairs for training purposes[END_REF][START_REF] Hernandez-Ossa | Virtual Reality Simulator for Electric Powered Wheelchairs using a Joystick[END_REF]].

Figure 3.24 -IPQ score means and standard deviations by criterion i.e. General Presence (GP), Involvement (Inv), Realism (Real) and Spatial Presence (SP).

Discussion

This section discusses the overall study (subsection 3.3.6.1) before discussing results regarding SoP (subsection 3.3.6.2) and Cybersickness (subsection 3.3.6.3).

Overall Study

Overall, the study presents interesting results and represents one of the first real and virtual comparative study in a clinical context. Moreover, conducting a study with wheelchair regular users in a technological research field is a challenge rarely overcome. Yet, it was a mandatory step in the development of a user-centered simulator. The challenge of designing such a VR experience for people with disabilities, in particular with neurological disorders, is that they can be more sensitive to discomforts such as Cybersickness because of potential visual, visuo-spatial or cognitive impairments. In fact, the majority of data disposal was due to faulty equipment or disruptive elements during passages such as loud sounds or software bugs. In the end, the main hypothesis H is validated based on performance comparison results shown in Figure 3.20. Indeed, the completion time distribution is similar in both the virtual and real conditions for secondly performed condition (Figure 3.20b). While performance differences in the first condition is only statistically significant for circuit 2, no conclusion can be drawn without additional data for circuit 3. This observed difference can be explained by the novelty of VR which can be a difficult technology to apprehend at first for beginners (Figure 3.20a). In fact, the comparison between first and second passages under each condition shown in Figure 3.21a and Figure 3.21b reveals a greater learning margin in the virtual condition which supports the idea that VR requires an adaptation time. Furthermore, those performance results also show, in a limited measure, that a learning process has happened similarly under both conditions. Nonetheless, a more precise performance criterion than completion time could be used to further compare both virtual and real power wheelchair navigation. For example, performances could be assessed using the Power Mobility Road Test as in [START_REF] Kamaraj | Interrater Reliability of the Power Mobility Road Test in the Virtual Reality-Based Simulator-2[END_REF]. Also note that the reliability of subjective data, such as questionnaire responses, can always be questioned. Objective measures such as skin conductance level for Cybersickness could also have been collected using systems like in [START_REF] Gavgani | Profiling subjective symptoms and autonomic changes associated with cybersickness[END_REF]. However, such physiological measures would have required additional sensors considered too much disruptive for the participants by therapists and therefore not foreseen in the protocol approved by the Research Ethics Committee. Finally, according to the USE Questionnaire scores reported in Figure 3.22 and oral feedback, participants were thrilled about the study, the simulator and the QoE. This study main limitation is the performance evaluation based only on completion time while other criterion could have been analyzed such as power wheelchair and joystick trajectory. Comparative investigations including those criteria are planned, focusing on user behavior and consequences rather than only time performance.

Sense of Presence

Focusing on SoP, despite a high level of general presence, we notice an average level of involvement criterion. One way of improving this score would be to enhance the virtual environment by adding effects such as ambient sounds or by populating the virtual environment. Another improvement of the QoE would be to limit the external disturbances during the experiment, in particular the excessive noises emitted by the motion platform itself [START_REF] Pithon | Wheelchair simulators: A review[END_REF]]. Indeed, the involvement presence criterion is directly linked to the user susceptibility to forget the real world and concentrate on the virtual goal. Finally, although the relationship between SoP and Cybersickness is debated in the literature, it is conceivable that the discomforts felt by users have had a negative impact on this criterion, preventing them from completely detaching themselves from the real world [START_REF] Weech | Presence and cybersickness in virtual reality are negatively related: A review[END_REF]. However, this theory could not be verified through statistical tests on the SoP and Cybersickness link, as related results were not significant.

Cybersickness

Regarding Cybersickness, results from both SSQ and VRSQ are more nuanced as the majority of participants still felt slight to moderate discomforts even though they were able to finish the tasks. While these discomforts could be explained by participants by self-induced Cybersickness [START_REF] Sevinc | Psychometric evaluation of Simulator Sickness Questionnaire and its variants as a measure of cybersickness in consumer virtual environments[END_REF], they are still too present to plan long sessions on our simulator.

One solution to enable the use of the simulator, in this tested state, in a clinical context would be to detect in advance or in real time people likely to feel too much discomfort. Detecting motion sickness susceptibility is the purpose of the MSSQ that has been fulfilled by each participant before performing the task in the virtual condition. However, we did not report MSSQ results since even though, on average, people with a higher MSSQ score have a higher SSQ score there is no statistically measurable cut-off value for the MSSQ score. Further, studies focusing on the MSSQ and SSQ within this particular clinical context should be conducted to be able to precisely detect which person will not stand the VR experiment provided it is statistically validated. Otherwise, other tools or models to detect susceptibility or dropout could be considered such as the prediction dropout formula proposed in [Balk, Bertola, and V. W. Inman 2013] or washout algorithms proposed in [START_REF] Aykent | Study Of The Influence Of Different Washout Algorithms On Simulator Sickness For A Driving Simulation Task[END_REF].

Regarding the potential Cybersickness causes, Figure 3.23 shows various leads to explore to reduce discomforts. For example, as suggested by the positive correlation between angular accelerations and Cybersickness, the maximal accelerations' value could be diminished or the motion platform cues modified. Nonetheless, some identified factors would require further investigation for the correlation to be fully understood. For example, the observable negative correlation between velocities and Cybersickness scores could be explained by the fact that higher velocities reduce completion time [START_REF] Venkatakrishnan | A Structural Equation Modeling Approach to Understand the Relationship between Control , Cybersickness and Presence in Virtual Reality[END_REF]]. However, in that case, similar correlations should also be observable when considering exposition time which is not what results suggest. Other techniques to reduce Cybersickness presented in the literature could be integrated into the simulator such as including more static reference points [START_REF] Whittinghill | Nasum virtualis: A simple technique for reducing simulator sickness[END_REF]. It is also possible to imagine shorter tasks with more progressive difficulty increase to allow more comfortable and shorter learning sessions. Finally, as Cybersickness seems closely linked to the display interface, VR headsets are concurrently compared to other display interfaces in another clinical study SIMADAPT2 to determine which one provokes less Cybersickness using the simulator. Note that for this ongoing study, the simulator motion cues have been refined in order to further reduce Cybersickness.

Conclusion

This chapter has presented a high fidelity multisensory VR based power wheelchair simulator dedicated to driving training and clinical rehabilitation. Its main particularity comes from its innovative 4 DoF platform which provides additional motion feedback reinforcing its simulator fidelity as well as QoE in terms of SoP and Cybersickness. In addition, the simulator is dedicated to power wheelchair domain and adaptable to the diversity of impairments and needs. Indeed, its motion platform is compatible with off-the-shelf wheelchair seating, controllers and ergonomic accessories. Plus, its highly realistic VE have a configurable complexity and are compliant with many kinds of display interfaces such as the HMDs, screens or Immersia. Thus, this power wheelchair driving simulator aims to provide comfortable virtual experiences with high SoP and skill transfer for training and rehabilitation purposes.

In the second part of this chapter, the power wheelchair driving simulator was used within a pilot user study assessing the impact of the vestibular feedback provided on user SoP and Cybersickness during a driving task in VR. Participants were asked to drive the virtual power wheelchair along a path in a VE reproducing a real city square. Every participant completed the path twice in a counterbalanced order: one with visual feedback only, and one with visual and vestibular feedback. We used subjective questionnaires (NASA-TLX, IPQ and IVEQ) to assess the quality of the VR experience after completion of each task. The results validate our stated hypothesis: the addition of the vestibular feedback to the visual feedback provided by the visual display interface rendering the VE increases SoP and decreases Cybersickness for users. Therefore, the vestibular feedback contributes to better user QoE while using the simulator to drive a wheelchair in a VE. Those positive results imply that the simulator is more likely to be accepted and used by the targeted population (therapists and end-users). Indeed, the positive impact of the proposed vestibular feedback on increased SoP and reduced Cybersickness provides solutions to deal with issues such as user lack of involvement and Cybersickness effects that represent important barriers to the use of VR technology by this target population. In a nutshell, our results highlight the importance of providing vestibular feedback in order to increase the quality of VR experience and therefore the benefit of our simulator for training and rehabilitation programs.

Finally, we presented a study with regular power wheelchair users consisting in the completion of a clinically validated task with both our wheelchair simulator and a standard power wheelchair. The objective of this second study was to compare user performance between both real and virtual conditions, as well as evaluate the QoE provided by the simulator in terms of SoP and Cybersickness. Conducting a study with regular users was a mandatory and challenging step in the development of a user-centered simulator. Indeed, it is a challenge that we took up to propose the best possible experience according to the target population. Overall, we proved that regular users are able to perform a clinically validated task similarly regarding the completion time, both with a VR based power wheelchair simulator and a real power wheelchair. We also assessed high levels of SoP through the IPQ resulting in a valuable QoE even though some improvements could be made to enhance the level of the SoP involvement criteria. If Cybersickness levels were also found to be high when compared to the literature, the investigation on factors and related works allowed us to draw guidelines for future work in order to improve the simulator acceptability within a clinical context. However, we could already consider our simulator in other contexts such as algorithm testing or urban planning which require less VR exposition time to be effective. Finally, this study was the first clinical study in which people with disabilities and therefore end-users were able to use our simulator in a targeted context. All the participants' feedback regarding the simulator and overall study was positive which is promising for the future.

In future works, further studies should investigate sensory feedback like vestibular, haptic, auditory and visual feedback in order to better identify their impact and limits. Those studies will continue to include regular power wheelchair users will continue to include regular power wheelchair users and people with disabilities in order to better understand and answer their needs. In addition, it would be interesting to collect and analyze objective measures (e.g. gaze direction, electrodermal activity) to objectively quantify the impact of those feedback on SoP and Cybersickness and to complete the subjective assessments. From future studies results and interpretations, guidelines can be drawn and developments made, in close collaboration with power wheelchair users and clinicians, in order to further improve the simulator fidelity and QoE. For example, another clinical study SIMADAPT2 is concurrently conducted with people with disabilities of which results are still being analyzed. The study aims to compare the QoE in different simulator configurations such as using the HTC Vive Pro HMD, Immersia immersive room or a screen. Its results should highlight limits and advantages of each configuration as well as point out most urgent issues. In this way, as studies and improvements are made, the simulator will become increasingly safe, effective and comfortable, making it suitable for use in a clinical context.

Nevertheless, the simulator already represents a powerful tool that can be used in other contexts such as in the development of smart power wheelchair algorithms like the one presented in the next Chapter 4.

4

A smart power wheelchair tool for path planning

Introduction

The Chapter 3 has presented a tool dedicated to innovative training in order to improve its accessibility and efficiency. In particular, the simulator allows infinite replay of specific and complex situations in which users can learn by doing without any risk. Thus, users should be better prepared for complex situations such as outdoor spaces leading to improved navigation. Nevertheless, training is not necessarily a solution for everyone. Indeed, some severe disabilities result in an almost total loss of certain cognitive abilities that cannot be learned or trained. Sometimes, people with disabilities need an assistive system to help them compensate for their inabilities. This idea gave rise to smart power wheelchairs (Chapter 1) and especially to power wheelchairs that are able to autonomously or semi-autonomously navigate. In other words, these power wheelchairs are able to move safely without being directly steered by an operator (autonomous mode) or are able to improve the trajectory of the driver (semi-autonomous mode). This type of smart power wheelchair compensates for the inabilities of some people with disabilities and greatly improves power wheelchair accessibility and driving quality. Nevertheless, these intelligent systems rely on complex algorithms and control steps that can still be greatly improved.

This chapter presents then the work aiming at improving path planning, one of the autonomous systems key steps, by proposing a new algorithm dedicated to non-holonomic autonomous robots such as power wheelchairs.

First, path planning related works are further explored in Section 4.2. Then Section 4.3 presents a new local path planner and Section 4.4, a new global path planning algorithm. Finally, the Section 4.5 discusses both contributions. This chapter is related to the ICRA conference paper [ICRA2021].

Path planning and related works

Path planning is an important field of robotics, control theory and artificial intelligence [START_REF] Lavalle | Rapidly-Exploring Random Trees: A New Tool for Path Planning[END_REF]. It refers to the process of finding a way from a start state to a goal state under constraints. In particular, path planning is crucial for autonomous and semi-autonomous robot navigation in unknown environments. It allows the robot to find safe control states or a safe path to reach a given goal state. Among the multiple path planning algorithms that exist, the Rapidly-exploring Random Tree (RRT) [Steven M LaValle 1998] algorithm stands out for its efficiency in quickly exploring unknown spaces and for its low structure complexity, which allows it to be easily optimized or upgraded. Indeed, over the years, many versions of RRT have been proposed [M. [START_REF] Lavalle | Rapidly-Exploring Random Trees: Progress and Prospects[END_REF][START_REF] Janson | Fast marching trees: A fast marching sampling-based method for optimal motion planning in many dimensions[END_REF][START_REF] Otte | RRTX: Asymptotically optimal single-query sampling-based motion planning with quick replanning[END_REF] among which an asymptotically optimal version RRT* [START_REF] Karaman | Incremental Sampling-based algorithms for optimal motion planning[END_REF] that has largely contributed to its widespread use. RRT and RRT* both generate a collision-free path composed of piecewise linear paths between states. Both algorithms are based on 3 simple steps illustrated in Figure 4.2 which consist in a greedy exploration of an unknown environment coupled with the generation of a tree between safe found states. However, a trajectory composed of linear piecewise paths is not suitable for non-holonomic robots, in particular for differential robots such as power wheelchairs. Indeed, their kinematic and dynamic constraints prevent them from following paths with too much curvature which considerably restricts their movements and makes their driving more complex. In addition, within a differential robot transport scenario, user comfort is closely linked to angular accelerations and jerk energy [START_REF] Labakhua | Smooth trajectory planning for fully automated passengers vehicles[END_REF]]. As such, comfort also depends on the smoothness of the trajectory i.e. the trajectory curvature [START_REF] Solea | Trajectory planning with velocity planner for fullyautomated passenger vehicles[END_REF][START_REF] Bevilacqua | Path planning maximising human comfort for assistive robots[END_REF]]. Even when walking, people tend to limit curvature maximum value and variations [START_REF] Arechavaleta | An optimality principle governing human walking[END_REF]. In order for a path generated by a path planner to be both feasible by a differential drive robot and comfortable for a transported user, it must be smoothed by limiting curvature variation and curvature maximum value. To this end, 3 different approaches exist.

The first one consists in handling curvature constraints at the control level while following a reference path. In [START_REF] Dececco | PC-sliding for vehicles path planning and control : Design and Evaluation of Robustness to Parameters Change and Measurement Uncertainty[END_REF]], a smooth path following method respecting kinematic constraints and based on Clothoid is presented. Authors in [START_REF] Park | A smooth control law for graceful motion of differential wheeled mobile robots in 2D environment[END_REF] propose a Lyapunov-based feedback control law along with a path following strategy consisting in reaching reference path states one after the other. Their control law regenerates a feasible local path between each state and provides comfortable motion based on curvature velocity adaptation. However, relying on control to ensure path smoothness can lead to a suboptimal path, including unnecessary turns as the reference path is not smooth.

The second common approach applies a smoothing algorithm on the reference path after its planning and before the control step. Post-smoothing algorithms take a reference path composed of different states or control points and tweak piecewise edges to generate a path respecting smoothing constraints. Multiple smoothing methods exist based on different interpolation mechanics and typical curves like Dubin's, Clothoid or Bézier curves. In [START_REF] Choi | Continuous Curvature Path Generation Based on Bézier Curves for Autonomous Vehicles[END_REF], low degree Bézier curves are used in corners and sharp turns to obtain a continuous curvature path i.e. G2-continuous. The works [START_REF] Yang | An Analytical Continuous-Curvature Path-Smoothing Algorithm[END_REF] and [START_REF] Yang | Continuous curvature pathsmoothing algorithm using cubic Bézier spiral curves for non-holonomic robots[END_REF] present a method based on Bézier transition curves, also known as Bézier spirals, to smooth a series of states into a G2-continuous path. In [START_REF] Zhou | Bézier curve based smooth path planning for mobile robot[END_REF], authors also use Bézier curves to smooth sharp turns and connect piecewise linear paths with each other. The algorithm in [START_REF] Bevilacqua | Path planning maximising human comfort for assistive robots[END_REF]] generates a comfortable path by joining the states while minimizing curvature variation, integral and curve length. It uses the G1 Hermite Interpolation Problem with Clothoid and then tweaks angles to achieve G2-continuity. Authors in [Renny Simba, Uchiyama, and Sano 2016] generate a C2-continuous and locally controllable path from a set of points by inserting Quintic Bézier curves between segments. In [START_REF] Heiden | Gradient-Informed Path Smoothing for Wheeled Mobile Robots[END_REF], authors propose an innovative method called Gradient Informed Path Smoothing (GRIPS). Unlike other algorithms, GRIPS deforms the path shape by locally optimizing the state locations. As such, this algorithm is able to locally correct suboptimal states.

However, post-smoothing algorithms require extra execution time and sometimes additional expensive collision checks [START_REF] Bevilacqua | Path planning maximising human comfort for assistive robots[END_REF] while the path planner already spent time to ensure collision-free states which results in an unoptimized behavior. In addition, a post-smoothing generated path might be globally suboptimal as states disrespecting curvature constraints are selected in the first place. Starting from GRIPS, if a local correction of the state locations in order to integrate more constraints is a viable solution, one could ask why not directly integrate these constraints when generating states and path. This is the main idea behind the third approach to enhance path smoothness i.e. incorporating curvature constraints inside the path planner algorithm to generate feasible and comfortable path on-the-fly. This third approach is the basis of many solutions such as in [START_REF] Mcleod | Real-time adaptive non-holonomic motion planning in unforeseen dynamic environments[END_REF][START_REF] Silva | Clothoid-based global path planning for autonomous vehicles in urban scenarios[END_REF], each adapted to a specific global path planning algorithm.

Regarding RRT based global path planners, multiple solutions to smooth the final path have also emerged over the years using interpolation curves and post-smoothing methods in a realtime approach. The solution proposed in [START_REF] Yang | An efficient Spline-based RRT path planner for non-holonomic robots in cluttered environments[END_REF]] executes a local check of path feasibility before state connection and generates a valid path based on Bézier piecewise curves with null curvature at each state, thus ensuring G2-continuity. Authors also present different sampling, collision-checking and pruning techniques to enhance performances of the RRT, then defining the Spline RRT (SRRT). However, SRRT fails to generate piecewise path on-the-fly as each new state connection requires the complete re-parameterization of the path from the start to the new state instead of simply appending a new independent piecewise Bézier curve path as presented in [START_REF] Neto | Feasible RRT-based path planning using seventh order Bézier curves[END_REF]. Indeed, their solution uses independent Bézier curves as piecewise paths after approximating the cost to go to a new state using Dubin's curves. However, while the use of seventh-order Bézier curves ensures curvature continuity with null curvature at each state, it also leads to heavy polynomial calculations. Furthermore, the Bézier curves and their curvature values are not involved in the evaluation of the distance cost to a new state: this can still lead to inconsistent state choices in terms of comfort. In [Park and Kuipers 2015], authors proposed a new local path planner based on a Lyapunov control law to generate piecewise curves and to evaluate distance between states. The method takes into account comfort constraints and eliminates inaccessible ones. [START_REF] Sobue | RRT-Based Path Planning Considering Initial and Final Pose under Curvature Constraints for Nonholonomic Wheeled Robot[END_REF]] also proposed a different local path planner based on Clothoid G1 fitting to extend constraints and to ensure the elimination of inaccessible states. However, discontinuities between piecewise Clothoid path remain, due to Clothoid representation complexity and to G1 fitting algorithm. Finally, authors in [Chi, C. Wang, et al. 2018] and [C. Wang et al. 2019] include the Line-of-Sight algorithm (LOS) in their path planning process to check if two states can be connected under non-holonomic constraints in addition to the usual collision check. This algorithm is an efficient tool to optimize the trajectory generation as it eliminates inaccessible states, but it does not ensure G2-continuity of the global trajectory and does not help in the evaluation of 2 possible local paths.

All those methods proved themselves to be efficient and functional. Yet, they are still suffering from drawbacks, either because of the use of complex piecewise curves or high degree splines or because they do not fulfill all comfort and non-holonomic kinematic constraints. As such, in this chapter is proposed a new local path planner based on low degree Cubic Bézier curves. Combined with path planning algorithms such as RRT*, it generates comfortable and non-holonomic robot compliant paths on-the-fly.

Cubic Bézier Based Local Path Planner

This section exposes the problem of local path planning in subsection 4.3.1 that the previously presented literature solutions solve. Then, subsection 4.3.2 presents a new local path planner algorithm able to solve the stated problem in a different and more suitable way.

Problem Statement

Considering a space X with obstacles whose position and geometry are a priori known, and 2 states s init , s goal . In order to facilitate the understanding, in the following problem statement, X is a two-dimensional space, even if the method is applicable in any dimension. X f ree refers to X space free of obstacle.

Path planners like RRT address the problem of finding a valid path from s init to s goal if it exists. A path is considered valid if it meets all path planner constraints. The most usual global constraint is for the path to be collision-free i.e. belonging to X f ree . However, in order for the path to be feasible by a non-holonomic robot and comfortable for a transported user, more constraints need to be satisfied. Hence, a path is comfortable for a user if its maximum curvature value and curvature variations are minimized as a pedestrian would naturally do [START_REF] Arechavaleta | An optimality principle governing human walking[END_REF]. Indeed, as stated in Section 4.2, curvature is inversely proportional to angular acceleration and is linked to jerk energy, which are known to be discomfort factors [START_REF] Solea | Trajectory planning with velocity planner for fullyautomated passenger vehicles[END_REF]. A path is then said feasible by a non-holonomic robot if it fulfills its kinematic and dynamic constraints. Those constraints are also represented by the maximum curvature of the path, as the maximum curvature is inversely proportional to the minimum curvature radius that the robot is able to achieve. Finally, to enhance path stability, the path should be G2-continuous, meaning that its curvature should be continuous.

If the path is defined as a parametric curve g(t) where t stands for the curve parameter in R, then the curvature κ(t) can be calculated as

κ(t) = | ġ(t) × g(t)| | ġ(t)| 3 . (4.1)
As shown in (4.1), the path parameterization should be at least second order differentiable. In addition, in order to obtain a valid path, its absolute maximum curvature value must be less than the maximum value achievable by the robot and tolerated by the user.

To summarize, the generated path must fulfill 3 main constraints :

         |κ(t)| ≤ min(κ robot , κ user ), g(t) is G2-continuous, g(t) ∈ X f ree , (4.2)
with κ robot the maximum curvature achievable by the robot and κ user the maximum curvature tolerated by the user. Note that the curve should also globally limit curvature variations, thus limiting sharp turns.

While the third constraint is generally fulfilled by the path planner itself, the following section presents a new local path planner to produce piecewise paths that meet curvature constraints and result in a global G2-continuous path once merged together.

Proposed Local Path Planner

To generate a path, several path planners, like RRT, connect piecewise curves between states. In most of them, those piecewise curves are linear and do not respect any constraint other than not crossing an obstacle. Here is proposed a new local path planner based on Cubic Bézier curves to connect new samples to the tree if possible. Bézier curves are parametric curves whose shape can be modified by tweaking a set of control points. The main advantage of Bézier curves lies in their simple parameterization based on Bernstein polynomial B i (t). Cubic Bézier curves are then defined by a set of four control points P 0 , P 1 , P 2 , P 3 and a third order Bernstein basis polynomial such that P(t), the Cubic Bézier curve parameterization, is defined by

P(t) = w 0 * B 0 (t) * P 0 + w 1 * B 1 (t) * P 1 + w 2 * B 2 (t) * P 2 + w 3 * B 3 (t) * P 3 , (4.3) B 0 (t) = (1 -t) 3 , B 1 (t) = 3 * t * (1 -t) 2 , B 2 (t) = 3 * t 2 * (1 -t), B 3 (t) = t 3 ,
with w i being the weighting basis coefficients. In this project, w i = 1 for each i in order to simplify calculations and understanding as they do not impact the overall method.

Using equations (4.3) and (4.1) we can compute the Cubic Bézier curve's curvature for any value of t. In particular, as shown in [Thomas W. [START_REF] Sederberg | Computer aided geometric design[END_REF], its initial curvature at t 0 = 0 is given by

κ(t 0 ) = w 0 w 2 w 2 1 n -1 n h |P 0 -P 1 | 2 = 2 3 h |P 0 -P 1 | 2 , (4.4)
with n being the Bézier curve order and h the perpendicular distance from P 2 to the line P 0 P 1 as shown in Using those expressions, we can ensure that each piecewise curve composing the final path meets the maximum curvature constraint stated in (4.2). Indeed, we can evaluate any piecewise curve curvature, and we can invalidate the curve if its value exceed maximum curvature value κ max . As the final path is a composition of those piecewise Bézier curves, its final curvature will not exceed the maximum predefined value.

The last constraint to fulfill is the curvature continuity of the final path i.e. the curvature continuity between piecewise curves. Let us consider a state s candidate connected to the global tree and accessible through a piecewise Cubic Bézier curve P(t p ), with t p 0 ≤ t p ≤ t p 3 with t p the curve P parameter in R, P i the control points of curve P and t p i the parameter value so that P(t p i ) = P i . Furthermore, let us imagine the state s new as the new state to connect to s candidate using a new piecewise Cubic Bézier curve Q(t q ), with t q 0 ≤ t q ≤ t q 3 with t q the parameter, in R, of curve Q, Q i its control points and t q i the parameter value so that Q(t q i ) = Q i (Figure 4.4). We need to connect both piecewise curves Q and P while keeping the curvature continuous in order to meet the G2-continuity constraint.

In particular, we need to ensure that, at a link state s link between the two piecewise Bézier curves Q and P, both P(t p ) curvature κ p (t p ) and Q(t q ) curvature κ q (t q ) are equal (Figure 4.5), in other words that κ p (t link ) = κ q (t q 0 ) with P(t link ) = Q(t q 0 ) = s link . Note that in most of related works, piecewise curves are connected at their end point such as s link = s candidate [X. [START_REF] Wang | Collision-free path planning method for robots based on an improved rapidly-exploring random tree algorithm[END_REF][START_REF] Neto | Feasible RRT-based path planning using seventh order Bézier curves[END_REF]. In contrast to the literature, in the proposed method, both states s candidate and s new are not used respectively as start point and end point of the Bézier piecewise curve. Instead, their positions are used as third and fourth control point Q 2 and Q 3 respectively of the Bézier piecewise curve. This results in the following advantages. First, the final heading of the robot stays tangent to line s candidate s new as a classical RRT path with linear piecewise curves would suggest and user would want. Secondly and more importantly, the first control point Q 0 , that is equal to the link state s link , also belongs to the curve P(t p ) at a given t link with t p 0 ≤ t link ≤ t p 3 as illustrated in Figure 4.5. This way, the final trajectory is not forced to transit through the state s candidate , the turn is "anticipated" and the curvature reduced. Thus, at a given t link , the positions of three of the four Q(t q ) control points are already known, namely Q 0 , Q 2 and Q 3 . However, Q(t q ) and P(t p ) still need to be G2-continuous meaning that position, derivative and curvature values of Q(t q 0 ) and P(t link ) must be equal. To do so, we can tweak the last unknown control point Q 1 .

Firstly, in order for Q(t q 0 ) and P(t link ) positions to be equal, s link must belong to both P(t p ) and Q(t q ) curves. This constraint is fulfilled as far as we take a point on P(t p ) curve as first Q(t q ) curve control point Q 0 . Secondly, we can ensure that the derivative of Q(t q 0 ) is equal to P(t link ) if the Q 1 control point relies on the tangent of P(t link ). Finally, using equation (4.4), we can express the G2-continuity constraint as a system to solve for the Q 1 position according to

         Q 0 = P(t link ) = Q(t q 0 ),t p 0 ≤ t link ≤ t p 3 , Q 1 ∈ Ṗ(t link ), k 0 = 2 3 h 0 |Q 0 -Q 1 | 2 , (4.5)
with Ṗ(t link ) being the P tangent of P(t link ) at t link location (Figure 4.5), k 0 the curvature value of P(t p ) at t link and h 0 the perpendicular distance from Q 2 to the line Q 0 Q 1 (Figure 4.3). Regardless of the curvature sign, we find 2 solutions to the system (Equations 4.5), namely

   x q 1 = ± 2 3 | h 0 k 0 | 1 1+m 2 link + x q 0 ,
y q 1 = m link * (x q 1x q 0 ) + y q 0 , (4.6) with x q i and y q i the coordinates of the Q i control point and m link the slope of Ṗ(t link ). Once the correct solution sign is selected depending on the P(t p ) current direction, the final control point Q 1 position is known and the curve Q(t q ) can be drawn as in Figure 4.5. Now, the maximum curvature of Q(t q ) can be evaluated and the new state and piecewise curve can be validated or rejected depending on the curvature constraint. Note that the computation of Q(t q ) does not require any change in the P(t p ) curve. This ancestor independence provides more flexibility to the path planner algorithm and better performance as the path does not need to be fully re-parameterized with each new state. It is yet to set the convenient t link which determines s link and Q 0 positions and greatly influences the Q(t q ) curvature profile and maximum. Figure 4.6 shows different possible configurations and the resulting P(t p ) and Q(t q ) curves. Furthermore, depending on the P(t q ) curve shape, a certain range of t link values will produce a curvature discontinuity, such as the situation presented in Figure 4.7.

Indeed, when P is S-shaped, for a certain range of t link near the inflection point, neither of the two solutions in equation (4.6) is both in the right direction and of correct sign. This is due to the configuration of the control points. To alleviate this issue, adequate conditions can be raised. If P is S-shaped, t link will provide a valid solution if the configuration meets the conditions    sign(x q0 ) = sign(k 0 ) if y p 3 ≥ y q 0 + m link (x p 3x q 0 ), sign(x q0 ) ̸ = sign(k 0 ) if y p 3 < y q 0 + m link (x p 3x q 0 ), (4.7) with x q i , y q i , x p i , y p i respectively the P(t p ) and Q(t q ) control points coordinates and x q0 the x derivative of P(t link ) whose sign gives P direction.

Another impossible configuration happens when curvature k 0 is null. In that case we can set Q 1 equal to Q 2 and the resulting path will remain G2-continuous as long as previously stated conditions are fulfilled (equation (4.7)). Note that the validity of t link only depends on P(t p ) curve's shape and control points. Thus, a consistent t link value for future cubic Bézier curve connection can be computed regardless new state position. This proposed local path planner allows then to generate a Cubic Bézier piecewise curve between 2 states and to evaluate its curvature. Then, this curvature value can be used as a piecewise curve validation criterion to fulfill constraints (equation (4.2)), as well as a local piecewise path cost value in the overall algorithm process.

Note that this presented method is applicable in any dimension as it relies on n-dimensional properties. The use of a two-dimensional space in this presentation is only to facilitate understanding.

Cubic Bézier Based RRT* (CBB-RRT*)

This section presents a new version of RRT* called CBB-RRT* and based on local path planning method presented in section 4.3.2 in order to illustrate its implementation within a global path planning algorithm. RRT* was chosen because it is the simplest asymptotically optimal RRT version and largely used in various domains. However, the local path planner could be implemented as a replacement of the linear local path planner in the exact same way in various RRT versions such as in [X. [START_REF] Wang | Collision-free path planning method for robots based on an improved rapidly-exploring random tree algorithm[END_REF][START_REF] Kang | Sampling-based motion planning of manipulator with goal-oriented sampling[END_REF][START_REF] Chen | A Fast and Efficient Double-Tree RRT*-Like Sampling-Based Planner Applying on Mobile Robotic Systems[END_REF]Chi, C. Wang, et al. 2018;[START_REF] Choudhury | Regionally accelerated batch informed trees (RABIT*): A framework to integrate local information into optimal path planning[END_REF]Gammell, Srinivasa, and Barfoot 2015;[START_REF] Moon | Kinodynamic planner dual-tree RRT (DT-RRT) for two-wheeled mobile robots using the rapidly exploring random tree[END_REF][START_REF] Arslan | Use of relaxation methods in sampling-based algorithms for optimal motion planning[END_REF]. In addition, even though the presented method to generate local paths was thought to be used with the RRT algorithm, it is adaptable to other global path planner based on the concatenation of piecewise curves. This section first exposes RRT* principles in subsection 4.4.1 before presenting the new version of RRT* based on the previously proposed local path planner in subsection 4.4.2. Then it compares this new version with a classic RRT* algorithm in subsection 4.4.3.

RRT and RRT* principles

As shown in section 4.2, RRT is a path planner that allows fast exploration of an unknown environment [START_REF] Lavalle | Rapidly-Exploring Random Trees: A New Tool for Path Planning[END_REF]]. RRT generates a collision-free path by combining piecewise linear paths between random states. Over the years, many enhanced versions have been proposed. One of the most used version is the RRT* version proposed in [START_REF] Karaman | Incremental Sampling-based algorithms for optimal motion planning[END_REF] that generates an asymptotically optimal tree by introducing a rewiring step to the RRT tree extension method as illustrated in Figure 4.8. In RRT*, a random state is found but not directly linked to the nearest in-tree state. State proximity is determined using euclidean distance i.e. a state is considered to be near to another if its euclidean distance is under a certain value η.

First, the nearest in-tree state is used to create a new state in the direction of the random state at η maximum distance. Then, the new state is connected to the near in-tree state that provides the cheapest local piecewise path cost becoming the new in-tree state. This two-steps approach allows the use of different evaluation cost methods to find the nearest state, the near states and the final parent state of the steered state. Finally, once the new state is in tree, the rewiring step optimizes the trajectory by changing its piecewise linear path. During this step, the steered state becomes the parent of its near in-tree states if the cost to reach them is lower than the actual.

CBB-RRT* algorithm and rewiring strategy

A Cubic Bézier based version of RRT* (CBB-RRT*) has been implemented using the proposed Cubic Based local path planner (algorithm 1) to test it within a real global path planning algorithm. In this algorithm s any are states whereas S any represent sets of states on which classical operations can be performed such as Empty() which empties the set or PopLast() which remove and returns the last state of the set. As in RRT*, the InitTree() method initializes the tree T with a root state, and RandomState() method uniformly generates a random state s random . The Extend() method extends T by one new state s new using the local path planning In its overall process, CBB-RRT* only differs from RRT* algorithm by its rewiring strategy in order to be compliant with the proposed local path planner. Indeed, the Cubic Bézier based local path planner generates piecewise paths dependent from their parent curve shape and parameterization. Thus, rewiring a state will recursively invalidate descendant piecewise path. In other word, if a piecewise path changes, continuity with next piecewise paths is broken which invalidates all path. Therefore, using the proposed local path planner requires another rewiring strategy than the RRT* one. As pictured in Figure 4.9, trees generated by CBB-RRT* and their overall exploration areas are smaller. This is due to a more constrained state validation but also to the different rewiring strategy. Furthermore, overall CBB-RRT* tree structure and descendants seem different from RRT* ones even though composing states are similar. Indeed, using the local path planner as a cost evaluation function, CBB-RRT* prioritizes reachable states with smaller curvature turns and generates a continuous path with a bounded curvature as shown in Figure 4.10. As no curvature constraint is considered in RRT*, no evaluation of the generated path curvature is possible and no curvature profile is available without further process on the generated path.

Discussion

This section first discusses usability limitations of both proposed global and local path planner (subsection 4.5.1) before proposing ideas to optimize both (subsection 4.5.2) and two different possible designs of a dynamic version of CBB-RRT* (subsection 4.5.3).

Usability and Limitations

While relying on RRT* features like fast exploration and asymptotical optimality, CBB-RRT* generates a smooth and comfortable path that meets all previously stated constraints (equation (4.2)). Indeed, the use of the local path planner guarantees path curvature continuity and limitation on which comfort and feasibility depend. Because path curvature is bounded by a specified value, it is achievable by any non-holonomic robots such as power wheelchairs. In addition, the path provided by CBB-RRT* is parametrized. Path can be discretized and position, heading and curvature are known at any time. This is a huge advantage at control step as the robot can adapt its velocity to respect comfort constraints. Furthermore, the local path planner could be used within any other path planning, path smoothing and control algorithms such as more advanced RRT versions like NC-RRT [X. [START_REF] Wang | Collision-free path planning method for robots based on an improved rapidly-exploring random tree algorithm[END_REF]], Risk-DTRRT [Chi, C. Wang, et al. 2018], DT-RRT* [START_REF] Chen | A Fast and Efficient Double-Tree RRT*-Like Sampling-Based Planner Applying on Mobile Robotic Systems[END_REF], BIT* [Gammell, Srinivasa, and Barfoot 2015] or RRT# [START_REF] Arslan | Use of relaxation methods in sampling-based algorithms for optimal motion planning[END_REF]. In particular, it would allow the development of more advanced versions of CBB-RRT*, such as a dynamic version of which two possible designs are proposed in next subsection 4.5.3. Beyond control and path planning domains, the local path planner could be useful in data interpolation or design fields [S. M. [START_REF] Hu | An extension algorithm for B-splines by curve unclamping[END_REF] as a solution to 123 G2-continuous piecewise connection with only third degree polynomial curves [START_REF] Wolberg | Monotonic cubic spline interpolation[END_REF].

However, using the local path planner, CBB-RRT* breaks piecewise curve symmetry and requires a specific rewiring strategy to work. This is due to the ancestor dependency of Cubic Bézier piecewise curves. As such, it takes more iterations than RRT* for the same amount of exploration and its rewiring complexity is higher. Also, generating piecewise Cubic Bézier curves instead of linear paths is more expensive in terms of control points calculations, collision checks and data transfers. Nonetheless, many optimizations can be developed to enhance CBB-RRT* overall performance as proposed in the followings.

Optimization ideas

Note that for comparative purposes, each CBB-RRT* algorithm step has been modified as little as possible whereas it could be optimized for the specific use of the presented local path planner. For example, a more precise proximity evaluation function would allow to refine the nearest state selection and connect random states more often. To this end, the proximity function could take into account heading difference between states, or piecewise curve length approximation like in [START_REF] Neto | Feasible RRT-based path planning using seventh order Bézier curves[END_REF] with Dubin's curve, or piecewise curvature value using the local path planner. Even though the rewiring strategy has been extended and differs from the original, it can be optimized by a redesign based on more recent strategies [START_REF] Otte | RRTX: Asymptotically optimal single-query sampling-based motion planning with quick replanning[END_REF][START_REF] Moon | Kinodynamic planner dual-tree RRT (DT-RRT) for two-wheeled mobile robots using the rapidly exploring random tree[END_REF]. Furthermore, the sampling strategy that generates random states can also be improved by using or combining various solutions, such as goal oriented sampling [START_REF] Kang | Sampling-based motion planning of manipulator with goal-oriented sampling[END_REF][START_REF] Akgun | Sampling Heuristics for Optimal Motion Planning in High Dimensions[END_REF], incremental direct sampling [START_REF] Choudhury | Regionally accelerated batch informed trees (RABIT*): A framework to integrate local information into optimal path planning[END_REF]Gammell, Srinivasa, and Barfoot 2015], ellipsoidal direct sampling [START_REF] Gammell | Informed RRT*: Optimal sampling-based path planning focused via direct sampling of an admissible ellipsoidal heuristic[END_REF] and weighted sampling [START_REF] Janson | Fast marching trees: A fast marching sampling-based method for optimal motion planning in many dimensions[END_REF]. Finally, other trajectory optimization algorithms could be implemented inside CBB-RRT* such as the LOS algorithm briefly mentioned in section 4.2

Regarding the local path planner, some choices would deserve further attention and investigation. For example, tweaking the weight of the Cubic Bézier basis coefficients w i could change the curve shape and provide smoother local piecewise curve while still meeting constraints as they are involved in the initial curvature (equation (4.4)). Also, if the use of polynomial based Cubic Bézier curve was motivated by calculation simplicity, adapting the method to other Cubic Bézier based curves could be considered such as T-Bézier curves [START_REF] Li | Planar T-Bézier curve with approximate minimum curvature variation[END_REF]] or H-Bézier curves [Zhao and G. Wang 2007]. Indeed, those non-polynomial Bézier based curves provide more flexibility and tweaking parameters than polynomial based one which could be explored in order to further control the generated trajectory shape. However, finding adequate equations forms required by the method and adapting calculations is a complex task. As a preliminary work, we have identified the initial curvature equation (4.8) of cubic H-Bézier curves, namely

κ(t 0 ) = (λ -s) 2 s (c -1) 2 (λ -2s + λ c) h |P 0 -P 1 | 2 , ( 4.8)
with c = cosh(λ ), s = sinh(λ ).

Further investigations should be conducted using this equation. Finally, evaluation of piecewise curve maximum curvature and the finding of the ideal t link value could be optimized using lookup tables or more advanced strategies.

Dynamic version design

One of the biggest CBB-RRT* limitation is its inability to handle moving obstacles. Indeed, RRT*, on which it is based, is a static global path planner which explore a static environment. However, in complex and populated environments such as outdoor public places, moving robots such as power wheelchairs must implement a dynamic path planner. In order to prepare the implementation of a CBB-RRT* version in a smart power wheelchair, this section proposes two different possible designs of a dynamic version.

The first version takes advantage of the algorithm and integrates it into a dynamic overlay also called a "meta algorithm". In the same way as proposed in [START_REF] Connell | Dynamic path planning and replanning for mobile robots using RRT[END_REF], the CBB-RRT* will be re-executed at regular intervals, just after an update of the obstacles' position. This way, every moving obstacle will be taken into account during each CBB-RRT* planning phase as static obstacles as illustrated in Figure 4.11. While this version is efficient, it does not allow for extensive exploration of the environment or extensive optimization of the generated paths. Indeed, the exploration and the generation of paths starts again with each new obstacles' position update, overwriting the previous finds.

On the contrary, the second designed version is able to keep track of the past generations as it is inspired by the Risk-RRT and Risk-RRT* algorithms from [START_REF] Fulgenzi | Risk based motion planning and navigation in uncertain dynamic environment[END_REF]] and [START_REF] Chi | Risk-RRT*: A robot motion planning algorithm for the human robot coexisting environment[END_REF]. Both of these algorithms integrate a module able to predict moving obstacles future positions based on Gaussian Processes. These predictions are based on the virtual or real environment observations and computed in parallel to the execution of the path planning algorithm. Thus, they can be taken into account when evaluating the cost of each new trajectory. While a Risk-CBB-RRT* algorithm would be more effective and would allow keeping track of the past trajectories, it would be more complex to develop, set up and execute. In particular, tuning the Gaussian Processes models and find adequate parameters require many tests.

Conclusion

This chapter has presented a new Cubic Bézier based local path planner that generates G2-continuous Cubic Bézier piecewise curves. This local path planner could find interests in many different fields. In a non-holonomic transport robot path planning context like power wheelchair navigation, trajectory curvature is directly linked to feasibility and user comfort. As such, this chapter has also presented the CBB-RRT* algorithm, a classical RRT* version using the proposed local path planner. This algorithm generates smooth, comfortable paths, feasible by non-holonomic robots without any additional steps.

However, several improvements and optimizations of both local and global path planners are still possible by conducting further research and/or combining it with other innovative algorithms. This way, more specific and more advanced versions could emerge. In particular, the development of a version able to manage dynamic obstacles is planned following one of both presented designs.

In order to further explore CBB-RRT* limits and advantages, it is necessary to test it in real conditions and compare it with other RRT* versions or other solutions. However, even without a financial limit, testing it intensively in complex scenarios could lead to extensive material damage and would be far too time-consuming, especially if each new improvement requires several tests. Finally, making the most of this path planner and the user comfort constraints it integrates would require individual parameterization that would be complex to implement at an industrial level without specific methods or tools. Indeed, even if different profiles of parameters are proposed, they will never be as well adapted to the user as a profile made-to-measure through extensive tests in several more or less complex situations. Hence, without individual parameterization, this path planner is doomed to be generic and not fully user-centered. Thus, adequate assistive development and testing tools have to be found.

5

Adaptive fidelity VR based simulator

Introduction

As shown in previous chapters, enhancing power wheelchair navigation through autonomous solutions and innovative training turns out to be promising. In one hand, VR based power wheelchair simulation is a significant tool to propose safe while complex situations in order to acquire the necessary experience to drive a power wheelchair safely. In other hand, For individuals whose abilities cannot be trained, it is still possible to develop smart solutions such as the presented path planning algorithm that takes into account specific needs of power wheelchair navigation context such as user comfort. However, these two lines of work and all that they implied, have highlighted the two major barriers to power wheelchair navigation enhancement; the lack of user inclusion in development processes and the lack of dedicated assistive development tools.

Main barriers to power wheelchair navigation enhancements

First, as stated in the introductory Chapter, the processes of designing and developing power wheelchair navigation solutions do not systematically include regular power wheelchair users. In other words, many power wheelchairs and related tools and infrastructures are not user-centered [Erdogan and Argall 2017b]. Hence, those projects are often detached from end-users needs and expectations by considering power wheelchairs only as generic mobile robots with a seat rather than a whole motion device with a driver [START_REF] Leaman | A comprehensive review of smart wheelchairs: Past, present and future[END_REF]. This sometimes results in power wheelchair related tools or infrastructures presenting flaws with important aspects being neglected [START_REF] Faria | A Survey on Intelligent Wheelchair Prototypes and Simulators[END_REF]. For example a majority of outdoor and public spaces are not suitable for power wheelchair navigation since they were not specifically designed [START_REF] Torkia | Power wheelchair driving challenges in the community: A users' perspective[END_REF]]. Sometimes, the power wheelchair itself, namely its structure and motion capacities, cause navigation difficulties [START_REF] Salatino | An observational study of powered wheelchair provision in Italy[END_REF][START_REF] Rice | A systematic review of risk factors associated with accidental falls, outcome measures and interventions to manage fall risk in non-ambulatory adults[END_REF]. Even though literature and researchers seem to become aware of the need to include end-users in the loop [START_REF] Götzelmann | Towards the inclusion of wheelchair users in smart city planning through virtual reality simulation[END_REF]Erdogan and Argall 2017b], this is still a new weak trend because it requires adapted development tools that do not exist yet. This leads us to the second major barrier that alters power wheelchair navigation enhancement, i.e. a lack of development assistive tool. Including end-users in the design and developments processes requires appropriate tools in addition to new methods. In particular, it requires a tool adapted to any context and foremost a tool usable throughout the complete process as authors in [START_REF] Braga | IntellWheels: Modular development platform for intelligent wheelchairs[END_REF] suggest.

The role of VR based simulators

As reported in Chapter 2, other research domains have successfully involved end-users in their design and development processes using VR based simulators of various fidelity levels. In fact, as VR allows simulating safe and controllable virtual situations with infinite possibilities, and VR based simulators allow simulating and experience any situations, in a more or less realistic way depending on their fidelity level. This way, a VR based power wheelchair simulator could help to gather precious end-users feedback and expectations. From a developer perspective, it could also help to virtually test each solution in any ecological situation regardless of real life context constraints such as cost and danger [START_REF] Baltazar | Autonomous wheelchair for patient's transportation on healthcare institutions[END_REF]. For example, regarding the path planner proposed in Chapter 4, a low fidelity level power wheelchair simulator could be useful to conduct rapid software tests all along future optimizations, whereas a high fidelity level simulator would allow a safe individual parameterization of the algorithm in almost real-life situations. As such, using VR based power wheelchair simulators could largely ease many design and development steps from user centered conception to individual customization. Going further, using the same power wheelchair simulator throughout the complete design and development process of a solution would limit project time and costs. In particular, its use at each process task, as illustrated by Figure 5.1, would ease interactions between end-users and developers, hence improving the overall quality of the solution in the same way as quasi-Agile method. However, in order for a VR based simulator to be adapted to any development step, specific considerations are required in its design, especially regarding its fidelity level. This chapter then presents guidelines to design adaptive fidelity VR based simulators. In Section 5.2 a new simulator fidelity model is proposed. Then, it paves the road to user-centered power wheelchair solution developments using a revised version of the simulator presented in Chapter 3 following those guidelines (Section 5.3). Finally, this chapter discusses the presented contributions in Section 5.4 before concluding in Section 5.5.

Design

The work presented in this chapter is not yet related to a publication since it is still in progress.

Adaptive fidelity simulator

In order to answer development issues, this section presents design guidelines to build an assistive development tool in the form of a VR-based adaptive fidelity simulator. Subsection 5.2.1 proposes a new simulator fidelity model on which are based the guidelines presented in subsection 5.2.2.

Simulator fidelity model

In simulation, the fidelity term has been extensively misused to refer to other concepts like SoP and realism or as a high quality experience. In particular, as shown in Chapter 2, the term fidelity is confusing as it can designate either the simulation fidelity or the simulator fidelity [START_REF] Tun | Redefining Simulation Fidelity for Healthcare Education[END_REF]. Actually, simulation fidelity appears to be application dependent, highlighting a strong relationship with the user profile and situation's nature, on the opposite of simulator fidelity which is context independent [START_REF] Tun | Redefining Simulation Fidelity for Healthcare Education[END_REF][START_REF] Rehmann | A Handbook of Flight Simulation Fidelity Requirements for Human Factors Research[END_REF]. In order to avoid ambiguities and misunderstanding that infest literature, as in [START_REF] Hamstra | Reconsidering fidelity in simulation-based training[END_REF], we recommend abandoning the term "simulation fidelity" in favor of more precise and consensus terms like realism, immersion and SoP. Nonetheless, we propose to maintain the term "simulator fidelity" and to clarify its definition suggested in [START_REF] Tun | Redefining Simulation Fidelity for Healthcare Education[END_REF]] by considering it as the intrinsic characteristic of the simulators and its capacity to propose a realistic virtual experience. This way, simulator fidelity refers to a tangible, measurable and context-free property distinct from simulation oriented concepts such as SoP, immersion and realism.

Definition -The simulator fidelity corresponds to the simulator intrinsic capacity to propose a realistic virtual experience in which the user will evolve, interact and feel similarly as if he was in a similar real experience.

In order to further clarify the notion of simulator fidelity, we also propose a new multidimensional independent simulator fidelity model inspired by models presented in [START_REF] Liu | Simulation fidelity[END_REF][START_REF] Rehmann | A Handbook of Flight Simulation Fidelity Requirements for Human Factors Research[END_REF]. Our model focuses on simulator and overcomes the limits of interdimensional dependencies of the one proposed in [START_REF] Liu | Simulation fidelity[END_REF] while being more application independent than the one in [START_REF] Rehmann | A Handbook of Flight Simulation Fidelity Requirements for Human Factors Research[END_REF]]. We then define simulation fidelity as a composition of 3 specific dimensions, namely Environment Fidelity, Sensory Fidelity and Functional Fidelity as shown in Table 5.1. Each dimension is independent of one another and participates in a specific way to the simulator propensity to provide a virtual experiment similar to its referent real situation.

Environment fidelity regroups all environment related parts of the simulation in which the simulated object or situation evolves close its real referent. In the case of power wheelchair VR simulation, this dimension refers to the realism of the virtual environment, its aspect and physical engine.

Sensory fidelity refers to the multiple sensory feedback involved in the simulation and how realistic those feedback are compared to what a user feels in the referent situation. Within a VR simulation, the visual and auditory modalities are classically involved and depend on the VR display device used. To enhance the quality of experience, many other types of feedback and Functional fidelity is related to the hardware and software simulator workflow and its proximity to the referent workflow. It provides information on how the simulator device looks, sounds, functions and works. For example, within a power wheelchair simulation context, a high functional fidelity simulator will present a realistic power wheelchair simulated chain of control from input control to output data, including a sensory platform similar to a real power wheelchair in shape and operation. Compared to literature, this proposed model is based on simulator concrete features resulting in large dimensions that can be split in multiple sub-dimensions. For example, it does not have any psychological-cognitive or task dimensions compared to the model proposed in [START_REF] Liu | Simulation fidelity[END_REF]. Indeed, those both so-called dimensions can be seen as the direct consequences of an immersive and high SoP VR experience. Hence, they are not considered as simulator features that enhance the immersion and realism capabilities of the simulator but rather as independent concepts. In addition, the proposed model better describes the fidelity as a simulator feature and allows comparison between existing simulators. Finally and more importantly, this model represents a favorable ground on which to build guidelines for the design of variable level fidelity simulators, also called "adaptive fidelity simulator", which are exposed in next section.

Definition -An adaptive fidelity simulator is a simulator with a variable level of simulator fidelity

Adaptive fidelity simulator design guidelines

Since simulators are generally dedicated to a single development step and aim to assist a specific task. Their architecture is static and determines their level of fidelity in each dimension. Indeed, once the simulator is operational, changing its fidelity level, and especially its Functional Fidelity level, usually requires a major redesign of its architecture. However, each design and development step would benefit from a simulator with a different level of fidelity. For example, early tests only require a high Environment Fidelity whereas late individual parameterization requires the highest possible fidelity level in every dimension. Therefore, the same simulator cannot be used throughout these development processes without having a variable fidelity level. Thus, in order for a VR based simulator to have an adaptive fidelity level, its architecture should follow the following guidelines.

Firstly, its software and hardware architecture should be modular, meaning that it should be composed of multiple independent modules dedicated to specific tasks in the workflow. This property allows the simulator to be independently developed and managed. In addition, it allows each module to be activated or deactivated depending on the developers needs and development step. For example, some compatibility tests of the path planner proposed in Chapter 4 would only require the VE and visual module whereas a complete individual parameterization would require high sensory and functional fidelity. Secondly, each module of an adaptive fidelity simulator has to impact only one dimension of the fidelity model or has to be composed of precisely bounded submodules impacting only one dimension as illustrated in Figure 5.2. This way, evaluating the fidelity level is easier and changing a module or a submodule will only modify the level of one fidelity dimension. While this guideline can be seen as a constraint, it represents an additional tool to design the simulator architecture and to precisely define modules. Indeed, it is not always easy to identify clear boundaries between modules to reach separation of concerns and complete independence. Imposing a separation of modules according to the impacted fidelity dimension allows to refine these boundaries.

VR simulator work�ow

Property -An adaptive fidelity simulator as a primary development tool has a modular architecture with each module impacting at best only one of the three fidelity dimensions.

Adaptive fidelity power wheelchair simulator

In order to provide an example of an adaptive fidelity simulator following the previously presented guidelines, this section presents a revised version of the simulator proposed in Chapter 3. It first presents the new version design in subsection 5.3.1 before giving an example of the proposed design adaptability by extending the simulator features in subsection 5.3.2. Finally, subsection 5.3.3 illustrates its relevancy within a prototyping use case.

Power wheelchair simulator design

The VR based power wheelchair simulator presented in Chapter 3 was firstly dedicated to training. It required a redesign in order to be used as a primary development tool adapted to any kind of power wheelchair related project. Thus, its architecture has been revised following the guidelines presented in previous Section 5.2.2 as pictured in Figure 5.3. While its software modularity was already ensured by a ROS based workflow, and its hardware modularity by an innovative motion platform design, some parts needed to be reviewed and enhanced to be fully adaptive, in particular regarding fidelity.

As presented in Chapter 3, the power wheelchair simulator includes a motion platform electrically and mechanically similar to a standard power wheelchair. Thus, thanks to this similar dimensioning, the simulator user can find the same positions and sensations as when using a real power wheelchair which can be equipped it with the same accessories. In addition, the simulator already includes a control module based on a standard power wheelchair Power Module capable of transforming the signal from many different standard power wheelchair controllers into user commands. This way, the user can control the simulator using any desired type of power wheelchair controller such as joystick, sip-and-puff or head-array. Both modules, in brown in Figure 5.3, were already ensuring a high level of Functional Fidelity since they provide similar physical interactions and functions as a real power wheelchair.

Finally, especially 2 modules benefited from a revision in order to follow the proposed guidelines.

• The Game Engine has been separated in submodules each impacting only one fidelity dimension. Its Virtual Environment submodule determines the level of Environment Fidelity, depending on 3D models realism, scenarios and possible virtual events. Then, the Game Engine includes 2 submodules which impact Sensory Fidelity, one handling the visual display and one in charge of the auditory stimuli, both independent which allow fine-tuning and improvements.

• The Motion Engine implements two different submodules each in charge of a different type of motion feedback; vestibular and haptic. This way, one type of motion feedback can be deactivated, offering more customization possibilities.

This revised version of the simulator presented in Chapter 3 can be perfectly adapted and integrated into a development process, at any step, while remaining usable in many contexts such as training.

Extending the simulator features

While the adaptive fidelity level allows the simulator to be used in several development steps, its modular architecture has another major advantage. It allows each module to be easily replaced or enhanced without risk of degrading the virtual experience on other aspects. This way, the simulator can be extended to suit specific needs and situations.

For example, two different Physics Engine solutions have been implemented and tested. The Physics Engine is the Game Engine submodule in charge of simulating the VE's physics like collisions, interactions etc. Unity implements a basic Physics Engine called PhysX with limited features. Some more advanced Physics Engine exist such as the one called Bullet. Thanks to its modular architecture and the well-defined scope of each module, the two solutions PhysX and Bullet have been easily compared in order to select the most suitable for the simulator. PhysX was finally selected because its simplicity allows a higher computation speed.

The modular architecture also allows additional modules to be added. In order for the simulator to be able to simulate realistic complex outdoor environments, it should reinforce its Environment Fidelity by including crowd in VE (Figure 5.4). However, Unity does not feature a complete crowd simulation tool since it involves complex simulation mechanisms and software challenges. Thus, the simulator Environment Fidelity can be extended by adding an existing crowd simulation tool to the software workflow. Authors in [START_REF] Grzeskowiak | Crowd against the machine: A simulation-based benchmark tool to evaluate and compare robot capabilities to navigate a human crowd[END_REF]] present one of the latest promising new crowd simulation tool. This open-source benchmark tool allows the simulation of mobile robots into crowds. As such, it gives high control over the crowd behavior and uses standard robot controls and features. Moreover, this tool is based on ROS as a communication middleware and Unity to simulate crowd, exactly like other simulator modules. Therefore, without further developments for compatibility, this crowd simulation tool has been included inside the Game Engine, as showed in Figure 5.5. This additional module allows not only to simulate crowds but also to evaluate the robot behaviors that can be integrated, e.g. power wheelchair navigation. Of course, the crowd simulation module can be deactivated and reactivate endlessly in the same way as all other simulator modules illustrated in Figure 5.3. Thus, with this additional crowd simulation module, the simulator has a higher Environment Fidelity level and can simulate more realistic VE which can be useful in the implementation and tests of the path planner presented in Chapter 4.

Figure 5.5 -Integration of the crowd simulation module in the simulator workflow.

Prototyping a path planning algorithm

Chapter 4 has presented a new path planning algorithm called CBB-RRT* dedicated to non-holonomic robots like power wheelchairs. The chapter concluded after presenting two different designs for a dynamic version of the algorithm, capable of avoiding moving obstacles. Not only their designs were inspired by several visualizations made possible by the simulator such as Figure 5.6, but it is easy to imagine how the simulator, in its different levels of fidelity, can be useful at different steps of development. Indeed, first implementations will be tested using variable Environment Fidelity simulators only to ensure that it works as intended. Then, as the development progresses, the simulated situations will have to be more and more complex, ecological and realistic, reinforcing this Environmental Fidelity as well as the Sensory Fidelity and Functional Fidelity in order to test the algorithm in almost real conditions of use. Simulators with high Functional Fidelity will also allow to test this algorithm compatibilities with other smart power wheelchair solutions and algorithms upstream of an implementation onto a real power wheelchair. Finally, a simulator with a level of fidelity as high as possible will allow us to conduct studies and experiments with end-users and therapists in order to ensure the relevance of the algorithm implementation.

Discussion

This section discusses limitations of our proposed simulator fidelity model in Subsection 5.4.1 and the overall power wheelchair simulator design in Subsection 5.4.2.

Simulator fidelity model

The proposed simulator fidelity model has proven to be useful in the process of designing a simulator as a development tool. In particular, it allows a finer identification of the module scope and delimitations. However, the model is only theoretical and limited in its use to subjective evaluations. Aside from relative topics researches like SoP, realism and immersions, at this stage, no study specific to this model has been conducted to validate its consistency. To move towards more objective analyses, mathematical models to quantify each dimension and measurement techniques have to be found.

Nevertheless, the proposed fidelity model allows to precisely differentiate the concept of "simulator fidelity" from the "simulation fidelity". It also allows to subjectively categorize or position a simulator relatively to the literature regardless of the application context by providing a multidimensional and dimension independent scale.

VR Power Wheelchair Simulator

Even though the proposed simulator can reach high level fidelity in the 3 dimensions, it still presents limits to be discussed. First, our simulator allows to reach a high level of Functional Fidelity thanks to an innovative mechanical platform. However, its limited motion platform, structural complexity and relatively high cost have to be considered. Second, the levels of the other two fidelity dimensions are considered high, although they can still be improved. Indeed, all the sensory modalities stimulated by a real power wheelchair driving experience are not fully stimulated by the simulator. It is the case of the sense of smell, of the feeling of embodiment or even of the auditory feedback which is included in our workflow but not fully exploited yet. Moreover, vestibular and haptic stimuli are difficult to reproduce due to technological limitations and would require further work. Finally, the environment fidelity is still very limited by the current computer power, 3D rendering techniques, virtual physic engines and network efficiency, which all represent complete and complex research domains.

Nevertheless, the overall idea of using an adaptive fidelity simulator could benefit other industrial domains or robotic projects. Indeed, in many projects, developers are slow to test their tools or to have them tested by the main end-users, which can lead to delays, costs, errors and especially failures. The revised simulator is then a perfect tool to early integrate, throughout a project, the opinion of users and experts and recenter development around the end-user, from smart solutions to smart solution designs, in an almost Agile perspective.

Conclusion

This chapter has presented guidelines to design an adaptive fidelity simulator before applying them to the VR based power wheelchair simulator presented in Chapter 3. The particularity of an adaptive fidelity simulator is that it can be adapted to any contexts thanks to its modular design based on a new simulator fidelity model. In particular, such simulator can be easily used at any development process step as a validation, testing or evaluation tool.

Applied to the context of power wheelchairs, using a VR based simulator throughout the complete design and development process could profoundly ease collaboration with regular power wheelchair users. This way, end-users expectations and needs would be in the center of new power wheelchair solutions considerations which constitutes one step closer to smart user-centered design.

Conclusion and Future Works

Conclusion

The primary objective of this thesis was to find solutions to enhance power wheelchair navigation inside every type of environments, from simple indoor corridors to complex and crowded outdoor public spaces. Power wheelchair navigation is the result of the driver's skills combined with power wheelchairs "intelligence". Thus, this thesis has addressed those both navigation aspects as pictured in Figure 6 On one hand, a VR based multisensory power wheelchair simulator has been proposed in Chapter 3. This simulator was first designed as a training tool to improve learning and thus navigation in complex environments. Although many simulators already exist with effective skill transfer as detailed in Chapter 2, the presented simulator easily stands out from the literature thanks to the various innovations it incorporates. In particular, its 4 degrees of freedom motion platform generates natural and realistic vestibular and haptic feedback, similar to real power wheelchair navigation motion feedback and in close correlation with virtual motion. As such, immersion and realism are enriched ensuring a high Sense of Presence thus a better skill transfer and training efficiency. Moreover, stimulating additional sensory modalities to the visual in a carefully synchronized manner reduces the cognitive mismatches responsible for Cybersickness. This way, as our pilot and clinical studies have confirmed, the simulator generates high Sense of Presence and low Cybersickness even in a clinical context. In addition, the simulator modular software architecture and the motion platform design, electrically and mechanically compliant with any standard power wheelchair accessories, allow the simulator to be adapted to any training context and user needs. Thus, the presented simulator allows an effective, comfortable and personalized training and rehabilitation. Outside the power wheelchair domain, the simulator and the different results presented in this chapter remain valid and usable in other projects. In particular, every VR based simulator could benefit from additional sensory stimuli such as vestibular feedback or haptic feedback. Indeed, vestibular and haptic feedback as additional information should be of interest in domains like robot teleoperation and telepresence such as in [START_REF] Giordano | Visual-vestibular feedback for enhanced situational awareness in teleoperation of UAVs[END_REF]. It could reinforce immersion of teleoperation systems [START_REF] Cambuzat | Immersive Teleoperation of the Eye Gaze of Social Robots Assessing Gaze-Contingent Control of Vergence, Yaw and Pitch of Robotic Eyes[END_REF]] and enhance the quality and precision of maneuvers for real robot experienced operators as they will retrieve realistic sensations.

On the other hand, some people have complex disabilities that result in inabilities almost impossible to compensate through training. Other solutions such as smart power wheelchairs are to be considered to allow them to correctly and safely drive a power wheelchair. As presented in Chapter 1, smart power wheelchairs are power wheelchairs equipped with computer based systems able to compensate for user inabilities. In particular, autonomous navigation smart systems allow people with more or less driving difficulties to travel through complex environments like outdoor environments. One key step of autonomous navigation workflow is the path planning step which consists of the autonomous generation of safe trajectory for a robot to follow. Chapter 4 has presented a new local path planning algorithm, dedicated to power wheelchairs. This algorithm focuses on mechanical constraints and usage context of smart power wheelchairs thus allowing them to generate more comfortable and safe trajectories to improve their navigation.

The general feeling resulting from both contributions is that improving power wheelchair navigation is a complex and difficult task. Indeed, it involves many areas of expertise, requires many skills and must address many constraints since each enhancement should not be at the expense of another navigation property. In addition, as disability is a condition resulting from many possible causes, each power wheelchair user has his own needs and expectations. This observation is in contrast to reviewed power wheelchair related projects that seem to be mostly disconnected from the users. It seems that even power wheelchairs themselves are not really adapted to "classic" industrial development methods nor to the economy of our society which favors genericity. This is why, in addition to finding innovative solutions such as the many examples of smart power wheelchairs, it is important to design new methods and tools to develop them. Indeed, power wheelchair related projects are lacking smart design and development methods and tools to accompany developments and make them more relevant, more flexible and faster. This way, more time and means could be invested in exploring more specific innovative solutions such as control paradigms and interaction devices, driven by user needs. Thus, inspired by those issues and the contributions outcomes, the Chapter 5 has presented a revised version of the VR-based power wheelchair simulator. This enhanced version allows the simulator to be used throughout the complete power wheelchair innovations design and development processes, allowing them to be tested and tried out in any virtual situation. This way, researchers can investigate the relevance, limitations and benefits of a solution upstream, well before its actual development, and in close collaboration with users.

Future works

Both presented contributions, the non-holonomic local path planning algorithm and the VR based power wheelchair training simulator, open the way to many short-term and long-term research projects.

Firstly, as discussed at the end of Chapter 4, in the long term, the local path planner algorithm could be improved, especially its evaluation and heuristic methods. Furthermore, it is yet to be implemented in many different global path planning algorithms to further investigate its limits and explore its combination with other algorithms. In addition, the method consisting of joining 2 Cubic Bézier curves in a G2continuous way could reveal itself useful in other domains such as computer-aided design. In the same way, the presented global path planner CBB-RRT*, implementing the local path planner and inspired from RRT*, could widely be optimized and enhanced since its current version was only used as a comparison control with the RRT* algorithm. For example, two dynamic versions of the CBB-RRT* algorithm have been proposed in Chapter 5, and are scheduled for implementation. Based on a dynamic CBB-RRT* version, the development of a complete shared control smart power wheelchair by combining it with other innovative algorithms like the ones from the ADAPT project is planned in a short-term work [RAM2021].

Regarding the VR-based power wheelchair training simulator, while its efficiency in terms of SoP, skill transfer and comfort are convincing, the overall discomforts it generates within long exposure prevent its use in restricted contexts such as clinical training and rehabilitation. In particular, although moderate, the Cybersickness felt on average is still too high to work with sensitive or fragile people as people with disabilities can be. Thus, many improvements and studies are already ongoing to enhance the simulator quality of experience, especially clinical studies with regular power wheelchair users and people with disabilities. The pilot and clinical studies presented in Chapter 3 have already established that adding sensory stimuli to the visual is an effective way to improve the quality of experience. As such, in the long run, methods to compute motion feedback will be refined to perfectly synchronize each sensory stimuli and reduce Cybersickness. In parallel, multiple studies will investigate ways to further develop other sensory feedback such as visual and auditory.

Nonetheless, the simulator has already evolved a lot since its first day and especially in its application scope and nature. It has moved from an innovative training tool to an adaptable development assistive tool as presented in Chapter 5. Indeed, working on both contributions has broadened our vision of power wheelchair related solutions development and has revealed its major flaws. In particular, power wheelchair industry and research are sorely lacking methods and tools adapted to power wheelchair domain to better include users in development and design processes as well as better address their need for adaptation. The thesis participation, by imagining a powerful assistive development tool through the VR based power wheelchair simulator, opens the way toward smart power wheelchair design and developments.

As such, following this thesis and the related European project ADAPT, we could imagine numerous research axis with the long-term objective of elaborating a complete power wheelchair related solutions' development method more oriented on user and specific needs. For example, it would be useful to develop a method, based on the simulator, for the therapists, to assess the level of power wheelchair driving of a user. Such method would guide clinicians in developing a customized virtual training program if possible. Another research axis could focus on the development of a detailed smart power wheelchair development process, inspired by agile developments methods and based on the intensive use of the simulator. This process could then be used in the development on our own user-centered smart power wheelchair based on ADAPT related outcomes as mentioned earlier. Abstract: Mobility is the basis for an active and comfortable life, especially in terms of independence, social activities and professional career. As such, the loss of mobility is a major problem frequently experienced by people with disabilities. Over the years, many assistive devices have been developed to help these people maintaining a certain degree of mobility, with the most used being the power wheelchair. However, despite their efficiency in regaining mobility, power wheelchairs appear as a mixed blessing as they are hard to access and hard to use. Driving a power wheelchair is a combination of the driver's skills and the wheelchair's onboard intelligence. Thus, this thesis builds on these two research axes to propose ideas and user-centered solutions to facilitate and improve power wheelchair navigation in complex situations. In particular, one of the contributions consists in a power wheelchair driving simulator able, thanks to virtual reality, to simulate any situation. This simulator can be used for adapted driving training, but also for the development of smart power wheelchairs related solutions such as the second contribution which consists in a comfortable path planner. In fact, it paves the way for intelligent designs of power wheelchair navigation solutions.

  Figure A.1 -Simulateur de fauteuil roulant électrique basé sur la RV : un outil de formation, de réadaptation, de conception et de développement.

Figure A. 2 -

 2 Figure A.2 -Répartition par âge dans la population américaine des civils en situation de handicap en 2014 rapportée de [Kraus 2015].

Figure

  Figure A.3 -Axes de recherche de la thèse

Figure 1 -

 1 Figure 1 -VR based power wheelchair simulator : a training, rehabilitation, design and development tool.

Figure 2 -

 2 Figure 2 -Age Distribution in the US Population of Civilians with Disabilities in 2014 reported from [Kraus 2015].

Figure 3 -

 3 Figure 3 -Thesis workstream.

Figure 1 . 1 -

 11 Figure 1.1 -Three examples of power wheelchair structure innovation.

Figure 1 . 2 -

 12 Figure 1.2 -Simplified standard power wheelchair control chain.

Figure 1 .

 1 Figure 1.3 -Simplified smart power wheelchair control chain. Dashed arrows refer to potential data flow.

Figure 1 .

 1 Figure 1.4 -Human aware path planning in indoor environment from [Vishnu Karakkat Narayanan 2016].

Figure 2 . 1 -

 21 Figure 2.1 -The Sensorama machine, considered as the first VR simulator [Heilig 1962].

Following

  its precursive article, Sutherland described the first Head Mounted Device (HMD) in [I. E. Sutherland 1968] as a system allowing the use of natural head movements to view VE, pictured in Figure2.2 HMD consists of a headset tracked by computer systems which display the VE from a first-person point of view while visually obscuring the real world. However, as HMD consists of screens that are very close to the eyes, they might induce discomforts[START_REF] Fuchs | Les casques de réalité virtuelle et de jeux vidéo[END_REF]].

Figure 2 . 2 -

 22 Figure 2.2 -The first Head Mounted Device (HMD) imagined by Sutherland in [I. E. Sutherland 1968].

  (a) Immersive Room example. (b) HTC Vive headset, controllers and infrared stations.

Figure 2 .

 2 Figure 2.3 -Two types of display interface commonly used.

Figure 2 . 1 Figure 2

 212 Figure 2.4 -The Immersia Immersive Room in Rennes, one of the largest VR research platforms in the world [Grani et al. 2014].1

Figure 2 .

 2 Figure 2.6 -Sankey diagram from [Chang, H. T. Kim, and Yoo 2020] illustrating the variety of research exploring Cybersickness content-related factors.

  (a) ViEW simulator from [Morere et al. 2018]. (b) Simcadrom simulator from [Hernandez-Ossa et al. 2020].(c) VR-SIM2 simulator from[START_REF] Kamaraj | Interrater Reliability of the Power Mobility Road Test in the Virtual Reality-Based Simulator-2[END_REF]].

Figure 2 .

 2 Figure 2.7 -Three examples of existing power wheelchair simulators.

  Figure 3.1 -The proposed power wheelchair simulator in Immersia.

Figure 3 . 2 -

 32 Figure 3.2 -The proposed power wheelchair simulator used with a screen.

  Figure 3.4 -Motion axes of a power wheelchair (wc).

  Figure 3.5 -Illustration of the 4 degrees of freedom of the simulator (in orange) related to the fixed reference frame (in blue).

Figure 3

 3 Figure 3.6 -Overall simulator workflow with examples of compliant devices.

Figure 3

 3 Figure 3.7 -Implemented architecture with examples of devices compliant with the simulator.

  Simulator in Immersia with Rennes 3D scene -Courtesy of Rennes Metropole. (c) Simulator in Immersia with PSH experimental room 3D scene.

Figure 3 . 8 -

 38 Figure 3.8 -Power wheelchair simulator first implementation usage example.

  (a) Rennes virtual environment.(b) Real place picture.

Figure 3 . 9 -

 39 Figure 3.9 -Virtual replication of Rennes urban area.

Figure 3 .

 3 Figure 3.10 -Illustration of feedback motion platform with rotation axes.

Figure 3 .

 3 Figure 3.13 -Top view of the path the participants had to complete in both experimental conditions.

  Move along arrow direction Move along arrow direction -slight turn Move along arrow direction -sharp turn Pause on the cross and continue forward Turn 180 degrees and go backward Arrival -park inside rectangle

  3.14). The questionnaire items were presented in their French-validated versions to our participants, but for readability purposes we provide their English-validated equivalent here. For the IVEQ, we indicate the item number used in the French version of the questionnaire [Tcha-tokey 2018], and the item number used in its English version [Tcha-Tokey et al. 2016].

Figure 3 .

 3 Figure 3.14 -Reported ratings showing significant differences between C V and C M . Scales are displayed in vertical axis.

Figure 3 .

 3 Figure 3.15 -Power wheelchair simulator within a clinical context.In order to evaluate the overall quality and efficiency of the simulator in a clinical context, we conducted a second study with people with disabilities and with haptic and vestibular feedback. The presented study aims then to provide a first overview of user performance comparison within a power wheelchair navigation task between VR and real conditions as well as to evaluate the Quality of Experience (QoE) provided by our simulator in terms of SoP and Cybersickness in a clinical context. The first subsection 3.3.1 clarifies the study objectives and hypotheses. Subsection 3.3.2 details the study apparatus. Following subsections 3.3.3 and 3.3.4 respectively presents the study procedure and participants. Then, results presented in subsection 3.3.5 allow comparisons between real and virtual user performances and evaluations of the QoE provided by the simulator in terms of SoP and Cybersickness. Finally, results are discussed and guidelines are drawn for future work in subsection 3.3.6. This section resulted from a research project published in [VR2021].

Figure 3

 3 Figure3.17 -Flowchart of user study procedure. Each configuration of condition nature and order has its own color.

Figure 3 .

 3 Figure 3.18 -Real circuit number 2 designed by clinicians.

Figure 3 .

 3 Figure 3.19 -Virtual circuit number 3 designed by clinicians.

  Condition C r 2 vs C v 2 .

  Circuit completion time in virtual condition C

  Circuit completion time in real condition C r (C r 1 ∪ C r 2 ).

Figure 3 .

 3 Figure 3.21 -Circuit completion time comparison between first passage P 1 and second passage P 2 for both conditions C v and C r .

Figure 3 .

 3 Figure 3.23 -SSQ and VRSQ correlated factors. Factors are reported on x-axis. SD stands for Standard Deviation. Each value inside a disc represents the correlation coefficient r. The color indicates positive (blue) or negative (red) correlation.

  Figure 4.1 illustrates path planning step position inside a simplified autonomous navigation workflow.

Figure 4 . 1 -

 41 Figure 4.1 -Path planning step in a simplified autonomous navigation workflow.

Figure 4 . 2 -

 42 Figure 4.2 -RRT workflow which has the advantage of being simple and efficient.

  Figure 4.3.

Figure 4

 4 Figure 4.3 -The initial curvature value at t 0 = 0 depends on other control point positions. The Cubic Bézier curve is in blue and its three first control points are denoted P 0 , P 1 and P 2 .

Figure 4

 4 Figure 4.4 -Default state connection case with P(t p ) a C-Shaped Bézier Curve in blue, s candidate an accessible state and s new the new state to connect.

  Figure 4.5 -Default case solution and its curvature profile. Vertical axis gives curvature κ(t) and horizontal axis gives parameter t. In this solution, t link = 0.4 i.e. P(0.4) = S link .

  (a) C-Shape P curve, t link = 0.5. (b) C-Shape P Curve, t link = 0.5. (c) S-Shape P Curve, t link = 0.2. (d) S-Shape P Curve, t link = 0.7.

Figure 4

 4 Figure 4.6 -Both S and C Cubic Bézier shapes P Curve cases and arbitrary set t link value. Curve curvature direction, sign and value are represented by green normals.

Figure 4

 4 Figure 4.7 -S-Shape P Curve with t link = 0.4 producing an invalid solution.

Figure 4 . 8 - 8 s

 488 Figure 4.8 -RRT* simplified workflow.

  (a) RRT* in a simple environment. (b) CBB-RRT* in a simple environment.(c) RRT* in a complex environment.(d) CBB-RRT* in a complex environment.

Figure 4

 4 Figure 4.9 -RRT* and CBB-RRT* with η = 4.0, N = 2000, κ max = 1.0. Red triangle represents the start state and its direction and red circle represents the goal. Blue lines represent complex environment solution paths.

Figure 4 .

 4 Figure 4.10 -Path curvature profile of the solution visible in Figure 4.6.(d). Vertical axis gives curvature κ(t) and horizontal axis gives parameter t.

  Figure 4.11 -Example of CBB-RRT* run in a crowded VE with moving obstacles as static obstacles.

  Figure 5.1 -3 main development steps with an adaptive fidelity VR based simulator as an assistive development tool.

Figure 5 . 2 -

 52 Figure 5.2 -Applying guidelines to a VR based architecture.

Figure 5

 5 Figure 5.3 -Adaptive fidelity VR based power wheelchair simulator architecture. Each module impacts only one simulator fidelity dimension. Each module box color correspond to fidelity dimension color.

Figure 5

 5 Figure 5.4 -First person view from a virtual power wheelchair of a crowded virtual environment.

Figure 5

 5 Figure 5.6 -Example of CBB-RRT* run in an empty VE representing a complex outdoor space from Rennes city.

  .1.

Figure 6 . 1 -

 61 Figure 6.1 -Thesis workstream and contributions

Titre:

  Navigation en fauteuil roulant électrique : De la simulation en réalité virtuelle vers des conceptions intelligentes réelles Mot clés : Réalité Virtuelle, Fauteuil Roulant Electrique, Simulateur, Navigation Résumé : La mobilité est la base d'une vie active et confortable, notamment en termes d'indépendance, d'activités sociales et de carrière professionnelle. Ainsi, la perte de mobilité est un problème majeur fréquemment rencontré par les personnes en situation de handicap. De nombreux dispositifs d'assistance ont été mis au point pour aider ces personnes à conserver un certain degré de mobilité, le plus répandu étant le fauteuil roulant électrique. Cependant, malgré leur efficacité, les fauteuils roulants électriques ne font pas l'unanimité car ils sont difficiles d'accès et difficiles à utiliser. La conduite d'un fauteuil roulant électrique résulte de la combinaison des compétences du conducteur avec l'intelligence embarqué du fauteuil. Ainsi, cette thèse s'appuie sur ces deux axes de recherche pour proposer des idées et des solutions centrées-utilisateurs afin de faciliter et d'améliorer la navigation en fauteuil roulant électrique dans des situations complexes. En particulier, l'une des contributions consiste en un simulateur de conduite de fauteuil roulant capable, grâce à la réalité virtuelle, de simuler n'importe quelle situation. Ce simulateur peut être utilisé dans le cadre de programmes adaptés d'entraînement à la conduite mais aussi pour le développement de fauteuils roulants et algorithmes intelligents comme la seconde contribution, un algorithme de planification de chemin confortables. De fait, cette thèse ouvre la voie à des conceptions intelligentes de solutions de navigation en fauteuil roulant électrique. Title: Power Wheelchair Navigation : From Virtual Reality Simulation Towards Real Smart Designs Keywords: Virtual Reality, Power Wheelchair, Simulator, Navigation

Table of Contents

 of Smart power wheelchair categories . . . . . . . . . . . . . . . . . . . 43 1.2.3 Autonomous and semi-autonomous navigation . . . . . . . . . . . . . 44 1.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2 State of the art : Virtual Reality based power wheelchair simulation 49 2.1 Virtual Reality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Cybersickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Simulator Fidelity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Power Wheelchair VR Simulation . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Training efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Addressing Sense of Presence (SoP) . . . . . . . . . . . . . . . . . . . 2.2.3 Addressing Cybersickness . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Beyond training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.3.2 Proposed Local Path Planner . . . . . . . . . . . . . . . . . . . . . . . 113 4.4 Cubic Bézier Based RRT* (CBB-RRT*) . . . . . . . . . . . . . . . . . . . . . 118 4.4.1 RRT and RRT* principles . . . . . . . . . . . . . . . . . . . . . . . . 119 4.4.2 CBB-RRT* algorithm and rewiring strategy . . . . . . . . . . . . . . . 119 4.4.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.5.1 Usability and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.5.2 Optimization ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 4.5.3 Dynamic version design . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 5.4.1 Simulator fidelity model . . . . . . . . . . . . . . . . . . . . . . . . . 139 5.4.2 VR Power Wheelchair Simulator . . . . . . . . . . . . . . . . . . . . . 139 5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 6.2 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Sankey diagram from [Chang, H. T. Kim, and Yoo 2020] illustrating the variety of research exploring Cybersickness content-related factors. . . . . . . . . . . 2.7 Three examples of existing power wheelchair simulators. . . . . . . . . . . . . 3.1 The proposed power wheelchair simulator in Immersia. . . . . . . . . . . . . . 3.2 The proposed power wheelchair simulator used with a screen. . . . . . . . . . 3.3 Power wheelchair simulator proposed in [Devigne, Babel, et al. 2017]. . . . . . 3.4 Motion axes of a power wheelchair (wc). . . . . . . . . . . . . . . . . . . . . . 3.5 Illustration of the 4 degrees of freedom of the simulator (in orange) related to the fixed reference frame (in blue). . . . . . . . . . . . . . . . . . . . . . . . . .16 Real setup with Quickie Salsa M2 power wheelchair. . . . . . . . . . . . . . . 3.17 Flowchart of user study procedure. Each configuration of condition nature and order has its own color. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.18 Real circuit number 2 designed by clinicians. . . . . . . . . . . . . . . . . . . 3.19 Virtual circuit number 3 designed by clinicians. . . . . . . . . . . . . . . . . . 3.20 Mean circuit completion time for first condition (C r 1 vs C v 1 ) and second condition (C r 2 vs C v .21 Circuit completion time comparison between first passage P 1 and second passage P 2 for both conditions C v and C r . . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.22 USE score means and standard deviations by criterion. . . . . . . . . . . . . . 98 3.23 SSQ and VRSQ correlated factors. Factors are reported on x-axis. SD stands for Standard Deviation. Each value inside a disc represents the correlation coefficient r. The color indicates positive (blue) or negative (red) correlation. . . . . . . . . 100 3.24 IPQ score means and standard deviations by criterion i.e. General Presence (GP), Involvement (Inv), Realism (Real) and Spatial Presence (SP). . . . . . . . . . . 101 4.1 Path planning step in a simplified autonomous navigation workflow. . . . . . . 108 4.2 RRT workflow which has the advantage of being simple and efficient. . . . . . 109 4.3 The initial curvature value at t 0 = 0 depends on other control point positions. The Cubic Bézier curve is in blue and its three first control points are denoted P 0 , P

	2.6
	List of Figures	15
	List of Tables Résumé en Français 4 A smart power wheelchair tool for path planning Conclusion and Future Works 4.1 5 Adaptive fidelity VR based simulator 6.1 Bibliography	19 21 129 141 145

Introduction: Power wheelchair and social outcome 31 Mobility issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Power wheelchair challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1 State of the art : Smart Power Wheelchairs 39 1.1 Power Wheelchair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1.1.1 Power wheelchair structure . . . . . . . . . . . . . . . . . . . . . . . . 40 1.1.2 Power wheelchair control chain . . . . . . . . . . . . . . . . . . . . . 40 1.2 Smart power wheelchair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 1.2.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 1.2.2 2.1.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.1.2 Sense of Presence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.1.3 3 High fidelity Virtual Reality based power wheelchair simulator 3.1 Simulator design and development . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Simulator requirements . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Multisensory design . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Evaluation of the Vestibular feedback impact: pilot user study . . . . . . . . . . 3.2.1 Pilot user study objectives and hypothesis . . . . . . . . . . . . . . . . 3.2.2 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Clinical usability evaluation through a clinical user study . . . . . . . . . . . . 3.3.1 Clinical user study objectives and hypotheses . . . . . . . . . . . . . . 3.3.2 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.5 4.2 Path planning and related works . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Cubic Bézier Based Local Path Planner . . . . . . . . . . . . . . . . . . . . . 45.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.2 Adaptive fidelity simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.2.1 Simulator fidelity model . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.2.2 Adaptive fidelity simulator design guidelines . . . . . . . . . . . . . . 134 5.3 Adaptive fidelity power wheelchair simulator . . . . . . . . . . . . . . . . . . 135 5.3.1 Power wheelchair simulator design . . . . . . . . . . . . . . . . . . . 135 5.3.2 Extending the simulator features . . . . . . . . . . . . . . . . . . . . . 136 5.3.3 Prototyping a path planning algorithm . . . . . . . . . . . . . . . . . . 138 5.4 3.6 Overall simulator workflow with examples of compliant devices. . . . . . . . . 3.7 Implemented architecture with examples of devices compliant with the simulator. 3.8 Power wheelchair simulator first implementation usage example. . . . . . . . . 3.9 Virtual replication of Rennes urban area. . . . . . . . . . . . . . . . . . . . . . 3.10 Illustration of feedback motion platform with rotation axes. . . . . . . . . . . . 3.11 The high-fidelity power wheelchair simulator, composed of an HMD for visual immersion, a joystick to control the virtual power wheelchair, and a vestibular feedback platform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.12 Participant point-of-view during trials. The black part in the bottom-right corner corresponds to the arm of a virtual wheelchair, which is spatially co-located with the real joystick and vestibular feedback platform. . . . . . . . . . . . . . . . . 3.13 Top view of the path the participants had to complete in both experimental conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.14 Reported ratings showing significant differences between C V and C M . Scales are displayed in vertical axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.15 Power wheelchair simulator within a clinical context. . . . . . . . . . . . . . . 32 ). Each configuration color correspond to procedure flowchart colors in Figure 3.17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 and P 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 4.4 Default state connection case with P(t p ) a C-Shaped Bézier Curve in blue, s candidate an accessible state and s new the new state to connect. . . . . . . . . . 115 4.5 Default case solution and its curvature profile. Vertical axis gives curvature κ(t) and horizontal axis gives parameter t. In this solution, t link = 0.4 i.e. P(0.4) = S link .116 4.6 Both S and C Cubic Bézier shapes P Curve cases and arbitrary set t link value. Curve curvature direction, sign and value are represented by green normals. . .

Table 3 .

 3 2 -Existing symbols and corresponding instructions.

Table 3 .

 3 3 -Questions presenting significant differences in participant ratings between conditions C V and C M according to the Wilcoxon signed-rank test.

	Question	Label	C V M (SD) C M M (SD) p-value
	IPQ INV3	"I still paid attention to the real envi-	-0.75 (1.71) -1.56 (1.37) .041
		ronment."
	IPQ INV4	"I was completely captivated by the	0.5 (1.66)	1.56 (0.70) .026
		virtual world."
	IPQ REAL2 "How much did your experience in	1.19 (1.18) 2.12 (0.78) .032
		the virtual environment seem consis-
		tent with your real world experience
		?"
	IVEQ 1	"My interactions with the virtual en-	6.62 (1.65) 7.62 (1.41) .049
		vironment seemed natural."
	IVEQ 5	"The sense of moving around in-	6.38 (2.62) 8.31 (1.99) ≪ .01
		side the virtual environment was com-
		pelling."
	IVEQ 15	"I became so involved in the virtual	6.31 (2.52) 7.88 (1.65) .044
		environment that it was as if I was
		inside the game rather than manip-
		ulating a gamepad and watching a
		screen."
	IVEQ 61	"I suffered from vertigo during my	5.06 (2.84) 2.62 (2.89) .01
		interaction with the virtual environ-
		ment."
	TLX 6	"How insecure, discouraged, irri-	7.06 (5.76) 4.06 (4.78) .017
		tated, stressed and annoyed were
		you?"
	3.2.4.3 Sense of Presence

  Table 3.4 -Results of the different statistical tests performed on completion time T i . P 1 and P 2 represent passage 1 and 2 in a given condition. Symbols represent test hypothesis result with ! when test null hypothesis was rejected. For each test, the p-value is reported under each hypothesis.

	Wallis test	0.515	0.624
	P 1 vs P 2 , virtual	T P 1 > T P 2	T P 1 > T P 2
	Wilcoxon Signed Rank paired test	1.3e-05	2.5e-4
	P 1 vs P 2 , real	T P 1 ! ̸ = T P 2	T P 1 ! ̸ = T P 2
	Wilcoxon Signed Rank paired test	0.15	0.3

  V. W.[START_REF] Balk | Simulator Sickness Questionnaire: Twenty Years Later[END_REF]] report 2 studies with a Total Severity SSQ scores of 21.84 and 27.25 that resulted in a dropout rate of 23.23% and 71.43% respectively. According to our scores, our simulator dropout rate should lie somewhere between these two rates which are both too high to consider the frequent use of our simulator in a clinical training context.

		Circuit 2	Circuit 3
	Nausea	13.63 (16.3) 20.61 (25.49)
	Occulomotor	20.84 (22.84) 20.62 (22.48)
	Disorientation 17.9 (25.09) 27.28 (34.69)
	Total Severity 20.44 (22.45) 25.58 (25.52)
	Table 3.5 -SSQ Scores. Mean and (Standard Deviation).
		Circuit 2	Circuit 3
	Occulomotor	16.96 (16.89) 14.67 (15.83)
	Disorientation 6.43 (10.02)	9.07 (15.4)
	Total Severity 11.7 (12.58) 11.87 (13.56)
	Table 3.6 -VRSQ Scores. Mean and (Standard Deviation).

Table 5 .

 5 1 -The 3 proposed simulator fidelity dimensions with examples of respective factors. devices have been developed to provide additional sensory modalities like haptic or vestibular feedback.

		• 3D models representation
	Environment • Virtual physic engine
		• Ecological virtual situation
		• Visual feedback
	Sensory	• Auditory feedback
		• Haptic and vestibular feedback
		• Mechanical design
	Functional • Human-machine interface
		• Global workflow

http://www.irisa.fr/immersia/

http://www.clcorporation.com/

The proposed CBB-RRT* rewiring strategy is then an extension of the RRT* rewiring strategy that occurs inside Extend() method. For all near in-tree state, we verify if it has been rewired with HasBeenRewired() method. If it has been rewired, the U pdateDecendant() method is applied.

All s near children are then gathered in S children using the GetChildren(). For all children, if a new piecewise path from s near that meets all constraints can be found using the MeetConstraints() method, then the piecewise curve is updated using U pdatePiecewieCurve() method and a recursive call happens to try to rewire all descendants. Otherwise, all child descendants are gathered in S descendant using GetDescendants() method, and removed from the tree using the RemoveVertices() method and saved in a state stack S. To avoid losing too many states, all states in S will be re-processed by CBB-RRT* as a random state. Indeed, if S is not empty (Algorithm 1 Line 3), the last state from S will be used as the new random state (Algorithm 1 Line 7)

Simulation results

To show the impact of the local path planner once implemented in a RRT version, CBB-RRT* and RRT* have been executed in similar known 2D environments and compared. For both algorithms the random states came in the same order from the same uniformly sampled set. In all simulations, the maximum distance and near criterion has been arbitrary set to η = 4 and the number of iterations to N = 2000. In CBB-RRT*, the link parameter value has been set to t link = 0.5 for every C-Shaped Cubic Bézier piecewise curve and set to a multiple value of curve inflection t when S-Shaped. Within a dynamic path planning scenario, the maximum curvature value κ max can be set according to robot linear velocity to ensure respecting robot kinematic constraints and comfort standard like the ones stated in [START_REF] Solea | Trajectory planning with velocity planner for fullyautomated passenger vehicles[END_REF]. For those static simulation, the maximum curvature was arbitrary set to κ max = 1.0.