Olfa... Nils

REMERCIEMENTS

Une thèse, c'est trois ans de travail, mais aussi trois ans d'une belle aventure humaine. J'ai eu la chance de rencontrer plein de personnes extraordinaires qui ont toutes contribué d'une certaine manière à l'élaboration de cette thèse.

First of all, I would like to thank the jury for assessing and attending my PhD defence. Merci Indira Thouvenin d'avoir présidé à distance ma soutenance, and thank you Takuji Narumi for attending even with the time difference. Many thanks to Martin Hachet and Niels Henze for taking the time to read my manuscript and giving constructive and nice feedback.

Je tiens à remercier grandement mes supers encadrants de thèse sans qui tout ce travail n'aurait pas été possible. Merci tout d'abord à Anatole de m'avoir acceptée en thèse, de m'avoir encouragée jusqu'au bout à rester dans la recherche même si je choisis pour le moment une autre voie ! Un grand merci à Ferran et à Ludovic, merci pour votre esprit, pour votre gentillesse, votre aide pour le développement ou les corrections d'article. J'ai pu évoluer et apprendre énormément pendant ces trois années de doctorat grâce à cet encadrement incroyable. Vous avez su me guider pour que petit à petit je prenne confiance et puisse avoir mes propres idées. Je tiens également à remercier les deux membres de mon comité de suivi, Marie Babel et Nicolas Mollet, qui m'ont boostée par leurs encouragements pendant mes premières années de thèse. Merci à Elise Bannier qui a été ma mentor pendant mon début de thèse et qui a su me donner de précieux conseils. Merci à l'Inria via le Défi Avatar pour le financement de ma thèse. Les réunions de ce projet furent de grands moments d'échanges scientifiques. Je remercie également le service recherche de l'INSA Rennes, principalement Justine Gromaine et Aurore Gouin, pour leur aide et leurs réponses à mes interrogations.

Je n'aurais sûrement jamais fait de thèse si je n'avais pas découvert pendant mon stage des équipes incroyables, pleines de gens fascinants et tous si différents. Merci Hybrid, merci pour les Mardis Jeux, les soirées Among Us, les movies foodies, les pauses café. Chaque personne que j'ai pu croiser dans cette équipe a un peu contribué à cette thèse, je ne vais mentionner qu'une partie de toutes ces personnes. Un merci tout particulier à Rebecca et Etienne mes supers anciens cobureaux. C'est devenu super triste et vide quand vous êtes partis ! Je remercie évidemment Victor/Rodras pour son soutien moral en toute circonstance, mon voisin psy, mon fournisseur de peluches (le petit axolotl, Lady Gagaviota...) et de vidéos de chats. Merci à Thomas H. a.k.a. Wouf pour nos discussions, les visites avec Rakia, les relectures si utiles de mes papiers, les pilules de motivation. Merci Adrien pour le soutien moral, pour l'organisation de supers soirées en ligne qui ont sauvé le confinement de l'équipe. Merci à tout le reste de la clique : Gwendal a.k.a. la Loutre ou le stajièr, Thierry, Alexandre, Hakim, Martin, Tiffany

Introduction

Avatars and Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . immersion, in terms of body perception, performance or behaviour. As there are already several studies and applications relative to sports in VR, we use the example of a virtual tennis game in this introduction. Each direct interrelation between the different entities is illustrated by a quote from an imaginary user.

Quote 1: "This is just a fake body, it is not my real body!" First, it is necessary to investigate the relation between users and their avatar, to evaluate whether users identify with this virtual body as much as they identify with their real body. VR definitely has advantages compared to desktop video games, as it completely immerses users in terms of sensory information. VR offers new sensory information that can help users feel like they are actually the virtual character representing them. This is possible not only by using visual information, but also additional stimulation such as haptic feedback (tactile and force feedback). Inspired by the rubber-hand illusion (RHI) [START_REF] Botvinick | Rubber hands 'feel' touch that eyes see[END_REF]] which gives a synchronous tactile stimulation on a rubber hand and the hidden real hand, thus creating an illusion of owning the rubber hand, the idea emerged to use such visuotactile stimulation in VR [START_REF] Slater | Towards a digital body: the virtual arm illusion[END_REF]]. This can give the feeling of being the avatar, i.e. a sense of embodiment, even when the avatar has a different age [START_REF] Tajadura-Jiménez | Embodiment in a child-like talking virtual body influences object size perception, self-identification, and subsequent real speaking[END_REF]] or a different gender [START_REF] Slater | First Person Experience of Body Transfer in Virtual Reality[END_REF]. If this sense of embodiment is high, users believe their virtual representation is their real body, then they can act through this avatar. However, it is still not clear whether interacting with this avatar increases or decreases the sense of embodiment.

Quote 2: "It is difficult to accurately control the avatar, I missed the ball because of that."

Here we focus on the relation between the avatar perception and the interaction technique, and most specifically the impact of interaction input first. Transposing an activity like tennis into VR is not an easy task. One of the challenges to do it is for example to correctly track users' movements. Interaction techniques can use various methods to track users (e.g. controllers, cameras, inertial sensors), which all have their own advantages and drawbacks. Most of them are cumbersome, or still cause tracking losses. Also, will the user hold a real racket, or just a simple controller? All interaction input design choices might have effects on users' body perception. Indeed, when performing actions, users act through their virtual avatar. Using their avatar to perform actions might change the relationship they have with it. Acting with an avatar uses visuomotor stimulation, and studies showed that this type of stimulation can strongly give the impression of embodying this avatar [START_REF] Kokkinara | Measuring the Effects through Time of the Influence of Visuomotor and Visuotactile Synchronous Stimulation on a Virtual Body Ownership Illusion[END_REF]]. In the nineties, researchers had the opposite opinion that interacting with input devices could on the contrary create a sense of disembodiment, because input devices make users focus on these devices instead of their own body [START_REF] Davies | Osmose: towards broadening the aesthetics of virtual reality[END_REF]. In their experience "Osmose", the authors therefore privileged creating a link between users' breath and the VE, enabling users to influence the environment by their breath. This gave them a feeling of connecting to this new environment. While this is understandable considering the technical possibilities at that time, this has now evolved and input devices that use directly users' body are becoming increasingly common (e.g. detecting gestures using controllers and gloves for object manipulation [START_REF] Hayatpur | Plane, Ray, and Point: Enabling Precise Spatial Manipulations with Shape Constraints[END_REF] or using Kinect to track users' body for navigation [START_REF] Dam | A study of navigation and selection techniques in virtual environments using microsoft kinect®[END_REF]). In the current context, it is possible to imagine forms of interaction with the environment that directly use the real body as an input, thus avoiding a disembodiment but on the contrary, creating a sense of embodiment towards the virtual body used for interaction.

quickly [Pan and Steed 2019]. While being embodied in a novel body, people can perceive themselves differently, or even show different behaviours. This is called the "Proteus effect" [START_REF] Yee | The Proteus Effect: The Effect of Transformed Self-Representation on Behavior[END_REF], and it starts being investigated in relation to interaction. For example, if we keep the example of the tennis game, it was already found that users can move more if their avatar looks thinner than their opponent's during a tennis game on Nintendo Wii [Peña et al. 2016]. Another example, if the avatar resembles a stereotype of someone who can play the djembe well, then users' actual performance can be better than playing with an avatar in a suit, and this performance is correlated with the level of embodiment [START_REF] Kilteni | Drumming in immersive virtual reality: the body shapes the way we play[END_REF]. But, sometimes the avatar does not seem to impact interaction, for instance seeing a virtual representation of your hands does not improve your performance in a motor-skill task [START_REF] Ricca | Influence of hand visualization on tool-based motor skills training in an immersive VR simulator[END_REF]]. Even though avatars offer a spatial reference which helps to perceive the environment [START_REF] Draper | Exploring the Influence of a Virtual Body on Spatial Awareness[END_REF][START_REF] Mohler | The Effect of Viewing a Self-Avatar on Distance Judgments in an HMD-Based Virtual Environment[END_REF], they also sometimes hinder interaction, for example by creating occlusions [Tran et al. 2017]. Avatars are also essential as they are an important clue of what is possible in the VE, they are here to indicate to users what they can perform or not. For example, embodied in a bat [START_REF] Andreasen | What is it like to be a virtual bat?[END_REF], they can potentially fly but they probably cannot grab a 3D object. Considering the environment affordances (the actions offered by an environment) and the avatar's characteristics (e.g. anthropomorphy, realism, shape, degrees of freedom), users should be able to quickly identify possible actions. Interaction in VR should therefore be designed by thinking about the users' virtual representation, so that the appearance reveals the possible actions. Avatars can therefore have various and complex effects on interaction, depending on their characteristics, which are still not fully understood.

Motivation and Research Axes

The interest of investigating avatar-based interaction is two-fold. On the one hand, it is linked to this influence of the avatar on interaction, as studies start demonstrating that users would benefit from having better interaction possibilities with a full-body avatar [START_REF] Kilteni | Drumming in immersive virtual reality: the body shapes the way we play[END_REF][START_REF] Banakou | Virtually being einstein results in an improvement in cognitive task performance and a decrease in age bias[END_REF]. This impact of having a novel body on users' behaviour can have great applications in several domains such as education or psychotherapy. For instance, for an application against fear of heights, users could be represented by a flying superhero or a bird avatar. If users manage to easily and efficiently control their avatar and fly with it, this might help them fighting their fear. On the other Introduction hand, it is also linked to the potential contributing effect of interaction on the avatar perception. Having interaction that is compatible with full-body avatars may help to increase embodiment.

While there is therefore a great interest in investigating avatars and interaction together, the knowledge on avatar embodiment and interaction tend to evolve in parallel. There are not many studies investigating the apparent interrelations between both, which could influence the level of embodiment or the way users interact. Nevertheless, the motivations and current challenges to better understand these interrelations are numerous. This thesis aims to extend current knowledge linking the user, the avatar, and the interaction by investigating the interrelations between them. Our work focuses on three main research axes (RA).

RA1: Influence of the user's characteristics on the sense of embodiment

This axis aims to deepen the understanding of the link between the user and the avatar, i.e. the first interrelation presented with Quote 1. One motivation of this thesis is to better understand how the sense of embodiment is elicited. Even though there is a growing number of studies on the sense of embodiment, it is still a recent research topic in VR and we lack knowledge on how it is elicited. The factors investigated concern mostly the avatar's characteristics, the type of sensory stimulation or the tracking apparatus. Most studies therefore consider the sample of participants as a whole, without considering inter-individual differences. Yet, body perception is a very personal aspect, and studies often show high standard errors in the participants' level of embodiment. Researchers do not know yet why some people easily embody virtual bodies, while others seem refractory to the sense of embodiment. As individual characterictics have already been studied in VR for other aspects of user experience such as the sense of presence, it seems interesting to study such individual differences in the context of embodiment. This question will be investigated in Chapter 2 through the evaluation of whether the user's personality traits can affect embodiment. While this question investigates the unknown effect of the user's characteristics on avatar perception, it does not take the interaction into account.

RA2: Influence of the interaction technique on the sense of embodiment

This axis corresponds to Quote 2 (for interaction input) and Quote 3 (for interaction feedback), which aims to explore one aspect of the interrelations between interaction and avatar embodiment. Studies on interaction techniques often use interaction-based crite-ria such as performance or usability. Few studies investigate the sense of embodiment. Nevertheless, in the real world, exploring the environment by interacting with it is a way to know and appropriate our bodies. One component of embodiment is related to the control of the virtual body, which is deeply linked to the possibility of performing actions. When an interaction task is used in a study, it is rarely used as an experimental condition. Therefore, little is known on how the body is perceived depending on the way users interact. Several parameters can change when interacting, such as the input characteristics or the action feedback. The influence of such factors on embodiment needs to be more deeply investigated. This question will be explored in Chapter 3 where we will investigate the impact of locomotion techniques on embodiment, which had not been investigated before. Chapter 4 will focus on manipulation techniques and investigate the impact of a novel type of feedback on embodiment for the specific case of anisomorphic manipulation techniques. Also, contrary to locomotion techniques, there are already several studies on the influence of manipulation on the sense of embodiment. These works can be used to propose new methods of developping techniques more compatible with avatars. In Chapter 5, we will therefore propose design guidelines for manipulation techniques that take avatar embodiment into account.

Figure 1 -Illustration of the different research axes, linking the interaction, the user, the avatar, and the sense of embodiment (SoE).

RA3: Influence of the avatar on the interaction

We discussed in the previous section that avatars can sometimes help (e.g. by in-Introduction creasing spatial awareness) or hinder interaction (e.g. by creating occlusions), which was illustrated with Quote 4. The studies investigating such influence of avatars on interaction are recent and still rare, as simpler virtual representations were used when most of the interaction techniques were invented. As a third research axis, we decided to investigate this possible influence of the avatar on interaction more deeply. While Chapter 3 will study the impact of embodying a full-body avatar when navigating, Chapter 4 will focus on manipulation techniques and most specifically anisomorphic manipulation, and how different appearances could impact performance.

Scope and Outline

In this thesis, we investigate two domains relative to VR: interaction and avatar embodiment. We focus on fully immersive VR applications used in Head-Mounted Displays (HMD). We study avatars defined as full bodies or body parts representing users in the VE. The notion of avatar embodiment studied in this thesis is based on the definition by Kilteni et al. [2012a], which may differ from other definitions of embodiment used in the Human-Computer Interaction community for example, where it relates more on the link between interaction and the user's real body. Our work focuses on avatars viewed from a first-person perspective, but related work using third-person perspective will be mentionned. The outline of this thesis will be as follows:

Chapter 1: Related Work on Interrelations Between Avatars and Interaction

We will first introduce related work on avatar embodiment, 3D interaction, and the studies investigating the interrelations between these two domains. While a first part will mostly present the context of this thesis and important aspects of VR, the following sections will develop the notion of embodiment, the impact of avatars on interaction, and the impact of interaction on avatar perception.

Chapter 2: Understanding Individual Differences in the Sense of Embodiment

The second chapter will focus on the sense of embodiment and tackle the question of individual differences in the levels of embodiment. We will present a user study on the influence of personality traits (Big Five traits and locus of control) and body awareness on the sense of embodiment. 123 participants took part in this study. A two-minute visuomotor task was used to elicit a sense of embodiment towards the avatar. At the end of the experiment, a virtual threat was induced to observe participants' reaction.

Chapter 3: Studying the Interrelation Between Locomotion Techniques and Embodiment

In this chapter, we will explore the impact of interaction on embodiment by focusing on locomotion. We will detail a user study that we conducted exploring the influence of locomotion techniques on the sense of embodiment. Three locomotion techniques were tested: real walking, walking-in-place and head steering. Each participant used only one technique and did the experiment twice, once with a full virtual body, and once with only 3D models of the controllers.

Chapter 4: Investigating Dual Body Representations During Anisomorphic 3D Manipulation

This chapter will focus on another type of interaction, manipulation, and most specifically on anisomorphic manipulation. It aims at investigating the use of a dual virtual representation when distorting users' motion for object manipulation. Two experiments were conducted, respectively investigating two types of motion distortions (amplified motion or decreased motion). Dual body representations with different visual appearances were compared to single body representations.

Chapter 5: Designing Avatar-Friendly 3D Manipulation Techniques: Practical Guidelines

In Chapter 5, we will leverage the knowledge on manipulation techniques and avatars to propose guidelines and leads of future research. We will present these guidelines for designing "avatar-friendly" manipulation techniques compatible with avatars, based on an analysis of existing literature (presented in Chapter 1). These guidelines are classified into three categories: Input Devices, Control and Feedback. These guidelines could help VR developers designing manipulation techniques that take avatars into account.

Chapter 6: Conclusion

Finally, a general conclusion will recall the different contributions as well as draw future research perspectives.

"What I know is all quicksand"

Giant Rooks

Chapter 1

RELATED WORK: INTERRELATIONS BETWEEN AVATARS AND INTERACTION

This chapter presents the related work on the sense of embodiment and interaction in virtual reality. It first introduces the main concepts of this thesis, namely virtual reality, 3D interaction and user experience in virtual environments. Then, it focuses on the sense of embodiment and how it is defined, elicited and measured in virtual reality. Two sections develop the existing interrelations between avatars and interaction. The first one studies the impact of avatars on interaction, while the second one focuses on the impact of interaction design choices on self-avatar perception.

General Concepts

Virtual Reality

Virtual Reality (VR) is a concept that emerged during the second half of the twentieth century. The term designates a reality that is "virtual", i.e. "created by computer technology and appearing to exist but not existing in the physical world" 1 . This term became popular in the late eighties, but the concept of simulated environments started earlier, for example with the Sensorama simulator created by Morton [START_REF] Heilig | Sensorama simulator[END_REF], providing various sensory stimulations to simulate a motorcycle ride. Since then, VR hardware has evolved. The concept of VR has been placed at one end of the Milgram's Reality-Virtuality Continuum [Milgram and Kishino 1994]. On the other end of this continuum, there is the real world. VR is the opposite of the real world, as everything is simulated in it, which creates a whole new artificial world. Between both ends, there is what is commonly called mixed reality, as it is composed of a certain ratio of real elements and virtual/simulated elements. This continuum has been revisited recently [Skarbez et al. 2021b], as it was mostly focusing on visual displays while VEs can stimulate all users' senses. The new version of the continuum stipulates that perfect VR is currently an unachievable goal, and that most of the current VR applications are actually a part of mixed reality (see Figure 1.1). Several definitions of VR have been proposed. For example, [START_REF] Steuer | Defining virtual reality: Dimensions determining telepresence[END_REF] proposed a definition after analysing existing definitions: "A virtual reality is defined as a real or simulated environment in which a perceiver experiences telepresence". Here we present another definition, a technical definition, that was proposed in 2003.

Virtual reality is a scientific and technical field that uses computer science and behavioural interfaces to simulate the behaviour of 3D entities in a virtual world, which interact in real time with each other and with one or more users in pseudo-natural immersion through sensory-motor channels.

Technical definition of Virtual Reality [Arnaldi et al. 2003]

Figure 1.1 -Revisited Milgram's Reality-Virtuality Continuum by Skarbez et al. [2021b].

VR immerses users in a brand new world, a virtual world. All the components of this world can be controlled by a computer. What users see, hear, touch or smell can be controlled. This opens infinite possibilities, to experience the real world in a safe and customisable manner or to experience unrealistic worlds to stimulate our imagination. To immerse users, there are different apparatus that can be used. In this thesis we will focus on Head-Mounted Displays (HMD). Ivan Sutherland and his team created what is considered as the first HMD in 1968 [START_REF] Sutherland | A head-mounted three dimensional display[END_REF]]. Nowadays, HMD are less cumbersome and can be wireless, letting users move freely. But other types of hardware can be used such as Cave Automatic Virtual Environment (CAVE), an immersive room made of screens on which the VE is projected [START_REF] Cruz-Neira | The CAVE: audio visual experience automatic virtual environment[END_REF]].

Interacting with Virtual Environments

In the virtual world, there is the possibility of acting and having influence on the VE, i.e. interacting with the environment. The user is able to perform actions and the environment responds with feedback. The actions that can be performed are in theory all the actions people perform in the real world, like walking, jumping, or grabbing, catching, pinching objects. Many techniques have tried to follow different types of knowledge of the real world, that can be classified using the Reality-based interaction framework [START_REF] Jacob | Reality-based interaction: a framework for post-WIMP interfaces[END_REF]]. This framework is composed of four categories of real-world knowledge: Naive Physics, Body Awareness & Skills, Environment Awareness & Skills, and Social Awareness & Skills. All techniques using this knowledge form a new generation of interaction techniques after the generation of desktop interfaces. We can also say that this type of interaction offers a high fidelity [McMahan 2011] to the real world, i.e. they imitate the way people interact in the real world. But in VR, people are not limited by real-life physical constraints, so they can have "superpowers", like reaching remote objects or passing through walls. These superpowers can replace realistic interaction or extend it and offer new functionalities in the virtual world.

Interaction in a VE can be modelised using an action-perception loop (see Figure 1.2). Users' input can be of various types, e.g. motion, voice, button trigger. It is transmitted to the application via input devices, treated by the environment which gives feedback thanks to output devices. The feedback can be coherent with the input. For example, a user motion can be directly mapped to a similar motion done by the user virtual representation. In this case, we talk about one-to-one mapping, or isomorphic interaction. But sometimes, a transformation is applied to the input to obtain a different feedback, thus creating distorted motion. In this case, we talk about anisomorphic interaction. The gain applied to the input is called a Control-Display gain (CD gain), as the display (feedback) is different from the user control (input). It is the gain applied to the input to compute the position of the displayed representation. It has been studied in the 2D [START_REF] Casiez | The impact of control-display gain on user performance in pointing tasks[END_REF]] and 3D contexts [START_REF] Argelaguet | A survey of 3D object selection techniques for virtual environments[END_REF]. This gain can be constant or adaptive (it varies depending on some conditions). A CD gain lower than one means the displayed motion is smaller than the real motion. A CD gain greater than one means that users' motion is amplified.

Related Work

User Input Devices

Output Devices

Avatar Figure 1.2 -Action-perception loop: the user can control the avatar thanks to the input devices, so as to interact with the VE. In response to the user's actions, the VE provides feedback perceived by the user thanks to the output devices.

After having processed the input, the VE gives feedback to users. There are various types of feedback that can be given, related to each of the five human senses: visual, auditory, haptic and more rarely olfactory and gustatory. The three first types are the most common to give feedback after an action. They can either confirm the consequences of users' actions, or just inform of the current state of the application. Without this feedback, users cannot efficiently interact with the VE [START_REF] Wingrave | Towards preferences in virtual environment interfaces[END_REF].

Interaction with the VE can take many forms. One simple and established taxonomy is the one by [START_REF] Bowman | Interaction techniques for common tasks in immersive virtual environments: design, evaluation, and application[END_REF] classifying interaction into navigation, selection, manipulation and system input. In the case of navigation, users' motions result in camera translation and rotation. Selection and manipulation let users choose objects and apply transformations to these objects (translate, rotate or scale them). System input enables users to modify parameters in an application, to access a menu or to write text. In this section, we will present previous work on selection and manipulation, as well as on navigation. We will not focus on system input, as most techniques used for system input are similar to the ones used for selection and manipulation.

Selection and Manipulation

Selection and manipulation are either separated or considered as one global type of interaction category. Selection is the action of choosing the object the user will interact with. It is composed of two phases: first, users position the selection tool on the desired target; second, they confirm the selection by clicking on a button for example. Selection techniques vary in terms of selection tools, the most used ones being a virtual hand and a ray. They can be classified using other criteria, for example the provided degrees of freedom [START_REF] Argelaguet | A survey of 3D object selection techniques for virtual environments[END_REF]. Manipulation tasks encompass all the modifications that can be done on the selected virtual object. Manipulation is often summed up to four canonical tasks: positioning, rotation, scaling, as well as selection if we consider it as a subcomponent of manipulation [START_REF] Poupyrev | 3d manipulation techniques[END_REF][START_REF] Bowman | 3D User Interfaces: Theory and Practice[END_REF]]. Numerous manipulation techniques have been proposed in order to cope with the complexity of 3D manipulation [Mendes et al. 2019]. Selection and manipulation can be anisomorphic. The CD gain can be lower than one to provide a higher control for precise positioning [START_REF] Frees | Precise and rapid interaction through scaled manipulation in immersive virtual environments[END_REF]. It can also be greater than one to provide higher speed of manipulation when precision is not crucial, or to reach remote objects [START_REF] Poupyrev | The Go-Go Interaction Technique: Non-Linear Mapping for Direct Manipulation in VR[END_REF]. Creating distorted motion by modifying the CD gain can also be used to provide haptic feedback, to lead the user to a physical prop [START_REF] Kohli | Redirected touching: The effect of warping space on task performance[END_REF][START_REF] Azmandian | Haptic Retargeting: Dynamic Repurposing of Passive Haptics for Enhanced Virtual Reality Experiences[END_REF]. This technique applies an offset to the virtual hand so the user will reach the real tangible object.

Locomotion

Locomotion techniques enable users to translate and rotate in the VE. Numerous studies talk about navigation, which is more specific to task involving wayfinding. Locomotion in VR has been widely studied [START_REF] Zayer | Virtual Locomotion: A Survey[END_REF], and many techniques have been created to tackle the problem of limited physical space, like walking-in-place [START_REF] Slater | Taking steps: the influence of a walking technique on presence in virtual reality[END_REF] or teleportation [START_REF] Bozgeyikli | Point & Teleport Locomotion Technique for Virtual Reality[END_REF]]. Some of these techniques use virtual movements (i.e. virtual steering) or physical motions but with lower interaction fidelity (e.g. walking-in-place), i.e. which are not similar to the way people interact in real life [McMahan et al. 2012].

As for manipulation, navigation can be anisomorphic. A CD gain greater than one can be used to travel a longer distance [START_REF] Interrante | Seven league boots: A new metaphor for augmented locomotion through moderately large scale immersive virtual environments[END_REF] or to increase rotation to reorient the user towards a certain direction [START_REF] Steinicke | Estimation of detection thresholds for redirected walking techniques[END_REF]].

Several taxonomies have been proposed to classify all the proposed locomotion tech-niques. The first taxonomies were mainly focused on the implementation aspects, like the velocity selection, the target selection [START_REF] Bowman | Travel in immersive virtual environments: an evaluation of viewpoint motion control techniques[END_REF]]. With the growing mastery of navigation algorithms, the taxonomies have focused more on the paradigms used. [START_REF] Arns | A New Taxonomy for Locomotion in Virtual Environments[END_REF] made the distinction between physical and virtual navigation. Another taxonomy has been proposed more recently, separating locomotion techniques into four categories: room-scale-based, motion-based, teleport-based and controller-based [Boletsis 2017]. Nowadays, the tendency is to focus more on the user and its perception of locomotion [START_REF] Albert | User-centric Classification of Virtual Reality Locomotion[END_REF].

Immersion and Presence

There are various user experience criteria in VR, such as enjoyment or comfort. In this section we focus on two aspects that have been extensively explored in the VR literature: immersion and presence. Immersion is the objective level of realistic sensory modalities provided to users [START_REF] Slater | A note on presence terminology[END_REF]]. It highly depends on the different output devices used, as well as the software part. A highly immersive application provides rich sensory stimulations such as high-quality graphisms, sound and touch feedback. As VR immerses users into another alternative world, it can give them the impression of being elsewhere and not in the real world anymore. The feeling of "being there" has been called the sense of presence. Several studies investigated factors influencing the sense of presence. For example, having a virtual body can increase the sense of presence [Slater and Usoh 1993b]. Presence differs from immersion, as it does not solely depend on the apparatus but is a psychological construct in users' mind, which can vary depending on each individual mental representations. It is a reaction to immersion [START_REF] Slater | A note on presence terminology[END_REF]] and it makes users react realistically to the virtual world. Slater [2009] introduced two components to substitute the sense of presence: Plausibility (Psi) and Place Illusion (PI). Place Illusion globally corresponds to the previous sense of presence, which gives to users a similar sensation as being in a real place. Plausibility refers to the credibility of the scenario. Plausibility is high if users think the events in the virtual world are really occuring. This thesis focuses on VR, a simulated world in which users can feel like they are really situated in it and where they can interact. An important element that makes presence higher and make interaction possible is the new virtual body that is given to users.

Embodying an Avatar

In VR, users have the possibility to be represented by an avatar, i.e. virtual body parts or a full body. They can feel a sense of embodiment towards this avatar, i.e. feel like this avatar is their real body [Kilteni et al. 2012a]. In this section, we will present related work on the sense of embodiment, from its emergence to its measures, its impact on users, and the factors influencing it.

Emergence of Avatars in Computer-Mediated Technologies

With the emergence of computer-mediated technologies and the internet, people started to need ways of expressing themselves to other people online. Because communication through text was highly limited, they also quickly needed a way to show a representation of themselves to other users, to express their identity. It started with profile pictures, usually called avatars, a term that first appeared mostly in video games or novels. This term has been extended to call all types of users' representation in a VE. From video games or chat platforms to VR, these avatars are users' virtual identity. They can be customised and serve as users' proxy in the virtual world. The definition of the word avatar sometimes vary between communities and researchers. A review by [START_REF] Nowak | Avatars and computer-mediated communication: a review of the definitions, uses, and effects of digital representations[END_REF] on the different uses of the word avatar led to this definition:

An avatar is a digital representation of a human user that facilitates interaction with other users, entities, or the environment.

Definition of an avatar [Nowak and Fox 2018]

An avatar is therefore the means used to interact, with other users but also with the VE. With other users, it lets users communicate through gestures for example. It is essential for social interaction to be able to see other users and know what they are doing. For interaction with the VE, it influences users' capabilities (see Section 1.3.1.1). For example, thanks to their avatar, users can know their position in the virtual world. The avatar also represents how they want to expose themselves to other users in the case of multi-user applications. The chosen appearance can depend on the application context, it reveals both how users want to present themselves to others, and how they perceive themselves [Vasalou and Joinson 2009]. There is therefore a strong relation between users and their avatar, that has been extensively studied in several communities. Indeed, the question of the relation between users and their avatar is an interdisciplinary question, involving as much the fields of HCI (with the question of embodied interaction), than art or psychology [START_REF] Hamilton | Identifying with an avatar: a multidisciplinary perspective[END_REF]].

The Evolving Concept of the Sense of Embodiment

In VR, this relation between users and their avatar is even stronger. When using HMDs, users' visual sense is reduced to what is visible in the headset. They cannot see their real body anymore, thus being left with only a virtual representation of themselves. As their real body is hidden, people can have the illusion that their avatar becomes their real body. This illusion has been studied in VR since the nineties. First called Illusory Virtual Body Ownership (IVBO), researchers investigating this question now use more often the term sense of embodiment, defined by Kilteni et al. [2012a]. This definition decomposed the sense of embodiment into three subcomponents: the sense of self-location, the sense of agency and the sense of ownership. This proposed structure has the advantage of clearly defining three aspects of embodiment, that represent different criteria of experiencing a body as our own. The sense of ownership was the component already studied in experiments on IVBO. VR is particularly efficient at creating ownership, as other types of media have more difficulty in creating such an illusion that the body is part of our own. There is the idea of a link between the user and the avatar in this component, both on an affective and a sensory aspect: this body is a part of users' body and they receive every stimulation through this body. The sense of agency is related to control. It has been extensively studied in other domains outside VR [Pacherie 2007]. A strong sense of agency implies both identifying yourself as a cause of an action, and experiencing a logical feedback relative to a performed action. [START_REF] Jeunet | Do you feel in control? " : Towards Novel Approaches to Characterise, Manipulate and Measure the Sense of Agency in Virtual Environments[END_REF] differentiated these two aspects by calling them the feeling and judgment of agency, based on previous studies in psychology. Finally, the sense of self-location refers to the spatial location of the avatar relative to the user's actual position. The main factor influencing it is the perspective from which the avatar is seen. The sense of self-location is high when the avatar is seen from a first-person perspective (1PP), and low when seen from a third-person perspective (3PP) [START_REF] Blanke | Full-body illusions and minimal phenomenal selfhood[END_REF]. It can be also impacted by tactile stimulations to some extent [Lenggenhager et al. 2009]. This notion of self-location comes from original real-life experiments like the rubber-hand illusion (RHI), where the fake hand and the real hand were not at the same location. In VR, it is easier to have a co-located avatar when the tracking is correct. Therefore this component has created less interest in the VR community recently. There are still interesting applications in VR that can disrupt this sense, for example out-of-body experiences where the user can be placed outside the virtual body on purpose [START_REF] Bourdin | A virtual outof-body experience reduces fear of death[END_REF].

While this structure has established a common reference to all researchers in the domain, the knowledge on the sense of embodiment in VR is still limited and definitions may need to evolve in the future.

Measuring Embodiment in Virtual Reality

The research on subjective measures to the sense of embodiment has highlighted the complex interrelations between all aspects covering embodiment, and the difficulty to clearly separate them [START_REF] Roth | Construction of the Virtual Embodiment Questionnaire (VEQ)[END_REF]Peck and Gonzalez-Franco 2021]. These subjective measures often take the form of a questionnaire. Items were first inspired from questions asked for the RHI. They have evolved with the experiments becoming more and more complex, and introducing more factors and types of feedback. Nowadays there are questions on the tactile sensations for example [Peck and Gonzalez-Franco 2021]. Researchers also tried to identify objective measures that could be correlated to the sense of embodiment. As in the RHI [START_REF] Ehrsson | Threatening a rubber hand that you feel is yours elicits a cortical anxiety response[END_REF]], a threat introduced to the fake body can create a reaction if the user felt embodied. The reaction can be evaluated with physiological measures such as skin conductance response [START_REF] Armel | Projecting sensations to external objects: Skin conductance response evidence[END_REF]]. This reaction is a behaviour that was found correlated to the sense of embodiment [START_REF] Yuan | Is the rubber hand illusion induced by immersive virtual reality?[END_REF][START_REF] Zhang | Body ownership and response to threat[END_REF]. Other behavioural responses can be used as additional clues of embodiment, for example voice frequency [START_REF] Tajadura-Jiménez | Embodiment in a child-like talking virtual body influences object size perception, self-identification, and subsequent real speaking[END_REF] or movements [START_REF] Kilteni | Drumming in immersive virtual reality: the body shapes the way we play[END_REF]. Behaviour can show how much users identify with the character representing them.

Behavioural Impact of the Sense of Embodiment

These changes in behaviour and reactions are a consequence of embodying a different body. Embodiment is a powerful illusion that can have surprising cognitive effects. For example, embodying an avatar with a different skin colour can reduce implicit racial bias [START_REF] Banakou | Virtual embodiment of white people in a black virtual body leads to a sustained reduction in their implicit racial bias[END_REF]]. The avatar characteristics can influence users' thoughts and behaviour, they can start acting as someone with their avatars' characteristics would. This is called the Proteus effect [START_REF] Yee | The Proteus Effect: The Effect of Transformed Self-Representation on Behavior[END_REF]. People embodied in a child avatar can start talking with a higher pitch [START_REF] Banakou | Body ownership causes illusory self-attribution of speaking and influences subsequent real speaking[END_REF]. It can also influence users' cognitive performance when they embody an avatar looking like Einstein, and this effect is even higher for people with a low self esteem [START_REF] Banakou | Virtually being einstein results in an improvement in cognitive task performance and a decrease in age bias[END_REF]]. Another study found contradictory results, with no effect of being Einstein on cognitive performance, but an impact of the appearance of another user in the VE [Kocur et al. 2020b]. If the other user looks like Einstein, there is an increase in the cognitive performance, that may be due to a competitive behaviour. This is not a simple process and might depend on the context. Contrary to the study on cognitive performances, a study found that an avatar that looks like an artist decreases creativity compared to a look-alike avatar [START_REF] Rooij | The Creative Proteus Effect: How Self-Similarity, Embodiment, and Priming of Creative Stereotypes with Avatars Influences Creative Ideation[END_REF]. Embodying an avatar is not only about experiencing a novel appearance, it can sometimes have an impact on users' cognition.

Impact on Body Image and Body Schema

The illusion created by the sense of embodiment is related to users' own body perception. Everyone has their own mental self-representation. One common theory, the dyadic taxonomy, says that people have at least two mental body representations, generally called body image and body schema [START_REF] Gallagher | Body image and body schema: A conceptual clarification[END_REF]]. The body schema "consists in sensorimotor representations of the body that guide actions" [START_REF] Vignemont | Body schema and body image-Pros and cons[END_REF]. Contrary to body schema which does not exist apart from the environment, body image is "a conscious image or representation [...] differentiated from its environment" [START_REF] Gallagher | Body image and body schema: A conceptual clarification[END_REF]]. De [START_REF] Vignemont | Body schema and body image-Pros and cons[END_REF] stated that body image "groups all the other representations about the body that are not used for action, whether they are perceptual, conceptual or emotional". Embodying an avatar challenges users' mental representations of themselves. For [START_REF] Biocca | The cyborg's dilemma: Progressive embodiment in virtual environments[END_REF], a duel takes place in the virtual world between the physical body and the virtual body, to alter body schema. The avatar appearance can alter mental representations, but also acting through this avatar. Similarly as tools can impact body schema [Maravita and Iriki 2004], interacting through an avatar that has a different morphology like a three-arm avatar for example [START_REF] Laha | Evaluating Control Schemes for the Third Arm of an Avatar[END_REF]] can alter body schema (see Figure 1.3). Proprioceptive drift is one possible alteration of the body schema. This drift happens for example in the context of the RHI, where the real hand drifts towards the fake hand. In VR, such drift has also been observed for example with a long-arm illusion [Kilteni et al. 2012b]. When displaying a long virtual arm, participants experience a shape modification of their mental representation and feel like their real hand shifts towards the remote virtual hand. However in this study, proprioceptive drifts and ownership were not correlated, showing possible different underlying processes. It was also found that a remote virtual hand alters body schema especially when participants feel a sense of agency towards this virtual hand [START_REF] D'angelo | The sense of agency shapes body schema and peripersonal space[END_REF]. This sense of agency appears when the virtual hand movements are synchronous with the participants' ones.

Figure 1.3 -Control of an avatar with a different morphology, for example an avatar with a third arm. Image from [START_REF] Laha | Evaluating Control Schemes for the Third Arm of an Avatar[END_REF]].

Factors Influencing the Sense of Embodiment

VR enables the full control of a wide number of experimental factors, from the stimulation protocol to the appearance and morphology of users' avatar, which has resulted in a notable body of literature examining the impact of such factors on the perceived sense of embodiment. These factors can be: top-down factors, i.e. depending on users' mental representations and cognitive processes that can moderate the influence of stimulations; or, bottom-up factors, i.e. depending on the provided stimulations detected by sensory organs [Kilteni et al. 2012a]. Here we prefer a classification by external factors, depending on the VE and the avatar, and internal factors, depending on the user [START_REF] Fribourg | Contribution à l'étude des facteurs influençant le sentiment d'incarnation envers un avatar en réalité virtuelle[END_REF]]. This classification clearly separates controllable factors from factors solely depending on users.

External Factors

At the origin of virtual embodiment, there are real-world embodiment illusions such as the RHI [START_REF] Botvinick | Rubber hands 'feel' touch that eyes see[END_REF]]. In this experiment, a touch visually applied on a rubber hand that is synchronous with an experienced touch on the real participant's Related Work hand can give the illusion of owning the rubber hand. The central idea in this illusion is to deceive the brain by creating a plausible stimulation. The result of an event (a motion, a touch) must be logical in reaction to the initial event. Progressively this illusion was transposed to VR. First, IJsselsteijn et al. [2006] reproduced the RHI by projecting either the real hand or both the hand and the stimulation (with a paintbrush). A few years later, an experiment was conducted that created an illusion of owning a virtual hand, with results as strong as the RHI [START_REF] Slater | Towards a digital body: the virtual arm illusion[END_REF]. In this experiment, they used a hand-held "Wand" device, with a ball attached to it (see Figure 1.4). There was a similar virtual ball touching the virtual hand.

Figure 1.4 -First experiment in VR using visuotactile stimulation to elicit a sense of embodiment towards a virtual arm. Image from [START_REF] Slater | Towards a digital body: the virtual arm illusion[END_REF]].

In parallel, there were also studies focused not solely on the hand but on the full body. These studies started by the experiment of [START_REF] Petkova | If I Were You: Perceptual Illusion of Body Swapping[END_REF] inducing the illusion of owning a manikin body seen from a first-person perspective in a video feed. This experiment used a visuotactile paintbrush stimulation like in the RHI. A similar experiment was conducted in which subjects could see a virtual projection of either their real body or a fake body from a third-person perspective [Lenggenhager et al. 2007]. Most of these studies therefore used a visuotactile stimulation, i.e. they used an object (paintbrush, ball) to touch users' real body at the same time as the object virtual counterpart touched the virtual body. But this is not the only way to induce a sense of embodiment. The second main means to induce it is a visuomotor stimulation. In the real world, the RHI was conducted using a moving rubber hand following participants' real hand move-ments [START_REF] Kalckert | Moving a Rubber Hand that Feels Like Your Own: A Dissociation of Ownership and Agency[END_REF] and with a projection of the real moving hand [Tsakiris et al. 2006]. The same method can be used in VR, by making the avatar reproduce users' movements [START_REF] Kokkinara | Measuring the Effects through Time of the Influence of Visuomotor and Visuotactile Synchronous Stimulation on a Virtual Body Ownership Illusion[END_REF].

While visuotactile and visuomotor stimulations are the two main means of creating an embodiment illusion, there were also experiments reporting the illusion by using only a visuoproprioception stimulation, i.e. by only showing a virtual body where users' real body was located. If the virtual body was co-located with the real body and had a realistic skin tone, this was enough for the illusion to appear [Maselli and Slater 2013].

Visuomotor stimulation is currently the most used type of stimulation. It was found to be stronger than visuotactile stimulation [START_REF] Kokkinara | Measuring the Effects through Time of the Influence of Visuomotor and Visuotactile Synchronous Stimulation on a Virtual Body Ownership Illusion[END_REF]. This is to our advantage because the goal of the avatar is not to be solely observed by users, but also used to perform actions with the VE. If users perform movements in the VE, and that their avatar follows their movements, it is therefore possible to create a sense of embodiment. A recent study also found that visuomotor stimulation provokes a disembodiment faster than visuotactile stimulation [Lesur et al. 2020]. Tracking must therefore work well, as mismatches might decrease embodiment more quickly when using visuomotor stimulation. Spatial and temporal synchrony are extremely important, especially for the sense of agency [START_REF] Jeunet | Do you feel in control? " : Towards Novel Approaches to Characterise, Manipulate and Measure the Sense of Agency in Virtual Environments[END_REF]. While users can still feel in control when the offset between the action and the feedback is slightly manipulated, the sense of agency is however lost when the visual feedback becomes too obviously asynchronous [START_REF] Debarba | Self-attribution of distorted reaching movements in immersive virtual reality[END_REF]].

In addition to external factors concerning the type of stimulation, other factors were also found to affect the sense of embodiment, such as avatar appearance. Despite the fact that it is possible to feel some ownership when seeing only virtual hands and feet [START_REF] Kondo | Illusory body ownership of an invisible body interpolated between virtual hands and feet via visual-motor synchronicity[END_REF]], the avatar appearance has been shown to be of importance to maximise the ownership illusion. For example, it is usually stronger with an avatar with coherent clothes or skin tone [Maselli and Slater 2013], and potentially even higher with a personalised avatar or a self-representation [Waltemate et al. 2018;[START_REF] Gorisse | From Robot to Virtual Doppelganger: Impact of Visual Fidelity of Avatars Controlled in Third-Person Perspective on Embodiment and Behavior in Immersive Virtual Environments[END_REF]]. The sense of agency is less sensible to appearance. It can be elicited even with point-line avatars [START_REF] Wellerdiek | Recognizing your own motions on virtual avatars[END_REF]] and with virtual limbs in implausible positions [Tsakiris et al. 2006].

Internal Factors

External factors focus on different experimental conditions (e.g. stimulation, appearance, perspective), yet, they rarely consider individual differences. These individual differ-ences can be due to internal factors depending on users. While there are not many studies investigating the influence of such factors on embodiment, their influence has been more explored in studies on the sense of presence [Slater and Usoh 1993a]. In particular, personality models with different dimensions like the OCEAN model have been used in order to characterise inter-personal differences. The OCEAN model, also known as the "Big Five" personality traits, is a taxonomy of personality traits that uses common language descriptors in order to identify five personality dimensions: Openness to experience, Conscientiousness, Extraversion, Agreeableness and Neuroticism. For example, it was found that agreeableness was positively associated with spatial presence [START_REF] Sacau | The impact of personality factors on the experience of spatial presence[END_REF]]. Regarding the influence of extraversion, it was found to be positively [START_REF] Laarni | Personality-Related Differences in Subjective Presence[END_REF] or to be negatively correlated [START_REF] Jurnet | Individual differences in the sense of presence[END_REF] with presence.

In addition to the "Big Five", other personality traits that have been investigated are absorption (the disposition for having episodes of total attention that fully engage one's representational resources [START_REF] Tellegen | Openness to absorbing and self altering experiences ('absorption'), a trait related to hypnotic susceptibility[END_REF]) and dissociation (the lack of normal integration of thoughts, feelings, and experiences into the stream of consciousness and memory [START_REF] Bernstein | Development, Reliability, and Validity of a Dissociation Scale[END_REF]). Their influence on presence was studied and they were sometimes both found positively correlated with presence [START_REF] Sacau | The impact of personality factors on the experience of spatial presence[END_REF], sometimes only dissociation was associated with presence [START_REF] Murray | Absorption, dissociation, locus of control and presence in virtual reality[END_REF]] or neither of them was correlated [START_REF] Phillips | Correlations Between Physiological Response, Gait, Personality, and Presence in Immersive Virtual Environments[END_REF]. [START_REF] Kober | Personality and Presence in Virtual Reality: Does Their Relationship Depend on the Used Presence Measure?[END_REF] found that absorption was a good predictor of presence, no matter what presence questionnaire was used. Moreover, empathy is another trait which has been studied in the past, and demonstrated to be related to feeling a higher sense of presence [START_REF] Nicovich | Experienced Presence within Computer-Mediated Communications: Initial Explorations on the Effects of Gender with Respect to Empathy and Immersion[END_REF][START_REF] Sas | Presence Equation: An Investigation into Cognitive Factors Underlying Presence[END_REF]Ling et al. 2013]. Finally, the locus of control was also demonstrated to have an influence on the sense of presence. People with an internal locus believe they are in control of events, while people with an external locus believe in external influences (e.g. fate). Contradictory results were found, namely that either an external [START_REF] Murray | Absorption, dissociation, locus of control and presence in virtual reality[END_REF] or internal [Wallach et al. 2010] locus of control was improving presence depending on the study.

For the sense of embodiment, some internal factors such as body awareness [START_REF] David | Susceptibility to the rubber hand illusion does not tell the whole body-awareness story[END_REF]] and personality traits [START_REF] Jeunet | Do you feel in control? " : Towards Novel Approaches to Characterise, Manipulate and Measure the Sense of Agency in Virtual Environments[END_REF]] have been studied. However, the majority of the works addressing such internal factors have mainly focused on the RHI in the physical world. The influence of body awareness, a cognitive ability that makes us aware of our body processes, has been investigated but no correlation was found with the strength of the RHI [START_REF] David | Susceptibility to the rubber hand illusion does not tell the whole body-awareness story[END_REF]. Regarding personality and RHI, it has been found that the illusion is stronger for empathic people [START_REF] Asai | Rubber hand illusion, empathy, and schizotypal experiences in terms of self-other representations[END_REF][START_REF] Seiryte | The Empathy Quotient (EQ) predicts perceived strength of bodily illusions and illusion-related sensations of pain[END_REF]. The sense of ownership in the RHI was also found correlated with traits like the Novelty Seeking trait (from the TCI-R questionnaire) or Psychoticism (from the SCL-90-R questionnaire) [START_REF] Kállai | Temperament and psychopathological syndromes specific susceptibility for rubber hand illusion[END_REF]. Also, higher responses to the RHI have been reported for people suffering from personality or psychotic disorders: dissociative subtype of posttraumatic stress disorder (PTSD) [START_REF] Rabellino | I can't tell whether it's my hand": a pilot study of the neurophenomenology of body representation during the rubber hand illusion in trauma-related disorders[END_REF], schizophrenia [Peled et al. 2000;[START_REF] Thakkar | Disturbances in Body Ownership in Schizophrenia: Evidence from the Rubber Hand Illusion and Case Study of a Spontaneous Out-of-Body Experience[END_REF]] and schizotypal personality disorder [START_REF] Asai | Rubber hand illusion, empathy, and schizotypal experiences in terms of self-other representations[END_REF]Van Doorn et al. 2018]. Finally, recent works have started to focus on the potential role of personality traits in virtual embodiment. One example being the work of [START_REF] Jeunet | Do you feel in control? " : Towards Novel Approaches to Characterise, Manipulate and Measure the Sense of Agency in Virtual Environments[END_REF] which showed that the feeling of agency is linked to an internal locus of control.

The literature shows both a clear interest and important results regarding the influence of personality on users' sense of embodiment in the physical world. Some more recent work also revealed an influence of the locus of control, a personality trait, on the sense of embodiment in VR. This last result highlighted the potential role of individual differences in the elicitation of the sense of embodiment in VR and in this way, raised the concern of exploring deeper their possible link with the sense of embodiment in VR. For this reason, a part of this thesis (see Chapter 2) will explore this matter by investigating the potential effect of personality traits and body awareness, which are two factors varying from one person to another that can be linked to embodiment.

The Impact of Having a Virtual Body During

Interaction

In real life, the body is the means of performing actions through our motor system, and of receiving feedback through our sensory system. In VR, the avatar serves as the intermediary between the real body and the VE. It shows actions performed by users and can visually receive a feedback, as the user would receive in the real world. As we said before, there are various avatars possible, and the avatar chosen in an application can impact the way users interact.

First, an avatar affects users' perception of their capabilities and of the environment. It can also affect their perception of their own movements, even when these movements are distorted in the VE. These effects also highly depend on the coherency between the avatar and the input modality used. Finally, the avatar chosen can also impact performance, depending on the task.

Impact on Perception of Interaction Capabilities and Environment 1.3.1.1 Affordances and Environment Perception

In real life, people learn progressively which tasks they are able to do or not. From the youngest age, people learn that their hands can grab objects, but also where an object should be grabbed depending on its shape and centre of gravity. Legs can let humans walk, or step over obstacles. Arms have a limited length that do not let people grab remote objects. People use the perception of their own body to know what is feasible. In 1979, Gibson's ecological approach introduced this idea of a strong link between the environment and the human perception system [START_REF] Gibson | The Ecological Approach to Visual Perception[END_REF]]. People perceive what actions the environment offers by considering their own body abilities. In the VE, users also perceive the affordances of the environment, i.e. "the use or purpose that a thing can have, that people notice as part of the way they see or experience it"2 by taking their body into account. There are some affordances from the real world, when users can interact with some objects as they would in real life. There are also unrealistic affordances, such as superpowers offered by VR like the World-in-Miniature technique [START_REF] Stoakley | Virtual reality on a WIM: interactive worlds in miniature[END_REF], a miniaturised version of the environment that lets users move objects in this environment. Developers must be careful about affordances and design choices, as they must guide users and show them what actions are feasible or not. Users' avatar can give clues as to what is possible or not [Seinfeld et al. 2020a]. For example, the degrees of freedom offered by the avatar can limit the interaction. If users are represented by a sphere, they know they can probably translate this representation, maybe select objects by clicking on a button for example, but they will not be able to perform precise hand poses to grab objects. Also, depending on the hand appearance, people can have the impression of having a better tactile sensitivity [Schwind et al. 2018a]. The avatar, in relation to the affordances offered by the environment, tells users what they can probably do or not. It is similar to 2D desktop applications, where a cursor on a text indicates that it can be placed somewhere to add/delete some characters, or a hand cursor implies that users can drag and drop. Avatars can also be used to show extended abilities. For example, an avatar with an extendable arm can imply that users can reach remote objects [START_REF] Feuchtner | Extending the Body for Interaction with Reality[END_REF].

Also, similarly to real life [START_REF] Hall | The hidden dimension[END_REF]], the virtual body serves as a reference frame to interact with the environment. It is even more essential in VR, as users tend to show a size and distance perception bias, usually underestimating distances and object size [START_REF] Plumert | Distance Perception in Real and Virtual Environments[END_REF]. It has been demonstrated that displaying an avatar can improve these perceptions [START_REF] Mohler | The Effect of Viewing a Self-Avatar on Distance Judgments in an HMD-Based Virtual Environment[END_REF]]. In a multi-user application, the virtual body helps to understand the VE scale, but the other users' size can have more impact, especially if there are lots of users [START_REF] Langbehn | Scale matters! Analysis of dominant scale estimation in the presence of conflicting cues in multi-scale collaborative virtual environments[END_REF]. McManus et al. [2011] did not find an effect of a self avatar on distance estimation, contrary to previous works. They hypothesise that this is due to participants seeing their avatar in a mirror, which potentially decreased their sense of embodiment (because of visual differences), thus lowering the impact of cues provided by the avatar.

The avatar can also help users decide whether they can perform an action. Lin et al. [2012] showed that the presence of an avatar changed users' perception of being able to step over a pole, but had no significant influence on their decision to pass through a doorway, as recently confirmed by [START_REF] Bhargava | Comparative Evaluation of Viewing and Self-Representation on Passability Affordances to a Realistic Sliding Doorway in Real and Immersive Virtual Environments[END_REF]. However, the choice of rotating shoulders to pass an aperture and avoid collisions was found influenced by the presence of an avatar [Mestre et al. 2016]. Similarly, the avatar's gender can also have an influence on affordances, in particular in collaborative VEs. [START_REF] Buck | Interpersonal Affordances and Social Dynamics in Collaborative Immersive Virtual Environments: Passing Together Through Apertures[END_REF] studied two-person joint actions while passing through apertures, and found an effect of avatar's gender on participants' behaviour. However, these behaviours are a bit different and more complex than the ones observed in real-life.

For manipulation tasks, it was found that hands with a personalised size increase the correct estimation of object size [START_REF] Jung | Over My Hand: Using a Personalized Hand in VR to Improve Object Size Estimation, Body Ownership, and Presence[END_REF], and that this effect can also depend on the realism of the avatar's appearance [START_REF] Ogawa | Object Size Perception in Immersive Virtual Reality: Avatar Realism Affects the Way We Perceive[END_REF]. This is coherent with early results showing individual differences during manipulation of virtual objects and the importance of calibrating the experience for each individual [Wang et al. 1997]. Similarly, virtual foot size can influence affordance and environment perception. Having enlarged virtual feet affects both judgment of stepping over and estimation of the width of a virtual gap [START_REF] Jun | Big foot: Using the size of a virtual foot to scale gap width[END_REF]. For tasks involving full-body motions, the avatar also helps to estimate users' height compared to different types of obstacles. For example, having a full virtual body helps users know whether they can step off a ledge or pass under a pole [START_REF] Bodenheimer | The Effect of Avatar Model in Stepping off a Ledge in an Immersive Virtual Environment[END_REF]. In this between-subjects study, they tried three virtual representations: no avatar, line avatar and full-body gender-matched avatar. They found a significant difference between the no avatar condition and both line and full-body avatar, with people having more difficulties to estimate their abilities without an avatar. The fact that there was no significant different between line and full-body avatars supposes that avatar realism is not very important for affordance judgment, in the case of stepping off a ledge.

Visual Occlusions

Occlusions often serve as a depth cue, helping people compare depth between objects [Ono et al. 1988]. However, the avatar can occlude virtual objects and therefore hinder interaction. The more body parts are represented, the higher the risk of this occurring. This can prove critical in applications providing only visual feedback contrary to real life, where other types of feedback (haptic, auditory) can prevent people from being bothered by occlusions. For example, a study found that users perform better with a virtual hand than with a virtual whole arm [Tran et al. 2017]. The authors hypothesised that this is due to the whole arm hiding the scene more and creating occlusions. This is also consistent with the study by [START_REF] Argelaguet | The role of interaction in virtual embodiment: Effects of the virtual hand representation[END_REF], where users performed better with skeleton hands than with realistic hands which generate more occlusions (see Figure 1.5).

In order to minimize occlusions, some potential solutions have been considered. For example, the avatar's hands can become transparent [START_REF] Zhai | The "Silk Cursor": Investigating Transparency for 3D Target Acquisition[END_REF][START_REF] Buchmann | Interaction with Partially Transparent Hands and Objects[END_REF] when users approach a virtual object. This maintains an anthropomorphic representation of the user while keeping the virtual object visible through this representation. Providing additional feedback of the object hidden by the avatar (e.g. with a supplementary view from another perspective) [START_REF] Bichlmeier | The Virtual Mirror: A New Interaction Paradigm for Augmented Reality Environments[END_REF] is also an alternative. The latter has the advantage of not changing the appearance of the avatar at the exchange of higher task complexity.

Impact on Perception of Distorted Motion

Thanks to the avatar, it is possible that users do not notice motion distortion. Users' visual perception dominates proprioception [START_REF] Burns | The hand is slower than the eye: a quantitative exploration of visual dominance over proprioception[END_REF], making this illusion possible. For example, even if users perform a small movement in real life, if their avatar moves a lot, they will trust the visual feedback more and think that they performed a larger movement. Several studies investigated the thresholds beyond which users notice this modification of their movements. It was found that displaying a realistic hand instead of a spherical cursor increases the detection thresholds during remapped movements by more than 30% [Ogawa et al. 2020a]. When reaching for an object, participants did not detect the horizontal shift applied to their movement as much in the realistic hand condition as in the spherical cursor condition (see illustration in Figure 1.6).

Figure 1.6 -The participant is represented by either a realistic hand (on the left image) or a spherical pointer (on the right). The transparent hand represents the user's real hand, not displayed in the VE. Image from [Ogawa et al. 2020a].

Another study found that the subjects who felt a sense of ownership towards their avatar tended to detect distorted motion less [START_REF] Burin | Body ownership increases the interference between observed and executed movements[END_REF]. A study by [START_REF] Bourdin | Altered visual feedback from an embodied avatar unconsciously influences movement amplitude and muscle activity[END_REF] found that it is possible to impact muscular activity by altering avatar's motion, without users noticing. The task used was flexing the elbow to an angle of 90°, with an elastic band. The virtual arm was flexed by either the same angle, 75°or 105°. The sense of ownership and agency were not impacted by the distortion. While the avatar seems to help increasing detection thresholds for manipulation tasks, it was found that displaying feet during redirected walking does not impact sensitivity to translation gains [START_REF] Kruse | I can see on my feet while walking: Sensitivity to translation gains with visible feet[END_REF]. Similarly, no signifant result was found by [START_REF] Reimer | The Influence of Full-Body Representation on Translation and Curvature Gain[END_REF] when using a full-body representation. There was also no significant effect of virtual representation on detection threshold in a study on redirected jumping [Li et al. 2021]. The presence of an avatar therefore seems to have less impact on whole body movements.

Coherency between Avatars and Input Devices Can Influence Interaction

There is a strong relationship between the chosen user representation and the input device used [Seinfeld et al. 2020a], e.g. it is rare to use hand tracking to control a simple sphere cursor. The user representation can also impact the way users hold the input device, how they manipulate objects [START_REF] Kadri | The visual appearance of user's avatar can influence the manipulation of both real devices and virtual objects[END_REF], as well as their preferred input device. For instance, previous work demonstrated that users prefer hand tracking to controllers when represented by realistic virtual hands because it is more realistic and fun [START_REF] Moehring | Effective manipulation of virtual objects within arm's reach[END_REF]Lin et al. 2019]. However, designers usually choose controllers in most applications, probably because they are more reliable, accurate [START_REF] Moehring | Effective manipulation of virtual objects within arm's reach[END_REF] and commonplace. Various types of controllers exist, differing in terms of shape, buttons and other inputs available, weight or haptic feedback provided. It is questionable whether the way they are displayed in the VE should be generic or not. Using controllers therefore raises several questions: When using such controllers for interaction, what user representation should be chosen? But also, how does this choice impact the interaction performance? With most controllers, a virtual hand can be used as a generic representation that would directly manipulate virtual objects. In 1999, [START_REF] Bowman | Interaction techniques for common tasks in immersive virtual environments: design, evaluation, and application[END_REF] recommended the use of virtual hands rather than virtual tools like raycasting to ensure efficient positioning and rotation of virtual objects. In this case, the different discrete inputs (buttons on the controllers) can launch actions such as grabbing of virtual objects, a solution often used in current VR applications. But sometimes, the controller used is inspired by a real tool and specific to an application, especially in training applications. In this case, it might be preferred to display the 3D model of this tool in the avatar's hand, to provide realism and coherency with the haptic feedback provided by the input device [START_REF] Insko | Passive haptics significantly enhances virtual environments[END_REF]]. Using virtual tools in the same manner that we use real tools has the advantage that it is straightforward. Moreover, using virtual tools was found to activate the same regions in the brain as real tools [START_REF] Rallis | Getting a handle on virtual tools: An examination of the neuronal activity associated with virtual tool use[END_REF], which highlights that virtual tools are treated behaviorally by the brain in a similar manner to physical tools. Displaying virtual tools instead of hands can also be an explicit cue for possible actions in the VE [Seinfeld et al. 2020a]. Choosing a virtual hand or a virtual tool in the avatar's hand as the representation of an input device can therefore change the way the user's interact.

Impact on Performance

As seen in Section 1.3.1.1, the avatar helps users during interaction by providing spatial awareness [START_REF] Draper | Exploring the Influence of a Virtual Body on Spatial Awareness[END_REF]] and perceive their capabilities correctly. This can increase performance. When navigating, a realistic self-avatar can help having smoother trajectories and avoid collisions [Medeiros et al. 2018]. McManus et al. [2011] investigated the influence of a self-avatar on two types of interaction: grabbing and placing precisely a stamp tool, and a stepping stone task. They found that the avatar helped to increase performance, but not more than seeing an animated character perform the task. Additionally, avatar appearance can vary in terms of shape, size or texture, which can influence interaction. The more complex the representation, the more information users can obtain to potentially improve their performance. For instance, people perform better in a bowshooting task with a full-body, and tend to prefer this representation over other simpler representations (only controllers or floating hands) [START_REF] Gao | The Effects of Avatar Visibility on Behavioral Response with or without Mirror-Visual Feedback in Virtual Environments[END_REF]. It was also found that people can solve a puzzle more quickly with an avatar than without, but there was no difference between the conditions with feet tracking and without [Pan and Steed 2019]. Another study found a user preference for performing a tool-based pick and place task with a visual hand representation, albeit performance was similar to the condition of performing the same task without a visual hand representation [START_REF] Ricca | Influence of hand visualization on tool-based motor skills training in an immersive VR simulator[END_REF]. Similarly, after a two-week training, there was still no significant difference in the motor task performance between a group with a virtual hand representation, and without [Ricca et al. 2021]. The importance of viewing a full virtual body also depends on the task. Pastel et al. [2020] found that the level of body parts visible had no influence on the performance during a grasping task, while seeing a full body led to higher accuracy in a throwing task. In terms of realism, a visually faithful avatar does not outperform a generic avatar in a cognitive manipulation task [Lok et al. 2003] or a robot avatar in a pointing task [Schwind et al. 2018b], showing a potential low impact of human-likeness on performance. Apart from the avatar shape itself (arm length, number of limbs, anthropomorphic or abstract), the appearance can also conscienciously or not imply users' capabilities. For example, stereotypes can impact the way users interact, because they will inconsciously want to interact the way their avatar would, due to the Proteus effect (see Section 1.2.4). For instance, a user plays drums better when represented by a dark-skinned avatar with casual clothes than a light-skinned avatar with fancy clothes [START_REF] Kilteni | Drumming in immersive virtual reality: the body shapes the way we play[END_REF]] (see illustration in Figure 1.7). This effect can also appear when users compare their own appearance relatively to others' appearance. For instance, when playing virtual tennis on a Wii con-Figure 1.7 -Illustration from the experiment investigating the impact of avatar appearance on the way users drum in VR. Participants are represented either by flat shaded white hands (A), a dark-skinned avatar with casual clothes (B), or a light-skinned avatar with fancy clothes (C). Image from [START_REF] Kilteni | Drumming in immersive virtual reality: the body shapes the way we play[END_REF].

sole, users will tend to decrease their physical activity when they perceive their avatar as more obese than the opponent [Peña et al. 2016]. A self avatar's musculature can also impact performance, as it was found that embodying an avatar with a muscular appearance decreases perceived exertion during an isometric force task [Kocur et al. 2020a].

The Impact of Interaction Design on the Sense of Embodiment

The avatar can have an impact on interaction as seen in the previous section, but it is also true the other way around. There is a strong link between the interaction technique and the avatar. First, the avatar appearance is linked to the technique, as not all appearances can be controlled by every types of input devices for example, but also because the appearance shows the possible interaction (see Section 1.3.1.1). Second, the avatar is the proxy through which the user can interact, so the user controls the avatar that then interacts with the environment. To do so, users make the avatar move through their own actions. Their actions and the avatar ones must be coherent. As we saw previously (see Section 1.2.6.1), visuomotor stimulation is one of the main way to elicit a sense of embodiment towards a virtual body. As soon as users perform motions that are repercuted on their virtual representation, they can feel that this representation is their own body. This therefore seems logical that performing different types of interaction in the VE can affect embodiment. Nevertheless, this impact has not been deeply explored. Most studies on embodiment involving visuomotor stimulation used simple actions to perform, such as moving in front of a mirror [Waltemate et al. 2018]. Several studies used interaction tasks: navigation tasks [Medeiros et al. 2018], manipulation tasks [Lin et al. 2019] or a mix of both [Pan and Steed 2019]; but, these studies have not deeply investigated the impact of the task itself on embodiment. Recent studies started to explore factors influencing the sense of embodiment depending on the task performed [Fribourg et al. 2020a], which showed that factors having the highest influence on embodiment seem to be impacted by the type of task. For example, avatar appearance was found to be more important for users in a punching task than in other tasks less focused on upper limbs, like walking or kicking a soccer ball.

In this section, we review the current work on embodiment and interaction. The analysis is decoupled considering the three main design choices for an interaction technique: the input characteristics, the control mechanism and the feedback. The focus is mostly on manipulation techniques as most of studies explored this type of techniques, but we will also mention works on other interaction tasks.

Impact of Input Characteristics

Numerous input devices exist, varying for instance in shape, Degrees of Freedom (DoF), input modality and input interfaces (e.g. buttons, joysticks). If the user has a virtual representation, it means the input device must ensure all possible interaction with the VE but also the control of his/her virtual representation. While the input device is usually the same for both avatar control and interaction such as the case of the virtual hand metaphor, hybrid methods are beginning to emerge using different input devices for avatar control and object manipulation (e.g. hand tracking for hands control and a tablet for manipulation [START_REF] Surale | Tablet-InVR: Exploring the Design Space for Using a Multi-Touch Tablet in Virtual Reality[END_REF]).

Shape

Controllers have various shapes, but most of them are held in a power grip. When the shape resembles a real tool, this provides high interaction fidelity. Input devices adapted to the task can give better performances [START_REF] Pham | Is the Pen Mightier than the Controller? A Comparison of Input Devices for Selection in Virtual and Augmented Reality[END_REF][START_REF] Bhargava | Evaluating Multiple Levels of an Interaction Fidelity Continuum on Performance and Learning in Near-Field Training Simulations[END_REF] as the way the user holds them is more coherent with the task to perform [START_REF] Batmaz | Precision vs. Power Grip: A Comparison of Pen Grip Styles for Selection in Virtual Reality[END_REF]. Little work exists regarding the influence of device shape on embodiment, probably due to the various types of controllers and its potential low impact. However, there could be an impact of the shape on embodiment, especially depending on the associated virtual model. Depending on the way users hold a device, it can change the way they control their representation and manipulate objects, which can make them feel more or less in control. In particular, this may impact their perception of their avatar if the manipulation is not intuitive. More importantly, depending on the shape, it is crucial to choose an adequate mapping between the controller and the actions performed in the VE.

DoF

For most manipulation techniques, the virtual hands are the tool to interact with the virtual objects, except when there is a use of an intermediary element like the ray in raycasting techniques. When using a virtual hand, the DoF provided by the input device are used mostly to control this hand. Intuitively, we can think that the more DoF provided for hand control, the higher the level of control and the sense of embodiment. Supporting this theory, hand tracking was found to elicit a higher sense of ownership than controllers, probably because it provides a finer control of the users' virtual hand [Lin et al. 2019] (see Figure 1.8). However, this effect can also depend on the DoF provided by the user representation compared to the DoF provided by the input device. For example, while Argelaguet et al. [2016] found that agency was better with unrealistic hands (sphere and skeleton hand, so with limited DoF) using Leap Motion, Lougiakis et al. [2020] found no difference between different hand appearances with a similar protocol using controllers. A potential explanation for this could be that controllers offer less DoF and thus reduce expectations in terms of hand control. The more DoF are provided by the input device, the more control users want during manipulation, especially when realistic representations are used [START_REF] Argelaguet | The role of interaction in virtual embodiment: Effects of the virtual hand representation[END_REF]]. These results suggest that more research should be done on combinations of different input devices and avatars during 3D manipulation.

Input Modality and Interaction Fidelity

There are many ways to track users' input. Some apparatus are external to users, like camera-based tracking, while others must be attached to users, or held. For users' hand tracking, two main input modalities could be considered: full-hand tracking and controllers. While controllers are efficient and commonly used, manipulating objects directly with the hands remains the most realistic way both of interacting and of controlling the avatar. It allows fine manipulation as well as direct control of the virtual hand. This is possible thanks to optical devices (Leap Motion, Kinect) or wearables (mostly gloves). However, it implies having precise and robust finger tracking. As previously discussed, in theory hand tracking offers more DoF and therefore better control and probably a higher embodiment [Lin et al. 2019].

However, imperfect tracking can cause mismatches between the visual display and the users' real actions. When the hand movements are constrained by the controllers, there are fewer chances for users to notice mismatches with their real hands. Experiments in which finger tracking provides a good sense of embodiment are usually constrained experiments, for example requiring participants to keep their palm facing down [START_REF] Hoyet | Wow! I Have Six Fingers!" Would You Accept Structural Changes of Your Hand in VR?[END_REF]. Therefore, constraining movements could be one possible solution. Recent input devices (e.g. Oculus Touch, Valve Index) use capacitive sensors for the fingers, providing a good trade-off between offering the efficient tracking of a controller and more precise finger movements for manipulating objects. It would also be interesting to study the impact of hybrid input [START_REF] Huang | Evaluation of a Hybrid of Hand Gesture and Controller Inputs in Virtual Reality[END_REF]] (using both a controller and hand tracking) on the sense of embodiment.

In addition to reliability, controllers also often offer buttons as input, which can be useful to trigger actions in the environment and feel in control, instead of for example launching an automatic animation of grabbing an object when the hand is near it. Using buttons offer low-fidelity interaction, but this can be better in terms of performance and acceptance than moderate-fidelity solutions [McMahan et al. 2016]. The level of interaction fidelity does not always impact embodiment. For example, when performing a transition between two virtual scenes, techniques with a higher fidelity like turning on yourself or putting a virtual HMD was not found to elicit a higher sense of ownership than a simulated blink metaphor [START_REF] Oberdörfer | Effects of VE Transition Techniques on Presence, Illusion of Virtual Body Ownership, Efficiency, and Naturalness[END_REF]]. This study therefore investigated the case of a teleportation from one VE to another, but continuous navigation has not been investigated yet. To our knowledge, no study investigated the impact of locomotion techniques on the sense of embodiment. This question will be explored in an axis of this thesis (see Chapter 3).

The best scenario generally remains the high-fidelity case, where the user performs the entire action like in the real world, as a complete control of the avatar elicits a higher sense of embodiment than just triggering actions [Fribourg et al. 2020a]. An alternative form of input is brain signals. Work on Brain-Computer Interfaces (BCI) for precise control is still at its early stage. For the moment, it has been mostly studied for controlling walking [Luu et al. 2016;[START_REF] Alchalabi | A multi-modal modified feedback self-paced BCI to control the gait of an avatar[END_REF]. It was already found that BCI can elicit a higher sense of embodiment when making an avatar walk, than finger movements [START_REF] Cohen | Controlling an avatar by thought using real-time fMRI[END_REF].

More important than the input modality itself, what matters is the mapping applied to this input.

Impact of Control and Mapping

A great part of interaction techniques do not consider a one-to-one mapping between input motion and the resulting virtual motion. For example, modifications of the CD gain or constrained motions are commonplace in order to increase the precision of freehand manipulation, or to redirect users in the VE. However, such control mechanisms can introduce mismatches between the actions performed by the user and the motions of their avatar. As visuomotor coherency is one of the major inducers of the sense of embodiment [START_REF] Kokkinara | Measuring the Effects through Time of the Influence of Visuomotor and Visuotactile Synchronous Stimulation on a Virtual Body Ownership Illusion[END_REF], such changes in control could have a negative impact in the overall sense of embodiment.

Motion and Interaction Constraints

Constraints can be used to interact more quickly or respect real world physics. Most constraints applied during interaction are meant to avoid collisions, or to reduce DoF (limit the interaction to a particular surface or an axis for example). When constraining the in-teraction, it means that the avatar's motion is also constrained, which can create a visualproprioceptive mismatch and disturb the senses of agency and self-location [START_REF] Pritchard | Non-hierarchical Influence of Visual Form, Touch, and Position Cues on Embodiment, Agency, and Presence in Virtual Reality[END_REF]. First, several studies decided to handle collisions as it might seem a good idea to create a realistic environment that respect the laws of physics. For instance, when moving an object on a table, it is possible to apply semantic constraints based on real-life physics, as long as the motion of the user is coherent with this constraint (e.g. a horizontal motion on the surface of a table). However, especially for wide and fast motion, blocking the avatar outside objects can create huge offsets between the real hand and its virtual counterpart. This could cause a break in the sense of self-location but also ownership, which is sensitive to spatial location [START_REF] Ratcliffe | The Effect of Visual, Spatial and Temporal Manipulations on Embodiment and Action[END_REF]]. An alternative is to not handle collisions for this type of movements. If users experience a high sense of presence (i.e. the sense of being in the VE), it was found that they can intuitively avoid collisions, especially when using a realistic avatar [START_REF] Fribourg | Virtual co-embodiment: evaluation of the sense of agency while sharing the control of a virtual body among two individuals[END_REF]]. For finer motion, it was found that handling collisions is preferred by users (see in Section 1. 4.2.4).

Second, constraints separating DoF (for example to move precisely an object on one direction) can also create big mismatches between the user's position and the avatar's one. In such a case, it is possible to use explicit constraints. They can be explicitly defined by the users so they know what motion they can perform or not [START_REF] Hayatpur | Plane, Ray, and Point: Enabling Precise Spatial Manipulations with Shape Constraints[END_REF]. It is also possible to use gestures to determine customised constraints [START_REF] Gloumeau | Pin-NPivot: Object Manipulation Using Pins in Immersive Virtual Environments[END_REF]], which has the advantage of making users move their avatar and potentially appropriate it. To reduce DoF, the classical use of widgets (see an example on Figure 1.9) explicitly constrains the manipulation, which can be more predictable and impact less the sense of agency. Widgets can be seen as virtual objects that the user can use to indirectly manipulate objects. Common constraints on the manipulation still apply to the widgets though, for example the grabbing of the widget tool must seem realistic (see Section 1.4.2.4). While widgets are intuitive, they do not provide high-fidelity interaction using directly the avatar. New techniques of DoF separation adapted to the avatar could be invented.

Another way to handle constraints could be to dissociate the avatar, that provides a realistic representation of the user, from a second form of representation that is not affected by the constraints. It can be the tool used, a ghost [START_REF] Yang | Implementation and Evaluation of "Just Follow Me": An Immersive, VR-Based, Motion-Training System[END_REF] or a skeleton hand [START_REF] Argelaguet | The role of interaction in virtual embodiment: Effects of the virtual hand representation[END_REF].

Remapped Motion: Modification of CD gain

Avatars provide a direct visual feedback of the user's position and motion in the environment. If the CD gain differs from one, this relation between the user's motion and the avatar's one is altered and can impact the sense of embodiment. Typically, interaction methods employ either constant or adaptive gains.

Constant gains

The higher or lower is the CD gain, the higher will be the mismatch between the avatar's hand and the user's real hand. Although visual feedback dominates proprioception [START_REF] Burns | The hand is slower than the eye: a quantitative exploration of visual dominance over proprioception[END_REF], and people do not notice easily motion distortion (i.e. when their motion is amplified or decreased when achieving a task) [START_REF] Debarba | Self-attribution of distorted reaching movements in immersive virtual reality[END_REF] and can even adapt their motion to this distortion [START_REF] Bourdin | Altered visual feedback from an embodied avatar unconsciously influences movement amplitude and muscle activity[END_REF], if the mismatch is too important it can frustrate the user and break the sense of embodiment. A study found that while the senses of agency and ownership are quite resistant to visual-proprioceptive mismatches (induced by a constant offset between the real and virtual hand), the sense of self-location is very sensible to them [START_REF] Pritchard | Non-hierarchical Influence of Visual Form, Touch, and Position Cues on Embodiment, Agency, and Presence in Virtual Reality[END_REF]. Moreover, [START_REF] Kokkinara | The Effects of Visuomotor Calibration to the Perceived Space and Body, through Embodiment in Immersive Virtual Reality[END_REF] found that when users' movements are amplified, this affects their perception of the VE and agency (contrary to the study by [START_REF] Pritchard | Non-hierarchical Influence of Visual Form, Touch, and Position Cues on Embodiment, Agency, and Presence in Virtual Reality[END_REF]), but not ownership. When the user's motion is distorted and it creates a mismatch that is noticeable, the user can therefore feel out of control and the sense of agency can be affected. To avoid this, it is better to do not apply gain, especially on fast and wide movements because it would quickly create a large mismatch between real and virtual hand. As discussed in Section 1.3.2, realistic hands make remapped motion less noticeable [Ogawa et al. 2020a]. Furthermore, instead of modifying the virtual body's motion, the distortion can also be applied on the virtual world [START_REF] Azmandian | Haptic Retargeting: Dynamic Repurposing of Passive Haptics for Enhanced Virtual Reality Experiences[END_REF]. This is the same principle as redirected walking, the world is translated when users move their head. This is only adapted to manipulation tasks necessitating head motions. A hybrid solution mixing world and body movements distortion can avoid the drawbacks of both techniques. Other tricks can be used especially after the distortion during offset correction, such as correcting the offset when the user closes the eyes [START_REF] Zenner | Blink-Suppressed Hand Redirection[END_REF].

Adaptive gains

The gain applied could also be adaptive, i.e. its value can vary depending on the conditions. For example, the gain can depend on the distance of the object to the user, closer manipulation necessitating a lower gain to be precise, and further manipulation a higher gain [Ouramdane et al. 2006]. It was found that the acceptance of distorted motion is increased when the distortion is gradually introduced [START_REF] Porssut | Reconciling Being in-Control vs. Being Helped for the Execution of Complex Movements in VR[END_REF]. Altering the motion gain slowly in the context of physically tiring tasks still elicits a sense of ownership [Feuchtner and Müller 2018;[START_REF] Wentzel | Improving virtual reality ergonomics through reach-bounded non-linear input amplification[END_REF]. When distortion must be used in an application, it is better to adapt it depending on the situation. Different gains could also be applied depending on the direction of the movement, as users' notice more easily offsets on the horizontal axis than in other dimensions [START_REF] Esmaeili | Detection of Scaled Hand Interactions in Virtual Reality: The Effects of Motion Direction and Task Complexity[END_REF]].

An alternative to avoid the impact of distorted motion on embodiment could be to decouple the tool from the body. An isomorphic control would be kept for the avatar, while the manipulation would be anisomorphic [START_REF] Gloumeau | Pin-NPivot: Object Manipulation Using Pins in Immersive Virtual Environments[END_REF]]. The gains would only be applied on the tool, thus not affecting the avatar itself, for example in out-of-reach interaction. In this thesis, we propose another alternative, which is to use a dual body representation, made of an interactive representation showing distorted motion, and a co-located representation showing real motion. This alternative is presented in Chapter 4.

Out-of-reach Manipulation

A special type of manipulation that can create a strong mismatch and potentially impact embodiment is out-of-reach manipulation. In the space in which we can reach objects, i.e. our peripersonal space, the challenge is mostly focused on the range of motion, the hand poses, the feedback of actions, or the display of input device. However, outside the peripersonal space, it is necessary to choose how to represent the action, and how it impacts the avatar. Common out-of-reach manipulation techniques are the Go-Go [START_REF] Poupyrev | The Go-Go Interaction Technique: Non-Linear Mapping for Direct Manipulation in VR[END_REF]] and the raycasting techniques [START_REF] Bolt | Put-That-There": Voice and Gesture at the Graphics Interface[END_REF]].

The Go-Go technique applies a non-linear CD gain to the user's input. The more users extend their arm, the further the virtual hand goes. If the limit of CD gain is too high, the mismatch can be important between the user's real hand position and its virtual counterpart. This could potentially impact all the sense of embodiment components. Several choices of feedback can be considered in this problem [START_REF] Feuchtner | Extending the Body for Interaction with Reality[END_REF], but all of them can highly impact the sense of embodiment. In the case of full-body avatars, the hand could be detached from the virtual body. However, it has been found that body discontinuity reduces body ownership but does not necessarily impact motor performance [Seinfeld and Müller 2020]. A hand attached to the arm by a rigid wire disturbs embodiment but not skin conductance in reaction to a threat [Tieri et al. 2015]. A potential solution could be to have an extensible arm, which can maintain a correct sense of embodiment, until reaching a certain length [Kilteni et al. 2012b]. Other feedback can be imagined, like a robotic extensible arm, a ghost clone of the hand going towards the object (as already used in training [START_REF] Yang | Implementation and Evaluation of "Just Follow Me": An Immersive, VR-Based, Motion-Training System[END_REF]), or an outside assistance like a drone going to the object instead of the user's body. It depends on the context of the application, if the realism must be maintained or not.

The Raycasting technique originally comes from the pointing technique [START_REF] Bolt | Put-That-There": Voice and Gesture at the Graphics Interface[END_REF]] with an additional ray to provide visual feedback of selected objects [Mine 1995]. It has the advantage of being body-referenced but not part of the avatar. However, depending on the way it is represented, it may impact ownership by providing an unrealistic feedback. If we consider the basic raycasting in which the ray is linked to the hand, we can display the ray coming from a finger, probably the index because it is the finger associated to pointing. We could also display a laser pointer in the avatar's hand instead, to maintain realism. The choice can also be impacted by the device input, if we use hand tracking we might prefer the first option, while the second could be better when a controller is used, or even a tracked stylus [START_REF] Teather | Pointing at 3D targets in a stereo head-tracked virtual environment[END_REF]. Other raycasting techniques exist, referenced to other parts of the body, for example to the head. In this case, a virtual headlamp could be used as a more coherent feedback.

The two techniques both have their pros and cons. The Go-Go technique uses direct manipulation, which is more intuitive and uses the avatar to appropriate it. The raycasting technique might be safer for self-location and agency, as it does not modify the CD gain and the virtual body does not have to be modified or reshaped to use this technique.

More variants of feedback for out-of-reach techniques and their impact on embodiment should be investigated. The ideal would be to invent a technique that is as intuitive as the Go-Go technique but does not have to modify the avatar.

Control of Dexterous Hand Interactions

Grabbing virtual objects is probably one of the hardest challenges in manipulation. Because of the lack of haptic feedback in VE, if a one-to-one mapping is applied to hand movements, visual artifacts can appear: unrealistic hand poses or fingers passing through objects. This can affect embodiment. However, it is known that humans are more sensible to visual interpenetration than proprioceptive offsets [START_REF] Burns | The hand is slower than the eye: a quantitative exploration of visual dominance over proprioception[END_REF]. They tend to believe more what they see than what their proprioception tells them. Designers therefore often choose to handle collisions and to define hand poses on the virtual objects, so the user is not disturbed by interpenetrations. This solution is usually preferred by the users, even though it can decrease performance [Prachyabrued and Borst 2012b]. But, if users feel too constrained by the collisions, this may impact the sense of agency and selflocation. This also applies for defined hand poses: if they are too different from users' real poses, this could affect embodiment. People usually tend to adapt to the visual feedback provided, and can be disturbed for example when the input action required is different from the feedback. This was noticed for example in the experiment by Lok et al. [2003] in which participants had to do a pinch movement but observed a grasping animation. Several participants started performing a grasp movement. Such adaptation needed might potentially influence the sense of embodiment.

The preferred feedback during the grasping of a ball has been studied, which confirms that handling collisions for fine manipulation is preferred [START_REF] Canales | Virtual Grasping Feedback and Virtual Hand Ownership[END_REF]. Participants preferred visualising their hand outside the object, even though their real fingers were actually entering the sphere. This condition preserved the sense of ownership. Providing complete control of the virtual hand does not always seem to be the best choice.

Assistance in taking virtual objects is often used to make the manipulation more intuitive and realistic. This can be used without affecting agency and ownership [START_REF] Porssut | Reconciling Being in-Control vs. Being Helped for the Execution of Complex Movements in VR[END_REF]]. However, if too few hand poses are provided, users may feel limited in their actions, which could impact the sense of agency. If users can grab an object even with unrealistic hand poses, the application will lack realism. Since defining many hand poses in a VR application can be time-consuming, it would be interesting to study their influence on the sense of embodiment, especially agency.

One-to-One Mapping or Animation

With tracking solutions improving, it is tempting to track exactly users' motions and map them directly to the avatar. This is not always possible as most of the tracking systems are still cumbersome or expensive to deploy extensively. Moreover, when the tracking is imperfect, this can create breaks in embodiment as users can notice the discrepancies [START_REF] Koilias | The Effects of Motion Artifacts on Self-Avatar Agency[END_REF][START_REF] Kokkinara | The Effects of Visuomotor Calibration to the Perceived Space and Body, through Embodiment in Immersive Virtual Reality[END_REF]]. There are therefore some papers comparing tracking solutions such as Inverse Kinematics (IK) to animations or hybrid solutions. For example, a locomotion technique that was recently studied in relation with the sense of embodiment is Walking-in-Place (WIP). A first preliminary study investigated two different feedbacks during WIP: an avatar stepping like the user, or an avatar walking [Park and Jang 2019]. Participants reported a preference for the natural walking animation, although it would sometimes display unintended steps. Another study compared a fixed body, a pre-recorded animation and an animation synchronised with users' leg movements using a deep-neural network [Lee et al. 2020]. It was found that the synchronised animation was better for ownership. A second experiment in the same study showed that this effect emerges whether users look directly at the legs or at the avatar's shadow. In line with these results, a study investigating prioritised factors to elicit a global sense of embodiment found that when people can progressively improve several factors, they prioritise control over appearance [Fribourg et al. 2020a]. The choice of controlling their avatar with IK instead of having an automatically launched animation was done before improving avatar appearance, and this was particularly the case for a soccer task where it was chosen before selecting a 1PP. While people like having full control over their avatar, a perfect one-to-one mapping is not always necessary. Movements can be distorted to have a visually realistic interaction while still feeling in control [START_REF] Porssut | Reconciling Being in-Control vs. Being Helped for the Execution of Complex Movements in VR[END_REF]]. Movement assistance is a good trade-off to ensure both sense of agency and reliability.

Impact of Feedback

The feedback provided to the user while performing an action can also impact embodiment. First the avatar itself is part of the feedback and can impact embodiment; for example if it is modified during manipulation. However, the type and characteristics of the feedback provided during an action can also affect embodiment.

Avatar Appearance During Interaction

The avatar is the main source of feedback during motion in the VE. To increase usability or performance, its appearance can be modified during manipulation (see Section 1.3.1.2). However, these changes must be done carefully. Even though avatar appearance is not the most important factor in the sense of embodiment [Fribourg et al. 2020a], several studies showed its importance in inducing a good sense of ownership [Waltemate et al. 2018]. Designers must be aware that modifying it can impact how much users feel like the avatar is part of their real body. For example, the avatar's hands can be made transparent to avoid occlusions. But, if the hands are too transparent, this might impact the sense of ownership [Martini et al. 2015] and agency [START_REF] Buchmann | Interaction with Partially Transparent Hands and Objects[END_REF]. It is also possible to use skeleton hands [START_REF] Argelaguet | The role of interaction in virtual embodiment: Effects of the virtual hand representation[END_REF], which provide a good sense of agency but a lower sense of ownership than realistic hands. To ensure a good sense of ownership, it seems important to keep a realistic avatar.

When a tool is necessary for manipulation, or when a controller is used as input device, the feedback at the hand's level can be either the hand (controlled by the input device, for example by mapping buttons to the movements of the hand) or the tool held in the hand. The feedback chosen and its coherency with the input device used might impact embodiment. While some studies start investigating this question [START_REF] Alzayat | Quantitative Measurement of Tool Embodiment for Virtual Reality Input Alternatives[END_REF], this topic needs further research.

Perspective

Perspective is the user's point of view on the VE. Perspective is important to perform an action precisely, especially when the user can only rely on visual feedback. In applications using an avatar, various camera positions can be used, each of them providing a different amount of visual information. Perspective is generally described as a third-person perspective (the viewpoint is outside the user representation) or a first-person perspective (the user representation is co-located with the real body) (see Figure 1.10). A third-person perspective (3PP) is usually advised for navigation because it provides a better spatial awareness, but some recent work found that a first-person perspective (1PP) is actually preferred [Medeiros et al. 2018]. Similarly, [START_REF] Kokkinara | First person perspective of seated participants over a walking virtual body leads to illusory agency over the walking[END_REF] found that 1PP elicited higher senses of ownership and agency when seated users looked at their virtual avatar walking. For manipulation, a 1PP is usually preferred and more precise [START_REF] Salamin | The Benefits of Third-Person Perspective in Virtual and Augmented Reality?[END_REF][START_REF] Gorisse | First-and Third-Person Perspectives in Immersive Virtual Environments: Presence and Performance Analysis of Embodied Users[END_REF] as the user can directly manipulate objects like they would in real life. Moreover, a 3PP requires an additional cognitive load for considering both the transformation users want to apply to a virtual object and the offset between their vision and their avatar. In the literature on the role of perspective on the sense of embodiment, it was found that a 1PP is preferred to elicit embodiment. It was found that subjects experience a higher sense of ownership from a 1PP, even though it can be experienced from a 3PP to some extent with a synchronous motor feedback [START_REF] Galvan Debarba | Characterizing first and third person viewpoints and their alternation for embodied interaction in virtual reality[END_REF][START_REF] Gorisse | First-and Third-Person Perspectives in Immersive Virtual Environments: Presence and Performance Analysis of Embodied Users[END_REF]]. The sense of agency seems less impacted by the perspective, and can be felt either from 1PP or 3PP as long as the movements are synchronised. Regarding the sense of self-location, studies have shown that a 3PP usually provokes a drop in the sense of self-location [Maselli and Slater 2014;[START_REF] Gorisse | First-and Third-Person Perspectives in Immersive Virtual Environments: Presence and Performance Analysis of Embodied Users[END_REF]. A potential solution, more complicated to implement, would be to have both perspectives [Salamin et al. 2008].

In conclusion, it is better to have a 1PP to provide both an efficient interaction and a high level of embodiment.

Haptic Feedback

Visual feedback is the main feedback provided in VR. However, in real life, people receive other types of feedback that help during manipulation. Additional feedback like haptic feedback [START_REF] Hirota | Providing force feedback in virtual environments[END_REF] can also be provided in VR and can impact manipulation performance [START_REF] Swapp | Interaction with co-located haptic feedback in virtual reality[END_REF]]. Haptic feedback can be provided through tactile feedback (touch, to feel the texture of the object for example) or force feedback (e.g. users feel a resistance when they collide with an object) [START_REF] Burdea | Force and touch feedback for virtual reality[END_REF]. There are nowadays output devices that are put directly on the body [Spanlang et al. 2010] that provide vibrotactile feedback and can make the user more aware of their virtual body. Synchronous visuotactile feedback provided by an experimenter was one of the first methods used to elicit embodiment towards a virtual body [START_REF] Slater | Towards a digital body: the virtual arm illusion[END_REF]]. If users feel a touch and observe at the same time a stimulation on the virtual body that can cause this touch, the brain interprets that the virtual body must be their body. A study found that haptic feedback provided by wearable devices can increase the sense of embodiment [START_REF] Fröhner | Can Wearable Haptic Devices Foster the Embodiment of Virtual Limbs?[END_REF], especially force feedback. A recent study also supports these results, as they found that interaction force feedback had a positive effect on the sense of agency, but no main effect on the sense of ownership [START_REF] Akselrod | Contribution of interaction force to the sense of hand ownership and the sense of hand agency[END_REF]. With mid-air interfaces, audio and haptic feedback can be more efficient to increase the sense of agency than visual feedback [START_REF] Martinez | Agency in mid-air interfaces[END_REF]. In addition of the information it provides during manipulation, haptic feedback is therefore also a way of increasing the sense of embodiment and should be used when possible. It can also be beneficial during locomotion. For example, it was found that providing proprioceptive feedback using tendon vibration while looking at the avatar walking can enhance the sense of embodiment [Leonardis et al. 2014].

When it is not possible to provide haptic feedback, pseudo-haptic feedback can be used. This technique can create an illusion of weight by modulating the gain applied to users' motion [START_REF] Jauregui | Toward "Pseudo-Haptic Avatars": Modifying the Visual Animation of Self-Avatar Can Simulate the Perception of Weight Lifting[END_REF]]. However, this should be used with precaution when using avatars as it can create a mismatch between users and their avatar (see Section 1.4.2.2).

Auditory Feedback

Another type of feedback that can be provided to users is auditory feedback. Auditory feedback provides important information when manipulating objects in real life. Like haptic feedback, it can inform us of collisions, it can also help in perceiving textures [START_REF] Kyung | Multi-sensory Perception of Roughness: Empirical Study on Effects of Vibrotactile Feedback and Auditory Feedback in Texture Perception[END_REF]. However, its relation with the sense of embodiment has been less studied than other types of feedback. The major study on auditory feedback and virtual embodiment is from Tajadura et al. [2017] who found that we can enhance embodiment of a child's virtual body when the avatar's voice and appearance are coherent. One study investigated the role of auditory cues in the RHI. Synchronous auditory feedback seems to strengthen the illusion [START_REF] Radziun | Auditory cues influence the rubberhand illusion[END_REF]. With a task of clapping hands in a non-immersive VE, no significant effect of the auditory feedback on virtual body owner-ship was found, showing a potential low impact of this type of feedback in the ownership illusion [START_REF] Roth | A simplified inverse kinematic approach for embodied VR applications[END_REF]. Several studies exist on the link between body perception and sound [START_REF] Azañón | Multimodal contributions to body representation[END_REF]. For example, when the sound heard when a small hammer hits a person's hand is the sound of a hammer hitting a piece of marble, it can give the person the illusion that the hand is made of marble [START_REF] Senna | The Marble-Hand Illusion[END_REF]. Because the sound informs the user of a contact with an object, it can also be used to create a long arm illusion [Tajadura-Jiménez et al. 2015b]. During locomotion, audio frequency can impact body weight perception [Tajadura-Jiménez et al. 2015a]. However, to our knowledge, no study has been done on the impact of auditory feedback during interaction on the sense of embodiment.

Make the Avatar Central

To have interaction techniques compatible with an avatar, the idea is to make the avatar central for the interaction. Techniques that are based on the body itself (using it as input or as spatial reference) are inherently more compatible with an avatar. Techniques that have been invented to use proprioception for example, use the body as a reference [Slater and Usoh 1994;Mine et al. 1997]. This has also the advantage of making users process information more rapidly, as information placed on or near the body improves information detection in some tasks [Seinfeld et al. 2020b].

There are therefore interrelations between the sense of embodiment and interaction techniques. From the knowledge on these interrelations, it is possible to adapt existing techniques to make them more compatible with avatars, and to invent new techniques that will be inherently compatible with avatars. The state of the art shows more existing papers on manipulation techniques and virtual embodiment than for other types of interaction techniques. From the analysis of existing literature, we proposed several preliminary guidelines for manipulation techniques compatible with avatars that will be presented in Chapter 5.

Conclusion of the State of the Art

VR immerses users in a whole new world. In this alternative world, avatars are useful to interact with the environment, i.e. to manipulate objects or navigate in this environment. To fully experience having a new body, it is better to feel like it is our real body. Sense of embodiment in VR is a recent and ongoing topic of research, inspired by real-world illusions such as the RHI. It is still unclear how it is elicited and why its level differs between individuals. Moreover, while being able to act through a body is an efficient way to appropriate it, the impact of interaction on embodiment has been little studied. While some studies start showing interrelations between sense of embodiment and interaction in VR, especially for manipulation techniques, we lack knowledge on the impact of virtual representations on existing interaction techniques. We also do not fully understand yet how interaction design choices can affect the different components of embodiment. Interaction tasks in VR are various, from object manipulation to locomotion, as could be their interrelations with embodiment. There is therefore a need of better understanding these interrelations to design new techniques, more compatible with high-fidelity avatars. The goal is to have rich interaction and customised full-body avatars in future VR applications to fully experience all the advantages of VR.

As a first step, the next chapter will focus on the sense of embodiment and why it may be elicited differently between users.

"I need to be myself, I can't be no one else"

Oasis

Chapter 2

UNDERSTANDING INDIVIDUAL DIFFERENCES IN THE SENSE OF EMBODIMENT

Abstract: This chapter reports an exploratory study aiming at identifying user internal factors (personality traits and body awareness) that might cause either a resistance or a predisposition to feel a sense of embodiment towards a virtual avatar. To this purpose, we conducted an experiment (n=123) in which participants were immersed in a virtual environment and embodied in a gender-matched generic virtual avatar through a headmounted display. After an exposure phase in which they had to perform a number of visuomotor tasks (during 2 minutes) a virtual character entered the virtual scene and stabbed the participants' virtual hand with a knife. The participants' sense of embodiment was measured, as well as several personality traits (Big Five traits and locus of control) and body awareness, to evaluate the influence of participants' personality on the acceptance of the virtual body.

Introduction

The sense of embodiment is the central aspect linking users to their avatar. In the related work, we presented many studies that investigated external factors influencing the sense of embodiment. These factors are linked to the avatar itself (e.g., appearance [START_REF] Banakou | Illusory ownership of a virtual child body causes overestimation of object sizes and implicit attitude changes[END_REF]Peck et al. 2013], realism [Maselli and Slater 2013]) or to the apparatus (e.g., degree of control [START_REF] Debarba | Self-attribution of distorted reaching movements in immersive virtual reality[END_REF], nature of the stimulation [START_REF] Kokkinara | Measuring the Effects through Time of the Influence of Visuomotor and Visuotactile Synchronous Stimulation on a Virtual Body Ownership Illusion[END_REF]). However, they are "external factors", i.e., mostly linked to the avatar itself or to the experiment protocol, but not "internal factors", i.e. linked to the user's characteristics (e.g. personality or background experience). Indeed, while most studies are able to show general trends of the influence of such "external" factors, the inter-user variabil-ity remains non-negligible. In practice, we can observe that some people easily believe in the illusion, while others are on the contrary totally refractory. This observation led us to investigate how individual differences could influence the sense of embodiment in VR. Such individual differences have been found for the sense of presence [START_REF] Sacau | The impact of personality factors on the experience of spatial presence[END_REF][START_REF] Murray | Absorption, dissociation, locus of control and presence in virtual reality[END_REF], or for the RHI [START_REF] Asai | Rubber hand illusion, empathy, and schizotypal experiences in terms of self-other representations[END_REF][START_REF] Kállai | Temperament and psychopathological syndromes specific susceptibility for rubber hand illusion[END_REF]. Better understanding the emergence of different embodiment scores between individuals could be a key to also understand better how embodiment is elicited, and to better control participant samples in embodiment experiments. The aim of this chapter is to study such potential individual factors influencing the sense of embodiment, to better understand this phenomenon. We therefore conducted an exploratory experiment where we investigated the link between "internal" factors (personality traits and body awareness) and the sense of embodiment. This experiment was divided into three phases: adaptation, induction and threat. In the adaptation phase participants were able to freely explore the environment and their avatar, in the induction phase participants had to reproduce a series of visuomotor tasks (see Figure 2.1, left) and in the threat phase, a virtual character appeared in the environment and threatened the avatar's hand with a knife (see Figure 2.1, right).

Experiment Design

Participants

One hundred and twenty three participants (age min=18, max=60, avg=30.3±9.0, 58 women and 65 men) took part in our experiment. The majority of them were students and staff from our research center. All participants freely volunteered for the experiment and most of them were curious about VR. They did not receive course credits nor economical compensation. They were all naive to the purpose of the experiment and had normal or correct-to-normal vision. People wearing glasses could keep them if they were not generating any discomfort. All participants gave written and informed consent. The study conformed to the declaration of Helsinki, and was approved by the local ethical committee. Seventy-six participants reported to have no previous experience in VR, twenty-five to have some previous experiences in VR and twenty-two to be experts.

Experimental Protocol

Before the experiment: Upon their arrival, participants were first briefed about the experiment, read and signed the consent form. They were then equipped with the HMD and the controllers, were asked to sit on a chair in front of the table where the experiment would be conducted, and a calibration phase was performed to adapt the avatar to their dimensions. More precisely, the global scale of the avatar was first adapted to match the height of the participant. Then, participants were asked to take a seated T-pose (reach arms on the side), in order to measure their arm span using both controllers. The distance between the two controllers was therefore used to adjust the avatar's arm length, while the headset position was used to scale the avatar's spine so that the avatar's head position matched the user's one. Participants were then asked to freely discover the environment. We did not impose a fixed time during the adaptation phase. Yet, all participants were encouraged to explore the scene, their avatar, and to look into the mirror. When they were ready, they could start the task.

Experimental task: Participants sat in front of a real table and saw a similar co-located virtual table, while being immersed in the VE from a first-person perspective. They were asked to put their hands on the virtual table (on two white spots) receiving by this occasion passive haptic feedback from the physical table. They held in their hands the real controllers that were also represented in the virtual world for coherence concern. A virtual screen was positioned in front of them, on the table, and a virtual mirror was located on their left (Figure 2.1). We chose to use a mirror as it is supposed to induce a greater sense of ownership [START_REF] González-Franco | The contribution of real-time mirror reflections of motor actions on virtual body ownership in an immersive virtual environment[END_REF][START_REF] Jenkinson | New reflections on agency and body ownership: The moving rubber hand illusion in the mirror[END_REF]. Also, we decided to induce the sense of ownership using visuomotor feedback since it has been shown to be stronger than visuotactile synchronisation to induce body ownership [START_REF] Kokkinara | Measuring the Effects through Time of the Influence of Visuomotor and Visuotactile Synchronous Stimulation on a Virtual Body Ownership Illusion[END_REF].

2D trajectories were displayed on the screen (see Figure 2.2), which participants were instructed to reproduce in front of them, using either their right or left hand according to the instruction provided. The trajectories presented were chosen to be relatively simple (number eight, circle, triangle, etc) to avoid a high cognitive load, which could have distracted participants from their avatar and the environment. After each drawing, they had to put back both hands on the white spots on the table. The task lasted two minutes during which participants saw their avatar moving synchronously according to their movements. After the achievement of the task, a virtual character entered the room and stabbed the virtual hand with a knife. We measured the reaction to the threat (hand motion), in order to inspect its potential correlation with the sense of ownership.

After the experiment: Participants were asked to fill in a number of questionnaires. First they filled in a demographic questionnaire, then they answered questions about embodiment, as well as questions about presence. They also filled in several personality questionnaires, and a body awareness questionnaire. Collected data are presented in more detail in Section 2.2.4.

Apparatus

The experiment was developed using Unity 2018.1.6f1. Participants saw the VE through an HTC Vive PRO HMD, while their hand movements were tracked using the Vive con- trollers. The FinalIK plugin was used to animate the participants' avatar with Inversed Kinematics and to provide visuomotor feedback, based on the participants' head (HMD) and hands (controllers) movements. During the experiment, two avatar models were used to match the participant's gender (see the male and female avatars in Figure 2.3). Because appearance is a major contributor to the sense of embodiment, using personalised avatars might lead to high embodiment ratings for most participants [Waltemate et al. 2018], which would prevent us from exploring the influence of individual traits on embodiment. We therefore decided to use gender-matched generic avatars to obtain a higher variability in embodiment ratings, i.e., to obtain both low and high embodiment ratings across participants. Also, the animation of the virtual character threatening the participant's hand at the end of the task was recorded using an Xsens motion capture system prior to the experiment, and mapped onto another virtual character (see Figure 2.1, right).

Collected Data

Embodiment and Presence Questionnaires

To measure embodiment, participants were asked to fill in the subjective questionnaire proposed by Gonzalez-Franco and Peck [2018]. It is composed of questions divided in several categories: body ownership, agency, tactile sensations (not used in our experiment), location, external appearance and response to external stimuli (referred to as threat per-Chapter 2 -Understanding Individual Differences in the Sense of Embodiment ception in this chapter). Participants therefore answered 19 questions on a 7-point Likert scale.

Given the shortness (6 questions) of the Slater-Usoh-Steed (SUS) presence questionnaire [Usoh et al. 2000] typically used in such experiments in the past, we also decided to include this questionnaire. People rated each question on a 7-point Likert scale. Our goal was to confirm previous results linking personality to presence, despite the already important number of questionnaires in our study. In particular, assessing how similar our results are to previous work on the relation between personality and presence would also be of value to further validate potential results on the sense of embodiment.

Behavioural Response

In addition to the embodiment questionnaire, we recorded participants' hand movements during the threat (character stabbing the participant's virtual hand at the end of the experiment), in order to evaluate how much participants considered the avatar to be their own body. In this situation, typically used in previous studies to provide another measure of the sense of embodiment, participants who feel embodied in their avatar are more likely to remove their hand [START_REF] Ehrsson | Threatening a rubber hand that you feel is yours elicits a cortical anxiety response[END_REF]], suggesting that they consider the virtual body to be their own.

Psychological Variables

As we wished to explore the effect of several aspects of personality and ability on embodiment, we selected a number of questionnaires which participants filled in after the experiment. These questionnaires were chosen to explore aspects we believed could influence embodiment, while ensuring that the duration for answering all these questionnaires was reasonable. Our choice was also based on the few studies conducted on internal factors, using for example body awareness and locus of control as independent variables. Four questionnaires were therefore selected (BFI, TIPI, IPC, BAQ), which are presented below with our corresponding exploratory questions of interest. Research questions were preferred instead of precise hypotheses because of the lack of literature and the wide range of traits evaluated in our experiment. On average, participants took 20 minutes to answer all the questionnaires. It is also important to mention that the experiment was conducted on a French campus, and that we therefore used the French validated translation of these international questionnaires in our experiment. All the Likert scales used are the ones pro-posed in each validated questionnaire, going from the lower bound (strong disagreement) to the upper bound (strong agreement).

1) Big Five Personality traits taxonomy is a common way of describing one's personality, even though not the only one that exists. In this model, called the Big Five or OCEAN model [START_REF] Goldberg | An Alternative "Description of Personality": The Big-Five Factor Structure[END_REF]], personality is typically described by five dimensions, which are Openness to experience, Conscientiousness, Extraversion, Agreeableness and Neuroticism. While several questionnaires of various complexity exist to assess these personality dimensions (e.g., 240-item NEO PI-R, 44-item BFI) we chose two questionnaires to use in our experiment.

First, we used the 44-item Big Five Inventory (BFI) [START_REF] John | The Big Five Inventory-Versions 4a and 54[END_REF]] adapted to French by [START_REF] Plaisant | Validation du Big Five Inventory français (inventaire des cinq grandes dimensions de la personnalité)[END_REF], where each item is rated on a 5-point Likert scale. This is a relatively short questionnaire, compared for example to the 240-item NEO PI-R questionnaire, but still quite complete [START_REF] John | The Big-five Trait Taxonomy: History, Measurement, and Theoretical Perspectives[END_REF], and used in research [START_REF] Jacques | Personality and virtual reality team candidates: The roles of personality traits, technology anxiety and trust as predictors of perceptions of virtual reality teams[END_REF][START_REF] Bélisle | Avatars as information: Perception of consumers based on their avatars in virtual worlds[END_REF]. It therefore seemed more adapted to an experiment involving several questionnaires. In this regard, a first question of interest was to study whether some personality traits were potentially correlated with the different components of embodiment (Q1).

However, despite the popularity of the BFI questionnaire and its relatively short length (44 items), being able to evaluate quickly how a user's personality traits would affect embodiment prior to a VR experience would be greatly improved if shorter questionnaires could be used. Therefore, we decided to include a second personality questionnaire, namely the Ten Item Personality Inventory (TIPI) [START_REF] Gosling | A Very Brief Measure of the Big Five », en, in: Personality Domains[END_REF], and used the French version [START_REF] Storme | Psychometric Properties of the French Ten-Item », en, in: Personality Inventory (TIPI)[END_REF], where each item is rated with a 7-point Likert scale. In particular, our goal was to study the extent to which the TIPI questionnaire would enable us to explain embodiment felt in VR compared to the more complete BFI questionnaire (Q2).

Our research questions related to the influence of Big Five personality traits on the sense of embodiment were therefore: Q1: Are some of the users' Big Five traits correlated with their sense of embodiment in VR? Q2: Do TIPI and BFI questionnaires show similar personality traits correlations with the sense of embodiment in VR?

2) Locus of Control (LoC) (i.e., the degree to which people believe that they have control over the outcome of events in their lives as opposed to external forces beyond their control) is another set of personality traits, which was demonstrated to have an influence on the sense of presence [START_REF] Murray | Absorption, dissociation, locus of control and presence in virtual reality[END_REF]Wallach et al. 2010] and on the sense of agency [START_REF] Jeunet | Do you feel in control? " : Towards Novel Approaches to Characterise, Manipulate and Measure the Sense of Agency in Virtual Environments[END_REF]. We therefore included a questionnaire to measure one's LoC, and used the common 24-item IPC scale [Levenson 1981], translated in French by Loas et al. [1994], using a 6-point Likert scale. This questionnaire determines LoC according to three dimensions: Internal, Powerful others and Chance. These dimensions typically mean that someone with an external LoC will tend to think that everything happens because of fate (chance type of locus) or powerful people (powerful others type of locus), while someone with an internal LoC will tend to think that he/she can change events with his/her own will and actions.

As a previous study [START_REF] Jeunet | Do you feel in control? " : Towards Novel Approaches to Characterise, Manipulate and Measure the Sense of Agency in Virtual Environments[END_REF] showed that an internal LoC is positively correlated with the sense of agency, we expected to find the same results in our study (Q3). Moreover, while this seems in agreement with the fact that the LoC is directly related to the action, there is no information about the possible influence of LoC on the sense of ownership. Therefore, we investigate whether ownership could also be correlated with an internal LoC (Q4), since some studies found that the sense of ownership and the sense of agency are based on similar processes and can strengthen each other [START_REF] Kalckert | Moving a Rubber Hand that Feels Like Your Own: A Dissociation of Ownership and Agency[END_REF][START_REF] Dummer | Movement and the Rubber Hand Illusion[END_REF]].

Our research questions related to the influence of internal and external LoC on the sense of embodiment were therefore: Q3: Is an internal LoC positively correlated with the sense of agency, as previously found [START_REF] Jeunet | Do you feel in control? " : Towards Novel Approaches to Characterise, Manipulate and Measure the Sense of Agency in Virtual Environments[END_REF]]? Q4: Is the sense of ownership also correlated with an internal LoC?

3) Body Awareness is a cognitive ability that makes us aware of our body processes. Because it can change the way we perceive our real body, there is a possibility that it could also influence the perception of our virtual body. While body awareness was not found to influence the RHI in the physical world [START_REF] David | Susceptibility to the rubber hand illusion does not tell the whole body-awareness story[END_REF]], another study showed that it could be disturbed by the body ownership illusion [Tsakiris et al. 2006]. Furthermore, to our knowledge, no studies were conducted to investigate its influence on the sense of embodiment in VR. We therefore decided to also include this personal ability in our study, and used the 18-item Body Awareness Questionnaire (BAQ) [START_REF] Shields | The Body Awareness Questionnaire: Reliability and Validity[END_REF], where each item is rated on a 7-point Likert scale, translated in French by [START_REF] Dumont | Expérience subjective et différences individuelles dans l'intégration d'informations visuelle et kinesthésique[END_REF]. This questionnaire is a self-report assessment of the body awareness, estimating the attention and consciousness we have of our body processes, often used in research because of its high reliability and validity compared to other self-report instruments [Mehling et al. 2009].

Results

Our research question related to the influence of body awareness on the sense of embodiment was therefore: Q5: Is body awareness correlated with the sense of embodiment?

Results

In order to analyse the link between internal factors and the sense of embodiment, Section 2.3.1 first explores the relationship between the embodiment scores (ownership, agency, self-location, external appearance and threat perception) and the Big Five, IPC and body awareness data. The data from the TIPI questionnaire are not discussed as there were no significant results (Q2 is therefore answered negatively). Then, Section 2.3.3 analyses the behavioural responses and Section 2.3.4 the presence results.

Embodiment Questionnaire (Version 1) Analysis

The analysis in this section was performed using the embodiment questionnaire filled in by the participants, i.e. the version from 2018 [START_REF] González-Franco | Avatar Embodiment. Towards a Standardized Questionnaire[END_REF]]. An additional analysis inspired by the second version of the questionnaire will be presented in the following section.

Before conducting the following analyses, we analysed the potential effects of gender and experience in VR on the embodiment questionnaires. Regarding gender, we performed Mann-Whitney tests for each question trying to find significant differences over such potential confounding factors. The analysis only showed two significant differences for body ownership related questions (O2 and O5) between male and female participants, while no significant differences were found for the rest of the questions and factors. A summary of embodiment answers is presented in Table 2.1, separated by men and women answers when relevant.

In order to prevent such differences from adding noise to the rest of the analysis, the population was split into two groups (men and women) for the body ownership analysis. Regarding experience in VR and video games, we used Pearson correlations to explore a potential influence on embodiment. We only found a positive correlation between agency and the experience in video games. For this reason, experience in video games is only reported in the section on Agency. As we ran the same analysis for each aspect of embodiment, we summarise the procedure here for clarity. More precisely, we ran a separate Table 2.1 -Statistical summary of the embodiment questionnaire responses. For each question we report the median and the first and third quartiles. If there was a significant difference between the men and women answers, we report the summary for each group. O: body ownership, A: agency, L: self-location, EA: external appearance, T: threat perception. Pearson correlations were then computed (see summary in Table 2.5) to explore potential links between the different components of embodiment and the internal factors questionnaires results. As we did not find results for the sense of self-location, this part was removed from the analysis. A multiple linear regression was performed when correlations were found for a given component, as in other cases it would be difficult to find a good model with variables that are not correlated with the studied component. We used a backward stepwise method to select the best predictors, using the Akaike Information Criterion (AIC), i.e. we started with all the variables and progressively removed them so as to minimise the AIC value. We chose the AIC over the adjusted R 2 as it also accounts for the complexity of the model [START_REF] Faraway | Extending the linear model with R: generalized linear, mixed effects and nonparametric regression models[END_REF]]. All the multiple linear regression models computed are summarised in Table 2.3.

ID

Body Ownership

As answers to body ownership questions were significantly different for men and women, we performed two separate analyses for men and women participants.

Men. Two components were selected (O P C1,M and O P C2,M ), which explained 65% of the variance. O P C1,M was mainly influenced by the questions O1, O2, O4 and O5, while O P C2,M was mostly influenced by O3.

We only found a positive correlation between O P C1,M and the chance type of LoC (r = 0.248, p = 0.047). As we did not find correlations between O P C2,M and any of the variables, we do not consider it further.

Results

Table 2 We performed a multiple linear regression for O P C1,M using the different psychological variables. We obtained a model with internal LoC, chance LoC and body awareness (adjusted R 2 = 0.169, p = 0.003).

Women. Two components were selected (O P C1,F and O P C2,F ), which explain 63% of the variance. O P C1,F was mainly influenced by the questions O1, O2 and O3, while O P C2,F was mostly influenced by O4 and 05.

Then, we found a negative correlation between openness and O P C1,F (r = -0.293, p = 0.026), as well as positive correlations between O P C2,F and both the chance type LoC (r = 0.366, p = 0.005) and the powerful others LoC (r = 0.427, p < 0.001). The linear regression for O P C1,F gave us a model with openness, conscientiousness, internal LoC, powerful LoC, chance LoC and body awareness (adjusted R 2 = 0.239, p = 0.002).

Agency

One component was selected (A P C1 ) which explains 48% of the variance. It was mainly influenced by the questions A1, A2 and A4. We found a positive correlation between A P C1 and the internal LoC (r = 0.248, p = 0.006). The linear model found for A P C1 was composed of agreeableness, internal LoC and body awareness (R 2 = 0.079, p = 0.005). We also found a positive correlation between A P C1 and the level of experience in video games (r = 0.184, p = 0.04).

External Appearance

One component was selected (EA P C1 ), which explains 51% of the variance and was influenced positively by all the questions on appearance (EA1 to EA4). We only found correlations with the internal LoC (r = 0.195, p = 0.031) and chance LoC (r = 0.201, p = 0.026).

However, as it seemed surprising that external appearance was simultaneously influenced by opposite (i.e., internal and external) types of LoC, we performed further Pearson correlations separately on the male and female populations, and found that the external appearance was more strongly related to the internal LoC for men (r = 0.306, p = 0.013) and to the chance LoC (r = 0.311, p = 0.017) for women.

We performed two multiple linear regressions, by separating male and female populations. For men, the optimised model was composed of neuroticism, internal LoC and

Results

chance LoC (adjusted R 2 = 0.169, p = 0.002). For women, the optimised model was only composed of chance LoC (adjusted R 2 = 0.081, p = 0.017).

Threat Perception

One component was selected (T P C1 ), which explains 84% of the variance. All the questions about threat perception (T1 to T4) contributed positively to this component. A positive correlation was found with neuroticism (r = 0.258, p = 0.004). The linear regression gave us a model with agreeableness and neuroticism (adjusted R 2 = 0.088, p = 0.001).

Additional Analysis: Embodiment Questionnaire (Version

2)

We performed an additional analysis with the updated version of the embodiment questionnaire [Peck and Gonzalez-Franco 2021]. This version has 16 questions (instead of 25 in the first version) that are classified into four components obtained from a PCA. It was published after we performed the first analysis, but we wanted to support a posteriori the validity of our results. Because we did not include several questions in our study (question R2 about proprioceptive drift because the avatar was co-located, question R7 because we did not need a customised question, and questions R14 to R16 because we had no tactile stimulation), we could not perform the analysis recommended in the paper. An analysis with a PCA, similar to the one performed to obtain the new version of the embodiment questionnaire, was therefore performed instead. The goal was to see whether the components obtained were similar to the ones found in the second version of the questionnaire, and whether the results for our study were still similar.

In this study, we used 19 out of the 24 questions from the first version of the questionnaire. First, the Pearson correlations between the different questions scores were computed. If the questions were correlated (r > 0.3) with less than three other questions, or too highly correlated with other questions (r > 0.9), they were removed. At this step, questions A2, A4, L1 and EA3 were removed because they were correlated with less than three other questions. Then, the individual Kaiser-Meyer-Olkin (KMO) value for each remaining question was computed. Question O5 had the lowest KMO value (0.56) and was correlated (r > 0.3) with only three other questions, therefore we decided to remove it. At the end, only 14 questions remained.

On these 14 questions, a Polychoric PCA was conducted. Using the empirical Kaiser criterion (the eigen value must be greater or equal to one), three principal components were kept. The fourth component had an eigen value equal to 0.98, which is close to 1. To explain more than 60% of the variance, we decided to keep four components. We then performed an oblimin rotation and kept questions having a loading greater than |0.4|. As performed by Peck and Gonzalez-Franco [2021], we computed the score for each component with equal weight for each question, which gave the following formula:

-TC1: T1 + T2 + T3 + T4 (questions about perception of threat) -TC2: O1 -O2 + O4 + EA4 (questions about ownership and appearance) -TC3: O3 + A3 + L2 + EA1 + EA2 (questions mostly about feeling out of the body or losing control) -TC4: -O2 + A1 (one question about ownership and one about agency)

These components explain 65.4% of the variance. We then computed the correlations between these components and the different psychological variables (Big Five traits, LoC and body awareness). We found a positive correlation between TC1 and Neuroticism (r = 0.258, p < 0.01) which is in line with results from the first version of the questionnaire. We also found positive correlations between TC2 (asking globally about ownership) and both Internal (r = 0.239, p < 0.01) and Chance LoC (r = 0.252, p < 0.01). This is similar to correlations already found in the previous analysis, where external appearance was correlated to both Internal and Chance LoC. TC3 was positively correlated with both Neuroticism (r = 0.181, p < 0.05) and Chance (r = 0.186, p < 0.05). It is difficult to compare this result to the previous ones, as this component mixes several categories of questions. Finally, TC4 (asking about being in control and the avatar not being someone else) was positively correlated with Internal LoC (r = 0.287, p < 0.01), which is also in line with previous results.

Threat Response

In order to evaluate participants' response to the threat in a more objective manner, we also computed their accumulated right hand motion (the stabbed hand) during the threat period to determine whether they reacted or not to this threat. More precisely, we computed the accumulated right hand motion between the moment when the knife was above the hand (approximately 0.5s before the stab) and the moment when the character removed the knife (approximately 1.5s after the stab). Six participants were removed from

Results

the analysis because of missing data (controllers positions were not saved), one because he/she removed his/her hand without holding the controller, and one because he/she removed his/her hand before the stab.

Across participants, the average accumulated hand motion was 9.15 ± 19.7 cm (me-dian=1.93cm; min=1.05cm; max=114cm), which was positively correlated with the threat perception score (r = 0.561, p < 0.001). In addition, we computed Pearson correlations between the participants' accumulated hand motion and their psychological variables, to determine if their personality traits or abilities would influence the degree to which they reacted to the threat, but we did not find significant correlations.

However, as the threat response can also be considered as a binary variable (whether participants reacted or not), we then performed a further analysis by computing a multiple logistic regression model on whether participants reacted or not. In particular, we considered that participants reacted to the threat if their accumulated hand motion was greater than 5cm (threshold experimentally identified from the experimenter's records of whether participants actually reacted). With this criterion, 30 participants were considered to have reacted to the stab out of the 115 participants kept for this analysis. We then used AIC to select the variables to remove from the multiple logistic regression model, and found a model only composed of neuroticism (β = 0.027, p = 0.022) and chance LoC (β = -0.062, p = 0.140).

Personality Influence on Presence

As previously mentioned, we also asked participants to answer presence questionnaires to assess how similar our results on the relation between personality and presence were from previous work, as well as to strengthen potential results on the sense of embodiment.

While we used Polychoric PCA to analyse the results of embodiment, previous work on presence commonly used a simple mean score over the SUS questions. In order to compare our results to previous work, we therefore followed the same procedure. As for the sense of embodiment, we studied Pearson correlations to identify potential links between presence and personality traits. We found positive correlations with agreeableness (r = 0.227, p = 0.012) and with the internal LoC (r = 0.203, p = 0.024) (see Table 2.4).

We performed a multiple linear regression which gave us a model composed of agreeableness, neuroticism, internal LoC and chance LoC (adjusted R 2 = 0.134, p < 0.001).

Additional Results

In order to get a clearer understanding of the potential relations between the different aspects of embodiment, we also computed Pearson correlations between all the components that relate to the sense of embodiment. Across men and women participants, we first found a positive correlation between external appearance (EA P C1 ) and threat perception (T P C1 ) (r = 0.327, p < 0.001), showing that participants tended to be more sensitive to the threat on their avatar when they also rated higher questions on external appearance.

As body ownership analyses were performed separately on men and women, because of significant differences in answering some of the questions, we also looked at correlations separately in this context. First it is interesting to note that we found a positive correlation between external appearance (EA P C1 ) and all the men and women ownership components (O P C1,M : r = 0.345, p = 0.005; O P C2,M : r = 0.287, p = 0.020; O P C1,F : r = 0.564, p < 0.001; O P C2,F : r = 0.593, p < 0.001). For both men and women, we also found a correlation between the threat perception (T P C1 ) and their first ownership component (O P C1,M : r = 0.355, p = 0.004; r = 0.289, p = 0.028).

Discussion

This experiment on the sense of embodiment, in which 123 participants took part, is to our knowledge the first VR experiment measuring embodiment as well as several personality traits and body awareness. Our aim was to explore how internal factors (individual differences) could modulate virtual embodiment experiences. In this section, we discuss the obtained results for each aspect of embodiment, as well as future work.

Sense of Embodiment

For each aspect, we first discuss the global obtained scores. While we used PCA for the analysis, here we mention scores for the different aspects using summation equations provided by [START_REF] González-Franco | Avatar Embodiment. Towards a Standardized Questionnaire[END_REF] in order to provide a simpler interpretation for discussion. Then we discuss the results concerning the Big Five traits and the locus of control, and finally potential other noticeable results like differences between men and women or interesting correlations with other variables.

Body Ownership

Overall, body ownership scores were in the average (M = 4.3; SD = 1.1), with a high variability, i.e. people presenting either low or high levels of body ownership. This could be explained either by the individual differences of participants and/or the use of a generic avatar. Our results also show that the question related to the co-located virtual body (O1) was rated higher than the question related to the avatar visible in the mirror (O4), which seems to suggest that the use of a mirror could be detrimental in some cases, as it might emphasise the appearance differences.

Regarding the influence of personality traits, our results first demonstrated that body ownership is to some extend correlated with external dimensions of the locus of control, both for male and female participants. This result answers Q4, but not as expected. Since the sense of ownership and agency usually strengthen each other, we expected ownership to be correlated with an internal locus of control, as is the case for agency. However, our results suggest that body ownership is actually more influenced by external dimensions of the locus of control. Typically, people with an external locus of control tend to think that things happening to them depend mostly on the influence of other people or chance. Therefore, our results suggest that people with an external locus of control might feel embodied in a virtual representation more easily than people with an internal locus of control.

In conducting this study, we expected some of the Big Five personality traits to influence ownership (Q3). However, our results did not show any evidence of such an influence. Similarly, we also measured body awareness, i.e., the cognitive ability of being aware of body processes, which we supposed could also influence embodiment in general (Q5). Even though body ownership scores tended to be low for people with high body awareness, the results were not significant. Similarly, experience in VR and video games, which could have influenced body ownership, did not show any influence, suggesting that experience in virtual-type applications does not influence how one's accept a virtual body as its own. Finally, we also noticed that women gave higher scores to the question O5, which means that they had a higher feeling that the avatar in the mirror was someone else. It is difficult to assess what might explain this result, but a possible assumption would be the fact that the avatars were not personalised. More precisely, it is possible that the male avatar had more average physical characteristics regarding the population of the experiment than the female avatar (brown hair and average build for male avatar compared to blond hair and skinny body for female avatar). While this result shows that differences can appear between different user groups as it was previously found in other studies [START_REF] Schwind | These Are Not My Hands!": Effect of Gender on the Perception of Avatar Hands in Virtual Reality[END_REF], and that the visual resemblance of the avatar might also influence these results, further studies would be necessary to better understand these influences.

Agency

On average, agency scores were high (M = 5.1; SD = 0.7), showing that participants felt in control of the avatar's movements. First, we found that the sense of agency is correlated with the internal dimension of the locus of control, which positively answers our question Q3 and is in line with previous findings [START_REF] Jeunet | Do you feel in control? " : Towards Novel Approaches to Characterise, Manipulate and Measure the Sense of Agency in Virtual Environments[END_REF]]. Therefore, it seems that people who feel a higher control on happening events tend to also experience a higher control of their virtual body, and might therefore feel more responsible of the avatar's movements. However, we did not find correlations with the other personality traits from the Big Five. Interestingly, we also found a positive correlation with the level of experience in video games, showing that the more people have experience in video games, the more they feel they have control over their avatar. This result is also supported by participants (with high gaming experience) feedback, who reported that they felt in control both because the avatar was moving well according to their movements and because they felt that there was no latency in the displayed movements.

External Appearance

External appearance scores were overall below average (M = 3.0; SD = 1.3), meaning that participants did not really have the feeling that the avatar looked like them. Our results showed that the acceptance of the avatar's external appearance was positively correlated with the internal and the chance dimensions of the locus of control. This result is particularly surprising as it shows that external appearance is simultaneously influenced by opposite (internal and external) types of locus of control. However, further exploration showed that these effects were due to external appearance being more correlated with an internal locus of control for men, but with a chance locus for women. However, these results cannot be interpreted in terms of differences between men and women's personality traits and can only be interpreted separately. Women with a chance locus of control tend to have higher external appearance scores, i.e., they tend to think that the self-avatar is a look-alike avatar. This result is similar to the one obtained for ownership, which was also correlated for women with an external locus of control and could be explained for the same reasons evoked previously. In contrary, men with an internal locus of control tended to have higher external appearance score. This means that men thinking that they can control their own life tend to more believe their avatar is similar to them. Although those interesting results also highlight differences between groups of population, deeper studies would be required to clarify these effects.

Threat Perception

Threat perception scores were particularly low (M = 2.9; SD = 2.0), which is in accordance with the number of people who actually reacted to the stab (30 out of 115 whose reactions to the threat were recorded). This is supported by the feedback from several participants who did not react to the threat and reported that they felt that the VE seemed "safe", and therefore did not feel threatened. Moreover, we found that threat perception was correlated with neuroticism. Since people with a high degree of neuroticism tend to be anxious, it is understandable that these same people were more impacted by the introduction of the threat. The fear of a threat is also commonly considered as an expression of the sense of ownership in studies exploring the sense of embodiment. If we did observed in our results that the threat perception was also correlated with one component of ownership for both men and women, it is however not enough to make a link between neuroticism and the sense of ownership.

In addition to assessing threat through questionnaires, we also measured the right hand motion in reaction to the stab. The model which better explained the differences between people who reacted from those who did not react was also influenced by neuroticism, which confirms the influence of neuroticism on the response to threat.

Presence

Our goal in investigating whether we found similar effects of personality traits on presence than previous studies was to validate that our experimental setup provided a similar basis than previous studies, which would therefore simultaneously strengthen the value of any results found for the influence of personality traits on the sense of embodiment. As expected, we found similar correlations than in previous studies, namely a correlation between presence and agreeableness [START_REF] Sacau | The impact of personality factors on the experience of spatial presence[END_REF], as well as between presence and an internal locus of control [Wallach et al. 2010].

Conclusion

In this chapter, we presented an exploratory study on the impact of personality traits and body awareness on the sense of embodiment. The major finding of the experiment is that the locus of control is linked to several components of embodiment: the sense of agency is positively correlated with an internal locus of control and the sense of body ownership is positively correlated with an external locus of control. Interestingly, both components are not influenced by the same traits, which confirms that they can appear independently. Taken together our results suggest that the locus of control could be a good predictor of the sense of embodiment when the user embodies an avatar with a similar physical appearance. Given the amount of personality and cognitive models and questionnaires in the literature, it was not possible to be exhaustive, and we decided to focus on some of the most common models. As future work, other personality traits could be explored. While this experiment included a visuomotor task, we did not study the impact of this task on embodiment. Nevertheless, interacting with the VE requires using the avatar and can therefore impact the sense of embodiment. In the following chapters, we will explore embodiment during locomotion and manipulation tasks. The next chapter will focus on the influence of locomotion technique on embodiment, as it has not been studied yet in the community.

"This ride is a journey to, run boy run, the secret inside of you" Woodkid Chapter 3

STUDYING THE INTERRELATIONS BETWEEN LOCOMOTION TECHNIQUES AND EMBODIMENT

Abstract: This chapter explores the potential interrelations between locomotion and embodiment by focusing on the two following questions: Does the locomotion technique have an impact on the user's sense of embodiment? Does embodying an avatar have an impact on the user's preference and performance depending on the locomotion technique?

To address these questions, we conducted a user study (N = 60) exploring the relationship between the locomotion technique and the user's sense of embodiment over a virtual avatar seen from a first-person perspective. Three widely used locomotion techniques were evaluated: real walking, walking-in-place and virtual steering. All participants performed four different tasks involving a different awareness of their virtual avatar. Participants also performed the same tasks without being embodied in an avatar.

Introduction

Locomotion is an essential task in VEs, as it lets users move from one point to another, to explore the VE or to move towards an object. While there were already several studies investigating the link between manipulation techniques and embodiment [Lin et al. 2019], there was no study investigating the potential interrelations between locomotion techniques and virtual embodiment. Yet, locomotion techniques were found to influence the sense of presence, and the level of motion involvement could influence the way users perceive their virtual body. This chapter therefore investigates how locomotion techniques can impact the sense of embodiment, and how embodying an avatar can influence the way users navigate in the VE (in terms of performance and preference). To explore these effects, we conducted a mixed-design experiment in VR. We used three widely used locomotion techniques as a between-subject factor: real walking, walking-in-place and head steering. We chose these techniques because they are all continuous locomotion techniques, with different levels of physical engagement and interaction fidelity. Participants performed four tasks in the VE, with two conditions on their virtual appearance (within-subject factor): full-body animated avatar or only 3D models of controllers.

Experiment

Participants

Sixty-five participants volunteered to take part in our experiment. The majority of them were students and staff from our research center. Five participants were removed from the study: two because of problems in data recording, two because of tracking issues and one because of motion sickness during the first block. In the end, sixty participants (age min=20, max=56, avg=28.9±8.4, 25 women and 35 men) took part in our study. Participants did not receive any compensation. They were all naive as to the purpose of the experiment, and gave written and informed consent. The study conformed to the declaration of Helsinki. Twenty-five participants reported having no or little previous experience in VR (score 1 or 2 out of 7), twenty-four to have some previous experience in VR (score between 3 and 5) and eleven to be experts (score 6 or 7 out of 7).

Apparatus

The experiment was developed using Unity (version 2019.1.0f2). Users were tracked using an HTC Vive PRO HMD (equipped with the HTC wireless adapter so that partic-Figure 3.2 -Left: Setup in the physical environment. The HTC Vive with a wireless adapter was used to enable participants to physically walk in an 8m × 8m area. The tracking of the user's motions was enabled by the two hand controllers and two HTC Vive Trackers attached to their ankles. Two additionnal HTC Vive trackers were also positioned on a backpack to track participants' shoulders. Tracking was done using four HTC Vive lighthouses. Right: Overview of the virtual environment: the navigation area was constrained by the virtual fences which matched the limits of the physical space.

ipants were not hindered by the cable when navigating), two HTC Vive controllers, two HTC Vive trackers positioned on the ankles to track the feet, and two HTC Vive trackers positioned on a backpack to track the shoulders. We used four HTC Vive lighthouses to track an 8m × 8m area. The VE consisted of a flat grassy ground surrounded by fences, matching the dimensions of the physical space, with trees and hills in the background (see Figure 3.2).

The positions of the headset, controllers and trackers on the ankles were used to animate the avatar, using inverse kinematics (FinalIK plugin). Participants were represented by gender-matched avatars (visible in Figure 3.1). During calibration, participants were asked to keep their feet and legs straight to adjust the avatar's feet. They also had to stand straight to adjust the avatar's global scale based on their height.

Locomotion Techniques

To better understand the influence of the presence of an avatar depending on the locomotion technique, we selected different locomotion techniques based on Boletsis's taxonomy [START_REF] Boletsis | The New Era of Virtual Reality Locomotion: A Systematic Literature Review of Techniques and a Proposed Typology[END_REF]]: room-scale-based, motion-based, controller-based and teleportationbased. In particular, we were interested in techniques that are commonly used in VR, and that involved a similar motion in the VE but different levels of physical movement. There-fore, we chose the following techniques: Real Walking (RW; room-scale-based), Walking-In-Place (WIP; motion-based) and Steering (S; controller-based). Despite its inclusion in Boletsis's taxonomy, we did not include teleportation in our study as it creates a discontinuous movement unlike the three other selected techniques. The different techniques are detailed below:

-Real Walking (RW): Participants could physically walk in an 8m × 8m area. A one-to-one control mapping was kept between the physical and the virtual motions.

-Walking-In-Place (WIP): we implemented a WIP algorithm which detects walking patterns based on the position of the ankles [START_REF] Kim | Sensor-fusion walking-in-place interaction technique using mobile devices[END_REF][START_REF] Bruno | A new approach to walking in place[END_REF]], which were tracked using Vive trackers. Locomotion was initiated whenever a first step was detected, i.e., when the two ankles' position had consecutively passed above a given threshold (initial tracker position + 5cm). It was stopped whenever a step had not been detected in the last 0.8s. Because participants tend to take lower steps over time, the threshold was decreased to a value equal to the initial tracker position + 2cm after they started stepping. The thresholds were determined empirically through iterative design and several user tests. The direction was determined by the participant's head orientation.

-Steering (S): in this technique, participants navigated in the VE using a constant navigation speed while keeping the Vive controller button held down, which is a common approach in both VR and video games. We chose a head-steering implementation (i.e., navigation direction determined by the participant's head orientation), as it is commonly used, easy to get familiar with, and because the tasks in our experiment did not require looking in another direction than the one in which people were headed.

While previous work identified that people usually walk in real situations at a comfort speed of approximately 1.3m/s [START_REF] Bohannon | Comfortable and maximum walking speed of adults aged 20-79 years: reference values and determinants[END_REF]], several studies demonstrated that participants tend to walk slower in an immersive VE [START_REF] Mohler | Gait parameters while walking in a head-mounted display virtual environment and the real world[END_REF][START_REF] Agethen | Behavior Analysis of Human Locomotion in the Real World and Virtual Reality for the Manufacturing Industry[END_REF][START_REF] Berton | Studying Gaze Behaviour during Collision Avoidance with a Virtual Walker: Influence of the Virtual Reality Setup[END_REF], especially when wearing an HMD. We therefore set the navigation speed of both the Steering and Walking-In-Place techniques to 1.0m/s, which should approximately match the speed observed while walking with an HMD [START_REF] Agethen | Behavior Analysis of Human Locomotion in the Real World and Virtual Reality for the Manufacturing Industry[END_REF][START_REF] Berton | Studying Gaze Behaviour during Collision Avoidance with a Virtual Walker: Influence of the Virtual Reality Setup[END_REF].

At this point, it also seems important to point out that for all three techniques in our experiment, the avatar's movements were always driven by the participants' actual Chapter 3 -Studying the Interrelations Between Locomotion Techniques and Embodiment movements when they were embodied in a virtual avatar. This means that a) for the real walking technique, the avatar walked as the participant physically walked; b) for the walking-in-place technique, the avatar performed steps on the spot like the participant, while being translated forward in the direction in which participants were looking; c) for the virtual steering, since participants did not move forward in the real world, the avatar stood like the participant, moved its feet like the participant when they turned on the spot, or "slid" along the ground in the direction participants were looking towards.

Experimental Tasks

The experiment was divided into four tasks (see Figure 3.1), which were designed to ensure that participants were aware of their virtual body, i.e. that parts of the avatar were directly visible from the participant's perspective. The main design principle for defining the tasks was to ensure that participants were able to see different parts of their virtual body during the experiment in a consistent way.

-Training task: The first task was a training task, which goal was to get participants used to the VE and the locomotion technique. More precisely, participants were instructed to navigate in the VE, in order to pick mushrooms on the ground by touching them with either hand. This task lasted one minute.

-Corridor task: The aim of this task was to enable participants to see their entire avatar moving, while navigating in a VE. They were therefore instructed to walk back and forth in a corridor with mirrors at both ends. A line in front of the mirror indicated where subjects were to turn around so as to not go through the mirror. This task lasted two minutes.

-Path-following task: The aim of this task was to force participants to look at their avatar, in particular at their feet, while navigating. They were therefore instructed to follow a target moving on an eight-shaped trajectory, both displayed at the ground level. The target was always 50cm ahead of them so that participants had to tilt their head, thus ensuring that the avatar's legs were inside their field of view. This task lasted two minutes.

-Columns task: The aim of this task was to study people's behaviour while navigating around virtual obstacles. They were instructed to navigate in a VE filled with 2-metre high columns and to pick mushrooms as in the training task. In this task, people could therefore mostly see their hands and arms. The mushrooms were always placed at the same positions. They were displayed in groups of ten, with new mushrooms appearing once all those of a series were picked. The distance between columns was 1.45 times the shoulder width of the scaled avatar, to ensure that any participant could move through without necessarily turning their shoulders (which requires an aperture-to-shoulder ratio lower than 1.4 [START_REF] Warren | Visual Guidance of Walking Through Apertures: Body-Scaled Information for Affordances[END_REF]Mestre et al. 2016]). This task lasted two minutes.

The tasks were always presented in the same order: training, corridor, path-following and columns. As we were interested in evaluating the overall users' subjective experience, we considered that keeping the same order would reduce the variability in their subjective assessment. Furthermore, we did not compare the tasks with one another.

Experimental Protocol and Design

First, participants signed the consent form. Then they were equipped with the HMD, the controllers and the trackers.

We had two independent variables: Technique and Appearance. For the Technique, we used a between-subjects design, so each participant used only one of the three locomotion techniques presented in Section 3.2.3. There were twenty participants per group. For the Appearance condition, a within-subject design was chosen. Two levels were used: Full-Body Avatar (FBA) and No Avatar (NA). In the FBA condition, participants were represented by a full-body gender-matched avatar holding a 3D model of an HTC Vive controller in each hand, while in the NA condition, only the 3D models of the Vive controllers were displayed. Therefore, the experiment was divided into two blocks (FBA and NA). In total, participants performed 2 x 4 tasks. To minimize potential ordering effects, the blocks were counterbalanced and there was a 5-minute break between them. Participants therefore either performed all the four tasks (in the order presented above) in the FBA condition, then all four tasks in the NA condition, or the opposite (see Table 3.1). The whole session lasted about 40 minutes, including the participant's welcome, performing the experiment, and answering questionnaires.

As dependent variables, we used both objective (performance) and subjective (user preference, embodiment) criteria.

Chapter 3 -Studying the Interrelations Between Locomotion Techniques and Embodiment

Objective Data

Objective data were measured in only two tasks (path-following and columns tasks). No objective data were recorded during the training task as the aim of the task was only to make users familiar with the given locomotion technique. Similarly, there was no relevant performance criterion in the corridor task.

-Path-following task: The mean distance between the path to follow and the user's position was computed as an objective measure of performance.

-Columns task: We measured both the number of mushrooms picked during the columns task, and the number of collisions with the columns, as an objective measure of performance. Because the number of collisions can also depend on the distance covered by participants, we normalized the number of collisions by the distance covered (in metres). We counted collisions between the participants' shoulders (tracked by the additional Vive trackers) and columns, hereafter referred as shoulder collisions.

Subjective Data

Subjective questionnaires were also used to obtain user perception of the experience.

Embodiment questionnaire: We used the ownership, agency and self-location questions from the embodiment questionnaire proposed by Gonzalez-Franco and Peck [2018] (see Table 4.4). These questions were evaluated on a 7-point Likert scale from 1 (Strongly disagree) to 7 (Strongly agree). The questionnaire was administered only after the FBA block.

Representation questionnaire: After each block, participants were asked questions related to the virtual representation (R questions in Table 3.3). These questions were about both the virtual representation seen indirectly in the mirror and in other tasks from the first-person perspective. The goals of these questions were mainly to detect whether people were disturbed by their representation (R M irrorLogical and R OtherLogical ) and whether they appreciated it (R M irrorP leasing and R OtherP leasing ). Each item was measured on a 7-point semantic differential scale. Participants answered these questions once after each block. Comparison questionnaire: Participants were also asked to answer several additional questions after the last block, related to whether they preferred the presence of an avatar or not (see Table 3.4). Questions C pref erBody , C pathEasier and C columnsEasier were rated on a 7-point semantic differential scale while question C behaviourDif f erent was rated on a 7point Likert scale. Participants could also associate an adjective with each Appearance condition, explaining why they preferred to have an avatar or not, as well as make free comments about the experiment.

SSQ:

Additionally, the Simulator Sickness Questionnaire (SSQ) [START_REF] Kennedy | Simulator sickness questionnaire: An enhanced method for quantifying simulator sickness[END_REF]] was given to participants before and after the experiment, and we computed the difference between pre-experiment and post-experiment scores to verify that there were no differences in terms of sickness between the different conditions.

Hypotheses

Previous studies have shown the impact of physical implication on the sense of embodiment [START_REF] Synofzik | I move, therefore I am: A new theoretical framework to investigate agency and ownership[END_REF]. Moving in the VE seems to let the brain compare the movement intention with the feedback of the action, which is one of the ways to increase the sense of agency [START_REF] Synofzik | The experience of agency: an interplay between prediction and postdiction[END_REF] if there is a match. This sense of agency can strengthen the sense of ownership [START_REF] Kalckert | Moving a Rubber Hand that Feels Like Your Own: A Dissociation of Ownership and Agency[END_REF]]. Thus, we expected that the higher the match between proprioception and sensory feedback, the higher the felt embodiment would be, leading to the following hypothesis: H1 The sense of embodiment is influenced by the locomotion technique. In particular, we expected the sense of embodiment to be higher for techniques with a higher interaction fidelity (i.e., RW > WIP > S).

Chapter 3 -Studying the Interrelations Between Locomotion Techniques and Embodiment

In addition, because an avatar provides a better spatial awareness [START_REF] Draper | Exploring the Influence of a Virtual Body on Spatial Awareness[END_REF]], we expected that participants would avoid the columns more in the columns task with the FBA condition. Participants could also see the columns as a threat for their avatar. Thus our second main hypothesis was: H2 The presence of an avatar leads to less collisions with the virtual environment. Furthermore, we also included secondary hypotheses, related to the other collected variables:

H3 People find having a full-body avatar while navigating in a VE more pleasing and logical (R questions).

H4 People think that their representation is more disturbing when using WIP and S than RW (R questions).

Analysis

Mixed two-way ANOVA analyses were used taking into account both the Technique (between-subjects) and the Appearance (within-subjects) factors. We tested the normality assumption using the Shapiro-Wilk normality test. When the data were not normal, we applied an Aligned Rank Transformation (ART) on the data before performing the ANOVA analysis. Tukey HSD post-hoc tests (α = .05) were conducted to check significance for pairwise comparisons. Kruskal-Wallis tests were however conducted when analysing results depending only on the Technique (between-subjects), as the Shapiro-Wilk tests significantly rejected the null hypothesis according to which the data were normally distributed. Dunn's post-hoc tests were conducted to perform pairwise comparisons.

Effect of the Locomotion Technique on Embodiment

First of all, we used a Mann-Whitney's test to identify potential ordering effects between the FBA and NA conditions. As we did not find any significant effect, order will not be considered in the remainder of the analysis.

We performed Kruskal-Wallis tests to explore differences in embodiment ratings between the different techniques, using the questions about the senses of ownership, agency and self-location. We only found a significant effect of the Technique on the question SL located about self-location (χ 2 = 9.623, p < 0.01). Dunn's test revealed that the RW C pathEasier I felt that performing the path-following task was easier without an avatar (1) vs. with an avatar (7) 4 [3;6] C columnsEasier I felt that performing the columns task was easier without an avatar (1) vs. with an avatar (7) 4 [4;5] C behaviourDif f erent I have the impression that my behaviour was different with an avatar vs. without an avatar 5 [4;6] condition obtained significantly higher scores than WIP and S conditions (see values in Table 4.4). We did not find any significant difference between any of the three techniques for all the other questions. These results therefore do not support H1. Medians and quartiles for each question are available in Table 4.4. Although not significantly different, the scores for the questions O someoneElse and O someoneElseM irror were higher for the RW condition. We also computed the overall ownership, agency and self-location ratings using the recommendations from Gonzalez Franco and Peck [2018], and did not find any significant difference. Overall, the agency ratings (M = 5.00, SD = 0.81) as well as self-location ratings (M = 5.43, SD = 1.09) were high. For ownership, the scores were slightly lower (M = 4.60,

Analysis

SD = 1.21).

Users' Performance and Collision Avoidance

We performed a mixed two-way ANOVA to study the potential differences between the different techniques (between-subjects factor) and the avatar conditions (within-subjects factor) on the objective measures of the path-following (mean distance to trajectory) and columns task (shoulder collisions, number of collected mushrooms). We did not find any main effect of the Appearance or interaction effects on these objective measures (see Table 3.5). In particular, this result does not support H2 (no influence on the number of collisions). These results were also confirmed by participants' answers to the subjective questions about the ease of tasks (questions C pathEasier and C columnsEasier in Table 3.4, which results are detailed in Section 3.3.3.2). Participants did not find the task easier in one or the other Appearance condition, which is coherent with the objective data. Table 3.5 -Performance results: mean distance to trajectory (in cm), ratio of shoulder collisions, and number of picked mushrooms.

Users' Preferences

We also performed a mixed two-way ANOVA to explore the differences in the subjective answers between the different conditions (Technique and Appearance). Some questions were meant to indirectly compare appearance between the two blocks, while others were meant to directly ask participants which condition they preferred at the end of the experiment.

Representation questionnaire

For the questions about the virtual representation, we found a main effect of Appearance for the question R M irrorLogical (F 1,57 = 4.48, p < 0.05). Post-hoc tests showed that participants felt that being embodied in an avatar was more logical (M dn = 5, IQR = 3 -6) than without (M dn = 4, IQR = 3-6). We also found an effect of Appearance for the question Chapter 3 -Studying the Interrelations Between Locomotion Techniques and Embodiment R OtherP leasing (F 1,57 = 9.341, p < 0.01). Only the results of R M irrorLogical and R OtherP leasing support H3. Also, we observed that participants provided lower ratings for the R M irrorLogical and R M irrorP leasing questions compared to R OtherLogical and R OtherP leasing respectively. Being in front of the mirror seemed to have a negative impact on the participants' answers.

No effect of the locomotion Technique was found on questions about representation, which does not support H4.

Comparison questionnaire

Regarding the questions directly asking participants to compare conditions, the results show a slight preference for the condition with an avatar, with all medians ≥ 4 for C pref erBody . Yet, we observed a polarization for S (see Figure 3.3), some participants not at all preferring having a virtual body (≤ 2), and others showing a high preference (= 7). These results were not visible for the WIP and RW conditions in which participants provided more consistent answers with a slight preference over the avatar. Regarding the questions asking to compare the level of ease between the two blocks (see Table 3.4, C pathEasier and C columnsEasier ), participants did not find the path-following and column tasks to be easier in one condition or another (answers around 4), independently of the Technique.

Additional Analyses

While we did not find that the presence of an avatar affected the number of collisions with the environment, previous studies have shown that people being embodied in an avatar usually tend to avoid obstacles more in the VE [Mestre et al. 2016;Pan and Steed 2019]. Therefore, we decided to explore this effect in more details by analyzing whether the number of collisions could be influenced by the level of embodiment reported by participants. In order to investigate this effect, we computed the correlations (Spearman) between the embodiment questionnaire and the amount of collisions in the FBA condition (as we did not ask embodiment questions in the NA condition). Regarding self-location questions, we found a significant negative correlation between the question SL located and the ratio of shoulder collisions (r = -0.31, p < 0.05). We did not find similar correlations for the questions about ownership or agency. This result suggests that people who felt that they were co-located with their virtual body collided less with the environment. Variations

Discussion

This study explored the potential inter-effects between the use of locomotion techniques and avatars. The first goal was to study the effect of the locomotion technique on embodiment, while the second goal was to explore the impact of the presence of an avatar during navigation, depending on the technique. In this section, we discuss the results on the sense of embodiment, collision avoidance, and finally user preference.

Embodiment

Our first main hypothesis was that the choice of a locomotion technique would influence the sense of embodiment. In particular, we expected high-fidelity locomotion techniques, requiring more physical movements, to elicit a higher sense of embodiment, similarly to previous results on the sense of presence [START_REF] Slater | Taking steps: the influence of a walking technique on presence in virtual reality[END_REF]Usoh et al. 1999]. Contrary to our expectations, there was no significant difference on the level of embodiment between the locomotion techniques, suggesting that the choice of a technique does 91 Chapter 3 -Studying the Interrelations Between Locomotion Techniques and Embodiment not influence the participants' sense of embodiment.

Two potential reasons may explain this result. A first potential explanation is that participants had a total control over their avatar movements, no matter what technique they used, which has been shown to play a primary role in the sense of embodiment [Fribourg et al. 2020a]. For all tasks, when participants moved, the avatar moved accordingly, therefore there was always a coherence between participants' movements and the feedback. Even for the steering technique, participants had to reorient their body to perform the tasks and were aware of the upper-body motions (e.g. holding the controller in front of them, picking mushrooms). Even though participants were mostly stationary when using the walking-in-place and steering techniques, they still felt a high sense of embodiment, which is consistent with studies in which people embodied avatars even though they were not moving [START_REF] Galvan Debarba | Characterizing first and third person viewpoints and their alternation for embodied interaction in virtual reality[END_REF][START_REF] Kokkinara | First person perspective of seated participants over a walking virtual body leads to illusory agency over the walking[END_REF]]. However, contrary to related studies [START_REF] Kokkinara | First person perspective of seated participants over a walking virtual body leads to illusory agency over the walking[END_REF]], the avatar was not necessarily walking in these conditions (especially with the steering technique) in our study. Having an avatar sliding on the ground did not seem to affect participants' sense of embodiment.

A second explanation of our results could be that visual incongruities due to animation quality might have slightly disturbed participants. Even though the difference was not significant, we noticed slightly lower ownership scores in the walking condition, which would be in contradiction with our hypothesis. Because it is the most realistic and highfidelity technique of locomotion, people may have more expectations in terms of matching between the visual feedback and their proprioception. It is known that the match between visual and motor signals plays an important role in inducing a sense of ownership [START_REF] Kokkinara | Measuring the Effects through Time of the Influence of Visuomotor and Visuotactile Synchronous Stimulation on a Virtual Body Ownership Illusion[END_REF], and that motion artifacts can affect the sense of agency while walking [START_REF] Koilias | The Effects of Motion Artifacts on Self-Avatar Agency[END_REF].

In summary, our experiment suggests that total control of avatar movements might contribute more to embodiment than the coherence between avatar movements and camera motion, although artifacts or differences between participants' real movements and the avatar's movements can modulate their sense of embodiment. Further studies will be required to better assess the contribution of the upper-body and lower-body control, as well as the impact of animation artifacts on the sense of embodiment.

Collision Avoidance

Our second main hypothesis was that people would collide less with the columns when embodied in a full-body avatar, however it was not supported by the results. In general, we observed different behaviours among participants, some avoided obstacles while others went through them. Participants who ignored the columns reported that they did it to pick the mushrooms faster, and because they were not disturbed by going through them, contrary to people who avoided them. This result differs from other studies that have found that people tended to avoid obstacles when they were embodied in a realistic avatar, but these studies used obstacles on the trajectory of the hand [START_REF] Argelaguet | The role of interaction in virtual embodiment: Effects of the virtual hand representation[END_REF] or at lower height [Pan and Steed 2019]. We believe that the task and the obstacles could explain the difference in our results, as the avatar may have not contributed to avoid the columns. First, the task required participants to focus on finding and picking the mushrooms which could have diverted their attention. Second, the obstacles might not have been close enough to compel the participants to use a body reference to avoid collisions.

Preference

Logical and pleasing aspects

We expected that people would find the condition with a full-body avatar more logical and pleasing. For the logical aspect, this was the case for the task involving a mirror. However, some participants reported that the avatar's movements were sometimes "disturbing", for example that the knees would bend too much compared to what they were doing. The absence of an avatar was still perceived as less logical, where several participants reported negatively about seeing only controllers in the mirror condition. Participants did not find it significantly more logical to have a full-body avatar in other tasks. This may be due to the fact that most VR applications currently only use floating hands or controllers as virtual representations, and that participants were therefore not surprised by this simpler representation (controllers only). For the pleasing aspect, the results were significant only for the tasks not involving the mirror. Although participants appreciated having a body visible from a first-person perspective, they did not find it more pleasing to see the avatar in the mirror. A potential explanation could be that several participants reported being disturbed by the difference in external appearance (clothes, haircut, morphology) of the avatar compared to their own, yielding lower scores on this question.

Chapter 3 -Studying the Interrelations Between Locomotion Techniques and Embodiment

Preferred condition

There were several questions asking participants whether they preferred the condition with or without an avatar. In particular, we expected that participants would prefer the condition with an avatar, and would find the navigation tasks easier to perform in such cases. The high variance in the answers to the question "I preferred having a body" shows different categories of people. Some participants were really disturbed by an absence of body and preferred having an avatar. Such participants described the experience with adjectives like "realistic" or "immersive" to describe the condition with an avatar. Other subjects did not prefer any of the conditions, or tended to prefer the condition without an avatar, as the avatar could be seen as "an obstacle" or too different from them that it was more disturbing than helping. This could potentially be explained by them being more task-oriented. They described this condition with adjectives like "easy", "transparent", "unconstrained" or "less disturbing".

The most used words for the condition with an avatar were: funny (9), easy ( 8), disturbing ( 7), realistic (6), immersive (5) and interesting (5). For the condition without avatar, it was: easy ( 9), simple (6), interesting (5) and disturbing (5). While adjectives for the condition without an avatar were more focused on tasks achievement (easy, simple), it is interesting to point that positive adjectives related to immersion and realism only appeared in the condition with an avatar. However, while our results show a slight preference for having an avatar in the navigation tasks of our experiment, it is possible that this preference is not directly related to the task but that it might be common to virtual experiences. It would therefore be interesting to explore potential effects of the task on this preference in future studies.

Ease of tasks

Similarly to the work by Lugrin et al. [2018], the presence of a virtual body to perform the tasks did not seem to impact the user in terms of performance or preference. Similarly to their study using an action-based game, our experiment contained goal-oriented tasks, especially in the columns task. In particular, some participants of our experiment reported that they only needed the controllers to perform the tasks. They therefore seemed to have been more focused on achieving the task, possibly reducing the awareness of the presence of the avatar. For tasks where they had to notice the avatar (mirror task and path-following task mostly), some participants considered the avatar as an obstacle or

Conclusion

an annoyance that was diverting them from the task. Our results need to be considered relatively to the tasks, and other tasks could be tested. For example, tasks which need a body reference and a finer control of the avatar, like the stepping task in the work by McManus et al. [2011], could be investigated.

Limitations

A limitation of this study is related to the degree of realism of the avatars and their animation. For instance, the calibration only adjusted the global scale of the avatar, while other papers studying avatars and collisions used more precise calibrations [Mestre et al. 2016]. Several solutions are now starting to appear to easily and precisely calibrate an avatar to the participants morphology [START_REF] Pujades | The Virtual Caliper: Rapid Creation of Metrically Accurate Avatars from 3D Measurements[END_REF], which could help in the future to more accurately measure collisions with the environment. In terms of animation, several participants were also disturbed by the leg movements, especially when physically walking in front of the mirror. It was previously found that offset rotation of joints can affect embodiment [START_REF] Koilias | The Effects of Motion Artifacts on Self-Avatar Agency[END_REF]. It could therefore be interesting to run a similar study with higher-quality motion capture systems to evaluate whether differences in terms of embodiment could be influenced by the animation quality in such cases. Still, animating avatars with Inverse Kinematics as performed in this study is a common procedure in such embodiment studies [START_REF] Roth | A simplified inverse kinematic approach for embodied VR applications[END_REF][START_REF] González-Franco | The contribution of real-time mirror reflections of motor actions on virtual body ownership in an immersive virtual environment[END_REF].

Even though people felt a sense of embodiment while using walking-in-place and steering techniques, some participants noticed that the feedback was strange, especially in front of the mirror. It would be interesting to study different types of visual feedbacks for the techniques. As an example, several studies have started to compare different feedbacks for the walking-in-place technique [Park and Jang 2019;Lee et al. 2020], which can be walking animation, synchronous stepping or running animation.

Conclusion

The study presented in this chapter explored the interrelations between avatar embodiment and locomotion techniques. The study considered three locomotion techniques requiring different user involvement (walking, stepping in place, limited physical movement) and three main tasks involving a different awareness of the virtual avatar that participants had full control of. Overall, we found that people experienced similar lev-Chapter 3 -Studying the Interrelations Between Locomotion Techniques and Embodiment els of embodiment with the three locomotion techniques and that the coherence of the avatar's motion with respect to motion of the VE did not create any disruption in the sense of embodiment. Our results represent a first attempt to qualify the interrelations between locomotion and virtual embodiment, and suggest that the locomotion technique used has little influence on the user's sense of embodiment in VR when users have a full control of their avatar movements. In this experiment, users could see exactly the movements they were performing, but this is not always the case. We mentionned that contrary to locomotion, manipulation techniques have been more studied, but this is less the case for techniques that distort users' motion. In the next chapter, we will therefore focus on manipulation, and most specifically on anisormorphic manipulation. This type of interaction can impact embodiment as it creates a mismatch between real and virtual motions.

"Time is running out, a ghost keeping me alive"

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Chapter 4

INVESTIGATING DUAL BODY REPRESENTATIONS DURING ANISOMORPHIC 3D MANIPULATION

Abstract: In virtual reality, several manipulation techniques distort users' motions, for example to reach remote objects or increase precision. These techniques can become problematic when used with avatars, as they create a mismatch between the real performed action and the corresponding displayed action, which can negatively impact the sense of embodiment. In this chapter, we propose to use a dual representation during anisomorphic interaction. A co-located representation serves as a spatial reference and reproduces the exact users' motion, while an interactive representation is used for distorted interaction. We conducted two experiments, investigating the use of dual representations with amplified motion (Go-Go technique) and decreased motion (PRISM technique)

. Two visual appearances for the interactive representation and the co-located one were explored.

Introduction

Many techniques have been invented for VR that increase user performance but distort user motion. While this is not necessarily a problem when using a simple user representation (e.g. a sphere representing the user's hand), this might cause strange feedback when embodied in a full-body avatar. Nevertheless, representing users with high-fidelity avatars is common as they offer several advantages. Avatars were found to increase spatial awareness [START_REF] Draper | Exploring the Influence of a Virtual Body on Spatial Awareness[END_REF], or even to impact perceived effort during a physical task [Kocur et al. 2020a]. There are also an increasing number of applications using fullbody avatars, especially social VR applications. To maximize the sense of embodiment towards avatars, spatially and temporally congruent visuomotor stimulation is an efficient method [START_REF] Kokkinara | Measuring the Effects through Time of the Influence of Visuomotor and Visuotactile Synchronous Stimulation on a Virtual Body Ownership Illusion[END_REF]. However, distorting movements during interaction On the left image, a ghost representation enables remote manipulation while a realistic co-located representation provides feedback with respect to the real user's position. On the right image, a ghost representation provides feedback with respect to the user's real position while a realistic representation enables precise manipulation with the environment thanks to slowed motion. could be detrimental to the sense of embodiment, as spatial congruency would not be respected anymore. Also, if the virtual body movements are distorted, users lose the information of their real body position, which might impact their understanding of the interaction technique.

To keep the advantages of both anisomorphic interaction and spatial reference offered by the avatar, we propose to provide the visual feedback of both distorted and real motions by displaying two avatars simultaneously. This type of feedback is referred hereinafter as dual representation, as opposed to single representations where only one avatar shows one type of feedback (real or distorted). The aim of this dual representation is to offer both the feedback of real users' motions as well as distorted motions during anisomorphic manipulation. In the context of this study, we define the dual representation as made of an interactive representation, used for interaction and displaying altered movements, and a co-located representation displaying real movements. This type of feedback has already been explored in the context of finger collisions with objects for example [Prachyabrued and Borst 2014;[START_REF] Canales | Virtual Grasping Feedback and Virtual Hand Ownership[END_REF]], and we believe that it could be valuable to all interaction techniques involving motion distortions to support both the sense of embodiment and interaction capabilities.

In order to evaluate the impact of dual representations on the sense of embodiment and interaction performance, we conducted two within-subject experiments to compare

Extended and Multiple Body Representations

different user representations (both single and dual) during anisomorphic manipulation. To this end, two common interaction methods were considered: remote manipulation with a gain that increases movement [START_REF] Poupyrev | The Go-Go Interaction Technique: Non-Linear Mapping for Direct Manipulation in VR[END_REF], and precise manipulation with a gain that decreases movement [START_REF] Frees | PRISM interaction for enhancing control in immersive virtual environments[END_REF]]. Both manipulation techniques create offsets between virtual and real hands, by either amplifying or decreasing users' movements. The interactive and co-located representations had either a realistic visual appearance or a transparent/ghost appearance.

This chapter provides insight on which user representation to choose during 3D anisomorphic manipulation.

Extended and Multiple Body Representations

In the related work of this thesis, we presented common techniques involving motion alterations and the impact they can have on the sense of embodiment (see Section 1.4.2.2). While the precise impact of motion alteration on embodiment is still unclear, several studies showed that a mismatch between users' motion and their virtual avatar was detrimental to embodiment, especially to the senses of agency and self-location. Most of theses studies focused on cases where users saw only one virtual representation of their movements. In this chapter, we ask the question: what would happen if they could see multiple representations of their movements during interaction? Few studies have investigated virtual representations with additional body parts or full bodies. In this section, we will present these studies which investigated either extended or multiple body representations, which are a lead to explore to reconcile embodiment and motion alteration.

Extended Body Representations

Avatar extensions have been explored, such as human tails [START_REF] Steptoe | Human Tails: Ownership and Control of Extended Humanoid Avatars[END_REF]] or third arms [START_REF] Laha | Evaluating Control Schemes for the Third Arm of an Avatar[END_REF]]. These studies used a material reminiscent of a ghost to distinguish the additional part from the rest of the body. They found that people could experience a sense of embodiment towards these additional limbs. Another study investigated the use of an extended arm in augmented reality, while keeping a representation of the real arm [START_REF] Feuchtner | Extending the Body for Interaction with Reality[END_REF]. This feedback was less appreciated than only an extended arm, without the real arm. More recently, an appended limb has been used as a spatial reference to extend proprioception and increase target selection [Tian et al. Chapter 4 -Dual Body Representations During Anisomorphic 3D Manipulation 2020]. This study found that people could feel a sense of ownership towards this limb, especially when they could control and move it prior to the selection task. The authors also tested different transparency levels for the additional limb, and found no impact on selection performance.

Multiple Body Representations

A study investigated the experience of having two bodies in VR, but not spatially co-located neither interacting with the VE [START_REF] Heydrich | Visual capture and the experience of having two bodies-evidence from two different virtual reality techniques[END_REF]]. Similar studies with additional body parts were conducted in real life with the rubber hand illusion [START_REF] Ehrsson | How many arms make a pair? Perceptual illusion of having an additional limb[END_REF]], using video stream [START_REF] Chen | Body ownership and the four-hand illusion[END_REF][START_REF] Guterstam | Duplication of the bodily self: a perceptual illusion of dual full-body ownership and dual self-location[END_REF] or augmented reality [START_REF] Rosa | The supernumerary hand illusion in augmented reality[END_REF]. More recently, a study investigated "distributed embodiment", i.e. embodiment towards up to four bodies [Miura et al. 2021]. In this study, participants had split views over four first-person perspectives. The results tended to show that subjects switched attention between bodies, but kept a global parallel sense of embodiment towards all bodies. Another study explored the use of additional hands for interaction, to decrease object selection time but without investigating embodiment [START_REF] Schjerlund | Ninja Hands: Using Many Hands to Improve Target Selection in VR[END_REF]. Some VR applications have two superimposed representations, but they are usually used for guidance [START_REF] Yang | Implementation and Evaluation of "Just Follow Me": An Immersive, VR-Based, Motion-Training System[END_REF]] so one representation is not controlled by users. While studies using several controlled bodies often used similar textures for all representations, these guidance applications used a "ghost" metaphor [START_REF] Yang | Implementation and Evaluation of "Just Follow Me": An Immersive, VR-Based, Motion-Training System[END_REF], where the second representation used for guidance is more transparent than the main one [START_REF] Han | Ar-arm: Augmented visualization for guiding arm movement in the firstperson perspective[END_REF][START_REF] Chinthammit | Ghostman: augmented reality application for telerehabilitation and remote instruction of a novel motor skill[END_REF].

While people replicated the RHI with two arms or bodies, or used a second representation for guiding users, to our knowledge no study investigated the use of a second representation to show real movements during anisomorphic manipulation. For this reason, we conducted two experiments to explore the embodiment of a dual representation, with two different anisomorphic interaction techniques, involving either amplified or decreased movements.

Context and Experiments Overview

In this study, we were interested in the potential use of dual representations for interaction in VR. More precisely, the context of this chapter is the use of dual body rep-

Experiment 1: Dual Representations for Increased Motions During Out-of-Reach Manipulation

resentations when there is an offset created between users' real position and the virtual representation position during anisomorphic manipulation. In this context, we consider that dual representations are made of an interactive representation used for interaction with the environment, and a co-located representation showing users' real movements. Therefore, users have control over two avatars simultaneously, but the mapping and visual appearance differ. More precisely, when a motion distortion is applied to a part of the avatar, the hand in our experiments, the two avatars will dissociate, providing visual feedback of both the co-located and distorted motions. When no distortion is applied, a single default representation can be used (a realistic full-body avatar) to maximise embodiment [Martini et al. 2015;[START_REF] Latoschik | The Effect of Avatar Realism in Immersive Social Virtual Realities[END_REF]] and avoid a visual overlap between the two representations. In this paper, when talking about our different experimental conditions, we will always indicate the visual appearance of the interactive representation first (letter on the left), then the co-located representation one (letter on the right).

The context is close to the ghost metaphor [START_REF] Yang | Implementation and Evaluation of "Just Follow Me": An Immersive, VR-Based, Motion-Training System[END_REF] in which the trainer's movements are superimposed to users' one. However, in our context, users are in control of both representations at the same time.

Dual body representations could be adapted to other situations, but in this study we focus on anisomorphic manipulation techniques. These techniques usually increase or decrease users' motion. In this chapter, we therefore conducted two experiments investigating either amplified motions or decreased motions. The goal was to have two main types of motion alteration. We chose two very well-known manipulation techniques: the Go-Go technique which amplifies movements to reach remote objects [START_REF] Poupyrev | The Go-Go Interaction Technique: Non-Linear Mapping for Direct Manipulation in VR[END_REF], and the PRISM technique which decreases movements to gain precision [START_REF] Frees | PRISM interaction for enhancing control in immersive virtual environments[END_REF]].

Experiment 1: Dual Representations for Increased Motions During Out-of-Reach Manipulation

The first within-subject experiment investigated the use of a dual representation when interacting with remote objects using the well-known Go-Go technique [START_REF] Poupyrev | The Go-Go Interaction Technique: Non-Linear Mapping for Direct Manipulation in VR[END_REF]. When using this technique, users' movements above a certain threshold are amplified, enabling both close and remote object manipulation.

Participants and Apparatus

Twenty-four participants (age min=20, max=36, avg=25.0±4.1, 11 women and 13 men) took part in this experiment. On a 7-point Likert scale, 7 of them were VR experts (score equal to or greater than 6), 6 were knowledgeable (score between 3 and 5) and 11 were beginners (score equal to or lower than 2). The majority of participants were students and staff recruited on our campus. All participants gave written and informed consent. The study conformed to the declaration of Helsinki, and was approved by the local ethical committee. Participants did not receive any compensation. They all had a normal or corrected vision.

Participants were equipped with a Valve Index Head-Mounted Display and Knuckles enabling finger tracking, tracked by two base stations. The experiment was developed using Unity 2019.4.12f1. We used gender-matched avatars from the Rocketbox library. They were animated using the RootMotion Final IK plugin. For object interaction (selection and hand poses), we used the SteamVR interaction system.

Go-Go Technique Implementation

Our implementation is based on the original Go-Go implementation [START_REF] Poupyrev | The Go-Go Interaction Technique: Non-Linear Mapping for Direct Manipulation in VR[END_REF]. A one-to-one mapping is applied until the real hand position R r reaches a threshold value D, then it becomes non-linear. The virtual hand position R v is determined as follows:

R v =    R r if R r < D R r + k(R r -D) 2 otherwise
The threshold D was 2/3 of the real arm length. The factor k was computed to ensure that the maximum arm length was four times the real arm length. Therefore, when users had their real arm fully extended, the virtual arm was four times longer than their real arm. This k value enabled users to perform the task by reaching all the targets, while maintaining a relatively accurate interaction. To extend the arm, users' motion direction needed to be known. There are several ways of determining it, depending on whether the head, the shoulder or the controller positions are used to compute the direction vector. Different ways were tested, and finally the normalised vector linking the shoulder position to the controller position was kept, similarly to the implementation by [START_REF] Feuchtner | Extending the Body for Interaction with Reality[END_REF]. This was the most stable solution, as it did not depend on the head orientation. The Go-Go technique uses an adaptative gain, enabling both close and remote interaction. An ecological task involving both interaction in the peripersonal (close to the body) and the extrapersonal (far from the body) space was necessary. We chose the ecological task of picking apples. Participants were facing a virtual tree containing 20 apples (see Figure 4.1). They had to extend their arm to reach the apples placed in their extrapersonal space and pick them. Then, there was a sorting task. Participants had to bring back the apple to their peripersonal space to inspect it. They needed to look at them to see if they were flawless, or rotten, i.e. with stains on them. The goal was to make participants bring the apples back to them, to interact closer to their body and be aware of their dual representation. After looking at the apples, they had to put them in the appropriate basket situated just outside their peripersonal space beside the tree (flawless apples in the left basket, or rotten apples in the right basket). To pick/release the apples, subjects had to grab/release the Knuckles handle. When they grabbed the handle, this would snap the apple to the virtual hand and trigger a hand pose.

Additional Task: Maximum Reach Estimation Task

Interacting with remote objects can alter the mental arm representation, and give a sensation of real elongated arm [START_REF] Feuchtner | Extending the Body for Interaction with Reality[END_REF]. We therefore decided to add a task to estimate whether the perceived maximum reach distance was influenced by the Representation. For this additional task, participants were immersed in an empty scene, with only the Unity default skybox. They had no virtual body during this task and only saw a red virtual sphere in front of them. They were instructed to move this virtual sphere using the Knuckles controllers' pad to place them at the distance where they thought they could reach it with their arm fully extended. They had to keep their arms at their sides during the measure. This measure was repeated six times, three times with the sphere coming from away (at a distance of twice users' real arm length), and three times from near participants (at a distance of 0.3 times the real arm length), alternatively.

Experimental Design and Protocol

This experiment had a within-subject design with Representation as the independent variable. For each level of Representation, distorted (interaction) motions and real motions could be represented either by a realistic body (R), a ghost body (G) or nothing (Ø). For this experiment we chose three levels of Representation, defined as : R -Ø, R -G and G -R (see Figure 4.2). In R -Ø, only distorted motions were represented with a realistic elongated arm. In R -G, a realistic elongated arm was used for interaction, while real motions were represented by a ghost transparent arm. G -R corresponded to the opposite combination. We did not use other possible combinations, as the goal was to always have a different visual appearance for interactive and co-located representations (so for example the R -R combination was excluded), and only a realistic appearance when using a single representation (therefore no single ghost extended arm). Also, when using the Go-Go technique, the user must see where the virtual hand is to be able to interact during motion distortion, therefore combination Ø -R could not be used in this experiment. The order of the different Representations was fully counterbalanced. Participants were first welcomed, the experiment was explained to them and they had to read and sign the consent form. Before starting the main experiment, users were first immersed in the experimental scene but without any task to perform. They were represented by an avatar with a global scale calibrated to match their height. They were

Experiment 1: Dual Representations for Increased Motions During Out-of-Reach Manipulation

immersed 45 seconds to look at the scene and their avatar. The goal was to have a first perception of the virtual scene, with a normal calibrated avatar without extendable arms.

After the 45 seconds, they performed the maximum reach estimation task. After this first exposure, the main experiment began, which was divided into three blocks, one for each Representation. Before the experimental task began, they had 20 seconds of free exploration of their avatar and the environment. Then, they had to press the controller's trigger to start a training with only five apples. After pressing again the trigger, they could start the main task, with 20 apples. The apples were placed similarly in all conditions to be able to compare results between the different representations. At the end of each block, participants were placed in another scene to do the maximum reach estimation task. In total, the experiment session lasted around 50 minutes.

Experimental Data

Subjective Measures

Participants' sense of embodiment was measured using the questionnaires from Peck and Gonzalez-Franco [2021] (mentioned as PGF questionnaire hereafter) and from [START_REF] Roth | Construction of the Virtual Embodiment Questionnaire (VEQ)[END_REF] (mentioned as RL questionnaire). We decided to use both questionnaires because they have complementary questions. The questionnaire items were evaluated on a 7-point Likert Scale from 1 (Strongly disagree) to 7 (Strongly agree). For the PGF questionnaire, we customised question R7 as recommended in their paper. We used the question "I felt as if my real arm were becoming longer". For question R8, we asked "I felt a realistic sensation in my body when I saw my virtual body" as recommended. For R14 to R16, we used apples as the source of touch. We thought it would be clearer for participants than asking about the touch of the ground as recommended in the questionnaire paper. It is possible to consider that the passive haptic feedback provided by the Knuckles grip could elicit a sensation of touch, even though the shape was different from an apple.

In addition, six questions specific to this study were added. For the two conditions with a dual representation, questions related to senses of ownership and agency (from the RL questionnaire) were added for both virtual representations, the realistic (opaque) and the ghost (transparent) representations (see Table 4.1). We used the words opaque and transparent to have neutral words describing the representations that would not bias participants' responses.

Five questions on the global opinion regarding the virtual representation as well as usability were asked (see Table 4.2). Subjects were also asked to rank the conditions in order of preference after the experiment, and to explain why they chose this order. Table 4.1 -Additional embodiment questions asked after conditions involving a dual representation (in R -G and G -R).

ID

Objective Measures

Because previous studies showed a possible impact of the virtual representation on performance [Tran et al. 2017], we included a performance measure in this experiment by measuring the time to pick the 20 apples. Similarly, related work showed that having a virtual extended arm can impact arm length perception, because it alters body schema [Kilteni et al. 2012b]. We therefore included the maximum reach estimation task described in Section 4.4.3.2 after each main task, to evaluate whether the virtual representation would impact maximum reach perception.

Experiment 1: Dual Representations for Increased Motions During Out-of-Reach Manipulation

Hypotheses

Previous studies showed that from a certain length (four times the real arm length), an extended arm do not feel like the users' own arm anymore [Kilteni et al. 2012b]. Reminding users of their real arm might help to create a global sense of embodiment towards their representation, which could be higher than having only one visible arm. Also, having the constant feedback of their own arm might be good for the sense of agency, as they can always see a congruent feedback of their real actions, which is an important factor in eliciting a sense of agency [START_REF] David | The "sense of agency" and its underlying cognitive and neural mechanisms[END_REF]]. Therefore we propose as first hypothesis that dual body representations influence the sense of embodiment, especially the sense of agency (H1.1).

While some studies suggested that additional visible information can impact performance [Tran et al. 2017], we hypothesised that seeing real movements could help to understand the transformation applied in the case of anisomorphic manipulation. This should not be enough to increase performance in the case of the Go-Go technique, as the technique is simple and the task we used does not necessitate precision. We hypothesised that we should not observe differences in terms of performance between the conditions (H1.2), as dual representations should not hinder the task.

When using a single representation, an offset is created between the remote virtual hand interacting with objects and the real hand. Because of this mismatch between real and virtual movements, users might get frustrated. On the contrary, having a dual representation lets users see both their real and virtual movements, we hypothesised that this type of representation would be preferred. Also, it could be perceived as fun to embody two different virtual representations. Our third hypothesis was therefore that people prefer having a dual representation (H3.1).

Results

Considering the ordinal nature and the non-normal distribution of subjective questionnaires scores, we performed Friedman non-parametric tests (with α = 0.05) on the different embodiment components and the user experience questions, followed by post-hoc pairwise Wilcoxon signed-rank tests with Bonferroni correction. For objective measures, we used a one-way repeated measures ANOVA and Tukey's post-hoc tests when the normality assumption was verified by the Shapiro-Wilk test (for the estimated maximum reach distance), and Friedman tests followed by Wilcoxon tests when the normality as-sumption was not verified (for the time completion). For the additional questions on realistic and ghost representations in G -R and R -G, we performed Wilcoxon signed-rank tests.

Sense of Embodiment and Preference

Embodiment questionnaires For the RL questionnaire, we computed the global scores for the three components (Ownership, Agency and Change) as recommended. Globally, the Ownership (M dn = 5, IQR = 3.44 -5.81) and Agency (M dn = 6, IQR = 5.75 -6.5) scores were high in all conditions while the Change (M dn = 2.25, IQR = 1.25 -3.75) scores were very low. For all components, we did not find any significant difference.

For the PGF questionnaire, we also computed global scores for each component (Ownership, Appearance, Multi-Sensory and Response), as well as the Multi-Sensory sub-score, the Agency score, using the two questions directly related to the sense of agency. Components scores were globally low (Mdn = 3.75, IQR = 3 -4.67 for Ownership, M dn = 2.63, IQR = 1.75 -3.41 for Appearance, M dn = 3.42, IQR = 2.67 -4.17 for Multi-Sensory, M dn = 2.75, IQR = 2 -3.83 for Response and M dn = 4, IQR = 3.5 -5 for the Agency sub-component), with common questions getting relatively high scores (such as I felt like I could control the virtual body as if it was my own body or I felt as if my body was located where I saw the virtual body) while questions not adapted to the experimental protocol gave very low scores (such as questions on tactile sensations). For the Response component, there was a main effect of Representation (χ 2 = 7.525, p < 0.05). The Kendall's W value showed a small effect (W = 0.16). Pairwise tests showed that the score for R -Ø was significantly higher than for G -R (p = 0.01). This seemed mostly influenced by the question I felt a realistic sensation in my body when I saw my virtual hand. For the Multi-Sensory component, Friedman's test showed a main effect of the Representation (χ 2 = 6.1, p < 0.05), but the pairwise test did not reveal any significant difference between the conditions. The results of these two components are visible in Figure 4.3.

Additional questions

For the additional ownership and agency questions about the realistic and the ghost representations (G -R and R -G only), there were significant differences in agency questions scores between R -G and G -R (see Figure 4.5). For the question controllingOpaque, the scores were significantly higher in R -G than G -R (p < 0.05). Participants felt more in control of the realistic arm when it was used for interaction than when it was displaying real motions. For the question controllingTrans- Chapter 4 -Dual Body Representations During Anisomorphic 3D Manipulation parent, the scores were significantly higher in G -R than R -G (p < 0.01). Similarly to the realistic arm, control was higher when interacting with the ghost arm. For the question causingTransparent, the scores were significantly higher in G -R than R -G (p < 0.01). No significant difference was found for the questions on ownership. We compared scores for similar types of representation (interactive or co-located) depending on the visual appearance. The scores for the interactive representations were not significantly different between the two appearances, neither for the co-located appearance. For each dual representation condition, we also looked at the potential difference in the scores between the interactive and the co-located representation. For the controlling and causing questions, scores were significantly higher for the realistic extended arm than for the ghost short arm in R -G (p < 0.05). Preference R -Ø was the preferred condition, with 10 participants ranking it as their most preferred condition (see Figure 4.4). Its average rank was 1.67. R -G and G -R had the same average rank equal to 2.17. There was no significant difference on the user experience questions. The scores were average for the question liked (M dn = 4, IQR = 2.75-6), low for disturbing (M dn = 2, IQR = 1-5), high for questions easy (M dn = 6, IQR = 5.75 -7), clear (M dn = 6, IQR = 6 -7) and exciting (M dn = 6, IQR = 6 -7).

Objective Measures

For the mean estimated maximum reach distance, corresponding to the average of the six measures from the maximum reach estimation task, the sphericity was violated so a Greenhouse-Geisser correction was applied. We found a main effect of Representation 110

Experiment 1: Dual Representations for Increased Motions During Out-of-Reach Manipulation

(F 2.37,54.52 = 10.48, p < 0.001, η 2 p = 0.313). Post-hoc test showed that the baseline (the measure prior to the experiment) was significantly lower than measures after the different levels of Representation, as all the pairs with the baseline in them had a p-value lower than 0.001. However, there were no differences between the three levels of Representation. In the baseline, the estimated maximum reach was equal to 83.4 ± 15.2% of the real arm length. After the different conditions, it was respectively equal to 91.7 ± 16.2% of the arm length after R -Ø, 89.9 ± 16.9% after R -G and 90.6 ± 16.9% after G -R. We did not observe any order effect.

There was also no significant difference in the time completion between the different blocks. People took 105.7 ± 40.7 seconds in average in condition R -Ø, 96.6 ± 25.3 seconds in R -G and 99.3 ± 22.8 seconds in G -R.

Discussion

The main goal of this experiment was to explore the impact of dual representations on the sense of embodiment and user performance. Except for a difference on the Response component between R -Ø and G -R, embodiment scores did not highlight differences between the conditions, which does not support H1.1. Additional questions showed that for both visual appearances, people had a higher sense of agency towards the arm when they were interacting with it (even if it was sometimes extended), than when the arm was showing their real movements. This is interesting as it encourages to introduce more interaction tasks in future embodiment studies, to study its impact on embodiment and potentially increase embodiment towards deformed avatars. Also, the agency scores for the ghost arm were significantly lower than the realistic arm in R -G. The opposite was not true in G -R. This means than participants could feel control over a ghost extended arm because they were interacting with it, but they felt less control over a co-located ghost arm while interacting with a realistic extended arm.

Additionally, the maximum reach estimation task revealed an increased perceived maximum reach distance after all the conditions, compared to the measure prior to the experiment. This shows that interacting with an extended arm changed users' mental representations of themselves, and they perceived their real arm to be longer. This is similar to results found in other studies [START_REF] Feuchtner | Extending the Body for Interaction with Reality[END_REF]Lin et al. 2020].

Regarding user performance, we did not observe any significant difference in task completion time, which does not contradict H1.2. Participants performed similarly under all conditions. This is probably due to the fact that the co-located representation did not interfere during the task, as it was only an additional information not located where the manipulation was happening.

Almost half of participants preferred using only one representation, which does not support H1.3. They found it more "playful", or that knowing only where the interactive hand is was "the most important". Several participants also reported it as more "realistic" because they only had one arm, even though this arm was extended. This is in line with the study by [START_REF] Feuchtner | Extending the Body for Interaction with Reality[END_REF] that also considered an extendable arm in augmented reality, in which 67% of participants preferred not seeing their real arm, and could embody the extended arm when interacting with it. Still, some participants preferred having a dual representation, to have the information of their real arm position. Some of them preferred their real body represented by a realistic body. These participants considered the ghost arm as an "extension", a superpower they had in the VE. Other people preferred interacting with a realistic arm, as they felt they were not able to pick apples with an "intangible" arm, and were more precise with a realistic arm. These two opposite opinions explain the similar mean ranking for R -G and G -R. Even though the single representation was preferred, there seems to be some individual differences.

The results could also be greatly influenced by the type of mapping. For this reason, we conducted a second study investigating another type of motion distortion.

Experiment 2: Dual Representations for Decreased

Motions During Precise Manipulation

The goal of the second within-subject experiment was to investigate the use of a dual representation when forced to be always in sight during a task in the peripersonal space. We also wanted to test a technique with a different type of gain, i.e. decreasing users' movements. The PRISM technique was chosen as it scales down users' movements to increase precision.

Participants and Apparatus

In this second experiment, we also had 24 participants (age min=22, max=36, avg=26.8±3.3, 12 women and 12 men). None of them did the first experiment. 4 of them were VR experts, 13 were knowledgeable and 7 were beginners.

The apparatus was the same to that in the first experiment.

PRISM Technique Implementation

The PRISM technique adjusts the virtual hand motion (translation and rotation) depending on users' hand speed. For translation, we scaled users' motion depending on the speed measured in m/s. For rotation, the scale depends on the angular speed in degree/s. When implementing PRISM, the gains can be applied on global translation/rotation or independently on each axis. In our experiment, we used global scaling as it was found more intuitive after several tests. The different cases determining the gains applied are described here. The threshold values MinV, SC and MaxV were empirically adjusted to our task and its difficulty.

-HandSpeed < M inV . In this case, the motion is considered as noise and not intentional motion. We used M inV = 0.01m/s for translation and M inV = 5 degree/s for rotation.

-M inV < HandSpeed < SC. Users are performing a slow motion in order to be precise. The function determining the gain applied is linear (going from 0 for M inV to 1 for SC). We used SC = 0.1m/s for translation, and SC = 50 degree/s for rotation.

-SC < HandSpeed < M axV . In this case we use a one-to-one mapping. We chose M axV = 0.2m/s for translation and M axV = 60 degree/s for rotation.

-HandSpeed > M axV . This case shows an intention to remove the current offset created between the virtual hand and the real hand. When the speed is greater than M axV , the offset is instantly recovered.

Task

The task was similar to the 6-DOF task considered by [START_REF] Frees | PRISM interaction for enhancing control in immersive virtual environments[END_REF]. Subjects were instructed to grab a 3D object and place it at a given target position. The object was a cylinder, to have a simple hand pose to grab it, with an antenna on top of it to constrain its rotation on the three axes. The target consisted of the same object but transparent and red (see Figure 4.1). When the object was correctly placed, it turned green. The object was considered well placed when its centre was within 3 millimetres of the target's centre and its three axes of rotation were aligned with those of the target (with a tolerance of 2.25 degrees per axis). The objects were always shown in the same order across the different conditions.

Experimental Protocol and Design

Similarly to Experiment 1, the experiment followed a within-subject design with Representation as the independent variable. This variable had four levels (see Figure 4.6). We added a fourth condition, Ø -R, because the PRISM technique is compatible with having only the real movements displayed and the object slowed down, contrary to the Go-Go technique. The order of the different Representation conditions was counterbalanced using a 4 × 4 Latin square design. Participants were first welcomed, the experiment was explained to them and they had to read and sign the consent form. Then they were immersed in the VE where they first had 20 seconds to observe their virtual body and the environment. Then, they had to press the controller's trigger to start a training with only two objects to place. They had a maximum of 30 seconds to place each object after which they could start the main experiment by pressing again the trigger. They had three minutes to place as many objects as possible. In order to keep the exposure time the same for each condition, we preferred to fix the total exposure time because we expected stronger user variability in this task than in the first experiment task. The next object (and the associated target) would appear when the previous one was correctly placed. In total, the experiment session lasted about an hour.

Experimental Data

We used the same subjective questionnaire as in Experiment 1. Only the following questions were changed, in the PGF questionnaire:

-R7: I felt as if my body had changed -R14: It seemed as if I felt the touch of the virtual objects in the location where I saw the virtual body touched -R15: It seemed as if the touch I felt was caused by the virtual objects touching the virtual body -R16: It seemed as if my real body was touching the virtual objects As objective data, the number of completed placements was counted. The times when each object was displayed, picked, released and correctly placed were logged. The hand velocity (in m/s) as well as the offset between the virtual and the real hands were also saved at each frame, for both left and right hands.

Hypotheses

We globally had the same hypotheses as in the first experiment. This experiment was slightly different from the first one, both because the technique decreased users' movements and the interaction was happening in users' peripersonal space. The PRISM technique alters users' movements which creates an offset between the real and the virtual hands [START_REF] Farrer | Effect of distorted visual feedback on the sense of agency[END_REF]]. Yet, compared to the Go-Go technique, the offset introduced will tend to be smaller and will also increase progressively during the manipulation process. On the one hand, as the offset increases progressively and will tend to be small, the chances of noticing the offset are reduced. On the other hand, as the offset is dependent of the motion speed, the user might perceive the virtual hand motion as unpredictable. The dual representation could enable to decrease this effect of control loss. However, having two bodies with different mappings in the peripersonal space could be disturbing for users. One hypothesis was that dual representations influence the sense of embodiment, especially the sense of agency (H2.1).

We were still expecting similar performance between the different conditions. Because in all the dual representation conditions one representation is semi-transparent, we hypothesised that it would not add too much visual information to affect performance, so that we should not observe differences in terms of performance between the conditions (H2.2).

Finally, because with dual representations there would be two virtual hands very close to each other, we were expecting a less pronounced preference for dual representations compared to the Go-Go technique, but still a preference because it would not result in any loss of information about users' movements. The third hypothesis was that people would slightly prefer having a dual representation (H2.3).

Results

We performed a similar analysis to Experiment 1. Subjective data were analysed using Friedman's tests and objective measures using either one-way repeated measured ANOVA or Friedman's test depending on the Shapiro-Wilk test significance.

Sense of Embodiment and Preference

Embodiment questionnaires No significant effect of Representation on the components from the RL questionnaire was found. Ownership ((Mdn = 4.625, IQR = 3 -5.5)) and Agency ((Mdn = 5.125, IQR = 4 -6.062)) were above average. The Change component scores were low ((Mdn = 2, IQR = 1 -3.062)). Interestingly, the question It felt like the virtual body was my body was influenced by Representation (p < 0.05), with single representations having better scores than dual representations, and the pairwise tests showing that Ø -R was significantly higher than G -R. Other questions had similar results between Representations, resulting in no significant difference in the Ownership component.

For the PGF questionnaire, components for which we found a main effect of Representation are shown in Figure 4.7. Components scores were globally average (Mdn = 3.83, IQR = 2.67-4.67 for Ownership, M dn = 3.13, IQR = 2.13-3.5 for Appearance, M dn = 3.5, IQR = 2.96 -4.38 for Multi-Sensory, M dn = 3, IQR = 2 -3.67 for Response and M dn = 4, IQR = 3 -5 for Agency). For both the Response (χ 2 = 8.85, p < 0.05) and the Ownership (χ 2 = 8.38, p < 0.05) components, Friedman's test showed a main effect of the Representation. R -Ø had higher scores but the pairwise tests did not reveal any significant difference between the conditions. However, the question I felt as if my body was located where I saw the virtual body was significantly higher in R -Ø compared to R -G and G -R. Even though there was an offset with their real hand, participants felt co-located with their avatar. There was also an effect of Representation on the question I felt that my own body could be affected by the virtual world, with R -Ø having significantly higher scores than R -G. Friedman's test showed a main effect of the Representation on the global embodiment score (χ 2 = 9.63, p < 0.05). Embodiment score in R -Ø was significantly higher than in R -G (p < 0.05). There was no other significant difference. Additional questions For the additional questions, we did not find any significant difference (see Figure 4.8). But, we also compared the scores between each similar question (for example, controllingOpaque and controllingTransparent). The scores for the question on controlling the interactive representation (i.e. showing distorted motions) were higher with the realistic appearance (in R -G) than with the ghost appearance (in G -R) (p < 0.05). The scores for the question wasMyBody for the interactive representation were also higher with the realistic texture (in R -G) than with the ghost texture (in G -R) (p < 0.05). In G -R, the scores for wasMyBody and controlling were significantly higher for the co-located realistic arm than for the ghost interactive arm (p < 0.01).

Preference R -Ø was the preferred condition, with 13 participants ranking it as their most preferred condition (see Figure 4.9). Its average rank was 1.92. R -G came second with an average rank of 2.38, then Ø -R (2.58) and G -R (3.13) as the least preferred.

Objective Measures

The number of completions was slightly higher in R -Ø but no significant difference was found between the four conditions (F 2.76,60.63 = 2.43, p = 0.079, η 2 p = 0.100). People correctly placed 15.7 ± 4.9 objects in average in R -Ø, 13.4 ± 6.0 in G -R, 13.5 ± 5.1 in R -G and 13.3 ± 5.3 in Ø -R. We also counted the number of adjustment releases (when objects were released without being correctly placed), for which there was a significant effect of Representation (p < 0.01). Pairwise tests showed that the number of adjustment releases was significantly higher in Ø -R than in R -Ø. The average number of adjustment releases was equal to 15.8 ± 7.0 in R -Ø, 16. 4 ± 9.5 in G -R, 15.3 ± 7.8 in R -G and 19.7±7.4 in Ø -R. Also, neither the offsets created nor the hand velocity were significantly different between the conditions. The average offset was 3.39 ± 0.97cm.

Discussion

The goal of this second experiment was to study the influence of dual representations on embodiment and performance when the interaction took place in the peripersonal space. We expected embodiment scores to be higher with the dual representations. On the contrary, there was a tendency of higher scores in R -Ø but pairwise tests could not show significant results. Only the global embodiment score showed that embodiment in R -Ø was higher than in R -G. Indeed, participants reported being disturbed by the presence of two hands, which could explain this result. Between the two dual representations, the results on the sense of embodiment tended to show that in this experiment, the hand appearance (realistic versus transparent) had an impact. The scores for the questions about control and ownership were higher with the realistic hand appearance than with the ghost one.

We did not find a significant difference between the conditions for the performance measure (number of completions), which does not contradict H2.2. However, performance tended to be higher for R -Ø, and equivalent for dual representations and the single representation Ø -R. We also reported that the number of adjustment releases was high in Ø -R. It was indeed observed during the experiment that in this condition, where the hand would cross the object when there was an offset, people would tend to release and grab again the object to remove the offset. This is in line with papers showing that users are disturbed by interpenetrations [START_REF] Canales | Virtual Grasping Feedback and Virtual Hand Ownership[END_REF].

Also, the preference for condition R -Ø was slightly clearer than in the first experiment. But interestingly, R -G was often ranked second, showing a good acceptance of the ghost hand to show real movements. Some participants reported that it was easier to understand their virtual movements when they had two representations. The dual representation also enables keeping the contact between a virtual hand and the virtual object. This is different from the original PRISM implementation [START_REF] Frees | PRISM interaction for enhancing control in immersive virtual environments[END_REF] where the virtual representation moves away from the object (like Ø -R in our experiment), and the offset is represented by either a line between the hand and the object for translations, or two sets of 3D axes for rotations. Our visual feedback is more compatible with avatars, as it leverages avatars to represent the offset.

General Discussion

This section gives global discussion on the two experiments with some leads of future studies.

Impact of Dual Body Representations on Embodiment and Performance

Embodiment scores for dual representations were globally similar to the scores for single representations, especially when using the Go-Go technique. This tends to show that having two bodies still elicited a good global sense of embodiment, which is in line with previous studies [START_REF] Chen | Body ownership and the four-hand illusion[END_REF]Miura et al. 2021]. While we expected that showing real movements would increase the sense of agency, it was not higher compared to conditions when people could only see their distorted movements. This is in accordance with other studies which showed that people are not disturbed by small offsets [START_REF] Porssut | Reconciling Being in-Control vs. Being Helped for the Execution of Complex Movements in VR[END_REF][START_REF] Kokkinara | The Effects of Visuomotor Calibration to the Perceived Space and Body, through Embodiment in Immersive Virtual Reality[END_REF] or can embody an extended arm until a certain length [Kilteni et al. 2012b;[START_REF] Feuchtner | Extending the Body for Interaction with Reality[END_REF]. People even felt more in control of the extended arm than of the arm showing their real movements. But in the second experiment when the interaction happened in the peripersonal space, the avatar visual appearance seemed to have a higher impact on agency. Both virtual representations were visible and closer during object manipulation, which may have increased the comparison between both hands and the difference in embodiment scores. This may also be due to people focusing more on the objects than on their representation, and not being disturbed by the offset which was never big enough to be distracting. We also compared embodiment scores of the two experiments using a Student's t-test. For all conditions, the agency component score from the RL questionnaire was higher in the first experiment than in the second (p < 0.01 for G -R and R -G, and p < 0.05 for R -Ø). People therefore felt a lower sense of agency using the PRISM technique than using the Go-Go technique. The other components scores were similar in both experiments.

As expected, we could not find a significant impact of dual representations on performance. Contrary to papers showing that additional visual information can impact 4.6. General Discussion performance [Tran et al. 2017], in our study dual representations were neither beneficial nor detrimental to the task. It therefore seems possible to use dual representations in such anisomorphic manipulation tasks.

User Preference and Recommendations

The two experiments showed that people globally preferred having a single representation over a dual representation for manipulation. Still, results showed a good acceptance of all representations, dual or single. The questions on user experience had relatively high scores, demonstrating that people liked the different representations and found the interaction easy and clear with them. However, while the general preference was for displaying only the interactive representation, some people found dual representations useful. We hypothesise that individual differences might exist regarding the perception of such a dual representation. One potential explanation could be related to people's ability to estimate their real body position or whether they are task-oriented. Depending on users' preferences, they could choose the representation that better suits them.

The results from both experiments give us some insight on how to choose the best virtual representation during 3D anisomorphic manipulation. In general, we suggest to use a single realistic arm as the interactive representation, and to let users the possibility to activate a ghost co-located arm. However, when using a technique in the peripersonal space with small offsets, only keeping a single realistic interactive representation seems sufficient and preferred.

Measuring Embodiment

One of the challenges that we faced in both experiments was how to measure embodiment. While the most common method is the use of subjective questionnaires, it has several limitations as it relies on the participants' understanding of the questions. Moreover, existing questionnaires have not been designed to assess dual representations. To cope with these limitations, we added specific questions to address dual representations. Furthermore, we considered it a good opportunity to use two questionnaires [START_REF] Roth | Construction of the Virtual Embodiment Questionnaire (VEQ)[END_REF]Peck and Gonzalez-Franco 2021], namely PGF and RL, which could be more sensitive to different aspects of embodiment in such a situation. The two questionnaires have different components, but still some comparisons could be made. The RL Ownership and Agency scores were high, and the Change scores low, while the PGF questionnaire scores all tended to be below average.

The RL Ownership and Agency questions are commonly used in the literature and tended to be high in all conditions, while the Change component questions were found irrelevant by the participants. They reported that they had difficulties answering the questions, suggesting that this component may be used in experiments investigating morphological differences, but probably not in experiments with calibrated avatars. For the PGF questionnaires, all components scores tended to be below average, as some questions (e.g. about tactile sensations) not adapted to the experiment seemed to have lowered global scores and added noise to the results. The questions in this questionnaire are more varied, suggesting a better adaptability to experiments with rich sensory stimulation, as there are questions asking specifically about it.

Overall, the two questionnaires provided different and complementary results. More questionnaires could be designed, as VR setups and experiments are various, and having only one standardised measure of embodiment seems like a difficult goal [Skarbez et al. 2021a].

Limitations

Our experiments were designed to study two common types of motion alteration, either increasing or decreasing motion. However, other types of distortion could be influenced by the representation. For instance, another type of common distortion is collision handling. Dual representations of the virtual hand have been studied for fine manipulation involving collision handling [START_REF] Canales | Virtual Grasping Feedback and Virtual Hand Ownership[END_REF], where a dual representation provided a good tradeoff between performance and preference. It would be interesting to explore the use of dual representations when a collision happens after a larger arm movement, and not only finger movements. While not studied here, dual representations could be appropriate as collisions can create huge offsets between the virtual and the real hand.

Moreover, we decided to display the co-located representation as soon as there was a gain applied. It would also be possible to display the co-located representation only if the offset is greater than a certain threshold. It would avoid having an additional information for precise manipulation like PRISM, when the offset is not disturbing for users, and only display the real hand when users can notice the mismatch and feel a loss of control.

Conclusion

In this chapter, we investigated the potential use of dual representations during anisomorphic manipulation, to see whether it could ensure both embodiment and performance. We used two different manipulation techniques, namely the Go-Go technique which amplifies motion and the PRISM techniques which decreases motion. With both methods, participants managed to feel a sense of embodiment towards a dual representation. Additionally, no impact was found on performance, which shows that such representations could be used in VR applications. While interacting seemed more important than showing exact movements for agency during out-of-reach manipulation, people felt more in control of the realistic arm during close manipulation. Overall participants preferred having a single representation, but still some people reported the benefit of having a representation showing their real movements to understand the distortion.

The importance of investigating such types of feedback during interaction is crucial, as we do not know yet the optimal visual feedback for each type of technique that would ensure both performance and embodiment. While this study investigated a specific feedback in the context of anisomorphic manipulation, there are already several studies on avatars and manipulation, detailed in Section 1.3 and Section 1.4. Based on the analysis of these studies, we will propose in the next chapter the theoretical concept of "avatar-friendly techniques", i.e. techniques that take the avatar into account. Chapter 5

DESIGNING AVATAR-FRIENDLY TECHNIQUES: PRACTICAL GUIDELINES

Abstract: This chapter was born out of an analysis of the state of the art on avatars and manipulation. As the related work showed (see Chapter 1), the literature on avatars and manipulation techniques is more extensive than for other interaction tasks. This chapter therefore proposes a set of fourteen guidelines to help VR developers creating manipulation techniques compatible with avatars, which we call avatar-friendly techniques. It also suggests several topics that could be investigated further regarding manipulation techniques and avatars.

Introduction

VR stakeholders usually design applications based on their instinct, or empirical experience, because of a lack of simple design advice, in the form of guidelines or claims for example. However, proposing and validating design guidelines for VR is already a challenge in itself [START_REF] Wingrave | Reflecting on the Design and Implementation Issues of Virtual Environments[END_REF]. There are too many factors impacting interaction, and too many individual differences, that make generalization from experiments very challenging. A set of guidelines for designing VR applications has been proposed by [START_REF] Gabbard | A Taxonomy of Usability Characteristics in Virtual Environments[END_REF], already talking about user representation. For instance, these guidelines recommend to use an efficient embodiment (i.e. provide enough sensory information) and to let users control their appearance in the VE. But, these guidelines are general and not precise enough to design manipulation techniques. Guidelines for designing 3D manipulation techniques have also been proposed by [START_REF] Bowman | 3D User Interfaces: Theory and Practice[END_REF], however, they do not consider user representation. Other guidelines, heuristics and claims [START_REF] Sutcliffe | Heuristic evaluation of virtual reality applications[END_REF][START_REF] Tanriverdi | VRID: A Design Model and Methodology for Developing Virtual Reality Interfaces[END_REF], more or less general, have been proposed since, but the avatar is usually forgotten. Guidelines specific to manipulation, considering the avatar, would help VR developers and encourage the use of avatars. We propose in this chapter design guidelines, justified by existing literature, that can be used in early stages of a design pipeline. These guidelines are focused on design choices for manipulation techniques involving avatars, therefore we refer the reader to the guidelines of [START_REF] Gabbard | A Taxonomy of Usability Characteristics in Virtual Environments[END_REF] concerning the remaining of the VR application pipeline (e.g. to restrict latency). Our guidelines are principally aimed towards helping designers to elicit embodiment during manipulation tasks, while also providing insights when a trade-off between embodiment and performance is required. We call this type of techniques "Avatar-Friendly techniques".

Techniques which take the user's avatar into account in the design process to preserve both user performance and sense of embodiment

Avatar-Friendly Techniques

The guidelines (see in Table 5.1) are classified into three parts: input devices (ID), control and mapping (CM) and feedback (FB).

Guidelines

Input Devices

ID1: For specific applications or training, use an input device adapted to the task. For applications training the user on the use of a specific tool, use an adapted device resembling the real tool. Place the 3D model of the device in the avatar's hand (see guideline FB5). Using an adequate device for a task yields better performance [START_REF] Pham | Is the Pen Mightier than the Controller? A Comparison of Input Devices for Selection in Virtual and Augmented Reality[END_REF]. This is essential for example when learning technical gestures, but otherwise generic controllers can be used.

ID2: Prioritise full-hand tracking when possible. Use hand tracking technologies (Leap Motion, gloves) instead of controllers when the tracking works well. In case of tracking issues, consider the use of 6-DoF controllers, especially controllers with capacitive sensors for the fingers. Using gestures and direct manipulation is preferred to ensure embodiment, realism, enjoyment, but only as long as the tracking is sufficient [Lin et al. 2019;[START_REF] Moehring | Effective manipulation of virtual objects within arm's reach[END_REF]. Six-DoF controllers still yield good levels of embodiment in most experiments.

Control and Mapping

CM1: For wide and fast motions, do not apply constraints. When wide and fast movements are done by the user, do not apply constraints (such as avoiding collisions or maintaining a hand pose on an object). Constraints might create a noticeable mismatch, decreasing the sense of self-location and potentially the sense of agency [START_REF] Pritchard | Non-hierarchical Influence of Visual Form, Touch, and Position Cues on Embodiment, Agency, and Presence in Virtual Reality[END_REF][START_REF] Kokkinara | The Effects of Visuomotor Calibration to the Perceived Space and Body, through Embodiment in Immersive Virtual Reality[END_REF].

CM2: For wide and fast motions, choose a CD gain equal to 1. For wide motion, the best is to keep a gain equal to 1. A gain lower than 1 could be perceived as latency. A higher gain can quickly create huge offsets between the real hand and the virtual hand, affecting the sense of embodiment [START_REF] Kokkinara | The Effects of Visuomotor Calibration to the Perceived Space and Body, through Embodiment in Immersive Virtual Reality[END_REF].

CM3: For small motion and precise manipulation, provide assistance to the user's movements. Use CD gains lower than 1 to precisely approach an object and/or automatic realistic poses to assist the user in their precise movements. It is possible to use subtle modifications of the motion without disturbing the sense of embodiment [START_REF] Debarba | Self-attribution of distorted reaching movements in immersive virtual reality[END_REF]]. This must be used as assistance to provide a visually realistic hand pose to the user during manipulation.

CM4: For precise manipulation, handle collisions. Constrain the avatar's hand and fingers outside of virtual objects during manipulation. Users are more sensitive to collisions than a small mismatch between the position of their virtual hand that of their real one. Therefore, they prefer seeing their virtual hand outside of objects [START_REF] Canales | Virtual Grasping Feedback and Virtual Hand Ownership[END_REF].

CM5: Progressively increase the distortion gain to make it more acceptable. The CD gain does not have to be constant, it can evolve during the application. Decrease it slowly to help precise manipulation. Apply a gain to avoid tiring motion, and then set it back to 1. It was found that distorted motions are better accepted when the distortion is gradually introduced [START_REF] Porssut | Reconciling Being in-Control vs. Being Helped for the Execution of Complex Movements in VR[END_REF]Feuchtner and Müller 2018]. In this case, the sense of embodiment is less impacted.

Feedback

FB1: Provide a well-calibrated avatar. The avatar's body measurements (height, general scale, arm length) must match those of the user. Eye height is important to estimate object size [Leyrer et al. 2011]. Having a personalised hand size was found better for manipulating objects and estimating their size [START_REF] Jung | Over My Hand: Using a Personalized Hand in VR to Improve Object Size Estimation, Body Ownership, and Presence[END_REF]Wang et al. 1997].

FB2: Use first-person perspective. The viewpoint should be co-located with that of the avatar. First-person perspective is better both for accuracy in manipulation tasks and for the sense of ownership [START_REF] Gorisse | First-and Third-Person Perspectives in Immersive Virtual Environments: Presence and Performance Analysis of Embodied Users[END_REF]. This was already recommended by Gabbard to increase the sense of presence [START_REF] Gabbard | A Taxonomy of Usability Characteristics in Virtual Environments[END_REF]].

FB3: Use slightly transparent hands to prevent occlusions. Make the hand subtly transparent to avoid occlusions and still provide depth cues. It can become transparent when close to an object. Gabbard already proposed this guideline for selection (see guideline Select7 [START_REF] Gabbard | A Taxonomy of Usability Characteristics in Virtual Environments[END_REF]). Here we want to highlight that a slightly transparent hand, additionally of being beneficial for performance [Van Veldhuizen and Yang 2021], can also still elicit a sense of agency [START_REF] Buchmann | Interaction with Partially Transparent Hands and Objects[END_REF] and ownership [Martini et al. 2015],

which we confirmed in our study in Chapter 4 with the ghost representation eliciting a good sense of embodiment, especially with the Go-Go technique.

FB4: Preserve body continuity as much as possible. If anisomorphic motion is used for out-of-reach manipulation (Go-Go technique), use feedback such as a long arm illusion or a robotic arm, but do not break body continuity. Avoid a too high offset that would make the arm too long. Breaking body continuity during interaction can result in a loss of embodiment [Seinfeld and Müller 2020]. However, if the chosen feedback is a long arm, the embodiment can break when the arm reaches twice the length of the normal arm [Kilteni et al. 2012b]. In this case, other types of feedback could be used, like a "ghost" arm [START_REF] Yang | Implementation and Evaluation of "Just Follow Me": An Immersive, VR-Based, Motion-Training System[END_REF]] that manipulates the remote object instead of the real arm (see Chapter 4). Raycasting can also be a good alternative since it is more efficient, albeit less intuitive [START_REF] Poupyrev | Egocentric Object Manipulation in Virtual Environments: Empirical Evaluation of Interaction Techniques[END_REF]].

FB5: Maximize multisensory coherency. If a controller is used, display its 3D model into the avatar's hand. It is if the real hand pose is similar to the avatar's hand pose.

It also provides coherency between visual and passive haptic feedback [START_REF] Insko | Passive haptics significantly enhances virtual environments[END_REF]]. If various virtual tools are used in the application, new input devices have been invented to propose a passive haptic feedback adapted to the virtual tool [START_REF] Zenner | Shifty: A Weight-Shifting Dynamic Passive Haptic Proxy to Enhance Object Perception in Virtual Reality[END_REF].

FB6: Provide haptic feedback. Use devices that provide haptic feedback during manipulation. Haptic feedback can increase the sense of embodiment [START_REF] Fröhner | Can Wearable Haptic Devices Foster the Embodiment of Virtual Limbs?[END_REF]. It can also help to improve performance when hand tracking is used [START_REF] Moehring | Effective manipulation of virtual objects within arm's reach[END_REF].

FB7: Use realistic avatars when using distorted motion. Use realistic avatars to make distorted motion less noticeable by the user. One condition for this is to have good hand tracking. They have several advantages as they make remapped movements less noticeable [Ogawa et al. 2020a] and increase the sense of ownership [Waltemate et al. 2018]. In Chapter 4, we also showed that people preferred to interact with a realistic arm rather than a ghost arm during distorted manipulation. However, realistic avatars increase users' expectations in terms of control [START_REF] Argelaguet | The role of interaction in virtual embodiment: Effects of the virtual hand representation[END_REF], therefore they should mostly be used when the tracking works well.

Future Research Topics

The current state of the art lets us identify several guidelines for designing manipulation techniques. However, there is such a high variety of input or output devices, manipulation techniques and possible virtual representations that our knowledge remains partial. More studies are needed to precise the guidelines, and maybe make them evolve as VR material evolves. This section presents the current gaps in the literature on manipulation techniques and avatars and proposes a number of research topics that should be explored in the future. Most of these research topics arise from the fact that the design of manipulation techniques rarely takes the avatar into account in the design process. This completes the lines of research on user representation proposed by Seinfeld et al. [2020a].

Study perception of motion alterations using different user representations. Ogawa et al. [2020a] compared the detection thresholds for a spheric cursor and a realistic hand, and found that distorted motion was less noticeable with a realistic hand. More of this kind of studies need to be done to investigate the role of avatars on the detection of distorted motion. It is necessary to understand how to safely modify motion without the user noticing it, or on the contrary to make the alteration more understandable to better accept it (e.g. by displaying a ghost hand showing real movements, as we proposed in Chapter 4). In addition to detection thresholds, motion alterations can influence how users' perceive the task. For example, several works have shown that changes in the CD gain could elicit illusions of weight when lifting virtual objects [START_REF] Jauregui | Toward "Pseudo-Haptic Avatars": Modifying the Visual Animation of Self-Avatar Can Simulate the Perception of Weight Lifting[END_REF].

Study different possibilities of feedback and mappings of controller-based input when an avatar is involved.

The perceived sense of embodiment towards the virtual representation highly depends on the mapping and feedback used, based on the information provided by the input device. While there are several studies on hand tracking, there is a lack of investigation on the visual feedback of controller-based input [Lougiakis et al. 2020]. Different mappings for a chosen input device should also be tested.

Compare different input devices to control the avatar during manipulation.

There is an increasing number of controllers proposed that should be compared with one another. For one user representation, several devices can be used to control it [START_REF] Alzayat | Quantitative Measurement of Tool Embodiment for Virtual Reality Input Alternatives[END_REF]]. The type of input device was found to both affect interaction efficiency and embodiment [Lin et al. 2019]. It would be interesting to compare controllers allowing fingers movement (e.g. Valve Index controllers) to controllers that need to be grabbed (e.g.

Vive controllers).

Propose new techniques to separate axes during manipulation while maintaining embodiment.

Constraining manipulation is sometimes needed for the sake of accuracy. For example, the user might want to move an object on a plane, or on an axis. Inspired by 3D desktop interfaces using widgets, similar techniques have been invented for immersive VE [Mendes et al. 2016]. If the user interacts with these widgets via an avatar, additional occlusions and clutching problems can appear. If the avatar does not correctly hold the widget, the feedback can seem unrealistic and disturb embodiment. If the movement is only constrained on a certain axis, users might feel a loss of agency, so it does not seem like a good solution either. It could be interesting to imagine new techniques to manipulate objects independently on different axes without affecting embodiment.

Compare different visual feedback for common techniques.

Different visual feedback can be provided for one chosen technique. For unrealistic interaction, it may be better to provide virtual tools that suggest the use of the technique. For example, putting a laser pointer in the avatar's hand to use raycasting. In some cases, the avatar can be adapted to the technique (long arm for the Go-Go), but this modifies the avatar appearance and may impact more the sense of embodiment. The impact of visual feedback has been investigated for the Go-Go technique [START_REF] Feuchtner | Extending the Body for Interaction with Reality[END_REF], and we have proposed in Chapter 4 a first study exploring the use of dual representations with anisomorphic techniques. Yet, there is a need for more similar studies testing different feedback and their impact on performance and embodiment. Another solution could be to decouple the avatar from the tool used for manipulation. When using anisomorphic manipulation, the transformations could be applied only on the tool, not the avatar. This type of feedback would not affect the avatar itself, thus potentially preserving embodiment.

Study the influence of visual feedback during grasping (collisions, hand poses) on embodiment, especially on the sense of agency.

Nowadays, frameworks (e.g. SteamVR) make it easy to define hand poses for object ma-nipulation, to have a more realistic visual feedback. Users can be guided to defined poses with subtle assistance, with no impact on embodiment [START_REF] Porssut | Reconciling Being in-Control vs. Being Helped for the Execution of Complex Movements in VR[END_REF]. They are biased to self-attribute assisted movements [START_REF] Debarba | Self-attribution of distorted reaching movements in immersive virtual reality[END_REF]]. However, overly simplistic mappings during grasping might make the user feel less in control. New solutions start to be proposed to automatically compute hand poses in real time [START_REF] Tian | Realtime Hand-Object Interaction Using Learned Grasp Space for Virtual Environments[END_REF]] that could potentially improve embodiment. The moment users release the hand pose might also be crucial for feeling in control, especially when no haptic feedback is used, yet it has rarely been investigated for the moment [Prachyabrued and Borst 2012a].

Explore the impact of multimodal sensory feedback during manipulation on the sense of embodiment. While there are studies showing the importance of synchronous multimodal feedback on the sense of embodiment, there is a lack of literature on the importance of haptic and auditory feedback, especially during interaction tasks. Yet, the potential impact of such feedback was found on body perception [START_REF] Fröhner | Can Wearable Haptic Devices Foster the Embodiment of Virtual Limbs?[END_REF]Tajadura-Jiménez et al. 2015b]. Manipulating objects offers a source of potential feedback that might increase the sense of embodiment.

Conclusion

In this chapter, we proposed several guidelines to design techniques compatible with avatars. These guidelines concern input devices, control and feedback. We also proposed several research topics that still need some investigation. We hope that in the future, thanks to deeper research on this topic, we will be able to reach good trade-offs ensuring embodiment and efficient manipulation. Finally, the avatar-friendly concept can be extended to other types of interaction (navigation, system control) to provide vibrant 3D experiences to users, as it will be discussed in the next chapter among other perspectives.

"The end has no end"

The Strokes Chapter 6

CONCLUSION

The goal of this thesis entitled "Towards Avatar-Based Interaction in Virtual Reality" was to better understand the interrelations between the user, the avatar, and the interaction in VR, in order to have future rich interaction while maintaining a good avatar embodiment. Three research axes (RA) presented in introduction guided this research. In this chapter, the different contributions made are summarised, and some perspectives for future research are presented.

Contributions

First, it was important to better understand the relation between the user and the avatar to know how virtual embodiment was elicited. While several works focused on external factors, i.e. factors depending on the virtual environment or the avatar, this thesis explored internal factors depending on the user (RA1: Influence of the user's characteristics on the sense of embodiment). In Chapter 2, we presented our first contribution, investigating the potential impact of body awareness and several personality traits (Big Five traits and locus of control) on the sense of embodiment. While there was no apparent effect of the Big Five traits and body awareness, positive correlations were found between sense of embodiment and locus of control. In particular, an internal locus of control seems to be correlated with the sense of agency, while an external locus of control seems to affect the sense of ownership. These results can encourage the community to dig deeper into the influence of internal factors, to better understand individual differences in embodiment scores.

Another factor that had not been investigated deeply was the effect of interacting with the VE. To ensure embodiment while interacting, it is essential to know which techniques are better for virtual embodiment, and how they can affect it. While there was an increasing number of works on the impact of manipulation on embodiment, locomotion techniques had rarely been investigated and their impact on embodiment was unknown (RA2: Influence of the interaction technique on the sense of embodiment). Moreover, most papers on locomotion did not use avatars, thus not taking their potential impact on locomotion into account (RA3: Influence of the avatar on the interaction). Therefore, we decided to investigate the interrelations between locomotion techniques and avatars. An experiment was conducted, presented in Chapter 3, using three different locomotion techniques involving a different level of physical motion: real walking, walking-in-place and head steering. In all conditions, the avatar's movements were reproducing users' movements. The user representation was used as a within-subject factor, with two levels: only 3D controllers or a full-body avatar. No significant difference between the locomotion techniques was found for the sense of embodiment, showing that having an avatar reproducing users' movements may be more important than the technique interaction fidelity. However, participants were particularly disturbed by the legs artifacts caused by inverse kinematics, especially in the walking condition. More investigation on the impact of such artifacts could lead to a deeper understanding of the interrelations between embodiment and locomotion techniques.

In addition to locomotion, another essential task in VR is object manipulation. Several techniques, called anisomorphic techniques, distort users' motion to facilitate interaction, e.g. to reach remote object or to increase precision. These motion distortions can impact the sense of embodiment. Therefore, in Chapter 4, we presented two experiments that investigated the use of dual body representations with amplified motion (using the Go-Go technique) and decreased motion (using the PRISM technique). Dual body representations displayed both distorted and real movements. This first study investigating dual representations in this context showed that it was possible to feel a global sense of embodiment towards such representations (RA2), and that they had no impact on performance (RA3). While interacting seemed more important than showing exact movements for agency during out-of-reach manipulation, people felt more in control of the realistic arm during close manipulation. We also found that people globally preferred having a single representation, but opinions diverge especially for the Go-Go technique.

As we mentioned in the related work, the literature on manipulation techniques and avatars is more extensive than on other types of techniques. We analysed previous work on this topic to propose fourteen guidelines, presented in Chapter 5, to help VR developers to design avatar-friendly manipulation techniques, i.e. techniques which take avatar embodiment into account during the design process (RA2). The aim is to have techniques that can ensure both performance and virtual embodiment.

Perspectives

While this thesis is a new step towards having avatar-friendly interaction techniques, our studies have some limitations and there are still many potential leads to explore in order to achieve rich interaction with avatars in VR.

Improve Embodiment Measures

To better understand how the sense of embodiment is elicited, we need to measure it, which is not trivial. For this reason, most studies use subjective questionnaires to measure embodiment. In this thesis, we used such questionnaires in all of our user studies. These questionnaires vary a lot between different experiments, as they highly depend on the experimental conditions. There have been several attempts to create a standardised validated questionnaire [Peck and Gonzalez-Franco 2021;[START_REF] Roth | Construction of the Virtual Embodiment Questionnaire (VEQ)[END_REF]. Roth et al. [2017;[START_REF] Fribourg | Contribution à l'étude des facteurs influençant le sentiment d'incarnation envers un avatar en réalité virtuelle[END_REF] constructed a novel embodiment questionnaire by relying on factor analysis to propose new leads of standardised questionnaires. Interestingly, their work brought out a novel dimension to evaluate embodiment, named Change (in the perceived body schema), which was not present in the subcomponents proposed by Kilteni et al. [2012a], suggesting that novel dimensions might emerge from the formal construction of novel questionnaires, and which could be more related to interaction. It would be interesting to get more insight on current questionnaires to know when to use them and maybe develop new ones. Having only one standardised questionnaire working for all embodiment experiments seems like a complex task to achieve [Skarbez et al. 2021a], therefore it might be interesting to have numerous small questionnaires adapted to specific cases. Moreover, subjective questionnaires are not always adaptable to every experiment and they still highly rely on participants' understanding of the questions. Studies therefore often add some behavioural responses to add matter to the results. While these responses are often used as an additional measure, and several works show positive correlations between behavioural responses and the sense of embodiment [START_REF] Yuan | Is the rubber hand illusion induced by immersive virtual reality?[END_REF][START_REF] Zhang | Body ownership and response to threat[END_REF][START_REF] Kilteni | Drumming in immersive virtual reality: the body shapes the way we play[END_REF], it is complicated to know whether they rely on similar neurological processes than virtual embodiment [Ma and Hommel 2013]. The ideal measure would be to have access to users' own mental representations of themselves at any time, but this is not feasible yet. A few cognitive models have been proposed trying to explain the brain processes eliciting the sense of embodiment [START_REF] Braun | The Senses of Agency and Ownership: A Review[END_REF]. One main hope for the future is to be able to use brain signals, captured by EEG or MRI, to find characteristic brain signals when embodying an avatar [START_REF] Jeunet | Do you feel in control? " : Towards Novel Approaches to Characterise, Manipulate and Measure the Sense of Agency in Virtual Environments[END_REF]Alchalabi et al. 2019].

Offer Customised Parameters to Ensure Embodiment

This thesis highlighted some potential individual factors influencing the sense of embodiment (see Chapter 2). For the first study on this topic, we therefore chose a number of personality questionnaires to explore the potential influence of individual traits. Given the amount of personality questionnaires and cognitive models in the literature, it was not possible to be exhaustive, and we decided to focus on some of the most common models (i.e. Big Five, Locus of Control, Body Awareness). Further studies exploring the influence of other traits and inter-personal aspects could be interesting to improve our understanding. For example, other interesting traits that could be studied would be empathy, which was already shown to have an effect on RHI and presence [START_REF] Asai | Rubber hand illusion, empathy, and schizotypal experiences in terms of self-other representations[END_REF][START_REF] Seiryte | The Empathy Quotient (EQ) predicts perceived strength of bodily illusions and illusion-related sensations of pain[END_REF][START_REF] Sas | Presence Equation: An Investigation into Cognitive Factors Underlying Presence[END_REF], or absorption which was found linked to presence [START_REF] Kober | Personality and Presence in Virtual Reality: Does Their Relationship Depend on the Used Presence Measure?[END_REF]. Other personal information could be investigated such as cultural differences or racial information. More knowledge will also come from studies using machine learning to enable the identification of different users' profile, that react differently to VR and embodiment. Some studies already go in the direction of customised experiences, by using reinforcement learning to adapt the experience to each user [START_REF] Porssut | Adapting Virtual Embodiment through Reinforcement Learning[END_REF]Llobera et al. 2021]. The ultimate goal would be to be able to predict embodiment levels and have customised experience to optimise embodiment for each user. A pre-experiment questionnaire, with identifies important individual factors, could be proposed so as to predict a user's level of embodiment prior to the immersion in VR. Being able to create such a questionnaire could prove a valuable tool in the future to adapt the virtual experience to the users in order to maximise their sense of embodiment. This would however also require additional knowledge about which adaptations are more fitted for some categories of users than others.

Study the Importance of Task and User Focus

In VR, an infinity of tasks are possible that could have a different influence on embodiment. In our studies, we always had to choose which tasks to perform, and this choice was often done so as to ensure that people could see the avatar. However, other tasks could be explored.

In Chapter 4, we decided to focus on two types of anisomorphic manipulation techniques. As future work, it could be interesting to explore other tasks creating bigger offsets between the real and the virtual hand. For example, interacting with surfaces that handle collisions could create bigger offsets. We also only used visuomotor tasks in our studies, but it would be possible to replicate these studies with visuotactile stimulation for example, as it necessitates subjects to look at the virtual body. While we wanted to make users interact with the VE and thus using visuomotor stimulation, as it was the focus of this thesis, results might differ a little when using different sensory stimulation.

A recurrent problem in embodiment studies is that participants do not always focus on their avatar, thus making subjective embodiment assessment complicated and unreliable. In our studies, participants sometimes reported that they tended to forget the avatar while doing the task. For example, in the studies of Chapter 4, a few participants reported a difficulty to rank the different virtual representations as they focused on the task and not the avatar during the interaction. Such as in real life, the virtual body is not always necessary to perform a task [START_REF] Ricca | Influence of hand visualization on tool-based motor skills training in an immersive VR simulator[END_REF]. Therefore, exploring tasks involving more the actual user's virtual representation would also be interesting. In the future, it would be better to always know where users have their focus during an experiment, to determine if it has an impact on results, or if having the avatar in the peripheral vision is enough to estimate embodiment. To this end, eye tracking could be an interesting solution to use in embodiment studies to explore the effect of paying attention to the virtual body.

Provide High-Quality Motion Capture

In this thesis we used simple animation techniques (i.e. Inverse Kinematics) to animate avatars during user studies. While Inverse Kinematics is often used in embodiment studies, and quite efficient for animating upper limbs, it showed its limitations mostly in the experiment on locomotion in Chapter 3, in which some participants reported being disturbed by some artifacts in the legs movements. As previous work showed a user preference for high-quality motion capture over Inverse Kinematics [Fribourg et al. 2020a], it could be interesting to run a similar study with higher-quality motion capture systems to evaluate whether differences in terms of embodiment could be influenced by the animation quality in such cases. This was also due to the fact that while we used global calibration to match the avatar's height to the participant's, the avatar's morphology was still different. Several solutions are now starting to appear to easily and precisely calibrate an avatar to the participants morphology [START_REF] Pujades | The Virtual Caliper: Rapid Creation of Metrically Accurate Avatars from 3D Measurements[END_REF]]. In the future, it will be possible to have perfectly calibrated avatars and good motion tracking (with external sensors such as cameras, or wearables like inertial sensors).

Extend Design Guidelines to All Interaction Techniques

In Chapter 5, we proposed several guidelines for designing avatar-friendly manipulation techniques. Of course, this concept does not need to be limited to manipulation techniques, but can be extended to all types of interaction techniques. For instance, avatars start to be considered in the design of navigation [Medeiros et al. 2019] or system input techniques [START_REF] Grubert | Effects of Hand Representations for Typing in Virtual Reality[END_REF][START_REF] Knierim | Physical Keyboards in Virtual Reality: Analysis of Typing Performance and Effects of Avatar Hands[END_REF]. When the related work on avatars and other types of techniques is more developed, it will be possible to propose more guidelines. For locomotion techniques, we tried to go in this direction with Chapter 3 by investigating avatar embodiment when using different locomotion techniques. However, more studies are needed to propose guidelines for designing the optimised locomotion technique that ensures embodiment, which ideally also preserves ease of navigation, sense of presence and limits motion sickness. For system input, it would also be interesting to have design guidelines. Most of them would be similar to the ones for manipulation techniques, but other specific guidelines could be added such as using more body-centred widgets, which is an avatar-friendly design already used in most VR applications.

Rethink Evaluation Methods

In Chapter 5, we proposed guidelines for early design phases. As avatars can impact interaction (as detailed in Section 1. 3, e.g. influencing users' speed [Tran et al. 2017]), we believe that it is becoming important to also consider evaluating the influence of the avatar throughout the whole design process, as well as to consider novel evaluation methods assessing the compatibility between an avatar and an interaction technique.

Developers and researchers should therefore use embodiment as a novel criterion for assessing the quality of interaction. During iterations of the design process, different types of evaluation are typically performed, where designers use several criteria and heuristics to identify flaws in a current implementation (formative evaluation) or to compare a new final implementation to benchmarks or older implementations (summative evaluation). These criteria are mostly performance-oriented (e.g. accuracy, speed) or user-oriented (e.g. ease of use, predictability). Given the literature now available in regards to the sense of embodiment, we believe that it should progressively become a new criterion for measuring the quality of interaction, just as breaks in presence were already proposed as new criteria to measure usability [START_REF] Steed | Breaks in presence as usability criteria[END_REF]]. In the future, the goal would therefore be to design efficient interaction techniques that do not disrupt embodiment, in which case questions related to the sense of embodiment [START_REF] González-Franco | Avatar Embodiment. Towards a Standardized Questionnaire[END_REF][START_REF] Roth | Construction of the Virtual Embodiment Questionnaire (VEQ)[END_REF]] should be added to formative and summative evaluations to complete evaluations during the iterative design process.

Extend On-Body Interaction

Body-centred interaction is inherently avatar-friendly, as it focuses the interaction on the body, therefore making the virtual body useful and helping the appropriation of it. While it is already common to have body-centered information and widgets in VR applications, it could go further by using the skin as input for example, which has not been deeply explored. Self-touch was already found beneficial for embodiment [START_REF] Bovet | The critical role of self-contact for embodiment in virtual reality[END_REF][START_REF] Hara | Voluntary self-touch increases body ownership[END_REF]]. It would be interesting to use more on-skin interaction [START_REF] Weigel | ISkin: Flexible, Stretchable and Visually Customizable On-Body Touch Sensors for Mobile Computing[END_REF]Meier et al. 2021] and to see its impact on embodiment. Making the avatar central during interaction and interacting directly with the skin, with a congruent visuotactile stimulation, could make users regularly focus on the body and could elicit high levels of embodiment.

Embody Multiple Bodies

As highlighted in Chapter 4, multiple bodies have not been investigated a lot in VR studies for the moment, but they might be more explored in the future. It would be interesting to propose a definition and a taxonomy of such multiple representations. Several factors already appear differentiating in such representations: visual appearance, perspective (first-person versus third-person), control (isomorphic versus anisomorphic; synchronised versus alternate), location (co-located bodies or not). Dual representations could represent co-located bodies seen from a first-person perspective, while multiple bodies seen from different perspectives like in the study by Miura et al. [2021] could be called duplicated representations.

Multiple body representations could steer new psychological studies on embodiment, to understand if embodiment switches between several representations or if a "parallel" embodiment emerges, global to all representations [Miura et al. 2021]. In collaborative applications, it would even be possible to create shared embodiment, where multiple users could share the control, not only of one avatar [START_REF] Fribourg | Virtual co-embodiment: evaluation of the sense of agency while sharing the control of a virtual body among two individuals[END_REF]] but of multiple avatars. This could offer multiple points of view to the user, common with those of other users, which might be a way to stimulate empathy and collaboration, as it would develop a common perception of the virtual world.

To conclude, we hope this thesis will steer new studies on the interrelations between avatars and interaction and open more questions on this topic, to invent incredible avatarfriendly interaction techniques. 1.2 Action-perception loop: the user can control the avatar thanks to the input devices, so as to interact with the VE. In response to the user's actions, the VE provides feedback perceived by the user thanks to the output devices. . 2.1 From left to right: an example of a trajectory to draw during the experimental task; A view of the scene from behind; Another virtual character stabbing the participants' virtual hand at the end of the experiment to measure their response to the threat on their virtual body. . . . . . . . . .

LIST OF FIGURES

Facteurs externes influençant l'incarnation

Deux méthodes principales existent pour générer un sentiment d'incarnation. La première est la stimulation visuotactile, dans laquelle un objet (pinceau, balle) est utilisé pour toucher le corps réel des utilisateurs en même temps que l'objet virtuel équivalent touche le corps virtuel [START_REF] Slater | Towards a digital body: the virtual arm illusion[END_REF]. Le deuxième moyen principal est la stimulation visuomotrice. Pour cela, il faut faire en sorte que l'avatar reproduise les mouvements des utilisateurs [START_REF] Kokkinara | Measuring the Effects through Time of the Influence of Visuomotor and Visuotactile Synchronous Stimulation on a Virtual Body Ownership Illusion[END_REF]]. Cette méthode s'est avérée plus efficace que la stimulation visuotactile [START_REF] Kokkinara | Measuring the Effects through Time of the Influence of Visuomotor and Visuotactile Synchronous Stimulation on a Virtual Body Ownership Illusion[END_REF]. La synchronisation spatiale et temporelle est extrêmement importante, notamment pour le sentiment d'agentivité [START_REF] Jeunet | Do you feel in control? " : Towards Novel Approaches to Characterise, Manipulate and Measure the Sense of Agency in Virtual Environments[END_REF]]. En plus des facteurs externes concernant le type de stimulation, d'autres facteurs ont également été identifiés comme l'apparence de l'avatar [Maselli and Slater 2013;Waltemate et al. 2018;[START_REF] Gorisse | From Robot to Virtual Doppelganger: Impact of Visual Fidelity of Avatars Controlled in Third-Person Perspective on Embodiment and Behavior in Immersive Virtual Environments[END_REF].

Facteurs internes influençant l'incarnation

Certains traits de personnalité pourraient être liés au sentiment d'incarnation. Certains liens ont été trouvés entre la force de l'illusion de la main en caoutchouc et certains traits de personnalité [START_REF] David | Susceptibility to the rubber hand illusion does not tell the whole body-awareness story[END_REF][START_REF] Asai | Rubber hand illusion, empathy, and schizotypal experiences in terms of self-other representations[END_REF]. Des travaux récents ont commencé à s'intéresser au rôle potentiel des traits de personnalité dans l'incarnation virtuelle. Un exemple est le travail de Jeunet et al. [2018] qui a montré que le sentiment d'agentivité est lié à un locus de contrôle interne, c'est-à-dire que les gens qui se sentent à l'origine des événements de leur vie se sentent également plus en contrôle de leur avatar. Dans le chapitre 2 de cette thèse, nous présentons une expérience utilisateur réalisée avec 123 participants sur l'impact potentiel de la personnalité sur le sentiment d'incarnation. Plusieurs traits ont été étudiés: les traits du "Big Five" [START_REF] John | The Big Five Inventory-Versions 4a and 54[END_REF][START_REF] Plaisant | Validation du Big Five Inventory français (inventaire des cinq grandes dimensions de la personnalité)[END_REF]] (Ouverture à l'expérience, Conscienciosité, Extraversion, Agréabilité, Neuroticisme), le locus de contrôle [Levenson 1981;Loas et al. 1994] et la conscience corporelle [START_REF] Shields | The Body Awareness Questionnaire: Reliability and Validity[END_REF][START_REF] Dumont | Expérience subjective et différences individuelles dans l'intégration d'informations visuelle et kinesthésique[END_REF]. Un questionnaire subjectif a été utilisé pour mesurer le sentiment d'incarnation. En plus de ce questionnaire, une menace a été introduite à la fin de l'expérience pour observer la réaction de l'utilisateur. Cette méthode est courante dans les études d'incarnation, car la réaction à la menace est généralement positivement corrélée à l'intensité du sentiment d'incarnation [START_REF] Yuan | Is the rubber hand illusion induced by immersive virtual reality?[END_REF].

Nous avons globalement trouvé que le locus de contrôle semblait être lié à deux composantes de l'incarnation. Le sentiment d'appropriation semble être plutôt influencé par un locus dit externe (le fait de penser que ce qui nous arrive est dû à des éléments extérieurs tel que le destin), alors que le sentiment d'agentivité est positivement corrélé par un locus dit interne (le fait de penser que ce qui nous arrive est dû à nos propres actions). Nous avons également trouvé que la réaction et la perception de la menace étaient positivement corrélés avec le neuroticisme. Dans le chapitre 4, nous étudions un autre type de technique d'interaction, la manipulation d'objets. Plus précisément, nous nous focalisons sur la manipulation anisormorphique qui modifie les mouvements de l'utilisateur, par exemple pour amplifier les mouvements pour atteindre des objets lointains, ou pour ralentir le mouvement pour gagner en précision. Ce type de techniques peut avoir un impact sur le sentiment d'incarnation, car les mouvements de l'avatar sont différents des mouvements de l'utilisateur. Les sentiments d'agentivité et de co-localisation sont potentiellement les plus impactés, car il y a un décalage entre les mouvements réels et virtuels [START_REF] Kokkinara | Measuring the Effects through Time of the Influence of Visuomotor and Visuotactile Synchronous Stimulation on a Virtual Body Ownership Illusion[END_REF][START_REF] Pritchard | Non-hierarchical Influence of Visual Form, Touch, and Position Cues on Embodiment, Agency, and Presence in Virtual Reality[END_REF]. Nous avons donc réalisé une étude pour explorer une potentielle solution : l'utilisation d'une représentation double. Une représentation sert à montrer les mouvements déformés aidant à l'interaction, pendant qu'une autre représentation co-localisée

Conclusion

Les différentes contributions de cette thèse ont pour but d'aider le développement des techniques d'interaction compatibles avec les avatars, c'est-à-dire des techniques qui sont efficaces mais qui permettent aussi de maintenir un bon sentiment d'incarnation envers l'avatar. En étudiant à la fois comment l'incarnation apparaît selon les profils des utilisateurs, comment les différentes techniques d'interaction peuvent aussi influencer cette incarnation, cette thèse s'intéresse autant à l'action qu'à la perception. Dans le futur, il serait intéressant d'approfondir les connaissances sur l'incarnation en réfléchissant à de meilleurs moyens de la mesurer et de la maximiser pour chaque utilisateur. Il serait intéressant aussi d'explorer des nouvelles méthodes d'interaction comme l'interaction sur la peau, et d'étendre les directives de design aux autres techniques d'interaction et pas seulement la manipulation d'objets. A long terme, la possibilité d'avoir des interactions riches via un avatar permettra par exemple aux utilisateurs de tester et d'apprendre de nouvelles compétences en RV. Abstract: Virtual reality enables users to be immersed in an alternative world. In this virtual world, they can move around or interact with objects through their virtual body, also called an avatar, which tells them where they are and what they are doing. Users can even feel a sense of embodiment towards this avatar and have the impression that it is their real body. This illusion offers an interesting user experience and can have surprising consequences such as increasing a person's cognitive abilities. However, it is not clear yet how this illusion is elicited. Furthermore, current interaction techniques are sometimes not compatible with realistic avatars, especially because they sometimes distort the user's movements, and thus potentially the avatar's movements and body, which can influence embodiment. This thesis proposes several studies to better understand the relationship between user, avatar and interaction. It focuses on the sense of embodiment, investigating both individual factors and the impact of different feedbacks during interaction tasks (locomotion and object manipulation). Design guidelines for avatarcompatible manipulation techniques are also provided based on existing literature, as well as leads for future research. The ultimate goal is to have effective interaction that provides a high sense of embodiment.

Figure 1

 1 Figure 1.5 -Examples of different possible hand appearances for a manipulation task.Image from[START_REF] Argelaguet | The role of interaction in virtual embodiment: Effects of the virtual hand representation[END_REF]].

Figure 1 . 8 -

 18 Figure 1.8 -Two different input modalities: hand tracking versus controllers. Hand tracking is preferred and better for the sense of embodiment. Image from [Lin et al. 2019].

Figure 1

 1 Figure 1.9 -Example of a widget to constrain manipulation. Image from [Mendes et al. 2016].

Figure 1 .

 1 Figure 1.10 -First-person perspective vs. third-person perspective. Image from [Galvan Debarba et al. 2017].

Figure 2

 2 Figure2.1 -From left to right: an example of a trajectory to draw during the experimental task; A view of the scene from behind; Another virtual character stabbing the participants' virtual hand at the end of the experiment to measure their response to the threat on their virtual body.

Figure 2

 2 Figure 2.2 -Examples of four trajectories that participants were instructed to perform during the experiment with either their left or their right hand.

Figure 2 . 3 -

 23 Figure 2.3 -The two avatar models used in our experiments, which were matched to the gender of the participant.

Figure 2

 2 Figure 2.4 -Contributions (i.e. weights) of the embodiment questions to the different components (O P C1,M and O P C2,M (for men), O P C1,F and O P C2,F (for women), A P C1 , EA P C1 , T P C1 ).

Figure 3 .

 3 Figure 3.1 -Illustration of the four tasks performed by the participants in our user study, all in the full-body avatar condition. The same tasks were also performed without an avatar. From left to right: Training task, Corridor task, Path-following task and Columns task.

  14, SD = 2.96 M = 8.50, SD = 2.91 Ratio shoulder collisions M = 0.35, SD = 0.41 M = 0.37, SD = 0.38 Nb mushrooms M = 22.7, SD = 7.13 M = 23.45, SD = 6.41

Figure 3 . 3 -

 33 Figure 3.3 -Scores by Technique for the question C pref erBody ; no significant difference between the techniques but a high dispersion for the S condition.

Figure 4 .

 4 Figure 4.1 -Illustration of two types of dual body representations studied in this chapter.On the left image, a ghost representation enables remote manipulation while a realistic co-located representation provides feedback with respect to the real user's position. On the right image, a ghost representation provides feedback with respect to the user's real position while a realistic representation enables precise manipulation with the environment thanks to slowed motion.

  102

4. 4 .

 4 Experiment 1: Dual Representations for Increased Motions During Out-of-Reach Manipulation

Figure 4 .

 4 Figure 4.2 -The three levels of Representation in the first experiment with amplified motion. The interactive arm is either realistic (in R -Ø or R -G) or transparent (in G -R). When a co-located arm is displayed, a realistic representation (in G -R) or a ghost one (in R -G) is used.

Figure 4 . 3 -

 43 Figure 4.3 -Results for the two components Response and Multi-Sensory from the PGF questionnaire in Experiment 1, for which a main effect of Representation was found. Only the pairwise test on the Response component showed a significant difference between R -Ø and G -R (p < 0.05). There was no main effect for other components.

Figure 4 . 4 -

 44 Figure 4.4 -Ranking for the different conditions in the Go-Go experiment. R -Ø was preferred with 10 participants ranking it as first, followed by R -G and finally G -R.

Figure 4 .

 4 Figure 4.5 -Results of additional questions on the senses of ownership and agency for G -R and R -G in the experiment with the Go-Go technique. * p < 0.05, ** p < 0.01

Figure 4 . 6 -

 46 Figure 4.6 -Different levels of Representation in the second experiment with amplified motion. The interactive arm is either realistic (in R -Ø or R -G), transparent (in G -R) or not displayed (in Ø -R). A co-located arm is displayed, either a realistic one (in G -R and Ø -R) or a transparent one (in R -G).

Figure 4 .

 4 Figure 4.7 -Results for the two components Response and Ownership, as well as the global Embodiment score (from the PGF questionnaire) in Experiment 2, for which a main effect of Representation was found. Only the pairwise test on Embodiment scores showed a significant difference between R -Ø and R -G (p < 0.05). There was no main effect for other components.

Figure 4 . 8 -

 48 Figure 4.8 -Results of additional questions on the senses of ownership and agency for G -R and R -G in the experiment with the PRISM technique. * p < 0.05, ** p < 0.01

Figure 4 .

 4 Figure 4.9 -Ranking for the different conditions in the PRISM experiment. R -Ø was preferred with 13 participants ranking it as first.

1

  Illustration of the different research axes, linking the interaction, the user, the avatar, and the sense of embodiment (SoE). . . . . . . . . . . . . . . . 1.1 Revisited Milgram's Reality-Virtuality Continuum by Skarbez et al. [2021b].

1. 3

 3 Control of an avatar with a different morphology, for example an avatar with a third arm. Image from[START_REF] Laha | Evaluating Control Schemes for the Third Arm of an Avatar[END_REF]]. . . . . . . . . . . . . . . . 1.4 First experiment in VR using visuotactile stimulation to elicit a sense of embodiment towards a virtual arm. Image from [Slater et al. 2008]. . . . . 1.5 Examples of different possible hand appearances for a manipulation task. Image from [Argelaguet et al. 2016]. . . . . . . . . . . . . . . . . . . . . . . 1.6 The participant is represented by either a realistic hand (on the left image) or a spherical pointer (on the right). The transparent hand represents the user's real hand, not displayed in the VE. Image from [Ogawa et al. 2020a]. 1.7 Illustration from the experiment investigating the impact of avatar appearance on the way users drum in VR. Participants are represented either by flat shaded white hands (A), a dark-skinned avatar with casual clothes (B), or a light-skinned avatar with fancy clothes (C). Image from [Kilteni et al. 2013]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8 Two different input modalities: hand tracking versus controllers. Hand tracking is preferred and better for the sense of embodiment. Image from [Lin et al. 2019]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9 Example of a widget to constrain manipulation. Image from [Mendes et al. 2016]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.10 First-person perspective vs. third-person perspective. Image from [Galvan Debarba et al. 2017]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2. 2

 2 Examples of four trajectories that participants were instructed to perform during the experiment with either their left or their right hand. . . . . . .2.3 Thetwo avatar models used in our experiments, which were matched to the gender of the participant. . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Contributions (i.e. weights) of the embodiment questions to the different components (O P C1,M and O P C2,M (for men), O P C1,F and O P C2,F (for women), A P C1 , EA P C1 , T P C1 ). . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Illustration of the four tasks performed by the participants in our user study, all in the full-body avatar condition. The same tasks were also performed without an avatar. From left to right: Training task, Corridor task, Path-following task and Columns task. . . . . . . . . . . . . . . . . . . . . 3.2 Left: Setup in the physical environment. The HTC Vive with a wireless adapter was used to enable participants to physically walk in an 8m × 8m area. The tracking of the user's motions was enabled by the two hand controllers and two HTC Vive Trackers attached to their ankles. Two additionnal HTC Vive trackers were also positioned on a backpack to track participants' shoulders. Tracking was done using four HTC Vive lighthouses. Right: Overview of the virtual environment: the navigation area was constrained by the virtual fences which matched the limits of the physical space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3. 3

 3 Scores by Technique for the question C pref erBody ; no significant difference between the techniques but a high dispersion for the S condition. . . . . .4.1 Illustration of two types of dual body representations studied in this chap-ter. On the left image, a ghost representation enables remote manipulation while a realistic co-located representation provides feedback with respect to the real user's position. On the right image, a ghost representation provides feedback with respect to the user's real position while a realistic representation enables precise manipulation with the environment thanks to slowed motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 The three levels of Representation in the first experiment with amplified motion. The interactive arm is either realistic (in R -Ø or R -G) or transparent (in G -R). When a co-located arm is displayed, a realistic representation (in G -R) or a ghost one (in R -G) is used. . . . . . . . . . 4.3 Results for the two components Response and Multi-Sensory from the PGF questionnaire in Experiment 1, for which a main effect of Representation was found. Only the pairwise test on the Response component showed a significant difference between R -Ø and G -R (p < 0.05). There was no main effect for other components. . . . . . . . . . . . . . . . . . . . . . . . 4.4 Ranking for the different conditions in the Go-Go experiment. R -Ø was preferred with 10 participants ranking it as first, followed by R -G and finally G -R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Results of additional questions on the senses of ownership and agency for G -R and R -G in the experiment with the Go-Go technique. * p < 0.05, ** p < 0.01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Different levels of Representation in the second experiment with amplified motion. The interactive arm is either realistic (in R -Ø or R -G), transparent (in G -R) or not displayed (in Ø -R). A co-located arm is displayed, either a realistic one (in G -R and Ø -R) or a transparent one (in R -G). 4.7 Results for the two components Response and Ownership, as well as the global Embodiment score (from the PGF questionnaire) in Experiment 2, for which a main effect of Representation was found. Only the pairwise test on Embodiment scores showed a significant difference between R -Ø and R -G (p < 0.05). There was no main effect for other components. . . . . . 4.8 Results of additional questions on the senses of ownership and agency for G -R and R -G in the experiment with the PRISM technique. * p < 0.05, ** p < 0.01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 Ranking for the different conditions in the PRISM experiment. R -Ø was preferred with 13 participants ranking it as first. . . . . . . . . . . . . . . . 6.1 Illustration des différents axes de recherche, reliant l'utilisateur, l'interaction, l'avatar et le sentiment d'incarnation (SoE). . . . . . . . . . . . . . . . . . 6.2 Boucle d'action-perception : l'utilisateur peut contrôler un avatar grâce à des périphériques d'entrée, pour pouvoir interagir avec l'environnement virtuel. En réponse aux actions de l'utilisateur, l'environnement virtuel retourne un feedback qui est perçu par l'utilisateur via les périphériques de sortie. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 6.3 Première expérience en réalité virtuelle utilisant une stimulation visuotactile pour créer un sentiment d'incarnation envers un bras virtuel. Image venant de [Slater et al. 2008]. . . . . . . . . . . . . . . . . . . . . . . . . . 182 6.4 De gauche à droite : un exemple de trajectoire à dessiner pendant l'expérience; Une vue de derrière de la scène virtuelle; Un autre personnage virtuel en train de poignarder la main virtuelle du participant à la fin de l'expérience pour mesurer sa réponse à la menace sur son corps virtuel. . . . . . . . . . 184 6.5 Illustration des quatre tâches effectuées par les participants durant notre étude utilisateur, toutes dans la condition avec l'avatar au complet. Les mêmes tâches ont également été réalisées sans avatar. De gauche à droite : Tâche d'entraînement, tâche du couloir, tâche de suivi de chemin et tâche des colonnes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 6.6 Illustration de deux types de représentations doubles étudiées dans ce chapitre. Sur l'image de gauche, une représentation fantôme permet une manipulation à distance tandis qu'une représentation réaliste co-localisée fournit un retour par rapport à la position réelle de l'utilisateur. Sur l'image de droite, une représentation fantôme fournit un retour par rapport à la position réelle de l'utilisateur tandis qu'une représentation réaliste permet une manipulation précise avec l'environnement grâce à un mouvement ralenti.186 Ogawa, Nami, Takuji Narumi, Hideaki Kuzuoka, and Michitaka Hirose (2020b), « Do You Feel Like Passing Through Walls?: Effect of Self-Avatar Appearance on Facilitating Realistic Behavior in Virtual Environments », in: Proceedings of the 2020 CHI Conference on Human Factors in Computing Systems, CHI '20, Honolulu, HI, USA, pp. 1-14. Ono, Hiroshi, Brian J Rogers, Masao Ohmi, and Mika E Ono (1988), « Dynamic Occlusion and Motion Parallax in Depth Perception », in: Perception 17.2, PMID: 3226867, pp. 255-266. Ouramdane, Nassima, Samir Otmane, Frédéric Davesne, and Malik Mallem (2006), « FOLLOW-ME: a new 3D interaction technique based on virtual guides and granularity of interaction », in: Proceedings of the 2006 ACM international conference on Virtual reality continuum and its applications, pp. 137-144. Pacherie, Elisabeth (2007), « The sense of control and the sense of agency », in: Psyche 13.1, pp. 1-30. Pan, Ye and Anthony Steed (2019), « How Foot Tracking Matters: The Impact of an Animated Self-Avatar on Interaction, Embodiment and Presence in Shared Virtual Environments », in: Frontiers in Robotics and AI 6, p. 104. Park, Chanho and Kyungho Jang (2019), « Investigation of Visual Self-Representation for a Walking-in-Place Navigation System in Virtual Reality », in: 2019 IEEE Conference on Virtual Reality and 3D User Interfaces (VR), IEEE, pp. 1114-1115. Pastel, Stefan, Chien-Hsi Chen, Katharina Petri, and Kerstin Witte (2020), « Effects of body visualization on performance in head-mounted display virtual reality », in: Plos one 15.9, e0239226. Peck, Tabitha C. and Mar Gonzalez-Franco (2021), « Avatar embodiment. a standardized questionnaire », in: Frontiers in Virtual Reality 1, p. 44. Peck, Tabitha C., Sofia Seinfeld, Salvatore M. Aglioti, and Mel Slater (2013), « Putting yourself in the skin of a black avatar reduces implicit racial bias », in: Consciousness and Cognition 22.3, pp. 779-787. Peled, Avi, Michael Ritsner, Shmuel Hirschmann, Amir B Geva, and Ilan Modai (2000), « Touch feel illusion in schizophrenic patients », in: Biological Psychiatry 48.11, pp. 1105-1108. Peña, Jorge, Subuhi Khan, and Cassandra Alexopoulos (2016), « I am what I see: How avatar and opponent agent body size affects physical activity among men playing exergames », in: Journal of Computer-Mediated Communication 21.3, pp. 195-209.

Figure 6 . 3 -

 63 Figure 6.3 -Première expérience en réalité virtuelle utilisant une stimulation visuotactile pour créer un sentiment d'incarnation envers un bras virtuel. Image venant de [Slater et al. 2008].

  d'études liant les deux domaines. Pourtant, il existe des interrelations entre incarnation et interaction qu'il est nécessaire de mieux comprendre. Dans les prochaines sections, nous présentons nos différentes contributions pour mieux comprendre les liens entre avatars et interaction, afin de créer des techniques plus compatibles avec les avatars.

Figure 6 . 4 -

 64 Figure 6.4 -De gauche à droite : un exemple de trajectoire à dessiner pendant l'expérience; Une vue de derrière de la scène virtuelle; Un autre personnage virtuel en train de poignarder la main virtuelle du participant à la fin de l'expérience pour mesurer sa réponse à la menace sur son corps virtuel.

Figure 6 .

 6 Figure 6.5 -Illustration des quatre tâches effectuées par les participants durant notre étude utilisateur, toutes dans la condition avec l'avatar au complet. Les mêmes tâches ont également été réalisées sans avatar. De gauche à droite : Tâche d'entraînement, tâche du couloir, tâche de suivi de chemin et tâche des colonnes.

Figure 6 . 6 -

 66 Figure 6.6 -Illustration de deux types de représentations doubles étudiées dans ce chapitre. Sur l'image de gauche, une représentation fantôme permet une manipulation à distance tandis qu'une représentation réaliste co-localisée fournit un retour par rapport à la position réelle de l'utilisateur. Sur l'image de droite, une représentation fantôme fournit un retour par rapport à la position réelle de l'utilisateur tandis qu'une représentation réaliste permet une manipulation précise avec l'environnement grâce à un mouvement ralenti.

Titre:

  Interaction Basée Avatar en Réalité Virtuelle Mot clés : Avatars, sentiment d'incarnation, interaction, réalité virtuelle Résumé : La réalité virtuelle permet d'immerger des utilisateurs dans un monde alternatif. Dans ce monde virtuel, ils peuvent se déplacer ou encore interagir avec des objets grâce à leur corps virtuel, aussi appelé avatar, qui leur indique où ils se trouvent et ce qu'ils sont en train de faire. Les utilisateurs peuvent même se sentir incarnés dans cet avatar et ainsi avoir l'impression que c'est leur vrai corps. Cette illusion offre une expérience utilisateur intéressante et peut avoir des conséquences surprenantes comme augmenter les capacités cognitives d'une personne. Cependant, il n'est pas encore clair comment cette illusion est créée. De plus, les techniques actuelles d'interaction sont parfois peu compatibles avec des avatars réalistes, notamment parce qu'elles déforment parfois les mouvements de l'utilisateur, et donc potentiellement le corps et les mouvements de l'avatar, ce qui peut influencer le sentiment d'incarnation. Cette thèse propose plusieurs études pour mieux comprendre les relations entre utilisateur, avatar et interaction. Elle se concentre sur le sentiment d'incarnation, en étudiant à la fois des facteurs individuels et l'impact de différents feedbacks pendant des tâches d'interaction (locomotion et manipulation d'objets). Des conseils de conception de techniques d'interaction compatibles avec les avatars sont aussi proposés, ainsi que des pistes de recherche pour le futur. Le but à long terme est d'avoir des interactions efficaces qui assurent un haut sentiment d'incarnation. Title: Towards Avatar-Based Interaction in Virtual Reality Keywords: Avatars, sense of embodiment, interaction, Virtual Reality

  used the empirical Kaiser criterion to automatically select the number of principal components explaining sufficient amounts of variance, then performed a PCA with this number of components using an oblimin rotation, enabling us to interpret the selected components (see the summary of the obtained components in Figure2.4, and exact values in Table2.2).

							2.3. Results
		Table 2.2 -Contributions (i.e. weights) of the different questions to the men ownership
		(O M ), women ownership (O W ), agency (A), external appearance (EA), and threat per-
		ception (T ) components.
							A P C1
						A1	0.722
				O P C1,M	O P C2,M	A2	0.827
			O1	0.740		A3	-0.443
		Questions	O3 O2	0.102 -0.475	0.966 0.623	A4	Men Median[Q1,Q3] Women -0.713
	O1 O2	I felt as if the virtual body was my body O4 0.722 I felt as if the virtual body I saw was someone else O5 -0.756	EA1	4 [3,5] 3 [2,4] EA P C1 4 [3,5] 0.716
	O3	It seemed as if I might have more than one body	EA2	0.719	2 [1,4]
	O4 O5	I felt as if the virtual body I saw when looking in the mirror was my own body I felt as if the virtual body I saw when looking at myself in O P C1,F EA3 0.727 3 [2,5] 4 [2,5] 5 [3,6] O P C2,F O1 0.471 0.272 EA4 0.705
	A1 A2 A3	O2 the mirror was another person -0.846 It felt like I could control the virtual body as if it was my own O3 0.829 T P C1 O4 0.864 T1 0.919 body The movements of the virtual body were caused by my move-O5 -0.822 T2 0.913 T3 0.915 ments I felt as if the movements of the virtual body were influencing T4 0.917	6 [5,6] 7 [6,7] 2 [1,4]
		my own movements
	A4	I felt as if the virtual body was moving by itself		1 [1,2]
	L1	I felt as if my body was located where I saw the virtual body	6 [4, 6.5]
	L2	I felt out of my body				2 [1,4]
	EA1 It felt as if my (real) body were turning into an "avatar" body	3 [1,5]
	EA2 At some point it felt as if my real body was starting to take	2[1,5]
		on the posture or shape of the virtual body that I saw
	EA3 At some point it felt that the virtual body resembled my own	2[1,4]
		real body, in terms of shape, skin tone or other visual features
	EA4 I felt like I was wearing different clothes from when I came to	3[1,5]
		the experience
	T1	I felt that my own hand could be affected by the knife	2 [1,5]
	T2	I felt fear when I saw the knife			2 [1,5]
	T3	When the knife appeared above my hand, I felt the instinct	1 [1,5]
		to remove my hand from the table
	T4	I had the feeling that I might be harmed by the knife	2 [1,4]
					64

Polychoric Principal Components Analysis (Polychoric PCA) for each aspect of embodiment on the different questions, as Polychoric PCA takes into account the ordinal nature of Likert scales. This type of PCA has already been used in similar studies

[START_REF] Slater | Virtually Being Lenin Enhances Presence and Engagement in a Scene From the Russian Revolution[END_REF]

. As mentioned previously, a separate Polychoric PCA was run on men and women data in the case of ownership. As proposed in Gonzalez-Franco and Peck's questionnaire

[2018]

, we

Table 2 .

 2 4 -Multiple linear regression models for presence ( * : p < 0.05 ; * * : p < 0.01)

		Presence
	Variables	β P r(> |t|)
	Agreeableness 0.018 0.008 **
	Neuroticism	0.008 0.095
	Internal	0.061 0.001 **
	Chance	0.046 0.010 *

Table 2 .

 2 5 -Pearson correlations for ownership (men and women), agency, external appearance, response to threat and presence.

		O P C1,M O P C1,F O P C2,F	A P C1	EA P C1	T P C1	Presence
	Openness	-0.293*
	Conscientiousness
	Extraversion
	Agreeableness					0.227*
	Neuroticism					0.258**
	Internal			0.248** 0.195*	0.203*
	Powerful others		0.427**
	Chance	0.248*	0.366**		0.201*
	Body awareness
		( * : p < 0.05 ; * * : p < 0.01)

Table 3 .

 3 1 -The two possible orderings of the experiment based on the avatar factor. While the representation questionnaire was administered after each block, the embodiment questionnaire was only administered after the FBA condition.

	1) SSQ	Full-Body Avatar	Rep. + Embodiment	No Avatar SSQ	Rep.	Comparison
	2) SSQ No Avatar	Rep.	Full-Body Avatar	SSQ	Rep. + Embodiment	Comparison

Table 3 .

 3 2 -Summary for body ownership (O), agency (A) and self-location (SL) questionnaires. This table reports the median and interquartile range for each question. When significant differences (Kruskal-Wallis test) were found between techniques (NW, WIP, S), the descriptive statistics for each technique are provided.

	3.3. Analysis

Table 3 .

 3 3 -Summary for subjective questions on the virtual representation (R). This table reports the median and interquartile range for each question. When main effects of appearance factor or interaction effects were found, the descriptive statistics for each appearance are provided.

			Median[Q1;Q3]
	ID	Questions	FBA	NA
	R M irrorLogical	When facing the mirror, my virtual representation when	5[3; 6]	4[3; 6]
		navigating in the VE was confusing(1)/logical(7)
	R OtherLogical	In other tasks, my virtual representation when navigat-	6[4;6.25]
		ing in the VE was confusing(1)/logical(7)
	R M irrorP leasing When facing the mirror, my virtual representation when		4[3;5]
		navigating in the VE was disturbing(1)/pleasing(7)
	R OtherP leasing	In other tasks, my virtual representation when navigat-	5[4; 6] 4[4; 5.25]
		ing in the VE was disturbing(1)/pleasing(7)
	ID	Questions	Median[Q1;Q3] NW WIP S
	C pref erBody	I preferred not having a body (1) vs. having a body (7)	5[3;6.25]

* indicates that an interaction effect was found Table

3

.4 -Summary for comparison questionnaire. This table reports the median and interquartile range for each question. There was no significant effect (Kruskal-Wallis test) of the Technique factor.

Table 4 .

 4 2 -Questions on user experience asked after all the conditions.

	ID	Question
	liked	I liked my virtual representation(s).
	disturbing	My virtual representation(s) was/were disturb-
		ing.
	easy	It was easy to interact.
	clear	It was clear how I could interact with the envi-
		ronment.
	exciting	It was exciting to interact with the environment.

Table 4 .

 4 4 -Summary of all embodiment questions for the second experiment with the PRISM technique. This table reports the median and interquartile range for each question.

	ID	R -Ø	Median[Q1;Q3] R -G G -R	Ø -R
	RL
	wasMyBody	5[3; 6] 1,2	3.5[2; 5.25] 1,2	3[2; 5] 1	5[3; 6] 2
	bodyParts	5[3; 6]	4[2.75; 6]	4.5[2.75; 5.25]	5[3; 6]
	human	5[4; 6]	5[2.75; 6]	5[3; 6]	4[3; 6]
	belonged	5[2.75; 6]	4.5[3; 6]	4[2.75; 6]	4.5[3; 6]
	myMovements	5[3; 6]	5[3; 6]	5[3; 6]	4.5[3; 6]
	controlling	6[4.75; 7]	6[5; 6]	5.5[5; 6]	5[4; 7]
	causing	6[5; 7]	6.5[4.75; 7]	6[5; 6.25]	6[5; 7]
	inSync	5[4; 6]	4.5[3; 6]	5[4; 6]	4[3.75; 6]
	form	2[1; 5]	2.5[1; 4]	2[1; 4]	2[1; 4]
	weight	1[1; 4]	1.5[1; 3.25]	1[1; 3.25]	1[1; 3.25]
	height	1[1; 4]	1[1; 4]	1[1; 4]	1[1; 2.25]
	width	1[1; 2.5]	1[1; 2]	1[1; 3]	1[1; 2.25]
	PGF
	outOfBody	2[1; 5]	2[1; 3]	2[1; 4]	2.5[1; 5]
	drifting	3.5[1.75; 5]	3[2; 4]	2.5[2; 4]	2[1; 4]
	influencing	2.5[2; 4]	3[2; 5]	3[1.75; 4.25]	3.5[2; 5]
	avatarBody	3[1; 5]	3[2; 4.25]	2[1; 4]	2[1; 4.25]
	posture	2.5[2; 4]	2[2; 3]	2[2; 3]	2[1.75; 4.25]
	clothes	1.5[1; 5]	1[1; 3]	2[1; 5]	1.5[1; 3.25]
	hadChanged	1[1; 3.25]	1[1; 2.25]	2[1; 3]	1[1; 3]
	realisticSensation 4.5[3; 5.25]	3[2; 5]	3[2; 5.25]	3.5[2; 5]
	affected	4.5[2.75; 6] 1	3[2; 5] 2	2.5[1; 5] 1,2	5[2; 5] 1,2
	wasMyBody	5[3; 6] 1,2	3.5[2; 5.25] 1,2	3[2; 5] 1	5[3; 6] 2
	resembled	3[1; 5]	3[2; 4]	2[1; 4.25]	3[1.75; 5]
	located	6[5; 6.25] 1	4.5[3; 6] 2	4.5[3; 6] 2	5[4.75; 6] 1,2
	control	5[3; 6]	4.5[2.75; 5.25]	5[2.75; 6]	5[3; 5.25]
	touchLocated	2.5[2; 5]	3[2; 4.25]	2[1.75; 3.5]	2.5[1; 3.25]
	touchCaused	3[1; 5]	2[2; 4]	2[1.75; 3.25]	2[1; 4]
	touching	3[2; 5]	3[2; 3.25]	3[2; 4]	2.5[1; 5]
	Conditions sharing a superscript were not significantly different (Wilcoxon
	signed-rank test with α = .05)
			125

Table 5 .

 5 1 -Table recapitulating the proposed guidelines and the corresponding sections to justify these guidelines.

	Input Devices
	ID1 For specific applications or training, use an input device	Section 1.4.1.1
	adapted to the task
	ID2 Prioritise full-hand tracking when possible	Section 1.4.1.3
	Control
	CM1 For wide and fast motions, do not apply constraints	Section 1.4.2.1
	CM2 For wide and fast motions, choose a CD gain equal to 1 Section 1.4.2.2
	CM3 For small motion and precise manipulation, provide as-	Section 1.4.2.4
	sistance to the user's movements
	CM4 For precise manipulation, handle collisions	Section 1.4.2.4
	CM5 Progressively increase the distortion gain to make it	Section 1.4.2.2
	more acceptable
	Feedback
	FB1 Provide a well-calibrated avatar	Section 1.3.1.1
	FB2 Use first-person perspective	Section 1.4.3.2
	FB3 Use slightly transparent hands to prevent occlusions	Sections 1.3.1.2 and 1.4.3.1
	FB4 Preserve body continuity as much as possible	Section 1.4.2.3
	FB5 Maximize multisensory coherency	Section 1.3.3
	FB6 Provide haptic feedback	Section 1.4.3.3
	FB7 Use realistic avatars when using distorted motion	Section 1.3.2

Table 6 .

 6 1 -Tableau récapitulatif des directives de design proposées et les sections correspondantes qui justifient ces directives.

	Entrée

Related Work

Cambridge University Press. [2021a],Affordance (n.d.) In: Cambridge dictionary, url: https : //dictionary.cambridge.org/dictionary/english/affordance [visited on 03/08/2021].

montre les mouvements réels de l'utilisateur. Nous voulions voir l'impact potentiel de ce type de représentation virtuelle sur le sentiment d'incarnation et la performance. Nous avons réalisé deux expériences, l'une avec des mouvements amplifiés (avec la technique Go-Go [Poupyrev et al. 1996]), l'autre avec des mouvements ralentis (avec la technique PRISM [Frees et al. 2007]). Pour chaque expérience, les représentations doubles étaient comparées à des représentations simples avec un seul avatar. Dans chaque condition, les mouvements déformés et réels pouvaient être représentés par: un avatar réaliste, un avatar fantôme transparent ou aucune représentation.

Avec les deux techniques de manipulation, les participants ont réussi à ressentir un sentiment d'incarnation pour les différentes représentations doubles. De plus, aucun impact n'a été constaté sur la performance, ce qui montre que de telles représentations pourraient être utilisées dans des applications de RV. Alors que l'interaction semblait plus importante que la présentation des mouvements réels pour l'agentivité avec la technique Go-Go, les personnes se sentaient plus en contrôle du bras réaliste pendant la manipulation avec PRISM. Dans l'ensemble, les participants ont préféré avoir une représentation simple, mais certains ont tout de même signalé l'avantage d'avoir une représentation montrant leurs mouvements réels pour comprendre la distorsion créée par la technique d'interaction.

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RÉSUMÉ LONG EN FRANÇAIS

Cette thèse intitulée "Interaction Basée Avatar en Réalité Virtuelle" étudie les interrelations entre les avatars et l'interaction en réalité virtuelle (RV). L'objectif est de mieux comprendre comment différentes techniques d'interaction peuvent avoir un impact sur la perception de l'avatar, ainsi que la façon dont le choix d'un avatar peut affecter l'interaction. En particulier, nous nous intéressons à la façon dont ces interrelations peuvent affecter le sentiment d'incarnation. Les contributions de cette thèse aideront les développeurs à concevoir des techniques d'interaction compatibles avec des avatars réalistes au corps entier.

Cette thèse tente de répondre à trois axes de recherche :

-RA1: l'influence des caractéristiques de l'utilisateur sur le sentiment d'incarnation -RA2: l'influence de la technique d'interaction sur le sentiment d'incarnation -RA3: l'influence de l'avatar sur l'interaction L'interaction avec l'environnement virtuel peut être classée en quatre catégories [Bowman 1999]: navigation, sélection, manipulation et entrée système. Nous ne nous concentrerons pas sur la saisie système, car la plupart des techniques utilisées pour la saisie système sont similaires à celles utilisées pour la sélection et la manipulation.

La sélection est l'action de choisir l'objet avec lequel l'utilisateur va interagir. Les tâches de manipulation englobent toutes les modifications qui peuvent être effectuées sur l'objet virtuel sélectionné. La sélection et la manipulation peuvent être anisomorphiques. Le mouvement peut être diminué pour offrir un contrôle plus élevé pour un positionnement précis [START_REF] Frees | Precise and rapid interaction through scaled manipulation in immersive virtual environments[END_REF]. Il peut également être amplifié pour atteindre des objets éloignés [START_REF] Poupyrev | The Go-Go Interaction Technique: Non-Linear Mapping for Direct Manipulation in VR[END_REF]].

Les techniques de locomotion permettent aux utilisateurs de se déplacer et de pivoter dans l'environnement virtuel. Plusieurs techniques ont été inventées pour répondre aux contraintes d'espace limité, comme la téléportation ou la marche sur place.

Conseils pour le Design de Techniques d'Interaction

Compatibles avec l'Avatar

Pour terminer cette thèse, nous proposons dans le chapitre 5 des directives de conception pour créer des techniques de manipulation compatibles avec les avatars. Ces directives sont classées en trois catégories: entrée, contrôle et feedback. Elles sont basées sur une analyse de l'état de l'art actuel sur les techniques de manipulation et les avatars. Nous avons étudié à la fois l'impact des avatars sur la manipulation et l'impact des choix de design sur le sentiment d'incarnation (voir le détail dans le chapitre 1). En plus des directives de design, nous proposons également des pistes de recherche pour la suite, toujours focalisées sur les techniques de manipulation.