Oscar Eduardo De

La Cruz Fierro

Professor, Guillaume Morel

Florian Gosselin

Wael Bachta

Damien Chablat

Nabil Zemiti

Yann Perrot

Benoît Perochon

Pascal Chambaud

Philippe Pottier

Didier Houche

Michèle Vie

Yves Germain

Ludovic Villard

David Reversat

Florian Richer

Philippe Gauthier

Caroline Maureau

Jean-Baptiste Cazneuve

Juan Miguel Alvarez

Davinson Castaño-Cano

Susana Sánchez Restrepo

Ugo Vollhardt

Alexandra Dos Santos

Carlos Viña

Omar Islas

Valentin Marcel

Arthur Bouton

Vanessa Zervogianni

Nathaly Ruiz

Alessia Michelotti

Livia Tepshi

Malik Shukeir

Monika Kami

« Ska

Veronica Sorgato

Laure Simon

Fabien Rodrigues

Contributions to the Study of Intermittent Contact Haptic Interfaces by

Keywords: Haptic interfaces, Virtual reality, Intermittent-contact, Psychophysical tests, Non-contact tracking

Force feedback interfaces are robotic systems allowing natural motion interactions with virtual or remote environments. They are employed in several domains such as remote handling (e.g. nuclear, subsea, space), manufacturing, entertainment, education, medicine and rehabilitation, just to mention the most popular. In virtual reality (VR) applications, the user typically holds a handle that is mechanically linked to the endeector of the robot. This link has a non-negligible inuence since the presence of the robot can be felt (friction, inertia and vibrations of the mechanical structure) even in free space, decreasing the realism of the interaction.

Intermittent-contact haptic interfaces (IC-HIs) represent a promising approach to cope with this issue. These interfaces track and closely follow (without contact) the user movements in free space and come to his/her contact only when force feedback is required. This way IC interfaces aim to improve the realism of the interactions.

The thesis presented concerns the study and improvement of such IC-HIs: 1) First it appeared in our research that the aforementioned improvement of interaction realism has not yet been proven. Indeed, no comparison between classical contact haptic interfaces (CC-HIs) and IC devices had been done so far from a user perception perspective. To this end we decided to perform a series of psychophysical tests based on three elementary VR tasks employing an available state-of-the-art 2 degrees of freedom (DoF) interface that provides nger interactions and allows implementing both CC and IC congurations.

2) Then we noticed that, despite the fact that moving in free space without feeling the presence of the robot invites the user to make faster movements, which in turn tends to produce oscillations when the user avatar enters in contact with virtual objects, this type of movements has attracted, to our knowledge, only little attention in the literature. This prompted us to focus our eorts on the improvement of the control law of the interface, in particular on the transitions between free space and contact modes at high speeds.

3) Finally we noticed that, even though several VR applications are performed by means of a tool (e.g. a virtual scalpel or scissors as in medical simulators), almost all existing IC devices focus on bare ngers interactions. Considering this, and also noticing that tool tracking is far easier than a nger's conguration measurement (variable sizes i and shapes, deformation at contact), we decided to initiate the development of an IC interface allowing tool interactions: the design drivers and sensing approach towards the development of a 6DoF non-contact tool-based tracking system were dened.

Résumé

Les interfaces à retour d'eort sont des systèmes robotisés permettant d'interagir gestuellement de façon naturelle avec des environnements virtuels ou distants. Ces dispositifs sont utilisés dans diérents contextes tels que la téléopération (e.g. nucléaire, sous-marine, spatiale), le manufacturing, les jeux vidéo, l'éducation, la médicine ou la rééducation, pour ne citer que quelques exemples. Pour les applications en réalité virtuelle, les utilisateurs manipulent généralement ces interfaces à l'aide d'une poignée qui est reliée mécaniquement au robot. Ce lien a une inuence importante puisqu'il conduit l'utilisateur à ressentir la présence du robot même en espace libre (frottements, vibrations, inertie de la structure mécanique du robot), ce qui réduit le réalisme de l'interaction.

Les interfaces à contacts intermittents (CI) constituent une alternative prometteuse pour essayer de surmonter ces inconvénients. Elles proposent de suivre les mouvements de l'utilisateur à faible distance en espace libre et de ne venir à son contact que lorsque l'on veut appliquer un retour d'eort. Elles visent de cette façon à améliorer le réalisme des interactions.

Cette thèse s'intéresse à l'étude et à l'amélioration des performances d'une telle interface CI : 1) Nous avons tout d'abord constaté que l'amélioration du réalisme des interactions évoqué ci-dessus n'a jamais été prouvé dans la littérature. En eet, il n'existe pas de comparaison entre les interfaces haptiques à contact classique (CC) et les interfaces CI du point de vue de leur perception par les utilisateurs. Nous avons donc décidé d'eectuer une série de tests psychophysiques basés sur la réalisation de trois tâches élémentaires représentatives des interactions usuelles en réalité virtuelle. Ces tests ont été eectués en utilisant une interface existante à 2 degrés de liberté (DdL) permettant d'interagir avec l'index de l'utilisateur et pouvant être utilisée comme une interface CC ou en tant qu'interface CI.

2) Nous avons aussi observé que le fait de se déplacer en espace libre sans ressentir la présence du robot incite les utilisateurs à se déplacer plus rapidement, ce qui a tendance à rendre le robot oscillant lors des contacts entre l'avatar de l'utilisateur et son environnement. Ce type de mouvement n'a pas, à notre connaissance, beaucoup été étudié dans la littérature. Nous avons donc également travaillé sur l'amélioration de la loi de commande de l'interface CI, en particulier lors des transitions entre espace libre et contact.

iii 3) Enn, nous avons constaté que, bien que diérentes applications de réalité virtuelle sont réalisées à l'aide d'un outil (e.g. avec un scalpel ou avec des ciseaux virtuels dans les simulateurs en chirurgie), presque toutes les interfaces CI existantes n'autorisent que des interactions à mains nues. Sur la base de ce constat, et sachant que le tracking d'un outil est beaucoup plus facile que celui des doigts (dimensions et formes variables, déformation au contact) nous avons décidé d'initier le développement d'une interface CI à 6DdL adaptée aux interactions eectuées à l'aide d'un outil. Nous nous sommes plus particulièrement concentrés sur la cahier des charges d'un tel système et sur l'étude des capteurs associés aux système de tracking de l'outil.

Mots clés: Interfaces haptiques, Réalité virtuelle, Contacts intermittents, Tests psychophysiques, Tracking sans contact.

To my family.

To Victor and Lobo. With CC-HIs, the user is usually mechanically linked to the device's end-eector, typically a handle, whose movements, measured by the robot, are used to know the conguration (position and orientation) of his/her hand. This information is necessary to provide force feedback which is consistent with the virtual scene and the mechanical properties of the virtual object (VO) being touched. The mechanical link that is established when the user manipulates the haptic device has however a non-negligible inuence since he/she experiences the friction, inertia and vibrations of the mechanical structure, even in free space where he/she is expected to feel nothing. Such unwanted sensations decrease the realism of the interaction since the user feels all the time the presence of the robot.

In addition, the dierence between free space and contact is less distinctively felt than in the real world. In order to cope with these issues, several eorts can be made in terms of mechanical design, e.g. use of very lightweight and very sti structures (even if an optimal trade-o is dicult to attain) and more ecient transmission systems. Another approach consists in installing a force sensor at the level of the robot's end-eector in order to measure and compensate any resisting force in the direction of displacement. However, resisting forces can never be totally cancelled and none of these approaches completely eliminates the feeling of the presence of the robot in free space.

Intermittent-contact haptic interfaces (IC-HIs) represent an original and promising approach aiming to cope with the aforementioned issues. Its principle consists in removing the mechanical link between the human operator and the force feedback interface during manipulations in free space and come at his/her contact only when force feedback is required. This solution implies the need to track and closely follow the user's movements in free space and to prevent him/her to move in the constraint direction when a VO is being touched. This way, the user doesn't feel any force in free space (perfect transparency)

and the transitions from free space to contact are deemed to be felt more naturally as xxi the robot really touches the user at the simulated contact moment. This approach aims to improve the realism of the interactions, however it suers from several shortcomings.

First, its eciency has not yet been proven in terms of user perception. Second, even if IC interfaces are experimentally proven to be stable at low speeds, they tend to become oscillating at higher speeds. Finally, despite the fact that a lot of tasks are performed by the mean of tools in the real world, most of existing IC-HIs focus on bare nger interactions and are therefore not optimal for simulating tool-mediated tasks.

In the scope of the present PhD work, we propose to systematically address these issues. We rst focused our attention on the evaluation of the benets and identication of the limitations of the IC paradigm based on tests performed with an available stateof-the-art 2 degrees of freedom (DoF) IC-HI that provides nger interactions and allows implementing both CC and IC congurations. Then we worked on the improvement of the stability of such IC interface during interactions at high speeds. Finally, we proposed to extend the IC principle to an interface providing 6DoF interactions through a tool, as it is the case in several virtual reality (VR) applications, e.g. as in medical simulators, overcoming this way some issues associated with nger tracking.

The present PhD dissertation is organized as follows:

Chapter I -Research Context: This chapter introduces the basics of VR and how the human sense of touch contributes in such context to enhance the immersion of the user in a simulated task. Technical specications of CC interfaces (number of DoF, workspace, inertia, maximum exertable force, etc.) are presented along with the limitations of such devices to provide pure free movements. The IC paradigm is then presented together with developed platforms employing this principle. Its advantages and challenges are also discussed. Finally a description of the performed research based on the IC paradigm is given, focusing on the three above-mentioned key challenges: user perception evaluation, performance improvement for interactions at high speeds and extension of the IC paradigm to tool interactions.

Chapter II -Evaluation of the Benets of IC-HIs from a User Perception Perspective: IC haptic interfaces aim to provide more realistic interactions with virtual environments since they touch the user only when force feedback is required. This assumption has however not yet been proven. Unfortunately, technical specications usually available for existing CC and IC interfaces do not allow to directly infer their perceived rendering quality (real interactions and immersion) and do not ensure optimal performances for the completion of a task of interest. Indeed, any evaluation performed without human interaction would not really represent the actual device use. Fortunately, psychophysical tests represent a solution to this problem. They are a useful tool to evaluate the benets of CC and IC interfaces and compare them. To this end, three psychophysical tests representing elementary VR tasks were performed by a group of volunteers using an available interface that can be congured either as a CC or as an IC interface. The protocol, performance metrics and results are presented for each experiment. Conclusions xxii and perspectives are also given.

Chapter III -Improvement of Contact Rendering at High Speeds: A good force feedback interface should allow stable interactions, whether the user is moving in free space or getting in touch with a VO. In the case of IC haptic interfaces, this is particularly challenging since, besides displaying a stable behavior in both modes, the control law must ensure a stable transition between free space and contact. Therefore, the IC interface must shift from closely following the user movements to a completely stabilized (usually xed) position prior to contact. Stable transitions have already been accomplished in a prior work with an existing 2DoF IC interface, but only at speeds up to 0.2m/s. This is a relatively low speed, considering that typical movements in VR environments are performed at speeds up to 4.6m/s, and if the interface is perfectly transparent in free space the user will be tempted to move faster. Being stable only up to 0.2m/s thus limits the scope of possible applications. This chapter presents the contributions made in the control law aiming to improve the free space to contact transitions at higher speeds (tests performed up to ≈ 0.4m/s). In order to evaluate the benets of the implemented control law, a group of participants was invited to perform a user test consisting in tapping on a vertical wall at low and high speeds. Quantitative and qualitative results are given and discussed. Finally, conclusions and perspectives are drawn.

Chapter IV -Contributions to the Design of an IC-HI Tracking Module for Tool-Based Interactions: The design of an IC haptic interfaces providing nger interactions is particularly challenging due to the variable sizes and shapes of ngers from one person to another as well as deformation at contact. This issue makes tracking of the user particularly complex. Fortunately, several VR applications are performed by means of the manipulation of a tool, e.g. medical simulators, which is much easier to track than ngers (xed and known geometry, possibility to integrate active components directly in the tool). In this chapter we propose to extend the IC paradigm to a 6DoF tool-based interaction device, which has the advantage of overcoming the above-mentioned issues.

An IC device consists in two main parts, a tracking system and a force feedback system.

The former system is used to obtain the relative pose (position and orientation) between the user and the robot's end-eector. The later consists in an end-eector which shape and size are suited to provide the corresponding interaction forces at contact. The presented work focused on setting the design specications of an IC tracking system in terms of dimensions and sensor requirements. Preliminary test and characterization of a proposed sensing strategy are proposed. Finally, conclusions and perspectives are given.

In the very last part of this document, global conclusions and perspectives on the performed work are given.

Introduction

In our days, there is an increasing demand for simulators aiming to articially recreate real world environments. These systems are used for various applications such as assembly verication, e.g. virtually checking that a new system can be easily assembled before launching the production, training, e.g. ight simulators, or simply entertainment, for instance immersive video-games.

An ideal simulation environment should stimulate each one of our senses (sight, hearing, smell and touch) to give us the illusion of being present in the recreated environment (immersion) and allow us to interact with it. However, recreating the corresponding sensations requires complex devices while all of them are not always required. Indeed, it can be observed in practice that visual and touch feedback are sucient to cover a wide scope of applications, even when ne interactions are required, e.g. dexterous manipulation of virtual objects (VOs). Visual rendering is obtained with systems ranging from simple monoscopic screens to more complex congurations like head mounted displays or multi-screen immersive systems such as CAVEs, with techniques allowing to recreate photo-realistic images. The study of the sense of touch is unfortunately less advanced. It is addressed with haptic interfaces, i.e. complex mechatronic devices able to provide either tactile or force feedback.

Force feedback interfaces are widely employed in virtual reality (VR) environments, e.g. for the training of novice surgeons in medicine, for the simulation of a product assembly, for education purposes or for scientic research. However, despite the wide range of applications of these devices, they still require to be improved in order to provide force sensations that are totally realistic. This chapter introduces our work which, based on these observations focuses on the study of a novel type of force feedback interface aiming to increase the realism of the interactions. It is organized as follows: we will rst learn about the concept of VR (see section 1.2), then about the importance of the sense of touch (section 1.3) and how it can be reproduced by force feedback devices to enrich our interaction experience in several VR applications (1.4). Representative characteristics of common force feedback interfaces will be presented in section 1.5, along with the diculty to obtain a good mechanical transparency (section 1.6). In section 1.7, we will introduce intermittent contact haptic interfaces, a relatively novel and very promising approach aiming to cope with this issue.

Finally, we will show in section 1.8 that these systems still suer from several shortcomings and we will introduce the proposed research.

Virtual reality

Even though virtual reality sounds as a very modern concept, it has been around for more than half a century.

VR accounts for an interactive computer simulation allowing the user to visualize a virtual environment (VE) which recreates a scene of the real world. Interactive means that such simulation acquires, by means of a tracking system, information on the user's state and is able to provide sensory feedback to one or more senses. The main objective is to make the user feel as being immersed in the VE [START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF].

Four basic characteristic elements of VR can be identied: the virtual world (or VE), immersion, sensory feedback (as a response to user's actions) and interactivity.

• A computer-based VE contains the description of the simulated objects as well as the rules governing their interactions, e.g. the eect of gravity making virtual objects to fall as it does with those in the real life [START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF].

• In the present context, immersion implies the notion of being present in the VE. In simple words, it is the belief of having left the real world to be present inside the VE.

Immersion can be achieved if the VR system is able to provide realistic stimuli to all human senses [Mestre, 2015].

• Sensory feedback requires proper displays, e.g. a head-mounted display (HMD, see Fig.1.1 and Fig.1.2) able to visually immerse the user in the virtual world, and a force feedback interface, hold by the user, that will apply on him/her the forces generated when VOs are being touched.

• Finally, interactivity refers mainly to the fact that the VE is responsive to the user's actions (inputs). It requires a tracking system able to determine the movements of the user to ensure consistency between the real world and the VE. As an example, the visualized scene will adapt so that the user has the impression to move inside the VE.

Figure 1.1: NASA's rst HDM [Mestre, 2017].

Figure 1.2: Classic HMD and VR glove environment [START_REF] Havig | Virtual reality in a cave: Limitations and the need for hmds[END_REF].

The rst practical implementation of the VR paradigm was developed in 1957 and patented in 1962 by Morton Heilig, who is considered as the father of VR. In such a system, known as Sensorama (see Fig. 1.3), a single person could perceive, e.g. a motorcycle ride through a city via sight, smell, vibration and wind [START_REF] Sherman | Chapter 1 -introduction to virtual reality[END_REF]. Several other VR systems were developed. The GROPE I to III systems, created in the late 60s and early 70s, allowed the user to move and feel interaction forces between molecules thanks to a haptic interface (see Fig.1.4). Other examples of VR applications using force feedback will be described in section 1.4.

Figure 1.4: GROPE-III haptic display system [START_REF] Brooks | Project gropehaptic displays for scientic visualization[END_REF].

As stated in the above paragraphs, one of the main goals of a VR system is to create the sensation of presence. A step forward in this direction was achieved during the 90s with the concept of CAVE (Cave Automatic Virtual Environment). It consists of a room whose walls are in fact screens displaying a VE (see Fig. 1.5).

Figure 1.5: Example of a CAVE [START_REF] Havig | Virtual reality in a cave: Limitations and the need for hmds[END_REF]. This technology is however very expensive and requires an important volume to be installed, e.g. four equally sized walls of ≈ 1.8m × 1.8m. As a consequence, the current tendency is to use HMDs instead. This technology have made huge progress in the recent years and is now both ecient and aordable (see Fig.1.6).

HTC VIVE

Oculus Rift The following section will provide an insight on the importance of the sense of touch and, in particular, the role it plays when non-direct manipulation of remote/virtual objects and interaction with VEs takes place.

Sense of touch and haptic feedback

The sense of touch is of capital importance for our everyday lives. Its lack would make us experience serious diculties when performing tasks such as grasping and manipulating tools or working in contact with surrounding objects [Robles- De-La-Torre, 2006]. Thanks to this sense, which gives us the ability to perceive the environment physical characteristics (shape, size, texture) and regulate the forces that we apply on it, we are able to perform a wide scope of tasks with high level of dexterity.

In some circumstances however, the human operator cannot be in direct contact with the object being manipulated, e.g. because the environment is hostile (nuclear, underwater, space) or because it is inaccessible at the user's scale (micromanipulation, microsurgery). In such cases the task can be accomplished by means of a teleoperated system, i.e. a remote robot mimicking the movements of a master arm manipulated by the operator. The ability to control the movements of a remote system is also of great value in VR, the user remotely controlling virtual avatars instead of robots in this case.

The concepts of teleoperation (manipulation of a remote robotic system), VR (controlling a virtual avatar) and telepresence (allowing a person to feel as if he/she were present at a place dierent from his/her current location) have accentuated the importance for the development of systems that allow a human operator to sense the physical characteristics and forces applied on the objects being remotely (see Fig. 1.9a) or virtually (see Fig. 1.9b) manipulated [Bergamasco, 1995], i.e. by means of haptic interfaces.

(a) Teleoperation master arm with force feedback in a nuclear context (©CEA/Stropa) (b) VR assembly testing for the automotive industry (©CEA/Stropa) Figure 1.9: Teleoperated and virtual reality (VR) systems using force feedback.

Haptics was dened as a perceptual system that uses both cutaneous (including thermal) and kinesthetic inputs to derive information about objects, their properties, and their spatial layout [START_REF] Lederman | Haptic exploration and object representation[END_REF]]. To stimulate this sense, the user requires dedicated devices called haptic interfaces, i.e. devices allowing motion interactions with remote/virtual environments with a reproduction of the sense of touch, using kinesthetic (force/position) and cutaneous (tactile) receptors [START_REF] Hannaford | Haptics[END_REF].

We can distinguish four methods for creating haptic sensations articially: vibrotactile devices, force feedback systems, surface displays and distributed tactile displays [START_REF] Hayward | Do it yourself haptics: part i[END_REF]. The scope of the present work is limited to the force feedback devices category. The following section will describe their main applications with a focus on VR, which is of particular interest for the present work.

Force feedback devices application examples

Force feedback interfaces nd applications in numerous domains (most of them using VR) such as design, manufacturing, assembly, scientic visualization, entertainment, education, medicine, space, rehabilitation, micromanipulation, as well as molecular biology [START_REF] Hannaford | Haptics[END_REF]. The interface should then provide adequate kinesthetic information contributing to enhance the sense of presence in the VE [Reiner, 2004].

In the elds of design, manufacturing and assembly, haptic feedback can contribute to change traditional product development approaches by allowing the users to get the feeling of touching objects, perceiving the nature of their surfaces and their dynamics before producing any real prototype [Xia, 2016]. This way, users can gain a comprehensive understanding and accurate evaluation of the design and manufacturing process (see Fig.1.10a).

In scientic visualization (see Fig. 1.10b), haptic devices can be used to simulate object's physical properties, e.g. texture and/or interaction forces. This allows direct and immediate control over simulations as well as sensing of the results of the scenario of interest [M. and Taylor, 2005].

The entertainment industry has also beneciated from haptic developments. Force feedback technology enhances the game experience by providing more realistic sensations while playing a game [START_REF] Orozco | The role of haptics in games[END_REF].

Haptics is also of great interest in education. For example, a multimedia system for learning handwriting of alphabet letters/characters in dierent languages can make use of a haptic device to provide force feedback to guide the user's gesture at following a pre-recorded letter trajectory (see Fig.1.10c).

In medicine also, VR simulation-based training appears as a promising solution for skill transfer. Novice surgeons can acquire and/or improve their skills before operating on a real patient and experienced surgeons can learn new techniques and even rehearse when the patient to operate presents a complicated surgery case (see Fig. 1.10d), e.g. a congenital anomaly or a known dicult anatomy [START_REF] Aggarwal | From scalpel to simulator: A surgical journey[END_REF].

Force feedback interfaces can also be used to intelligently guide/regulate the motion of the user during an operation [START_REF] Bowyer | Active constraints/virtual xtures: A survey[END_REF], e.g. preventing the user to move towards a restricted region, contributing that way to improve the security of the patient and postoperative results.

More generally, robot-assisted minimally invasive surgery (RMIS) oers advantages to patients such as less trauma, shorter hospital stay and reduced recovery times [START_REF] Westebring | Haptics in minimally invasive surgery -a review. Minimally invasive therapy & allied technologies : MITAT[END_REF]. Robots in master-slave conguration can cope with motion constraints of surgical instruments, improving surgeon's dexterity [START_REF] Puangmali | State-of-the-art in force and tactile sensing for minimally invasive surgery[END_REF].

The surgeon is expected to act and feel as if he/she were holding directly the surgical (a) [START_REF] Borro | A large haptic device for aircraft engine maintainability[END_REF],

(b) [START_REF] Brooks | Project gropehaptic displays for scientic visualization[END_REF], (c) [START_REF] Palluel-Germain | A visuo-haptic device -telemaqueincreases kindergarten children's handwriting acquisition[END_REF], (d) [START_REF] Gosselin | Haptic systems for training sensorimotor skills: A use case in surgery[END_REF], (e) [Burdea, 2008], (f ) [START_REF] Sagardia | Vr-oos: The dlr's virtual reality simulator for telerobotic on-orbit servicing with haptic feedback[END_REF]] and (g) [START_REF] Bolopion | A review of haptic feedback teleoperation systems for micromanipulation and microassembly[END_REF].

tools being in contact with the patient. In such scenarios, any strategy to estimate/ sense the applied force is expected to improve the accuracy and dexterity of the surgeon [Okamura, 2009] and therefore reduce the tissue trauma and organic damage. The development of force sensors for RMIS is thus still an active research topic as reported in [START_REF] Puangmali | State-of-the-art in force and tactile sensing for minimally invasive surgery[END_REF].

One can also refer to physical rehabilitation which is a growing eld of use for haptic interfaces. Unlike a human therapist, robots can train patients for long periods of time without tiring. Robotic systems coupled with VR simulations also bring additional improvements to today's conventional physical therapy methods, since they introduce objective measures of performance (see Fig. 1.10e).

Space is an environment inaccessible to humans where force feedback systems can contribute to train operators and help them performing maintenance, reparation or exploration tasks while preventing and reducing risks. In [START_REF] Sagardia | Vr-oos: The dlr's virtual reality simulator for telerobotic on-orbit servicing with haptic feedback[END_REF] for instance, a VR platform for telerobotic on-orbit servicing missions helps to train users (providing visual and haptic feedback) for satellite maintenance tasks (see Fig.1.10f ).

When it comes to manipulation of tiny objects, haptic systems allowing the user to interact with objects at the micro scale are needed (see Fig. 1.10g). In molecular biology for example, the size and complexity of molecular structures make it dicult, if not impossible, to show all of their features in a physical model alone. In combination with augmented reality (AR) and voice commands, haptic feedback provides additional information about these models using a force display [START_REF] Sankaranarayanan | Role of haptics in teaching structural molecular biology[END_REF].

All the above mentioned applications require a device compatible with the targeted task. Several examples of such devices are presented in section 1.5, with focus on commercially available interfaces.

Commercially available force feedback interfaces

Force feedback systems are robotic mechanisms capable to measure the user's movements, this information being used to control the movements of his/her avatar, and deliver a force signal to his/her hand, usually through a stylus or a thimble [Campion, 2011].

The realism of the interaction is strictly related to the capabilities of the device to allow natural movements of the human operator's hands as well as to reproduce adequate stimuli on them. An ideal force feedback system should be transparent: the user should be able to move in free-space without feeling any force, i.e. to make pure free movements, and the device should prevent him/her to move in the constraint direction if a sti object is being touched, i.e. the device should be able to simulate any type of contacts, even hard ones [Couroussé, 2007].

It is worth noting that a perfect transparency cannot be attained in practice. Fortunately, most of the time it is not necessary to reproduce the whole bunch of physical interactions experienced everyday, and force feedback interfaces can be tuned to the requirements of the tasks of interest. It is thus important to identify what sources of kinesthetic information are relevant for the targeted tasks, and which degree of delity is needed [Robles- De-La-Torre, 2006].

Several performance metrics are usually employed to qualify a force feedback interface:

workspace, position resolution, continuous force, peak force, friction, apparent stiness, apparent inertia and bandwidth. All these notions, dened below with reference to e.g.

[MPB Technologies Inc., 2018b] contribute to the transparency of the device.

• The workspace is the volume that the device can cover, considering both translations (ranges usually expressed in the Cartesian space in mm, cm or m) and rotations (ranges usually expressed in degrees in yaw, pitch and roll).

• The position resolution is the smallest amount of movement which can be detected by the arm sensors. It is usually expressed at the level of the handle (i.e. in the Cartesian space) in µm or mm in translation and in degrees or radians for the rotations.

• The continuous force is the amount of force/torque that the device can exert for an extended period of time. It is usually expressed in the Cartesian space in N for the translations and in N.m for the rotations.

• The peak force is the maximum force that the actuators can exert, e.g. over a small period of time. The peak force can typically be between 2 and 10 times higher than the continuous force for typical actuators usually implemented in force feedback interfaces, allowing to momentarily stop the user against the environment, e.g. when taping or touching a hard object.

• The friction is a measure of the resistance of the device to movement. It is expressed in N for translations and N.m for rotations. It should be as low as possible.

• The apparent stiness is the maximum stiness that can be simulated by the device.

It informs on the dierent types of objects that can be simulated. Indeed many objects in VR environments behave like a spring, i.e. they deform linearly in response to an external force. The apparent stiness is expressed in N/m for translations and N.m/rad for rotations. The higher it is, the better solid virtual walls can be simulated.

• The apparent inertia is a measure of the mass (in kg) and inertia (in kg.cm 2 ) that is sensed by the user when he/she tries to move the handle of the robot. It should be as low as possible in order to give him/her the impression that he/she moves freely in free space.

• The bandwidth is the frequency (in Hz) up to which the device can be properly controlled. It should not be confused with the update frequency of the controller nor with the bandwidth of the human somatosensory system, i.e. about 300 -1000Hz for tactile sensing and 20 -30Hz for kinesthetic and proprioceptive sensing.

It is worth noting that, even if the afore-mentioned data are usually given in the Cartesian space, this information can be given instead in the joint space.

Six main manufacturers were identied in the market: 3D Systems, Force Dimension, Haption S.A., Quanser, MOOG Inc. and MPB Technologies Inc. Representative examples of their products will be briey described below.

The Touch device (see Fig. Fig.1.11c,right). It is particularly well suited for scale 1 virtual/remote manipulations.

It is also used for comanipulation in laparoscopic surgery as well as in rehabilitation [START_REF] Haption | Virtuose 6d[END_REF].

The High Denition Haptic Device (HD symbol indicates that the workspace is roughly cylindrical in shape. In the third column, the upper number indicates the total number of (sensed) DoFs, the second one the number of active (motorized) DoFs.

Limitations of existing haptic interfaces

As mentioned earlier, the apparent mass of haptic interfaces, as well as their friction, should be as low as possible, in order that the user doesn't feel the presence of the robot in free space. All existing devices were designed to answer this need. However, as can be seen in table 1.1, their values are not negligible. As a consequence, a perfect transparency is not attained.

Transparency in free space could be improved by implementing accompanying control strategies, e.g. measure the force exerted by the operator and exert an additional force in the direction of movement [START_REF] Diaz | Stability Boundary and Transparency for Haptic Rendering[END_REF]. Such solutions have however their limits and inertia and friction cannot be totally cancelled.

Part of the problem is related to the fact that force feedback interfaces usually require the user to be mechanically linked to them in order to know the user's position and provide force feedback that is consistent with the virtual scene. This link has a nonnegligible inuence as the user experiences the friction, inertia and vibrations of the mechanical structure even when moving in free space. In this case the dierence between free space and contact is less distinctively felt and muscular fatigue is expected to appear in case of long manipulations.

Medical simulators are particularly sensitive to this issue. In dentistry training for example, the need for the simulation of hard teeth (high stiness) and light tools (low inertia) places a great challenge in the design of force feedback interfaces [START_REF] Zhang | DentalTouch: A haptic display with high stiness and low inertia[END_REF].

A relatively novel paradigm known as intermittent-contact aims to cope with the limitations of conventional devices in order to improve the realism of the haptic interaction and relief the user when long manipulations take place. Its principle and the advances in this eld of research will be described in the next section 1.7.

Intermittent-contact paradigm

The intermittent-contact (IC) paradigm proposes to remove the mechanical link between the interface and the user in free space, obtaining a perfect transparency and letting the user touch the haptic device only when a contact occurs in the VE. This way, intermittent-contact haptic interfaces (IC-HIs) aim to improve the realism of the haptic interaction.

Two categories of devices implementing the IC paradigm can be identied. The rst one is known as Encountered-Type haptic interfaces (ET-HIs) and the second one as Close-Tracking-type haptic interfaces (CT-HIs). In the former, a robot manipulator, which end-eector has the shape of the simulated object, is controlled to make it be encountered the user's hand at the position where the VO is found. In the later, the device follows the user at a short and constant distance, without contact, and touches him/her only when a VO is reached.

These devices are particularly interesting to reduce the fatigue during long manipulations and to perceive small interaction forces as it is the case in medicine, e.g. the force applied on an organ. Their principle and relevance will be discussed in sections 1.7.1 and 1.7.2 respectively.

Encountered-type haptic interfaces

The ET-HI principle consists in imagining that the virtual space is superimposed with the real environment. The robot is then controlled to be positioned along its surface at the nearest position of the user's hand and simulate the VO properties (see Fig. 1.12).

This way, the user remains away from the robot in free space and he/she touches its endeector only when and where he/she is supposed to touch the VO, a perfect transparency is therefore achieved. To do this, the user's position must be tracked, e.g. using video

Free space

Virtual surface (VO) cameras or body-mounted position tracking sensors, and the robot must be controlled so that it can rapidly and accurately anticipate the user's movement intentions.

The ET-HI approach was rst proposed in [McNeely, 1993]: a robot manipulator, which end-eector has the shape of the simulated object, is controlled to make it encounter the user's hand at the position where the VO is expected to be found. This way the user is totally free in free space and he/she can feel the corresponding interaction forces.

The ET-HI approach was also used in [START_REF] Tachi | A construction method of virtual haptic space[END_REF] for the construction of a haptic space: the user's arm motion is measured by a passive master arm, allowing to compute the position and orientation of the user's ngertip. This information is used by a computer to calculate the nearest object to the user's hand in the virtual haptic space (see Fig. [START_REF] Tachi | A construction method of virtual haptic space[END_REF]).

Another ET-HI system was proposed in [START_REF] Yokokohji | What you can see is what you can feel-development of a visual/haptic interface to virtual environment[END_REF], Yokokohji et al., 1999].

Called WYSIWYF (What You can See Is What You can Feel), this concept allows the user to feel the object precisely where the user sees it. Employing vision-based tracking, the system can blend live video with the virtual scene, i.e. a portion of the user's hand is extracted from the captured image and is superimposed on the virtual scene (see Fig.1.14).

In [START_REF] Yokokohji | Design and path planning of an encountered-type haptic display for multiple ngertip contacts based on the observation of human grasping behavior[END_REF], an ET-HI device allowing the simulation of precision grasping tasks using three ngers (thumb, index and middle ngers) was presented (see Fig. 1.15).

The system consists of two modules, a base module composed of a robot manipulator (see .14: WYSIWYF system (adapted from [START_REF] Yokokohji | WYSIWYF display: A visual/haptic interface to virtual environment[END_REF]). [START_REF] Yokokohji | Design and path planning of an encountered-type haptic display for multiple ngertip contacts based on the observation of human grasping behavior[END_REF]).

When working with ET-HI devices, the user's hand is a kind of moving obstacle (see Fig. 1.16a) that should be avoided (see Fig.1.16b). Miscalculations or system slowness can lead to painful collisions. In order to cope with this issue, path planning techniques are necessary.

In [START_REF] Yokokohji | Path planning for encountered-type haptic devices that render multiple objects in 3d space[END_REF], a path planning algorithm for ET-HI devices that renders multiple VOs in 3D space was proposed. Here a convex polyhedron is constructed from the reference points of the virtual objects (see Fig.1.16c). As long as the user's hand is outside the polyhedron, the device stays on its surface. On the other hand, if the user's hand penetrates in it, the device avoids the user's hand and goes inside the polyhedron if necessary. Such algorithm not only considered the security of the user but also the eciency of the device movement. [START_REF] Yokokohji | Path planning for encountered-type haptic devices that render multiple objects in 3d space[END_REF]).

As previously explained, ET-HIs have the advantage over classical type haptic interfaces to be perfectly transparent in free space as they are not at all in contact with the user's hand. With this approach however, the robot may reach very high speeds, which is dangerous for the user, e.g. if bilateral contacts with concave surfaces have to be simulated. Another issue is that the amount of objects that can be simulated is limited to a restricted set of pre-manufactured objects, which often display only very simple mathematical shapes. Despite these limitations, this approach recently found a regain of interest as exemplied by the Lobby-Bot platform from Clarte [START_REF] Clarte | Lobbybot[END_REF] used for testing the perception of dierent materials (see Fig. 1.17).

Figure 1.17: LobbyBot ET-HI system.

Close-tracking-type haptic interfaces

The CT-HI approach is another way to implement the IC paradigm. Contrary to the ET-HI principle where the device follows the surface of the VO, it proposes to let the device follow the user at a short and constant distance, without contact, and touch him/her only when a VO is reached (see Fig. 1.18).

The CT-HI principle requires to measure the distance between the device and the user's body (typically his/her nger), using e.g. sensors installed on the end-eector. The device will then closely follow the user's movements without any path planning as long as the user remains in the reachable volume (workspace) of the interface. Despite this limitation, the security of the user is improved. Several examples of such devices will be given below.

Free space Transition Contact

Physical world

Virtual world In [START_REF] Hirota | Development of surface display[END_REF], the existence of an object is simulated thanks to a mechanism for surface displaying (see Fig.1.19). 3DoF tracking of the index nger is accomplished by means of magnetic sensors integrated in a moving head and magnets mounted on the nger (see Fig.1.19a). When the nger is being displaced in free space (i.e. no VO is being touched), the moving force feedback head follows it (tracking mode). [START_REF] Hirota | Development of surface display[END_REF]).

When a VO is about to be touched, the display mode is activated, the force feedback head stops at the VO position and waits for the nger to contact its inner surface composed of a tube (see Fig.1.19b).

In [START_REF] Yoshikawa | A touch and force display system for haptic interface[END_REF], a 2DoF arm (see Fig.

Near virtual object

Virtual object

In touch with virtual object (c) Control

Figure 1.20: 2DoF CT-HI system from [START_REF] Yoshikawa | A touch and force display system for haptic interface[END_REF].

A similar approach was used in [Gonzalez, 2015] for the development of a 2DoF CT-HI (see Fig. 1.21a). The tracking is however improved to get better performances: the endeector is instrumented with infrared proximity sensors allowing to reconstruct the nger shape and to precisely estimate the position of its center using distance measurements (see Fig.1.21b). The control of the device is more precise, especially regarding the transitions between free space and contact (see Fig.1.21c). Further technical specications on this CT-HI can be found in appendix A.

In [START_REF] Yoshikawa | A threedimensional touch/force display system for haptic interface[END_REF], a three-dimensional haptic display composed of two arms and a cap-like end-eector attached to their tips was presented (see Fig.1.22a). The user can insert his/her nger in the cap to interact with the virtual world. The device's sensor system is composed of optical glass-ber on-o sensors, allowing to roughly estimate the 6DoF conguration (position and orientation) of the nger in the cap (see Fig.1.22b).

In free space the device tracks and follows the ngertip without contact. At contact (when a virtual object is touched), the cap is controlled so its inner surface touches the nger (see Fig. Figure 1.22: 3DoF CT-HI system from [START_REF] Yoshikawa | A threedimensional touch/force display system for haptic interface[END_REF].

Finally, a recently developed CT-HI presented in [START_REF] Chabrier | Design and experimental evaluation of an infrared instrumentation for haptic interfaces[END_REF] allows two nger dexterous interactions (index and thumb ngertips) with digital mock-ups in VR (see Fig.1.23a). This interface should be able to precisely measure and follow both ngertips remotely without equipping the user with any marker on skin or nail, and serve as a contact surface when force feedback is required. To perform this, two 6DoF end-eectors were specially designed and tested. Each end-eector integrates 9 proximity sensors, 8 placed around the nger in two planes, the last one being in front of it (see Fig.1.23b). A 6DoF (position and orientation) robot is associated with each nger and connected to a base plate xed on the hand palm. All these elements are associated with a positioning arm (see Fig. 1.23c) in order to allow for as free as possible hand movements.

It is worth noting that the performance of CT-HI devices directly depends on the quality and speed of the measurement of the user's body conguration (typically his/her hand or nger). It is of capital importance to acquire this data with a high precision and at a high frequency in order to allow for the implementation of an ecient control strategy ensuring clean free space to contact transitions. Several techniques can be used therefore. Some of them will be described and discussed in chapter 4.

(b) Prototype end-effector with 9 proximity sensors [START_REF] Chabrier | Design and experimental evaluation of an infrared instrumentation for haptic interfaces[END_REF]).

Proposed research

Force feedback interfaces are intended to allow a user to interact naturally with a virtual/remote environment with haptic feedback. Therefore, they should be both light and frictionless enough so that they do not interfere with the user's movement in free space (transparency) and mechanically sti to provide realistic force feedback. Several eorts can be made to achieve these goals, e.g. by optimizing the mechanical design or by using force sensors to measure and compensate the resistance of the device to the user's movements in the direction of displacement. These solutions are however not sucient to achieve a perfect transparency and the performances of current force feedback devices still require to be improved, in particular for tasks lasting long hours and where perception of small forces is important, e.g. for medical simulators employing light tools.

The IC paradigm, presented in section 1.7, aims to solve this problem by physically disconnecting the user for the device in free space and letting him/her touch the robot only when it is required, this way providing only the necessary amount of interaction forces.

This principle can theoretically render force feedback interfaces perfectly transparent, allowing to increase the realism of the interaction. It has been implemented in two ways:

ET-HI and CT-HI devices.

In the former approach, the system anticipates the user's movements, positions the end-eector of the robot at the place where he/she is expected to touch a VO and waits for the user to encounter it. User tracking is commonly achieved by means of a motion capture system or a passive mechanical master arm attached to the user's arm. Such approach is however dangerous, as without meticulous path planning, the robot may follow trajectories near the user. Furthermore, if bilateral contacts are simulated the robot may attain very high speeds, compromising the security of the user.

The later approach proposes to closely track (advantageously with a system integrated in the end-eector of the robot) and follow the user's movements (in position and orientation) without contact in free space and stop the robot when a VO is being touched to make the user feel the interaction forces. With this approach, the security of the user is improved, even if his/her movements are restricted to the workspace of the robot. For this reason, in the present work we will focus on close-tracking-type interfaces.

It is worth noting that, despite their potential advantages, CT-HI devices still suer from several limitations. The objective of the doctoral thesis presented here is to increase knowledge about them. It is organized around three key questions that, according to the explored literature, have not yet been addressed for this type of devices. Each of these issues will be addressed in a specic chapter of this thesis, as explained below.

For practical purposes the term IC-HI will be used as an equivalent of CT-HI in the reminder of the present document.

• Chapter 2: Evaluation of the Benets of IC-HIs from a User Perception Perspective.

When using a force feedback interface in VR, the user should ideally experience what the avatar feels, either nothing when he/she is in free space, or realistic forces during contacts with the environment. He should also feel, a clear distinction between free space and contact modes. Compared to conventional devices, IC-HI interfaces should increase the realism of the interaction as they theoretically provide a perfect transparency in free space, a large range of forces when obstacles are touched and sharp transitions between these two states. These advantages should allow VR to get closer to reality.

As a consequence, we would expect that users prefer an IC-HI rather than keep using conventional devices. However, this has not yet been proven.

To answer this question, we made use of an existing 2DoF device developed at CEA, LIST [Gonzalez, 2015] that can be congured either as a classical contact haptic interface (CC-HI) or as an IC-HI. In order to compare the relative merits of both congurations, a series of phsychophysical tests were proposed to a group of volunteers. Three types of user tests, each one representing an elementary VR task, were performed: stiness identication, target pointing and obstacle detection. Each test was performed in both congurations (CC-HI and IC-HI), and information about the state of the system but also about the feeling of the user were acquired, allowing us to obtain both qualitative and quantitative results. This work is presented in chapter 2.

• Chapter 3: Improvement of Contact Rendering at High Speeds When designing IC-HIs and their controller, three phases should be considered: free space, contact and transitions between free movements and contact. In free space, the robot tries to keep the user limb, e.g. his/her ngertip, at the center of its end-eector. In practice, the limited dynamics of the robot reduce its capacity to instantaneously follow the user. The role of the controller is then to try to compensate for the resulting position error. IC-HIs usually work quite well in this phase, provided that the available gap between the end-eector and the user limb is sucient to absorb any position deviation without contact between them.

At contact, IC-HIs work like any other haptic interface. They can be controlled either in admittance or impedance These principles are well known and this phase is not a problem, as far as the controller gains preserve the stability of the device.

Transitions between free space and contact are more tricky. Let's take the example of a xed obstacle. When the user approaches the vicinity of the VO, the robot's endeector should be completely stabilized before contact so that the user has the impression of touching an immobile object. As can be seen in the literature, this can be made in various ways, either by abruptly shifting from free space control to contact mode when hitting the VO, or by progressively changing the reference position in the vicinity of the environment, so that the user limb seamlessly moves from the center of the end-eector to its periphery, allowing the user to touch it when required, or by having both mode always active and progressively changing their weight depending on the situation. The last one is the most recent solution and it proves to be the more stable [START_REF] Gonzalez | Smooth transition-based control of encounter-type haptic devices[END_REF].

However, it is still not capable to manage contacts at high speeds.

Motivated by this fact, part of our research was concentrated on the improvement of the contact rendering at high speeds. The proposed control strategy aims to dissipate the energy of the interface, prior to contact, by creating a pure damping zone on the frontier of the VO. To evaluate the benets of this approach, user tests were also performed.

Further details can be found in chapter 3.

• Chapter 4: Contributions to the Design of an IC-HI Tracking Module for Tool-Based

Interactions.

It can be seen in the literature that most existing IC haptic interfaces are intended for bare nger interactions. Despite their advantages, the design of such systems is particularly challenging since the size and shape of human ngers vary for each user. Also, ngers deform both when bending and during contacts with the environment. This makes it dicult to precisely determine their position, orientation and geometry.

Fortunately, a lot of tasks are performed by means of a tool and do not require direct nger interactions. In surgery simulators for example, the interaction usually takes place through a stylus-like interface.

Introduction

Since they touch the user only when force feedback is required, intermittent contact haptic interfaces, and in particular close-tracking-type devices (referred here as IC-HIs), aim to provide more realistic interactions with virtual environments than classical contact haptic interfaces (CC-HI). To our knowledge, however, this has not yet been proven.

Indeed, the information which is usually available regarding both CC and IC existing interfaces is often limited to technical specications (number of DoF, workspace, inertia, maximum exertable force, etc.) and example applications. Unfortunately, this is not sucient to ensure optimal performances for the completion of a VR task of interest nor to directly infer their perceived rendering quality. Such performance assessment requires the presence of the human operator in the loop and any evaluation performed without human interaction would not really represent the actual device use.

Psychophysical evaluation methods appear to be a good solution to this problem. By directly evaluating the perception of an external stimulus provided to a human being through a given device, such approach allows to take into account both the performances of the device itself, the capacities of the user, and their adequacy in the context of a specic task. Results being given with reference to the user, who is independent of the device, this approach also allows to make fair comparisons between two or more force feedback devices. It can be imagined for instance asking a user to perform a given VR task with dierent devices and measuring/calculating each time the same performance metric, related to the task itself and not to the employed device. The results obtained can be then analyzed to learn which device is better suited for the task of interest.

Psychophysical tests are thus a useful tool to evaluate the relative benets of CC-HI and IC-HI devices and compare them. In this work, we choose to focus on three tests representing elementary VR tasks. These evaluations, reported in this chapter, were performed by a group of volunteers using an available interface that can be congured either as a CC or as an IC interface.

This chapter is organized as follows: section 2.2 presents an insight on the dierent existing approaches for the assessment of haptic interfaces performances and the interest of a psychophysical evaluation approach. Section 2. [START_REF] Samur | Generic and systematic evaluation of haptic interfaces based on testbeds[END_REF]).

is provided (contact with a sti VO). Considering only the device technical specications is not sucient as the performances of the controller, which ensures a proper communication between the VE and device, have also a large inuence on the achievable stiness.

The quality of the immersion and of the perceived interactions thus depend on the quality of both the VE, the controller and the capacity of the haptic device to provide realistic interactions. All these elements should therefore be taken into account for the evaluation of the haptic rendering system. These elements representing research branches by themselves and as a result being in constant evolution, methods being resilient to such evolution is of particular interest in this case. Experiments involving human users may provide a pertinent approach, as will be developed in the following section.

Evaluation based on psychophysical tests

When considering the ability of a user to perform a given VR task requiring force feedback, the following question quickly arises: Which haptic interface better suits the task of interest?

The answer to this question is not straightforward since the device technical specications (DoF, workspace, inertia, maximum exertable force, etc.) alone do not provide direct information regarding the attainable performances for that task. The task's constraints should also to be taken into account. Whether the interface is intended to be used in a medical simulator or in a video game platform, the requirements will not be the same. Indeed the dynamics of such tasks are totally dierent and the device should t them to fulll the expectations. Similarly, the human operator should also be considered.

Indeed, the design of haptic devices should account for the human operator's capabilities, e.g. take into account the size of the hand or the reachable speeds and workspace with his/her arm.

In summary, as a haptic device is meant to be used by a human user to perform various tasks and its performance is highly aected by the user's behavior and tasks constraints [Samur, 2012], all these elements should be taken into account. In this con-text, psychophysical evaluation represents a pertinent approach. More specically, device evaluation based on psychophysical tests represents an adapted approach for haptic interfaces since it links device performance measures to the limits of human perception, obtaining as a result device-specic limits [Samur, 2012] regarding the task of interest.

Psychophysics has been dened as the scientic study of the relation between stimulus

and sensation [Gescheider, 2013], e.g. for the senses of vision, hearing and touch. Another more complete denition is the analysis of perceptual processes by studying the eect on a subject's experience or behavior of systematically varying the properties of a stimulus along one or more physical dimensions [START_REF] Bruce | Visual Perception: Physiology, Psychology and Ecology[END_REF].

Haptic rendering systems have been used in a variety of pshychophysical experiments:

• peg-in-hole [START_REF] Unger | Comparison of 3-D haptic peg-in-hole tasks in real and virtual environments[END_REF]],

• tapping [START_REF] Chun | Evaluating haptics and 3d stereo displays using Fitts' law[END_REF],

• targeting [START_REF] Oakley | Putting the Feel in 'Look and Feel[END_REF],

• haptic training [START_REF] Avizzano | Motor learning skill experiments using haptic interface capabilities[END_REF],

• joint task in a shared VE [START_REF] Basdogan | An Experimental Study on the Role of Touch in Shared Virtual Environments[END_REF],

• hardness perception [START_REF] Lawrence | Rate-hardness: a new performance metric for haptic interfaces[END_REF]] and

• object recognition [START_REF] Kirkpatrick | Application-based evaluation of haptic interfaces[END_REF].

Such experiments can be useful to assess the performances either of the haptic interface or of the haptic feedback itself. In the present work the attention is given to attainable performances with a haptic device.

For a VR task of interest a set of performance metrics can be dened in order to build a standard testbed that can be used with several devices. This should include both quantiable metrics, e.g. speed, force, time travel, and subjective performance values, e.g. survey, user's opinion [Samur, 2012].

Testbed evaluation approach aims then to provide general and complete results that can be taken into account in any VR application using the studied task [START_REF] Samur | Generic and systematic evaluation of haptic interfaces based on testbeds[END_REF].

This means that several haptic devices that are potentially interesting for the desired application can go through such testbed evaluation, the device obtaining the highest performances is expected to be used for that application since it will provide optimal performances.

Depending on the nature of the task, it can be classied into two haptic modes:

motor control and perception. A haptic mode is dened as a distinct style of using the haptic system, characterized by the nature of the user's attention, the path and duration of the movements, and the skin location contacting the object of interest [START_REF] Kirkpatrick | Application-based evaluation of haptic interfaces[END_REF]. A haptic mode involves then several factors that play a more or less important role depending on the nature of the task. Table 2.1 shows a taxonomy for each haptic mode assuming that the user is using his/her hand. This information can contribute to imagine a pertinent VR-based testbed based on the subtasks.

Table 2.1: Taxonomy of haptic modes (adapted from [Samur, 2012]).

Haptic mode Generic tasks Subtasks

Motor control In the literature, a comprehensive evaluation of dierent CC devices was found in [Samur, 2012]. On the other hand, despite the potential interest of the IC paradigm (which aims to provide a perfect transparency in free space and more realistic transitions between free space and contact) and the fact that it has been around at least since the 90s, it was observed a lack of work to assess its benets for VR tasks. Motivated by this observation, we decided to implement a certain number of psychophysical experiments based on VR tasks in order to assess the benets of a recently developed IC-HI device.

Inspired by the taxonomy provided in table 2.1, psychophysical experiments based on three dierent tasks that can collectively represent the building elements of a realistic haptic application were proposed: (1) stiness identication, (2) target pointing and (3) blind obstacle detection. Aiming to compare the relative benets of CC and IC haptic interfaces, all of them were performed in both conditions.

The rst experiment, called stiness identication, aimed to answer the following question: Does an IC haptic interface allow to better distinguish dierent stiness values than a CC-HI device? This experiment consisted in palpating a reference wall that displays a reference stiness (unknown to the user) that has to be guessed. To this end, the same wall could be switched to a variable stiness mode where the user could modify the displayed stiness. Switching between both modes could be done until both walls were perceived as displaying the same stiness. This kind of task is commonly performed by veterinarians and novice surgeons to learn palpation skills [START_REF] Forrest | Haptic stiness identication by veterinarians and novices: A comparison[END_REF].

In a second experiment we wondered if a target pointing task was easier to perform with an IC-HI or with a CC-HI? In order to obtain elements of answers, this experiment, called target pointing, proposed a motor control task which consisted in pointing targets of several sizes, located at dierent distances from a home position. Well dened metrics to evaluate the performance of this type of experiment have been dened in [MacKenzie, 1995].

The third experiment, called blind obstacle detection, aimed to answer the following question: Are free space to contact transitions more realistic employing an IC haptic interface than with a CC device? This experiment proposed a combination of dierent haptic modes since it asked the user to follow a vertical line (motor control) where he/she would encounter an invisible obstacle located at an unknown position (perception).

The performed experiments searched to provide answers to the above presented questions. While all of them are dierent, they share however certain common points from an implementation point of view. These elements are presented in the following section 2.3.

For practical purposes in the reminder of the present chapter, the terms CC condition (classical-contact condition) and IC condition (intermittent-contact condition) will make reference to the use of a CC and an IC device respectively.

General methods

In this section, some aspects which are common to the three performed experiments will be presented and described: participants (section 2.3.1), materials (section 2.3.2), experimental setup (section 2.3.3), procedure (section 2.3.4) and data processing methods (section 2.3.5).

Participants

A total of thirty people (19 men, 11 women, aged 22-60) were invited to be volunteers for our experiments. They were told that they would have to perform a VR task employing a force feedback interface. A brief description of these two elements was provided in certain cases during the recruitment process, however no concrete details about the experiment were given.

The population was mainly issued from people working in the Institut des Systèmes

Intelligents et de Robotique (ISIR), a robotics laboratory located in Paris, France. It accounted for administrative personnel, permanent sta, PhD students and interns. Only right-handed volunteers were chosen since, as it will be seen further in section 2.3.2.1, the experimental set-up was better suited for right handed participants.

Each one of the three experiments was assigned to a group of ten participants in a random manner, i.e. a list with proposed time slots was lled in order to make two appointments with each participant, one for the CC interface and another one for the IC interface. This means that each group was asked to perform only one of the three assigned tests using both a CC and an IC interface (see Fig. In order to prevent learning eects, a two-days rest interval between the tests performed with CC and IC interfaces was given to the subjects. Calendar shown in table 2.2 provides a representative chronology of the performed experiments for each subject, denoted here as S.

Materials of the study

In this section the materials employed during the experiments are described. The focus was given here to the elements that allowed to collect/generate data, in particular:

• the CC and IC haptic interfaces (section 2.3.2.1), which allows to collect information regarding the movements of the user as well as the interaction forces,

• the VE (section 2.3.2.2), which denition provides the necessary elements to generate its visual representation and calculate the corresponding interaction forces thanks to the associated control law (section 2.3.2.3),

• and nally, a questionnaire (section 2. 3.2.4), that allows to collect the feeling of the participants on particular aspects of the performed experiment.

CC & IC haptic interfaces

One of the main aims of the performed work was to compare the attainable performances in both CC and IC conditions for a same VR task. To perform this an available 2DoF robot was equipped with either a CC or an IC end-eector.

The robot is composed of two links 0.25m long each. Its workspace lies in a vertical plane. The actuation of the links is provided by two DC motors and cable capstan reducers allowing a particularly transparent behavior. Encoders (position sensors placed on the motors) are used to track the robot's displacements and counterweights are mounted on each axis to allow for gravity compensation (see Fig. This platform was originally equipped with an IC end-eector (see Fig. 2.4a). This element is composed of a 24mm wide hollow cylinder equipped with 16 infrared proximity sensors used to compute the relative position of the nger with respect to the cylinder, the later being also used as contact surface when force feedback is applied.

In order to provide typical CC feedback, the IC end-eector could be easily replaced by a CC end-eector mounted on the same robot (see Fig. Further technical details on the robot equipped with an IC end-eector can be found in appendix A.

Virtual environment

A VE recreates a scene of the real world. Its model is used for visualization purposes as well as to calculate the corresponding interaction forces.

In the present case the employed 2D VE consists of a black vertical rectangle (free space) surrounded by a thick green contour representing four virtual walls. The home position is a circular area of the free space employed as a starting point prior to a movement. Finally, user's nger avatar was represented with a white circle which displacement was coupled with that of the robot's end-eector. These elements are shown in gure 2.5.

As the interaction with the VE is performed by means of a haptic interface, this VE should be positioned in an area where the device performs well. Here, the VE from gure 2.5 is placed 0.2m in front of the robot's reference frame R 0 and it extends just above it (see Fig. 2.6). The dimensions of the free space rectangle are 0.15m × 0.20m. According to [Gonzalez, 2015], this robot equipped with an IC end-eector shows homogeneous performances in this area.

It is worth noting that gure 2.6 illustrates the VE as it is dened in the haptic space, i.e. the environment used to generate force feedback. It can dier from its visual representation, which can in particular be placed in a dierent location as shown later in gure 2.12 (the haptic virtual space is located close to the robot as shown on gure 2.6 while its visual representation is shown on a screen in front of the user, far away from the robot).

Home position

Finger avatar

Virtual walls

Free-space The corresponding interaction force with the VE, e.g. with a virtual wall, denoted here as F e , is calculated based on its model and acts as a unilateral constraint during the contact phase. Such principle works for both conditions CC and IC, however control in free space is dierent. The following section will provide the principle of the control employed on both interfaces.

Control of the haptic interface

The control strategy of either the CC or the IC interface (see Fig. 2.4) should manage the behavior of the device during free space and contact modes. In the following paragraphs the employed strategies for both modes as well as the transition between them will be presented, rst for an IC-HI and then for a CC-HI.

In free space the IC haptic interface should closely track the user's nger position without touching it. We note here:

X = X f /0 -X r/0 = X f /r (2.1)
the tracking error X between the center of the nger X f /0 and the center of the ring X r/0 (see Fig. 2.7, where the nger is modeled as a cylinder). This error can then be expressed in the joint space as follows:

q = J -1 (q) X (2.2)
where q = [q 1 q 2 ] T are the joint positions and J(q) the robot's Jacobian matrix expressed in its global reference frame R 0 .

Ring (End-effector)

User's finger Error minimization is achieved with a proportional derivative controller, which pro-vides the robot with a reference tracking torque τ t in the Laplace domain:

𝑿 𝑓/0 𝑿 𝑟/0
τ t = Z t q = (K t + B t s) q , (2.3)
where Z t is the impedance expressed in the joint space, K t and B t the proportional and derivative gains respectively (both diagonal matrices in the joint space) and s the Laplace variable. With this controller, a link equivalent to a spring-damper system is created between the centers of the nger and the ring which have their corresponding avatar representation in the virtual world (see Fig.

Z tcart = J T Z t J -1 .
The corresponding PD tracking gains are:

K t = 40 0 0 40 Nm/rad B t = 1 0 0 1 Nms/rad (2.4)
When the nger touches a VO, e.g. a wall, the resulting contact force based on its mechanical properties should be displayed to the user. Such force resulting of the interactions with the VE is noted here as F e and acts as an unilateral constraint. A viscoelastic compliant VE without tangential friction is assumed and a modied Kelvin-Voigt model [START_REF] Achhammer | Improvement of model-mediated teleoperation using a new hybrid environment estimation technique[END_REF] is used to calculate the resulting interaction forces as follows:

F e =        if d r/e < 0 & Ẋr/0 > 0 then F e = -d r/e (K e + B e s)n if d r/e < 0 & Ẋr/0 < 0 then F e = -d r/e K e n
else F e = 0

(2.5) where d r/e is the distance between the ring's avatar inner circumference and the closest point of a VO located at position x e , n is an unitary vector normal to the surface of contact and Ẋr/0 is the speed of the ring along n.

For explanation purposes, Ẋr/0 is assumed positive in the direction of motion. These elements are illustrated in gure 2.9.

Real world

Virtual world The PD gains K e and B e for force rendering are:

𝑿
K e = 2500 0 0 2500 N/m B e = 35 0 0 35 Ns/m (2.6)
The transition between free space and contact with the IC-HI is achieved by reducing the inuence of the tracking force F t (send to the robot as a tracking torque τ t ) by a factor β nearby the obstacle, i.e. the tracking force starts decreasing at a distance d f /e = d β from the VO which is located at position x e . Equation (2.7) shows how β can vary in function of d f /e , the distance between the nger's avatar and the VO (distances d f /e and d β are ilustrated in gure 2.8). However, factor β cannot be totally canceled in the vicinity of the VO since in this case the ring would not follow the nger when it moves away from it.

       if d f /e > d β then β = 1 if d f /e ∈ [0, d β ] then β = 1-β min d β d f /e + β min if d f /e ≤ 0 then β = β min = 0.1 (2.7) Here d β = R r -R f,max = 1mm (with R r = 12mm and R f,max = 11mm chosen so that ∀R f , R f,max > R f ).
1 This way by the moment the user encounters the ring, the tracking eect is almost canceled and F e = 0. Equation ( 2.3) can now be expressed as: In the case of the CC-HI device, the user's index nger is mechanically linked to the robot's CC end-eector (the center of the end-eector and user's nger are coincident).

τ t = Z t β q (2.
As a result the displacement of the interface in free space is performed thanks to the forces the user applies on it.

As for the contact, force rendering is performed the same way as in (2.5), i.e. the ring avatar is used to compute the interaction forces. Same controller gains were also used.

The control corresponding to the CC haptic interface, is summarized in the control block diagram from gure 2.11.

1 According to [Grenier, 1991] the perimeter of the largest index is 63mm, which gives a radius of ≈ 10mm.

Robot

Questionnaire

A questionnaire was employed to perform a complementary survey on particular aspects of the performed task at the end of each experiment. Such questionnaire was anonymous and the participants could spend as much time as they needed to ll it. In this section, only the questions which are common to the three experiments are provided.

These questions were:

• Did you nd the interface easy to use? 1) Strongly disagree Besides these common questions, 2 or 3 additional questions specic to each experiment were included in the questionnaire (see sections 2.4.2.3, 2.5.2.2 and 2.6.2.2).

Experimental setup

The experimental setup used for the tests was installed in an isolated room of the robotics laboratory ISIR. During each test the participant was sitting, wearing headphones and facing a screen where the VE is displayed by means of a graphical user interface (GUI). The robot was placed on a small table so that the user's right index nger could be placed comfortably inside the end-eector (no elbow rest was provided).

The robot was also hidden from the user's sight by a vertical wall. The experimenter was positioned in front of a supervision computer. This set-up is shown in gure 2.12. It is worth noting here that the participant visualized a GUI that contained only the VE (as shown in gure 2.5) and that its displayed size was adapted to t properly the available screen so that it could be clearly visualized from the user's location. A constant nger radius was employed for all participants to dene the size of the nger avatar, in practice R f = 7.5mm. This gure provides also typical duration times for common stages (welcome, survey and goodbye). Specic typical times for each experiment will be described later in the reminder of this chapter.

Welcome

The following stages describe the welcome of a participant:

1. The participant was met at the main hall of the laboratory and taken to the experiment's room.

2. Once in the experiment's room, he/she was invited to take a sit and answer a general information form (profession, age, knowledge about computer tools, human machine and haptic interfaces).

3. The participant was then provided with a letter of consent, which explained the global process of the experiment he/she was about to perform. This letter gave in particular information on the following aspects:

• the aim of the study,

• how a haptic interface allows to interact with a VR,

• a description of the CC and IC devices,

• a description of the VR task to be performed as well as,

• the recorded variables.

4. He/she was asked if there were questions about the global process.

• A brief resume of the letter of consent was explained orally in order to reinforce the understanding of the general procedure.

5. Finally, he/she was asked to sign the letter to agree on the experimental conditions.

Since this was a voluntary participation, he/she was informed that he/she could quit the experiment at any time and because of any reason without generating any particular issue.

Training session

The aim of the training session is to provide the participants with practical information on the execution of the experiment and to allow them practicing until they feel condent with it. This training session focused on the following aspects:

• explaining to the participant the experimental conditions,

• teaching him/her how to manipulate the haptic interface according to the experiment to perform,

• explaining the structure of the experiment and

• practicing the corresponding VR task.

These points will be developed in the following paragraphs.

Experimental conditions. During the presentation of the layout of the main elements of the experiment to the participant, it was pointed out that during the experiment he/she was going to be sitting on a chair, wearing headphones and facing a screen where the VE was displayed. In addition to this, he/she was told that the robot (placed on a small table so that his/her right index nger could be placed comfortably inside the end-eector) was going to be hidden from his/her sight by a vertical wall.

The headphones let him/her listen a softened pink noise (not disturbing for the inner ear) during manipulations. This was intended to reduce the inuence of surrounding parasitic noises, in particular those eventually generated by the haptic interface.

When any oral communication had to be established between the experimenter and the participant, the former talked to the later through a microphone located on the supervision computer. At this time the pink noise was turned o so the participant could listen to the experimenter's voice in the headphones. This solution allows to avoid removing the headphones each time oral instructions are required.

Haptic interface manipulation. As described in section 2.3.2.1 the employed haptic interface could be equipped either with a CC or with an IC end-eector. The 2DoF nature of this robot had to be taken into account when learning how to manipulate it in both CC and IC conditions, i.e. for displacing the nger avatar in free space, and if required for touching the virtual walls.

During the manipulation of the interface, the participant had to maintain his/her right index nger inside the robot's end-eector and to keep it perpendicular to the robot's working plane without pushing. Such task was somehow complicated, in particular in the IC condition, since in the absence of a mechanical link, nothing prevents the participant from moving his/her nger out the end-eector nor from changing its orientation without noticing it.

The correctness of the participant's gesture was veried by the experimenter and he/ she was told to correct it if necessary. Enough time was given to him/her in order to learn how to manipulate the haptic interface.

Structure of the experiment. Each experiment required the participant to perform a VR task. The action of performing such task is denoted here as a trial. A set consists then of a dened number of trials and a complete experiment is composed of a dened number of sets. The number of sets for each experiment will be specied later in this chapter. These denitions were explained to the participant prior to practicing the VR task.

Practice of the VR task. The participant had enough time to learn how to perform the VR task. Several trials were performed until he/she felt comfortable with it. In practice, at least one set of trials was performed.

Experiment

Prior to the experiment, the experimenter activates the corresponding VE by means of the GUI displayed on the supervision computer. In order to start, the participant is asked to put the headphones and to place his/her right index nger inside the end-eector of the haptic interface.

Oral instructions allowed to perform the transitions between trials. For a single trial, the experimenter proceeded in the following way:

1. The participant is invited to position the nger's avatar over the home position. Examples of employed phrases were: Once that a set of trials was completed, a longer break took place (1 -2min). During this time the experimenter asked the participant to put his/her arm aside. The experimenter also asked him/her how he/she was feeling with the execution of the VR task and if he/she had any questions. At the same time complementary instructions were given if necessary, e.g. in the case his/her gestures to manipulate the interface were not adequate.

Once the break was nished, another set of trials started until completing the number of required sets for the whole experiment. A scheme of the building blocks of a typical experiment is shown in gure 2.16.

Survey & goodbye

At the end of the experiment, the participant was asked to answer a survey. Finally a reward was given, e.g. a chocolate, prior to taking him/her back to the hall of the laboratory.

Data processing

The aim of the data processing was to identify meaningful dierences/tendencies between the CC and the IC interface. To this end, a statistical analysis on the performance metrics of interest was performed for each experiment. On the other hand, the perception of the user was measured based on the provided answers during the survey performed at the end of each experiment.

Statistical analysis

The generated data were post-processed in order to perform quantitative comparisons.

Boxplots were employed to analyze the results. Here the median appears inside the box as a horizontal line, the box represents the rst (Q1) and third (Q3) quartiles and whiskers represent minimum and maximum values (see Fig.2.17). This method allows to observe the dispersion of data around the median as well as outliers without making any assumption on the underlying statistical distribution. In a second time, the statistical signicance of the performance metrics was studied.

To do so, an analysis of variance (ANOVA) was performed. Such test relies on data normally distributed (normality validated with a Shapiro-Wilk normality test) and on the equality of variances (equality validated with a Levene's test). In the opposite case, a non-parametric statistical test was employed (Friedman test).

Finally, in both cases the corresponding post-hoc test was performed.

Perception measurement

In order to asses the perception of the participants for each experimental condition, the answers were counted as a ve-point Likert scale. Measured perception for each question was calculated using equation (2.9).

P e i = 5 j=1 n A j • j 5 j=1 n A j (2.9)
where: P e i is the measured perception for question i j is the Likert level A j is the selected option corresponding to Likert level j n A j is the number of participants that answered option A j .

Statistical signicance of P e i was assessed by means of a Wilcoxon one-tailed rank-sum test.

Experiment 1: Stiness identication

This experiment aimed to provide elements of response to the following question:

Does an IC haptic interface allow to better distinguish dierent stiness values than a CC device? Therefore, it proposed to palpate a horizontal wall (displaying a nominal stiness value) in order to guess (approximate) its value. To this end, the same wall could be switched to a variable stiness mode where the user could modify the displayed stiness.

Switching between both modes could be done until both walls were perceived the same.

In the following sections, some elements which are specic to this experiment will be described, in particular the participants (section 2.4.1), the specic employed materials (section 2.4.2) as well as the specic setup (see section 2.4.3). In section 2.4.4 the specic procedure for the execution of the task will be detailed. Section 2.4.5 presents the employed performance metrics. Section 2.4.6 provides the obtained results and observations.

Finally conclusions are given in section 2.4.7.

Participants

Ten subjects participated in this experiment: 7 males, 3 females. Their ages ranged from 24 to 36. All of them were right-handed.

Specic materials 2.4.2.1 Virtual environment

The VE employed for this experiment relies on the VE of reference displayed in gure 2.5. It contains however additional elements (see Fig. 2.18), in particular a horizontal wall located at a distance of 12cm (in the real world) from the bottom and an invisible zone that avoids the user from visualizing this wall as well as the nger avatar. The goal of this invisible zone is to avoid the inuence of visual feedback when palpating/pushing on the wall. The horizontal wall is modeled the same way as the surrounding green virtual walls, i.e. as a spring-damper system which behavior is dened in equation (2.5). As a consequence, a nger avatar pushing on it would displace downwards a longer distance if a low stiness is displayed or a shorter distance in case of a high stiness, allowing the participant to guess the dierence from visual cues.

Remote control

The horizontal wall described in previous section 2.4. These values were applied along n, referring in this case to a vector normal (pointing upwards) to the horizontal wall.

Switching between both modes as well as other actions could be accomplished by means of the remote control shown in gure 2.19. Such control is composed of three elements:

• the switch, that allowed to toggle between the reference and variable modes,

• the potentiometer, that allowed, in variable mode, to modify the displayed stiness of the wall (possible stiness values ranged from 50 to 2500N/m),

• and nally the push button allowed to validate the chosen K u value.

Questionnaire

In order to take into account the user's perception in relation to the experiment, he/ she was asked to answer a survey at the end of it. The survey for this experiment included the following questions:

5) Strongly agree

The same group of questions were asked to each participant at the end of each test in both conditions (CC and IC).

Specic experimental setup

The experimental setup for this experiment required to integrate the remote control so that the participant could easily manipulate it with his/her left hand. Figure 2.20 shows a top view of the experimental setup integrating the remote control.

Participant

Specic procedure

In the present experiment a trial consisted in the palpation of a horizontal wall in order to guess the displayed reference stiness. To this end, the same wall could be switched to a variable stiness mode which current value K u was retrieved from the potentiometer mounted on the remote control.

For each trial, the user was given a limited time (25s) to palpate the horizontal wall (with the index nger inside the robot's end-eector). He/she could switch between both stiness modes as much as desired in order to make his/her choice of K u (by pushing the button on the remote control). If the time given to perform the trial was over, the user had to press the button to validate the last K u dened with the potentiometer. It is worth noting here that contact with the end-eector in the IC condition was allowed any time.

At the beginning of each trial, the reference mode was activated in order to randomly display one of the following ve reference stiness values: 100 200 400 800 1600 N/m and their corresponding damping values:

1. 4 2.8 5.6 11.2 22.5 Ns/m It is important to mention that in order to apply any change of wall stiness, including changing the stiness mode, it was necessary to move the nger avatar to the visible zone, e.g. if the user switched to variable mode and/or modied the potentiometer's position, the nger avatar had to be displaced to the visible zone to apply such changes. The same was also valid when switching to the reference stiness mode in order to display the reference stiness value. A visual aid was provided to the participant, the home position being red in reference mode and green in the variable mode (see Fig. 2

.21).

A set was composed here of ve trials (one trial per reference stiness), with a 10s break each time. During each set each reference stiness was presented once to the user.

A total of three sets were performed (thus a total of 15 trials, i.e. 3 trials per reference stiness value) in order to obtain three K u values for each K ref value (see Fig. Transitions between trials and sets were performed by means the oral instructions introduced in section 2.3.4.3.

Performance metrics

The employed performance metric was based on the following formula:

D s = K ref -K u K ref × 100 (2.10)
where D s represents the dierence, in percentage, between the reference and user stiness values. A D s value close to zero indicates a better approximation of the K ref value, therefore a better performance.

Results & observations

As stated in section 2.4.5, the value D s was dened as the performance metric of interest for the present experiment. We remind here that this metric expresses the dierence, in percentage, between the reference stiness K ref and the user stiness K u . For low reference stiness values (K ref = [100, 200, 400]N/m), both interfaces show a D s value spread quite similar. Around one third of the data points are found between 0% and 20%. Positive values imply an under estimation of the stimuli K ref . On the other hand, around half of the data points are between -20% and 0%. Negative percentages imply that the user over estimated the stimuli K ref .

Conditions

Difference D s (%) C C -1 0 0 I C -1 0 0 C C -2 0 0 I C -2 0 0 C C -4 0 0 I C -4 0 0 C C -8 0 0 I C -8 0 0 C C -1 6 0 0 I C -1 6 0 0
For a medium stiness value (K ref = 800N/m), it can be stated that most of the data points are negative in both conditions. For this case there was a clear over estimation of

K ref .
Finally for a high stiness value (K ref = 1600N/m) the data points moved toward positive values. It can be seen that the tendency was to under estimate the stimuli, meantime in the IC condition over and under estimation of the stimuli looked similar. In this case the fact of not being mechanically linked to the interface may have inuenced the results with data points similarly distributed around the reference stimuli.

In general, based on the results presented in gure 2.24, it is dicult to infer a clear dierence between both interfaces. A post-hoc analysis of the Friedman test showed that there was not a statistically signicant dierence between both interfaces (p -value > 0.05). The table shows the corresponding median x and the p value for a Wilcoxon rank-sum test. Despite the above provided observations, no statistical signicant dierence was reported (p > 0.05 in all cases).

Conclusion

A stiness identication task was performed by a group of subjects in order to compare the benets of an IC interface to those of a CC interface. During the experiment the subjects had to palpate a horizontal wall and manage to approximate a K u stiness to a K ref stiness, the performance metric for this experiment being the value D s .

Results shown in a boxplot allowed us to observe that for low values users tended to over estimate the stimuli, meantime the opposite trend was observed for high values (K ref = 1600N/m). After data processing, no statistical signicant dierences were reported between both interfaces. This was also the case for the measured perception.

From a general point of view, it can be concluded that the usage of an IC interface did not signicantly modify the capacity of the subjects to perceive stiness during a palpation task.

Experiment 2: Target pointing

A second experiment was proposed to answer the following question: is a target pointing task easier to perform with an IC haptic interface than with a CC device? In order to provide elements of response to this question, this experiment proposed a motor control task involving travel and targeting. Starting from an initial (home) position, the user had to point several targets of dierent sizes and located at various distances from the initial position.

In the following sections, some elements which are specic to this experiment will be described, related in particular to the participants (section 2.5.1) and to the specic employed materials (section 2.5.2). In section 2.5.4 the specic procedure for the execution of the task will be detailed. Section 2.5.5 presents the employed performance metrics.

Section 2.5.6 provides the obtained results and observations. Finally, conclusions are given in section 2.5.7.

Participants

Ten subjects participated in this experiment: 5 males, 5 females. Their ages ranged from 22 to 60. All of them were right-handed.

Specic materials 2.5.2.1 Virtual environment

The VE employed for this experiment relies on the VE of reference presented in gure 2.5. It contains however additional elements (see Fig. 2.26), in particular the target. The visualized target (bottom gray circle) is vertically aligned with the home position (top gray circle). In order that it is not hidden by the nger's avatar, its size is expanded.

In practice, the diameter of the visualized target is equal to the nominal diameter of the target (W for width, in cm) plus the diameter of a reference nger 2R f (R f = 0.75cm).

The relative distance between the center of the home position and the center of the target is called A.

Questionnaire

In order to take into account the user's perception in relation to the experiment, he/she was asked to answer a survey just after it. This survey included the following questions:

• Q1.Were you able to reach the target easily? 1) Strongly disagree The setup employed for this experiment is the one previously described in section 2.3.3.

Specic procedure

In the present experiment a trial consisted in displacing the nger avatar, from the home position to the center of the target and to remain there until obtaining the message Target validated!. No particular instructions were given to the subject in terms of speed of the movement, however in order to obtain a valid trial the only constraint was to start and nish the movement performing a vertical movement, without moving sideways.

For each trial a limited time (10s) was given to move from the home position towards the target. The user had to manage to keep the nger avatar inside the target until visualization of the validation message. After validation, the user was asked to move his/her nger avatar back to the home position and wait (without removing his/her nger from the interface) for instructions to perform the next trial.

Dierent position and size values allowed to generate nine targets. The values employed for the position A of the target were: 4 8 16 cm the values employed for the size W of the target were: 0.25 0.5 1 cm Therefore in the present experiment a set was composed of nine trials, corresponding to the dierent possible combinations of distances and target sizes (as will be further explained below, these values were chosen in order to span a large range of tasks, from easy to very hard). A total of three sets were performed (27 trials in total, i.e. 3 trials per target conguration). This structure is illustrated by gure 2.27.

Prior to the experiment, the subjects had a training phase (15min). During this phase It is worth noting that, during the experiments performed with the IC haptic interface, the user was instructed to try to avoid touching the robot's end-eector. Transitions between trials and sets were performed by means the oral instructions, as explained in section 2.3.4.3.

Performance metrics

This experiment aims to assess the relative benets of both interfaces when trying to perform a travel and targeting task. Within this context, Fitts's law provides a comprehensive set of metrics that can be used in this case [MacKenzie, 1995].

According to this law, the diculty of a target pointing task can be quantied by means of information theory (measured in bits), that is:

ID = log 2 (2A/W ) (2.11)
where:

• ID is called the index of diculty (in bits),

• A is the distance or amplitude to move (cm) and

• W is the width or tolerance of the region within which the move terminates (cm).

The A and W values presented in section 2.5.4 were chosen in order to sample a wide range of indexes of diculty, giving as a result nine dierent combinations (targets).

The chosen values allowed ve diculty levels denoted here as easy (I D = 3), mediumeasy (I D = 4), medium (I D = 5), medium-hard (I D = 6) and hard (I D = 7). The time to complete a movement task can be predicted using a linear equation function of ID:

M T = a + b • ID (2.12)
where:

• M T is the movement time (in s),

• a is the ordinate at origin (in s) and

• b is the slope coecient (in s/bits).

Movement time values were recorded for each trial. Parameters a and b are constants that can be determined from experiments employing linear regression. Since these parameters are system dependent they could be used as benchmark metrics for performance comparisons between haptic devices [Samur, 2012].

These results allowed us to compute the index of performance IP which is of particular interest since it represents the amount of processed information per unit of time (bits/s), that is:

IP = ID M T (2.13)

Results & observations

During the experiment, several variables were recorded, including: the amplitude A of the movement, the target size W and the Cartesian position of the user's nger center X f /0 . The later was used to compute the movement starting and end times, both allowing to calculate the movement time M T .

It is worth mentioning that the data of two subjects could not be taken into account for data analysis due to inappropiate manipulation of the IC interface. One of them continuously grazed the wall when performing the movement while the other grasped the IC end-eector using his/her index nger and the thumb. By looking at the boxes in the case of a task with the easiest level (I D = 3bits), it can be observed that the CC condition obtained a higher median than the IC condition. For a medium-easy task (I D = 4bits), IP median and data points show higher values in the IC condition. Such tendency was also observed for medium (I D = 5bits), medium-hard (I D = 6bits) and hard tasks (I D = 7bits).

Friedman test was employed to assess the statistical signicance of IP , however results did show that there was no statistical signicant dierence between both conditions (p > 0.05 in all cases).

The measured perception P e for this experiment is shown in gure 2.30. The chart shows the measured perception and the ideal value is highlighted by a dotted line. Question Q1 aims to provide information about the task diculty which is related with the ID. Question Q2 provides information related to the movement time M T . Questions Q3 and Q4 are generic questions regarding the employed interface.

Based on this resource it can be noticed that the participants found the target easier to reach in the IC condition (Q1), on the other hand similar speeds (Q2) were perceived in both conditions. The IC interface was perceived to be easier to use (Q3) and less tiring (Q4) than the CC one. In general the measured P e values are close to each other, not showing a clear dierence with the exception of Q4.

The table shows the corresponding median x and the p value for a Wilcoxon rank-sum test. Despite the above provided observations, no statistical signicant dierence was reported (p > 0.05 in all cases).

Conclusion & perspectives

In the present section, a travel/targeting experiment was presented. The reported results showed that the index of performance trended to be higher in the IC condition.

The perception of the user regarding the experiment itself showed to be similar for both conditions in terms of ease and speed to reach the target. A similar feeling was reported in terms of ease to manipulate both interfaces. On the other hand, the IC interface was perceived as less tiring to manipulate.

Statistical analysis performed on the index of performance IP and on the measured perception P e stated however that there was no signicant dierence between both conditions.

The fact of not being mechanically linked to the interface in the case of the IC condition may have inuenced the user to displace faster during the movement. This may explain why the IP value trended to be higher for several IDs. To better compare the precision of the pointing task, the position of the user's nger relative to the center of the reached target could be studied.

It is worth noting that the proposed task did not include any free space to contact transition. An interesting complement to this study could be to add force feedback to the pointing task, e.g. to implement a serial tapping task as used by Fitts, i.e. a participant who taps as quickly and accurately as possible between two targets for several width W and distance A values. This kind of experiment would involve free space to contact transitions, therefore potentially revealing more realistic manipulations since breaks would only be done between each set and not between each trial, which in the performed experiments was judged to break the rythm of participants.

Experiment 3: Blind obstacle detection

Our last experiment aims at allowing to answer the following question: are free space to contact transitions more realistic employing an IC haptic interface than a CC interface?

In order to provide elements of response to this question, this experiment proposed a blind obstacle detection task, which combines motor control and perception haptic modes: the user was asked to follow a vertical line (motor control) where he/she would encounter an invisible obstacle (horizontal wall) located at an unknown and variable position (perception).

In the following sections, the elements which are specic to this experiment will be described, in particular the participants (section 2.6.1) and the specic employed materials (section 2.6.2). In section 2.6.3, the specic procedure for the execution of the task will be detailed. Section 2.6.4 presents the employed performance metrics. Section 2.6.5 provides the obtained results and observations. Finally conclusions are given in section 2.6.6.

Participants

Ten subjects participated in this experiment: 7 males, 3 females. Their ages ranged from 24 to 28. All of them were right-handed.

Questionnaire

In order to take into account the user's perception in relation to the experiment, he/ she was asked to answer a survey at the end of it. The survey for this experiment included the following questions:

• Q1.Were you able to detect the obstacle easily? 1) Strongly disagree For each trial the user was given a limited amount of time (10s) to start moving from the home position and encounter the obstacle. As soon as the user encountered the obstacle, he/she was asked to move back the nger avatar to the home position before having a 5s break (here the user was invited to keep his/her index right nger inside the interface). Once back in the home position, another trial could take place.

Five obstacle positions were presented randomly (x obs = 0, 2, 4, 8 and 12). Therefore in the present experiment a set was composed of ve trials (one per obstacle position).

A total of four sets were performed (20 trials in total, i.e. 4 trials per obstacle position), with a one minute break between sets. This structure is illustrated by gure 2.32. Prior to the experiment, the participants had a training (10min). During this phase they were taught how to manipulate the interface by employing appropriate gestures (as an example, in order to ensure good functioning when using the IC interface, it was important to keep the index nger perpendicular to the robot's 2D workspace, without changing its orientation and without moving it out of the robot's end-eector). It was also told to the user that the robot's end-eector shouldn't touch him/her in free space when using the IC interface. A schematic representation of the ow of all building phases for this experiment is shown in gure 2.33. The total time required to perform it was about ≈ 45min. Transitions between trials and sets were performed by means of oral instructions as introduced in section 2.3.4.3.

Performance metrics

During the experiment, several data were recorded, including the obstacle position

x obs , the nger position X f /0 and its velocity Ẋf/0 , the ring position X r/0 and its velocity Ẋr/0 as well as the interaction force with the VE F e (the later being computed from the obstacle and ring positions in the absence of direct force measurement).

These data allowed to calculate the following performance metrics for this experiment:

• v r (t cs ), which corresponds to the speed (along the vertical axis) of the interface's endeector (ring) when its avatar encounters the obstacle, i.e. when contact starts (the corresponding time denoted here as t cs ). This would provide the speed of the user in CC condition (since a mechanical link exists) and approximate user's speed in IC condition (since the end-eector is closely tracking and following the user).

• t cont , represents the amount of time the user stays in contact with the obstacle. It is dened as the dierence t cf -t cs , with t cf being the instant of time when contact was nished. This data informs on the user's reaction time.

• F emax (t) (with t ∈ [t cs , t cf ]) corresponds to the maximum estimated force (along the vertical axis) during contact.

High user speeds are deemed to be the signature of a highly condent user. On the other hand, long contact times and high forces would to indicate that the contact was hard to detect.

Results and observations

The analysis of the benets of both interfaces was assessed based on the performance metrics provided in previous section 2.6.4.

The data of three subjects had to be discarded for data analysis due to unexpected situations that generated extreme metric values. For instance, the recorded F emax values for one of them were zero for nearly half of the trials, while two other subjects manipulated the CC or the IC interface several times at much higher speeds (≈ 0.4m/s) than the rest of the subjects (≈ 0.10m/s), hence completely dierent position and force proles. Therefore data processing was based on data corresponding to only 7 subjects.

Figure 2.34 shows a boxplot where each v r point represents the mean of all trials for each subject at each obstacle position x obs . It can be observed that most of speeds remained lower than |v r | = 0.15m/s (taking into account the speed's absolute value, all speeds being negative as the user was moving downwards). Based on the medians, we can state that the participants reached in general higher speeds when manipulating the CC interface. This observation raises the following question related to the manipulation of the IC interface: why participants move slower in this case? A possible answer could be that they concentrated more on the gesture (which was dicult to perform in this conguration, i.e. follow a vertical line, with the right index nger inside the end-eector and perpendicular to the robot's working plane while at the same time avoiding to touch the robot) than on the task itself. Figure 2.35 shows a boxplot where each t cont point represents the mean of all trials for each subject at each obstacle position x obs . In general, it can be observed a clear trend to stay longer in contact with the obstacle with the IC interface (lower medians in the CC condition). It can be also noticed that the t cont value slightly increases in both conditions when the distance between the home position and the obstacle becomes shorter (the closer the obstacle, the longer the contact).

Figure 2.36 shows a boxplot where each F emax point represents the mean of all trials for each subject at each obstacle position x obs . Here it can be observed that less force was applied with the IC interface. This is somehow interesting since in this case the participant did not require to apply a lot of force to detect the obstacle, which is closer to reality.

Friedman test was employed on the presented data sets in order to asses for a statistically signicant dierence between both interfaces. The performed tests on each of the performance metrics did not show any signicant dierence between CC and IC haptic interfaces (p > 0.05 in all cases).

Conditions

Speed v r (m/s) x 0 0 _ C C x 0 0 _ I C x 0 2 _ C C x 0 2 _ I C x 0 4 _ C C x 0 4 _ I C x 0 8 _ C C x 0 8 _ I C x 1 2 _ C

Conditions

Contact time t cont (ms)

x 0 0 _ C C x 0 0 _ I C x 0 2 _ C C x 0 2 _ I C x 0 4 _ C C x 0 4 _ I C x 0 8 _ C C x 0 8 _ I C x 1 2 _ C C x 1 2 _ I C

Conditions

Force F e max (N) The measured perception (computed from the results of the survey) is shown in gure 2.37. It can be observed that subjects reported similar ease to perceive contact with both interfaces (Q1). On the other hand, they estimated that they applied smaller forces (Q2) using the IC interface (this being consistent with the observations reported in Fig. 2.36).

x 0 0 _ C C x 0 0 _ I C x 0 2 _ C C x 0 2 _ I C x 0 4 _ C C x 0 4 _ I C x 0 8 _ C C x 0 8 _ I C x 1 2 _ C C x 1 2 _ I C
Participants considered that their reaction time was faster in the IC condition (Q3), which is inconsistent with the results reported in gure 2.35. Finally users found the CC interface easier (Q4) and less tiring (Q5) to use.

Q1:

Were you able to detect the obstacle easily?

Conclusion

Generally speaking, no signicant dierence between both interfaces was found, however certain tendencies could be observed. For example, longer contact times and smaller user speeds prior to contact with the IC interface were unexpected but somehow not stunning since learning to use this kind of device was not straightforward. The presented experiment highlighted the fact that a mechanical link, even in free space, as is only present with the CC interface, reassures the user. For an IC interface, any slight haptic stimuli may be necessary to bypass this issue. On the other hand, this tendency appears quite logical. Indeed, in the IC conditions, the user has a bare nger and must be cautious while in the CC condition he has a kind of protecting layer which could unconsciously reassure him (with such a protection he can move quickly without risks of injuries). It would be interesting to test this hypothesis in a future test campaign.

Chapter conclusion and perspectives

Choosing a force feedback interface is not a straightforward task. Besides taking into account the device's metrics (DoF, workspace, inertia, maximum exertable force, etc.), it is fundamental to evaluate its performances in real conditions, i.e. while being manipulated by an user. To this purpose, device evaluation based on psychophysical tests (linking the device performance measures to the limits of human perception) represent a pertinent approach.

This is also true for IC haptic interfaces. Indeed, while the IC paradigm theoretically provides perfect transparency in free space and more realistic haptic interactions at contact, the benets of this type of devices are still not clearly known. Learning about their benets was the purpose of the presented research.

To this end, we performed three experiments: stiness identication, target pointing and blind obstacle detection. It was concluded from the rst experiment that the usage of an IC interface did not signicantly modify the capacity of the subjects to perceive stiness. On the other hand, the target pointing and the blind obstacle detection experiments highlighted somehow that a mechanical link plays an important role to reassure the user, particularly when manipulation occurs in free space. However none of the presented experimental results showed a signicant dierence on performance metrics regarding both types of haptic interfaces.

This is encouraging because it means that, even though an IC interface is less intuitive to manipulate when considering only 2DoF movements (such movements are dicult to perform in this conguration as the user has to move along a given trajectory while maintaining his/her nger inside the end-eector and perpendicular to the robot's working plane while at the same time avoiding to touch the robot), its employ did not impoverish the capacity of the participants to perform the proposed tasks.

In order to encourage the development of more performing IC interfaces it is important to learn on current devices capacities. Ergonomics of IC devices indeed plays an important role since users are intended to use them in the most natural possible way, e.g. the user should concentrate on the task itself and not on how to position his/her hand to make the device work properly. The development of IC haptic interfaces with higher degrees of freedom (≥2DoF) is thus expected to provide more natural manipulations. This will release the aforementioned usage diculties, and one can reasonably make the assumption that in this case IC interfaces will outperform CC devices. Further developments are however necessary to validate this hypothesis.

Finally, IC interfaces remain, from our perspective, a promising approach. We may think of a variety of IC devices congurations, among which end-eectors that can t already existing robotic arms (using the IC paradigm, even those ones that were not designed for haptic interactions can be employed for this purpose).

Introduction

A good force feedback interface should allow stable interactions, whether the user is moving in free space or getting in touch with a VO. In the case of IC haptic interfaces, this is particularly challenging since besides displaying a stable behavior in both modes, the control law must also ensure a stable transition between free space and contact (see Fig. 3.1).

First tested control strategies for IC-HIs were reported in [START_REF] Hirota | Development of surface display[END_REF], [START_REF] Yoshikawa | A touch and force display system for haptic interface[END_REF]] and [START_REF] Yoshikawa | A threedimensional touch/force display system for haptic interface[END_REF]. Such approaches relied on an abrupt transition between free space and contact modes. While simple, this solution can generate oscillations (based on non-passive energetic exchanges) and therefore a non-realistic contact sensation, especially when encountering a VO at high speeds.

On the contrary, an ideal IC interface must switch from closely following the user's movements to a completely stabilized (and usually xed) position prior to be contacted by the user. As abrupt transitions do not fulll this requirement, smooth transition strategies were proposed later. This way, stable transitions have already been accomplished in a previous work [Gonzalez, 2015] with an existing 2DoF IC interface (see section 2.3.2.1 or appendix A for more details on the interface), however only at speeds up to 0.2m/s. For faster movements, oscillations unfortunately reappear.

Contact Free-space

Virtual environment Finger avatar Figure 3.1: Free space to contact transition in real and virtual worlds. This is relatively embarrassing since in practice typical movements in VR environments are performed at speeds up to 4.6m/s [START_REF] Elgendi | Real-time speed detection of hand gesture using kinect[END_REF]. Providing stable free space to contact transitions only up to 0.2m/s thus limits the scope of possible applications.

In order to allow for a larger range of applications, oscillations must be reduced even for high speed contacts. This is the goal of the work presented in this chapter which introduces a contribution aiming to improve the free space to contact transitions at higher speeds (tests performed up to ≈ 0.4m/s). The eciency of our approach was validated using quantitative performance metrics. As we were also interested in evaluating how natural the contact was perceived, we performed user tests as well. To this end, a group of six participants was invited to perform a certain number of taps on a virtual wall at low and high speeds, employing an existing 2DoF IC haptic interface in order to test the current implemented control law (smooth transition strategy) and the novel approach we proposed.

The present chapter is organized as follows: in section 3.2 the current control law implemented on the available 2DoF IC interface (already presented in section 2.3.2.3) is briey recalled. In section 3.3 the proposed strategy allowing to perform stable free space to contact transitions at higher speeds (> 0.2m/s) is detailed. Section 3.4 presents results of the preliminary comparison cases between both control laws and section 3.5 presents the description and results obtained from user tests. Finally, conclusions and perspectives are drawn in section 3.6.

Smooth transition-based control

As detailed in section 2.3.2.3, the control of the IC-HI relies on two modes: free space and contact. The goal of the control in free space is to reduce the tracking error X in order to closely track and follow the user's nger without touching it (see Eq.( 2.1)). Such error minimization is achieved with a proportional derivative controller, which provides the robot with a reference tracking torque τ t (see Eq.( 2.3)).

On the other hand, the goal of the contact mode is to display to the user the mechanical properties of the VO being touched. Such force F e is calculated as an unilateral constraint assuming a viscoelastic compliant VE without tangential friction (see Eq.(2.5)).

Finally, the smooth transition between free space and contact modes is achieved by reducing the inuence of the tracking force F t (send to the robot as a tracking torque τ t ) by a factor β nearby the obstacle. Such transition is illustrated in gure 3.2. While allowing a smooth transition between free space and contact, this algorithm presents in practice an undesired behavior when contacting a VO at high speeds (>0.2m/s):

𝑑 𝑓

oscillations appear when the ring encounters a VO and therefore an unnatural contact is perceived by the user when his/her nger encounters the interface's end-eector, giving the impression of touching a moving object instead of a static one as in real life.

As it will be noticed, the contribution described in the remaining of the present chapter focuses on the transition strategy.

Oset transition-based control

Smooth transition-based control proved to be stable with interactions occurring at low speeds (≈ 0.2m/s) [Gonzalez, 2015]. However at higher speeds (> 0.2m/s) the problem is not completely tackled and the sensation felt at contact may be non-realistic.

In the present section we propose a dierent strategy to perform stable free space to contact transitions for faster movements. Taking the smooth transition-based approach as a base, the proposed approach adds bilateral damping contributing to the stabilization of the robot's end-eector before application of the force feedback. As will be shown later, this comes at the price of a slight shift of the virtual constraint, which remains however imperceptible for most users as proved by the results of our evaluations. Such approach is denoted here as oset transition-based control law.

Principle of the oset transition-based control

In free space, the user can move the interface freely, i.e. no interaction force exists.

When the ring's inner periphery penetrates in a VO, we propose to completely stop it before displaying the VO properties. To do this, a dissipative force is applied on the ring until the interface is static (in practice until | Ẋr/0 | < v th , with v th a threshold introduced to cope with the noise of the speed signal).

In practice, the speed threshold is tuned experimentally. It was set here at v th ≈ 0.02m/s, which corresponded to a static interface with a nger inside the ring. When the mentioned condition was true, the new VO position x ε was dened as the coordinate of the distal point on the inner periphery of the ring, then the VO properties (K e and B e ) were rendered to the user. This algorithm was implemented using a Finite State Machine (FSM) as shown in gure 3.3. Each state description is presented below.

• Transparent state: this state becomes active when the relative distance between the ring avatar to the VO is greater than d β , i.e. d r/e > d β . In this mode only the tracking force F t acts on the ring, implying F e = 0. As soon as the interface approaches the VO and the inner periphery of the ring penetrates into it (d r/e < 0) the braking state becomes active.

• Braking state: in this state a bilateral force F d is exerted on the ring (see Eq.

F e =        if d r/ε < 0 & Ẋr/0 > 0 then F e = -d r/ε (K e + B e s)n if d r/ε < 0 & Ẋr/0 < 0 then F e = -d r/ε K e n else F e = 0 (3.2)

Management of the tracking force

As previously explained, the inuence of the tracking force must diminish when the ring touches the wall, however it must be strong enough for the interface to follow the user's nger when it moves away from the VO. Also, it is important to have a continuous tracking force to ensure that the interface will behave correctly during transitions between free space and contact modes.

In the original control law the inuence of the tracking force F t decreased by a factor β function of d f /e (relative distance between the nger avatar and the virtual environment), to ensure its continuity. This approach makes factor β to reach its minimum value β min when the nger avatar is in contact with the VO.

For the control algorithm presented in section 3.3.1 we proposed to decrease factor β in function of an augmented avatar of the nger. By making its radius equal to R r (that of the inner radius of the ring), the minimum value of F t is already reached by the time the ring's avatar penetrates in the reference wall x e . Indeed, because of the tracking error X = 0, the nger's center position is always in advance to that of the ring in the direction of the motion. This way, the nger avatar will rst penetrate in the reference (x e ) then in the oset (x ε ) VO boundary. This strategy, as well as the corresponding applied forces are illustrated in gure 3.4. When the VO takes its new value at x ε , the augmented nger's avatar is already penetrating into it. At this moment β varies in function of d f /ε (see Eq.(3.3)), following the same principle as in (2.7) and illustrated in gure 3.2, ensuring the continuity of F t .

       if d f /ε > d β then β = 1 if d f /ε ∈ [0, d β ] then β = ( 1-β min d β )d f /ε + β min if d f /ε <= 0 then β = β min = 0.1 (3.3)
When moving away from the VO located at x ε , the augmented nger avatar can be far enough from it in order too fully reactivate the tracking force F t , i.e. d f /ε > d β . When the ring comes back in transparent state (d r/e > d β ) we make β vary again in function of d f /e . This way the continuity of the tracking force is ensured when moving away from the virtual object (see Fig.

Preliminary comparison of control strategies

The aim of this section is to make a preliminary comparison between the smooth transition-based (existing approach) and the oset transition-based (newly proposed approach) control laws.

In order to get valuable results, we will focus here on contacts with a static VO occurring at high speeds (> 0.2m/s), since in such conditions oscillations at contact were observed with the smooth transition based approach.

We are more specically interested in answering the following questions:

1. to which extent the oscillations are reduced with the oset transition-based approach?, 2. how long does it take to the IC interface to reduce its speed to ≈ 0m/s before the user touches it? and 3. how realistic the contact with a VO object is perceived?

Considering this, a VR tapping test on a static VO, i.e. a wall, was proposed to evaluate both approaches. In order to make quantitative comparisons between both approaches, specic metrics allowing to compare their respective performances during a typical encounter were dened.

For the sake of simplicity, in the reminder of this chapter, the smooth transition-based approach will be denoted here as VO-A, standing for virtual object A, and the oset transition-based approach will be denoted as VO-B, standing for virtual object B.

Performance metrics for the comparison between dierent control laws during a typical encounter

In order to compare both control laws, our attention was focused on the behavior of the IC interface when it encounters a VO with a certain speed (low or high as dened in section 3.4.2). We were particularly interested in the Cartesian speed and displacement of the IC-HI end-eector (or ring) during a typical encounter. We focused on two instants of time:

• t r/vo : instant of time at which the ring's inner periphery encounters the static VO at x e and

• t f /r : instant of time when the user's nger contacts the ring (contact detected by means of a capacitive sensor covering the inner surface of the ring).

Therefore the corresponding speeds:

• v r (t r/vo ): speed of the ring when it encounters the VO at x e and

• v r (t f /r ): speed of the ring when it rst encounters the user's nger.

As for displacement, we were interested in the amplitude of the very rst oscillation (rebound) after the encounter with the VO took place, as well as the maximal speed of the ring during this rebound. Based on this, we dened:

• d max : amplitude of the very rst rebound of the ring after encountering the VO and

• v rmax (> t f /r ): maximum speed during the rst rebound.

The above proposed metrics apply for both control strategies. In the case of the VO-B approach, we dened the following additional metrics:

• t vr≈0 : time taken by the interface to stabilize (time to reach a speed v r ≈ 0) and

• ε: oset added on the virtual constraint of reference x e .

The above-dened metrics are related to questions stated in previous section 3.4 regarding the reduction of the oscillations at contact and the time it takes for the interface to stabilize.

Proposed study cases

The experiments were performed using the 2-DoF IC-HI presented in Chapter 2 (see Fig. 2.3). Preliminary tapping tests allowed to observe the behavior of the device in conditions VO-A and VO-B for movements performed at dierent speeds: a user was invited to manipulate the 2DoF IC-HI in order to approach the left vertical wall of the VE of reference (see Fig. 2.5).

Due to the dynamics of the robot, the user entered in contact with the ring before reaching the wall for speeds > 0.5m/s. For this reason, a value of 0.4m/s was chosen as the maximum speed tested (called here high speed). To span a large range of experimental conditions, we also performed the same tests at a much lower speed. A value of 0.2m/s was chosen as a low speed to remain signicantly lower than the high speed value.

The robot's gains were adjusted experimentally in order to ensure an ecient nger tracking while minimizing oscillations at contact. Their values in free space and during contacts are given in (3.4) and (3.5) respectively. We use the same gains K t , B t and K e , B e in both conditions VO-A and VO-B. The dissipative gain B d is dened in (3.6).

A high value is chosen in order to stop the interface as fast as possible (in practice in < 20ms, see Table 3.2). With these values, no noticeable oscillations were observed. It is worth noting that the speed of movement is imposed by the user. In order to ensure that it is close to the aforementioned values, the speed prior to contact was recorded for each displacement to verify that its value was as close as possible to the dened low and high speeds.

Low speed case

The graphical representation of the device's position and speed for a typical encounter obtained at low speed is illustrated in gures 3. No noticeable dierence can be observed between VO-A and VO-B conditions. In both cases, the ring's speed and the rst rebound show a similar prole and also similar orders of magnitude for d max and v r values.

Based on these results, we conducted that the behavior of both control laws is very similar at low speeds.

High speed case

The graphical representation of the device's position and speed for a typical encounter obtained at high speed is illustrated in gures 3.9 and 3.10 for each condition. It can be observed that by the time the user's nger encounters the ring (at t f /r ), the corresponding ring's speed is closer to 0 in VO-B than in the VO-A condition. A reduction of the speed v r (t f /r ) was observed with the proposed approach VO-B.

It can also be observed that the d max value is smaller in the VO-B condition (important oscillations appeared with VO-A). As for the rebound speed v rmax (> t f /r ) it can also be seen that its absolute value |v rmax (> t f /r )| is bigger in VO-A than in VO-B.

These observations let us make the hypothesis that the sensation felt by the user would be more representative of a static object, therefore more natural, if the VO-B is employed.

Conclusion

Preliminary taps on a vertical wall were performed at low and high speeds. Taps at low speed allowed us to observe that the behavior of the interface was similar in both approaches. Taps at high speed allowed us to observe a reduction of oscillations with the newly proposed approach.

User-test-based comparison of control strategies

Preliminary tests let us to make the hypothesis that the speed of the ring when the nger encounters it |v r (t f /r )|, the amplitude of the rst rebound d max and the maximum ring's speed during the rebound |v rmax (> t f /r )| are smaller in VO-B condition compared to VO-A. The aim of the tests presented in this section is to test our hypothesis. To this end, a group of six subjects was proposed to perform a tapping test at low and high speeds in both conditions.

This section is organized as follows: details regarding the participants are given in section 3.5.1, the employed materials are presented in paragraph 3.5.2, the experimental setup in paragraph 3.5.3, the procedure in paragraph 3.5.4 and the proposed data processing in paragraph 3.5.5. Finally, results and elements of discussion are provided in section 3.5.6.

Participants

A total of six people (3 men, 3 women, aged 23-33) were invited to perform the VR tapping task employing an IC haptic interface. A brief explanation of VR and what a haptic interface is was provided during the recruitment process. However, no concrete details on the experiment were given.

This population was composed of people working in the Interactive Robotics Laboratory from CEA, LIST. It accounted for administrative personnel, permanent sta as well as PhD students.

The participants armed to be familiar with computer technology tools, e.g. oce software and multimedia content. Some of them were familiar with specialized software, tactile screens as well as joysticks. On the other hand, most of them already knew what a haptic interface was but most of them had never used one.

Only right-handed volunteers were chosen since the employed IC-HI is mainly suited for this prole. Each participant performed the proposed experiment during one single visit.

Materials employed for the study

In this section the materials employed during the experiments are presented. The focus is given here to those elements that allowed to collect/generate data, in particular:

the IC haptic interface, the VE and a questionnaire employed to perform a survey at the end of each experiment.

IC haptic interface

A description of the IC-HI employed for the user tests can be found in section 2.3.2.1 and in appendix A.

Virtual environment

The VE employed in this experiment is shown in gure 3.11. It is similar to the VE presented in Chapter 2 (see Fig. It is worth noting that the VO-B approach introduces an oset ε on the virtual constraint x e . Visualizing such oset may have an impact on the way the contact is perceived.

It was thus decided to display the nger avatar as stopping at the original virtual wall position irrespective of its real location (see Fig. 3.12). Such action introduces a potential visuo-haptic delay, i.e. the user may see his/her nger avatar touching the obstacle before really ling the contact. Fortunately, as was emphasized by [Vogels, 2004] and [START_REF] Knorlein | Inuence of Visual and Haptic Delays on Stiness Perception in Augmented Reality[END_REF], such visuo-haptic delay is imperceptible if it is lower than 45ms, which is the case here since as it will be seen in section 3.5.6.2 the interface stabilizes in less than 20ms.

Finger avatar

𝑥 𝑒 𝑥 𝜀

Finger avatar

Real avatar location

Seen by the user Figure 3.12: Finger avatar location in VO-B approach.

Questionnaire

A questionnaire was employed to perform a survey on particular aspects of the performed task. This questionnaire was anonymous and the participants could spend as much time as they needed to ll it. The employed questions were the following:

• Q1.Was the contact perceived 1) well before the nger's avatar reaches the wall?

2) slightly before?

3) at the moment the avatar reaches the wall? 4) slightly after? 5) well after?

• Q2.At contact, the wall was perceived as 1) clearly moving to the left?

2) moving to the left?

3) being static?

4) moving to the right? 5) clearly moving to the right?

• Q3.The sensation at contact was perceived as 1) very natural?

2) natural?

3) neutral? 4) unnatural?

5) very unnatural?

Experimental setup

The experiment was performed in an isolated room. The participant was standing up, facing the screen and wearing an anti-noise helmet. The haptic interface was placed on a table so that the user could comfortably place his/her right index nger inside the end-eector and so that a horizontal movement towards the left could be performed easily.

The interface was hidden from the user's sight by a vertical wall. It is worth noting here that the participant visualized a GUI that contained only the VE presented in section 3.5.2.2 whose displayed size was adapted to cover the largest possible portion of the participant's screen. The nger's avatar size was proportional to the participant's index nger diameter.

The experimenter visualized a dierent version of the GUI displayed on a supervision computer. It contained additional options allowing to turn on/o either the VO-A or the VO-B control laws, the force feedback as well as the tracking of the user's nger. Such additional options were not visible for the participant.

Procedure

This section explains the general procedure followed by each participant to perform the proposed experiment. This procedure describes the performed actions since the moment the participant arrives until he/she leaves the room where the experiment takes place.

The user is asked to perform a certain number of taps on a vertical wall located on his/her left at low and high speeds (≈ 0.2m/s and ≈ 0.4m/s respectively) using VO-A and VO-B approaches. This generates four test conditions:

• VO-A Low, • VO-B Low,
• VO-A High and In this gure, it can be observed that a specic training session was planned for each speed, i.e. for low and high speeds. This would allow the user to remember the sensation of moving at low or high speeds prior to the experiment.

Two XL blocks account for the experiments and survey at low speeds, and two XH blocks for those at high speeds. It is worth noting that the survey is lled in each XL or XH block. This way questions on the performed task are easier to answer, rather that answering everything at the very end of the experiment. The average length of the whole experiment was around 1h30.

Welcome

The following stages describe the welcome of a participant:

1. The participant is met at the main hall of the laboratory and taken to the experiment's room.

2. Once in the experiment's room he/she is invited to take a sit and is provided with a letter of consent which explains the global process of the experiment he/she is about to perform and gives details on the following aspects:

• The aim of the study.

• An explanation on how a haptic interface allows to interact with a VR.

• A description of the IC haptic interface.

• A description of the VR task to be performed 3. The participant is asked if there are any questions regarding the global process.

• At this moment a brief resume of the documents is given orally in order to reinforce the understanding of the general procedure.

4. Finally, he/she is asked to sign a letter of consent to validate his/her agreement with the terms of the procedure.

Since this was a voluntary participation, he/she was informed that he/she could quit the experiment at any time and for any reason without generating any particular issue.

Training

As stated at the beginning of section 3.5.4, two training sessions were proposed for each participant: one at low speed and one at high speed. The goal was to train the user to move his/her arm at speeds close to ≈ 0.2m/s (in the low speed case) and ≈ 0.4m/s (in the high speed case).

The training focused on the following aspects:

1. Explaining the experimental conditions to the participant:

Upon presentation of the layout of the dierent elements of the experimental setup, it was explained to the participant that during the experiment he/she was going to be standing up, wearing an anti-noise helmet and facing a screen where the VE was displayed by means of a GUI. In addition to this, it was told him/her that the robot (placed on a contiguous table so that he/she could comfortably place his/her right index nger inside the end-eector) was going to be hidden from his/her sight by a vertical wall.

The anti-noise helmet allowed to reduce the inuence of surrounding parasitic noises, in particular those eventually generated by the haptic interface. When any oral communication had to be established, the experimenter talked louder to the participant so that he/she could listen to his voice, even while wearing the helmet. This would avoid to remove it each time oral instructions were required.

Also, the user's nger diameter was measured prior to the haptic interface manipulation stage, for the purpose of adjusting the size of his/her nger's avatar.

2. Teaching him/her how to manipulate the haptic interface according to the experiment to perform:

The 2DoF nature of the haptic interface had to be taken into account when learning how to manipulate it. Here, it was of crucial importance that the user kept his/her right index nger inside the end-eector (straight and perpendicular to the working plane of the robot) with the nger pad oriented to the left, so that it can make a full contact with the wall (see Fig. The non-respect of the above-described gesture would impact the user's perception and the quality of the data recorded with a contact sensor installed in the inner surface of the ring. The correctness of the participant's gesture was veried by the experimenter and he/she was told to correct it if necessary. Enough time was given to him/her in order to learn how to manipulate the interface.

3. Explaining the structure of the experiment:

The experiment requires the participant to perform a VR tapping task. The action of performing one single tap is denoted here as a trial, this trial being considered as valid if the tap is performed at the expected speed, either low or high. A set corresponds to the fact of performing at least three valid trials for each one of the four conditions (VO-A Low, VO-B Low, VO-A High and VO-B High). Finally, a complete experiment is composed of a dened number of sets (here four sets corresponding to the four experimental conditions). These denitions were explained to the participant prior to practicing the VR task.

Practice of the VR task:

The participant was given enough time to learn how to perform the VR task and and feel comfortable with it.

Stages (1-4) were performed during the rst training session. During the second training session, points (2-3) were briey reminded and the attention was given to point (4).

In all cases, the participant only knew if it was low or high speed and no information about the VO being touched was provided.

Experiment

According on the condition in which training took place (either VO-A or VO-B), the experiment started with a dierent condition. This is illustrated in table 3.1. Each case represents a complete experiment session. Cases were employed alternatively for each participant, e.g. participant 1 performed the experiment using the order stated in case 1, participant 2 performed the experiment using the order stated in case 2, etc. Performing this way would help to avoid any learning eects regarding the VO being touched.

Table 3.1: Experiment structure cases.

Case 1 Training -VO-A Low Experiment -VO-B Low Experiment -VO-A Low Training -VO-A High Experiment -VO-A High Experiment -VO-B High

Case 2 Training -VO-B Low Experiment -VO-A Low Experiment -VO-B Low Training -VO-B High Experiment -VO-B High Experiment -VO-A High

Prior to the experiment, the experimenter activated either the VO-A or VO-B condition (selection of the corresponding control law) by means of the GUI displayed on the supervision computer. In order to start the experiment, the participant was asked to put the helmet and to place his/her right index nger inside the end-eector of the haptic interface.

Oral instructions allowed to perform the transitions between trials. For a single trial, the experimenter proceeded in the following way:

1. The participant was invited to position the nger's avatar approximately at the center of the starting line. Examples of employed phrases were: Once that the participant had accomplished the VR task, he/she was invited to come back to the starting line (if he/she felt tired he/she could remove his/her nger from the interface, however it was preferred no to do this so he/she kept in mind the sensation of moving at the low or high speed). At the same time the experimenter stopped recording data and veried speed and contact sensor data.

The correctness of the participant's gestures was inspected visually during each trial.

Data was also recorded for each single tap and its exploitability was veried in situ to verify the validity of the trial, i.e. correct speed (either ≈ 0.2m/s or ≈ 0.4m/s) and absence of contact with the ring before touching the obstacle. If needed, he/she was told to move slower or faster in order to better approximate the expected speed. Steps (1-3) were repeated until the obtention of at least three valid trials for each of the four conditions.

Once a set of trials was completed, the user was asked to take an obligatory break, e.g. 1 -2min. During this time, the experimenter asked the participant how he/she was feeling with the execution of the VR task and if he/she had any questions. After this, he/she was asked to answer to the survey before keep on going with the next set. An example of scheme of the building blocks of a typical experiment (without the welcome, training and goodbye blocks) is shown in gure 3.17 for case 2 from table 3.1.

Goodbye

At the end of the experiment, a reward was given to the participant before taking him/her back to the hall of the laboratory.

Data processing

The generated data were post-processed in order to perform quantitative comparisons.

Box-plots were employed to analyze the results. Here the median appears inside the box as a horizontal line, the box represents the rst (Q1) and third (Q3) quartiles and whiskers represent minimum and maximum values (see Fig. 3.18). This method allows to observe the dispersion of data around the median as well as outliers without making any assumption on the underlying statistical distribution. Boxplots were applied on the following performance metrics: v r (t r/vo ), v r (t f /r ), d max and v rmax (> t f /r ). In order to assess the perception of the participants and get complementary qualitative comparisons for each experiment condition, we used the results of the survey. The answers were counted as a ve-point Likert scale. Measured perception for each question was calculated using equation (3.7).

P e i = 5 j=1 n A j • j 5 j=1 n A j (3.7)
where:

P e i is the measured perception for question i j is the Likert level A j is the selected option corresponding to Likert level j n A j is the number of participants that answered option A j

Results and discussion

Between 10 and 15 taps were necessary in each case to obtain three valid taps. With a population of 6 participants, this implies that a total of 18 trials were employed for data analysis in each condition, i.e. 3 taps × ( VO-A or VO-B ) × 6 participants.

3.5.6.1 Performance evaluation 0.2m/s and 0.4m/s respectively (a positive value indicates that the ring moves in the same direction as of the user's movement).

Figure 3.20 shows the obtained results for the speed of the ring when it encounters the user's nger (v r (t f /r )). Its absolute value should be as low as possible to realistically simulate a static wall. It can be observed that, at low speeds, the spread of the data is similar in both conditions. At high speeds, a noticeable shift of the spread of this value for the VO-B condition evidences smaller absolute values than in the VO-A condition. oscillations. At low speeds, a slight reduction of this value can be observed for the VO-B case. At high speeds, such reduction is maintained. It is worth mentioning here that the orders of magnitude of d max are similar at low and high speeds, meaning that there may be possible improvements to do at low speeds for the VO-B approach.

VO-A Low VO-B Low

Finally, gure 3.22 illustrates the obtained results regarding the rebound maximum speed v rmax (> t f /r ). It can be inferred from these results that the ring is moving against the user (negative speeds). At low speeds, the absolute value of this speed is slightly smaller in the VO-B condition than in the VO-A case. At high speeds the absolute value in VO-A is higher than in the VO-B case.

Figure 3.22: Speed of the ring center at a time > to f /r .

Stabilization of the interface

The proposed approach VO-B stabilizes the interface at the price of slightly modifying the position of the VO. Table 3.2 provides mean and standard deviation for the stabilization time t vr≈0 and the generated oset ε at low and high speeds. Results show that, in average, the ring stabilizes in ≈ 3ms at low speed and ≈ 13ms at high speed. On the other hand the oset ε remained lower than 3mm. As according to [Vogels, 2004] and [START_REF] Knorlein | Inuence of Visual and Haptic Delays on Stiness Perception in Augmented Reality[END_REF], a visuo-haptic delay is imperceptible if it is lower than 45ms, we can expect here that a human operator wouldn't realize these dierences when performing a tap.

Perception of the participants

The participants were asked to answer three questions upon completion of at least three valid taps in each condition. Results for the measured perception are given in gure 3.23.

Q1 asks if the user perceived the contact before (score 1 or 2), just when (3) or after ( 4or 5) the nger's avatar touched the virtual wall. It provides information on the perception of the visuo-haptic delay (ideal result is 3). Results tend to prove that, both at low and high speeds, the delay of the haptic signal introduced by the VO-B approach tends to not be perceived, in particular at high speeds. This can be correlated to the fact that t vr≈0 < 45ms.

Q2 asks if at contact the touched wall was perceived as moving to the left (score 1 or 2), being static (3) or moving to the right (4 or 5). It tells us if the user was perceiving the rebound (ideal result is also 3). At low speeds, the VO was perceived as similar in both conditions. At high speeds, the perception of the VO-B was felt as being more static.

Finally, Q3 asks if the sensation at contact was felt very natural (1), natural (2), neutral (3), unnatural (4) or very unnatural (5). At low speeds no remarkable dierence was observed. At high speeds, the contact with the VO-B was perceived as more natural. 3.6 Chapter conclusions and perspectives

Conclusions

In this chapter, a new control law intended to improve the contact rendering with an IC haptic interface was introduced. The results of our experiments show that the proposed oset transition-based control allowed to reduce the speed of the end-eector before the user's nger encountered it. The rebound amplitude after contact was also reduced. As a consequence, the contact is perceived as more natural.

The proposed approach stabilizes the interface at the price of slightly modifying the position of the VO, therefore generating a delay of the haptic signal. We found however that the stabilization times remained under the perceptible visuo-haptic delay time, therefore it was not perceived by the participants.

Perspectives

The observed results allowed to notice that with the proposed approach applied on the available IC-HI, some improvement on the stabilization of the interface and realism of the perceived VO was accomplished. It would be interesting to extend the population of participants, e.g. up to 10 or 15 subjects, and perform statistical analysis to reinforce the signicance of the results.

Also, the presented approach was a specic development based on the dynamics of the available IC-HI. Dierent other strategies could be investigated as well, e.g. start applying the dissipative force prior to reach the VO, in order to stop the ring against it without any oset.

In all cases, it would be worth performing a sensitivity study, i.e. a generalized study of the inuence of the dierent parameters of the interface on its performances for the dierent approaches that allow to stabilize an IC haptic interface. To this end, it would be interesting to develop a 1DoF IC-HI with optimal performances as it would allow to span a larger set of parameters than the existing 2DoF device, thus allowing to perform a deeper study of a typical encounter.

An ecient tracking and clean free space to contact transitions depend mainly on the performances of these three elements, i.e. the quality of the tracking information, the adopted control strategy and the ability of the device to follow the controller orders.

Among these elements, the tracking system appears as particularly important as it is the entry point of the system. As an example, to ensure optimal transitions, the conguration of the user must be known precisely and at very high rates so that contacts in the virtual and real worlds are seen and felt at the same time, i.e. allowing to ensure that any existing visuo-haptic delay is imperceptible to the user.

In practice however, the tracking systems of most existing IC haptic interfaces are imprecise. One reason for this is that such devices are often used to interact with the VE using bare ngers [START_REF] Yoshikawa | A threedimensional touch/force display system for haptic interface[END_REF]. As a precise estimation of the conguration of a nger is a complex task, due to large variations in shape and size depending on the user and on the conguration of the hand, its position and orientation are only roughly estimated. Fortunately, several VR tasks are performed employing a tool instead of bare ngers, e.g. dentistry simulators. For such applications, which are very common in VR, it is more interesting to develop IC interfaces providing virtual tool based interaction, hence the requirement of a dedicated tool tracking system.

The following sections aim to provide a methodology towards the design of such a tracking module. We will rst present the tool interaction paradigm for IC haptic interfaces (see section 4.2) as well as dierent strategies for measuring the relative conguration of a handle in reference to the robot (see section 4.3). Then we will dene precise design drivers for the tracking system (see section 4.4). To answer these needs, we will rst make a comprehensive review of representative characteristics of common existing tracking systems (see section 4.5) and sensing technologies (see section 4.6), keeping in perspective the design of an IC non-contact tracking system. Then, we will present the results of a preliminary experimental characterization of a sensor, which was found to be suited for our application (see section 4.7). Finally in section 4.8 conclusions are given.

Tool interaction paradigm for IC haptic interfaces

A close-tracking-type interface (referred here as IC interface) requires a robot endeector equipped with sensors that allows to measure (to track), without contact, the conguration of the user (position or position + orientation) relative to the robot. Thanks to this information the robot will be able to closely follow the user's movements, e.g. his/ her nger position and orientation in free space. When a VO is being touched, the IC interface should be able to come into physical contact with the user and provide force feedback according to the VO mechanical properties, e.g. the object's stiness, ensuring realistic physical interaction between the user and the interface.

To date, developers of IC haptic interfaces have concentrated their eorts on de-vices providing interactions directly on the user's hand, as in [START_REF] Gonzalez | Smooth transition-based control of encounter-type haptic devices[END_REF], Chabrier et al., 2017]. In such approach, precise tracking of the user becomes a complex task since a nger has variable sizes and morphologies depending on the user. Furthermore, it deforms at contact. Estimation of the nger's conguration and shape without contact requires then the employ of a precise and high frequency measuring system, which is ideally as small as possible. Such system introduces in turn the need for precise, high frequency and small unitary sensors that, properly arranged in a dened volume, will provide raw data that will be converted into meaningful conguration information thanks to any adapted data treatment strategy. It is worth noting that it could be theoretically possible, if necessary, to obtain a very precise information about the nger conguration and shape. This would however require an increase of the number of sensors and therefore an increase of the size of the tracking system, as well as of the time needed to treat the data, which is not desirable as it would result in a bulky and heavy measurement system.

Fortunately, as it can be observed in chapter 1, tracking a nger is not always mandatory. Indeed, several VR applications employ haptic interfaces that are manipulated by means of a pen-like end-eector (a handle which is represented in the virtual world by an avatar of a desired shape, e.g. a surgical instrument), allowing kinesthetic (force/position) interactions with the VE. This is much easier to track than a nger as it has a known and xed shape and as it can be equipped with embedded sensors. The development of IC interfaces providing interaction by means of a handle (which avatar can represent any desired tool) is thus very interesting and promising.

As shown in gure 4.1, the tracking system (which can be local or external, see section 4.3) ensures the measurement of the handle conguration without contact in free space.

The robot controller uses this information to closely follow it. At contact, the robot will move so that its end-eector stops where the VO is expected to be, waiting for the handle (hold by the user) to encounter it and provide the corresponding interaction forces.

IC interfaces using a tool-based interaction paradigm aim to simplify the tracking and force feedback tasks. Indeed a tool, on the contrary to a nger, has xed size, shape and mechanical properties. Such characteristics should allow to increase the precision of the conguration calculation. The detection of collisions with surrounding VOs and the calculation of the interaction forces are also simplied since the handle avatar shape is known.

Furthermore, kinesthetic and tactile feedback are made naturally thanks to the mechanical link established between the user's hand and the handle [START_REF] Salisbury | Haptic rendering: introductory concepts[END_REF].

Such a tool based paradigm can nd a particular interest in several applications, in particular for dentistry simulators. In such systems, simulation of light tools used to interact with hard teeth requires haptic devices providing both low inertia (in free space)

and high stiness (at contact) [START_REF] Zhang | DentalTouch: A haptic display with high stiness and low inertia[END_REF]. While classical haptic interfaces can hardly answer these requirements, being either very transparent in free space but unable to render high stiness and large forces or vice-versa, an IC interface would allow to render hard contacts while remaining very transparent as the user can manipulate a handle (representing the dental tool) in free space without feeling the presence of the robot. This would guaranty the natural execution of the task and provide realistic force feedback with better control of the exerted force on teeth and tissues. As previously mentioned for nger-based IC-HIs, a precise estimation of the handle conguration is also fundamental here to improve the quality of the interaction since this information is used to control the robot behavior in free space and at contact. To answer this requirement, a study of dierent tracking approaches to measure the relative handle/ robot conguration is presented in the following section.

Real world Virtual environment

Handle/robot non-contact tracking

Several paradigms can be used to track the handle's conguration relative to the robot's end-eector (here IC haptic interface and robot end-eector will be used indistinctly). Three possibilities can be imagined.

External tracking system

One can use a camera based motion capture system to measure the global conguration of the handle and the robot (see Fig. 4.2). The information of interest, i.e. their relative conguration, would then be obtained at any instant of time by combining these data. This solution is very simple to implement and allows to obtain synchronized measurements of all data. With this approach however, it would be necessary to equip the handle and the end-eector with markers allowing to keep a better track of it. Also, except if using costly high end systems, accuracy and bandwidth are limited. Last but not least, errors associated with the handle and end-eector add up when calculating their relative conguration.

Hybrid tracking system

Another solution is to use a motion capture system to measure the conguration of the handle and the joint sensors of the robot to compute the position and orientation of the end-eector. This solution is relatively simple to implement since it does not require to modify the robot (see Fig. 4.3). Moreover, compared to the previous approach the information on the end-eector is more precise and acquired at a higher bandwidth.

However, the same limitations remain for the handle and the measure of interest (the relative handle/robot conguration): it is once again calculated by combining both infor-mation. In such conditions, inaccuracies of both systems add up, being in certain cases relatively important. In fact, it is generally assumed that the robot will move at low speeds, allowing to compute the end-eector's conguration using the joint sensors data combined with the robot kinematic equations. This solution is however not very precise.

In order to precisely calculate the conguration of the robot's end-eector, it would be necessary to employ the exible dynamic model of the robot [Jubien, 2014] which risks to be complex and needs computing resources to be calculated at a haptic rate (≥ 1kHz).

In addition, motion capture system's bandwidth are usually lower than those employed in robot controllers, introducing the need to use interpolation and/or predictive lters to ensure that both systems work properly together.

Local tracking system

The last and most interesting approach consists in integrating non-contact short range sensors (providing displacement information) directly in the end-eector. This solution gives a direct access to the information of interest and, provided an informed selection of sensors, this information is very precise and fast. This approach was used in [START_REF] Yoshikawa | A touch and force display system for haptic interface[END_REF], [Gonzalez, 2015] as well as in [START_REF] Chabrier | Design and experimental evaluation of an infrared instrumentation for haptic interfaces[END_REF]. In the former, the ring is equipped with a set of eight light-weight optical on-o sensors used to roughly estimate the user's ngertip position in a ring-like end-eector at a frequency of 2kHz. In the second, the end-eector is instrumented with sixteen infrared proximity sensors allowing nger shape reconstruction and precise estimation of its position at a frequency of 300Hz. In the later, nine infrared proximity sensors are used to identify the relative conguration between the ngertip and the surrounding cap in 5DoF at 1kHz. Therefore, eight sensors are positioned around the nger in two planes perpendicular to the nger axis and the last one is placed in front of the nger.

Despite the fact that it requires the development of a specic measuring system, this approach was considered the best suited for our application since the tracking of the handle would be done with a single measure, reducing the accumulation of tracking errors. The tracking system of an IC-HI is in charge of measuring, without contact, the relative conguration between the handle held by the user and the robot, either in 3DoF (position) or 6DoF (position and orientation). Its aim of is to provide the robot with the necessary information so that it can compensate for any position dierence and follow the handle's trajectory in free space and so that it can properly manage contacts with VOs.

These demands are partially similar to the requirements associated with motion capture systems usually used in VR to measure precisely and at a high frequency rate the 6DoF conguration of dierent parts of the user's body (e.g. head, eyes, arms, hands, ngers, trunk, legs and/or feet depending on the targeted application). Indeed this information is also used to control the conguration of the user's avatar and manage the contacts with the environment. This is also true for haptic interfaces, with a mechanical link between the user and the robot and with focus on the hand however.

In all cases, the global aim is to avoid tracking technologies that bothers the user and, as a consequence, reduces the immersion and quality of the interactions with the VE. In the case of haptics, a mechanical inuence of the sensor on the system has to be avoided for haptic applications, specially kinaesthetic ones [START_REF] Hatzfeld | Engineering Haptic Devices: A Beginner's Guide[END_REF]]. In the case of IC haptic interfaces providing tool based interactions, mechanical inuence of the tracking system is somehow forbidden. It is then not advisable to add heavy tracking systems to the hand of the user since this will potentially make the user uncomfortable and/or fatigue faster.

In summary, despite the fact that there is no universal tracking system (dierent technologies, which are more or less complex and performant, exist), VR applications and IC interfaces tracking systems share common requirements. An ideal tracking device would need to meet a series of criteria, sometimes not compatible between each other.

These requirements are shown in gure 4.5

Self-contained

Does not require additional elements placed on the human or environment

Complete

Allow 6DoF motion tracking

Robust

Temperature, moisture, magnetic field, radiofrequency noise

Small

≤ size of a chip

Accurate

(<1mm, <0.1°) Fast (>1kHz)

Occlusion insensitive

The device does not need a direct view of the sensor. Cheap

Wireless

Unlimited workspace

Ideal Tracking System

Figure 4.5: Ideal tracking system requirements (adapted from [START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF]).

Adaptation to the case of an IC-HI

Previously mentioned requirements hold for any VR tracking system. Some of them remain however quite general and require to be more specically instantiated in the context of an IC-HI local tracking systems. Each of the above mentioned criteria will be further discussed in the sequel.

Completeness, robustness, cost and size

These requirements are still valid in the context of an IC-HI local tracking system.

They hold as stated in gure 4.5.

Self-containment and wires

The use of a tool as interaction-media (instead of a nger or any other body part)

allows to equip the handle, if necessary (e.g. to allow for a higher measurement precision), with active elements (e.g. active emitters or receivers). A special care should however be taken to keep the handle wireless in order to avoid any additional eort caused by the cables. Fortunately, this can be easily avoided by supplying the active elements mounted on the handle with small embedded batteries.

Occlusions, workspace and accuracy

With a local tracking system, the handle is always kept in front of the end-eector (provided an adapted control of the device). As a consequence, there are inherently no occlusions. The counterpart of this advantage is that the workspace is directly limited by the robot's range of motion. This means that the robot should be selected adequately for the tasks of interest. Also, a sucient space should be left between the handle and the end-eector, so that the robot has a sucient time to react to any user's movement in free space and follow them without handle/robot collision. This introduces in turn some constraints on the local tracking system range of measurement and precision.

Tracking accuracy

The IC paradigm implies that force feedback should be provided to the user only when he/she touches the IC interface in order to provide clear free space/contact and contact/free-space transitions synchronized with the virtual scene.

From a control point of view, the robot is governed by two laws (or modes): the free space mode (that ensures tracking and close following of the handle) and the contact mode (responsible for providing the corresponding interaction forces with VOs). The transition between these two control modes is made when the handle avatar (HA) makes contact with a VO, i.e. when the minimum distance d HA/V O between them becomes negative. In the real world, it should correspond to the exact moment of the physical contact between the handle and the IC interface. A perfect synchronization of these two events in both real and virtual worlds is the goal to attain even if it is not that easy to achieve.

In order to reach an acceptable synchronization (i.e. an imperceptible visuo-haptic delay) it is necessary to precisely determine the distance d handle/robot between the handle and the robot (see Fig. 4.6) in order to provide a force feedback that corresponds to the to calculate the conguration of the tool. Next, the handle conguration is sent to the robot's controller which calculates the necessary torques that should be sent to the robot's actuators to cope with the handle displacement and reduce the position and orientation tracking error (see Fig. 4.7 for an illustration of the position tracking error X ). Of course, the robot will not react immediately, its reaction time depending on the actuators and robot's dynamics. As a whole, this measurement and tracking process introduces an inherent delay. As a consequence, the robot won't move exactly at the same time as the handle does.

This tracking error must be taken into account when dening the size of the inner volume size of the IC interface. This volume should be large enough to avoid the handle touching the robot while the user is manipulating it in free space. The IC haptic interface should however also remain as small and light as possible for an easy integration on a robot.

A careful optimization should thus be performed in order to nd the best possible tradeo between a small end-eector and an end-eector suciently large to ensure movements without handle/robot collisions in free space. Within this context, a gap between the handle and the IC interface just larger than the maximum tracking error appears as the best solution.

Tracking error 𝝐 𝑿 One may think of employing a real robot to perform a tracking error identication task, i.e. make the robot to follow a known trajectory with well dened speeds and accelerations, and identify the maximum tracking error Xmax for such platform. Such an experiment would however be complex to set-up.

IC interface Robot

Another method that is simpler (especially if the robotic platform is not available at the moment of the design) and that consumes less resources is to simulate the behavior of the whole system to identify the maximum tracking error. Therefore, it is necessary to make some assumptions regarding both the operator's dynamics (which will constrain the handle's movements), the control law and the robot (which will constrain the following dynamics). It is worth noting that, in a rst step, a 1-DOF simulation is sucient. Such approach that consists in simulating a trajectory-follow task employing a 1DoF IC haptic device model, which characteristics are representative of a whole force feedback device, has been employed in [Gonzalez, 2015] to dimension a 2-DOF IC-HI's end-eector.

Regarding the operator's dynamics, the movement of the user's hand can be modeled using a mathematical model that matches observed straight unconstrained point to point arm movements [START_REF] Tamar | The Coordination of Arm Movements: An Experimentally Conrmed Mathematical Model[END_REF]. This model, which results in a minimum jerk trajectory, was slightly modied in its notation by [Gonzalez, 2015] and its formula is given here in (4.1).

x

h (t) = x A + (x B -x A )(6t 5 rel -15t 4 rel + 10t 3 rel ) (4.1)
where

x h (t) is the hand position, x A and x B are the start and end positions respectively and t rel = t/t B is the motion relative time (with t B the end time and x h = x A , when t = 0s).

From equation (4.1), the arrival position x B which corresponds to a motion time t B can be expressed in function of the human speed ẋh,max and acceleration ẍh,max . Their mathematical expressions are given in equations (4.2) and ( 4.3) respectively.

x B = 128 ẋ2 h,max 45 √ 3ẍ h,max (4.2) t B = 16 ẋ2 h,max 3 √ 3ẍ h,max (4.3)
Speed ẋh,max and acceleration ẍh,max order of magnitudes should be representative of reasonable human arm movements. A non-exhaustive research allowed us to identify some reference values of typical hand's speeds and accelerations related to VR applications (see in Table 4.1). From this table, we chose medium values of speed and acceleration for our simulations, i.e. 1.6m/s and 23m/s 2 .

Regarding the controller, we used a PD coupling scheme between the handle and the robot. Proportional-Derivative controllers are usually employed with force feedback devices. One main reason is that it allows to eciently simulate sti surfaces (with a PD controller, the surface of virtual objects appears as if they were modeled by a Mass-Spring-Damper, which can be used to simulate a large variety of typical environments).

Also, provided the PD gains are chosen adequately, the system is passive, i.e. stable for any user behavior. 1): [START_REF] Tamar | The Coordination of Arm Movements: An Experimentally Conrmed Mathematical Model[END_REF], ( 2): [Elgendi et al., 2012a], ( 3): [Nagasaki, 1989] and ( 4): [Gonzalez, 2015]. Finally, regarding the robot, we chose to use the Skills haptic device as a reference.

Movement description

This haptic interface was developed at CEA, LIST for the simulation and training of maxilla facial surgery procedures [START_REF] Gosselin | Specication and design of a new haptic interface for maxillo facial surgery[END_REF]. It was more specically tailored to meet the requirements of corticotomy surgical procedure [START_REF] Hassan | Corticotomy-Assisted Orthodontic Treatment: Review[END_REF] x h . The Cartesian error is then used to compute the error at the joint level, which serves as an input for the PD controller to calculate the joint torque τ and then the saturated torque τ * s , which maximal and minimum values are xed by the peak torque The expression of the PD controller at the joint level is given in equation (4.4). In order to identify the controller gains providing the smallest possible tracking error X min (i.e. the smallest of the maximum tracking error values generated at each simulated round-trip displacement), a large range of values were tested in order to observe the error distribution. The proportional gain was chosen between 0 ≤ K p ≤ 10000N/m with a step of 100N/m and the derivative gain between 0 ≤ K d ≤ 100Ns/m with a step of 1Ns/m. Using this step sizes 10000 tracking error X values were obtained. Their distribution is shown in the abacus from gure 4.9.

τ pk = ±F pk • l r = ±7.5N • m.
τ t = K p l 2 r (θ h -θ * r ) + K d l 2 r ( θh -θ * r ) (4.4)
These results show that the smallest tracking error that can be attained is | X min | ≈ 3.7mm. This value is obtained when employing gains equal to K p = 3636N/m and K d = 90Ns/m.

It is worth noting however that these gains cannot be attained in practice. Referring to the Skills technical documentation [START_REF] Gosselin | Proces verbal de recette: Virtuose 6D Médical EVO II[END_REF], it was noticed that the gain K d that proved to be stable on real platform is limited to K dθ = 4Nm/rad/s at the joint level, which corresponds here to K d = K dθ /l 2 r ≈ 45Ns/m, which is half of the one obtained in simulation. Simulation results for a round trip movement using these gains are shown in gure 4.10. The corresponding tracking error value is equal to | X | ≈ 4.6mm. It can then be said that a spherical volume of radius r ≈ 4.6mm should be taken into account in the process of dening the size of the inner volume of the IC end-eector. For practical purposes, a sphere with a diameter of 1cm will be taken into account.

Working frequency

It is known that a servo rate of 1kHz is commonly employed for adequate haptic rendering [START_REF] Salisbury | Haptic rendering: introductory concepts[END_REF]. This value appears to be a good compromise allowing to present reasonably complex objects with reasonably sti values. Higher stiness, e.g.

to provide crisper contacts, would require to increase the working frequency, which implies to reduce the complexity of simulated objects or to employ more powerful computers.

Specications of an IC interface

An IC haptic interface allowing tool based interactions should be equipped with an adapted end-eector. For this design, it is important to take into account the following aspects:

• The handle, hold directly by the user's hand, should be light and easy to manipulate.

• The handle should be adapted to the tasks of interest. Here, with focus on surgery, we will make the assumption that the handle has a cylindrical pen-like shape, with a comfortable diameter of around 15mm.

• The tracking system's weight should be as small as possible so that the robot is able to displace it and provide expected tracking and force feedback behaviors. Weight has an inuence on the stability of the haptic loop.

• The end-eector should allow to constrain the handle in all directions (in position only or position and orientation).

The tracking system (providing 3 or 6 DoF information) requires to be placed between the haptic device and the handle being manipulated by the user. For the former, four main design drivers were identied: minimum distance of measurement (allowing to precisely control the transitions between free space and contact), range of measurement (which should be sucient to cope with any user's movement), high working frequency (for a stable control of the haptic device) and high accuracy (to reduce error accumulation).

The corresponding values are summarized in Table 4.3.

Designers usually use several unitary 1DoF sensors for the realization of such tracking system, however it remains interesting to explore already available tracking systems possibly suiting the development of an IC handle tracking system. Principle and representative characteristics of common existing tracking systems will be presented in next section 4.5. The required sensing technology, accuracy, size, working frequency and resolution will depend mainly on the measuring necessities and on the constraints of the environment where such sensors will be employed.

In the present section, our interest focuses on the tracking systems mainly employed .12: Mechanical linkage tracking paradigm (adapted from [START_REF] Rolland | A Survey of Tracking Technology for Virtual Environments[END_REF]).

Conclusion

Despite the eciency of a tracking system employing mechanical linkages (e.g. high resolution and high frequency), this approach is not suited to perform the tracking of the handle of an IC haptic interface, since the IC paradigm relies on obtaining the relative handle/robot conguration without any contact at all. This approach will thus not be further discussed.

By Ultrasonic waves

Ultrasonic sensors composed of co-localized emitter/receiver pairs are commonly used in mobile robotics and in the automotive industry as proximity sensors. In such case however, only the distance to the nearest object is required and obtained, and not the distance to a specic point or object of interest.

For precise tracking purposes, it is necessary to be able to compute the distance to specic points or surfaces. This can be made using separate ultrasonic emitters and receivers, as will be exemplied below with the time of ight method, or by purposely associating dierent emitter/receiver pairs with specic surfaces of the target, as will be explained in section 4.5.2.2 for the phase-shift method. Both methods and their respective merits will be discussed hereunder.

Time of ight method

By simply measuring the duration of the travel of an ultrasound wave between an emitter and separate receiver (i.e. the time of ight t tof ) it is possible to compute the distance between them. Knowing the travel speed of ultrasonic waves (which depends on the physical medium, e.g. in dry air with a temperature of 20 • C, the speed of sound is c = 343.2m/s). The traveled distance l can be calculated using (4.5). Receivers [R 1 , R 2 , R 3 ] are located at xed positions along the axes of a Cartesian coordinate system (adapted from [START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF]).

In order to obtain orientation information, it is necessary to calculate the 3D position [START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF]). Table 4.4 provides time of ight distance measurement representative performances based on ultrasonic sensors. Table 4.4: Time of ight distance measurement representative performances based on ultrasonic sensors [START_REF] Rolland | A Survey of Tracking Technology for Virtual Environments[END_REF], Mihelj et al., 2014[START_REF] Maxbotix | Innovative ultrasonic sensors[END_REF], Farnell, 2018] Sensor type Ultrasonic

Measured variable

Distance based on time of flight of an acoustic wave

Physical phenomenon

Transmission or reflection of acoustic waves Weight / Size Lightweight / Diameter in the order of 1cm

Measuring range

Few centimeters up to few meters, e.g. 20mm-10000mm

Working frequency

Imposed by the pulse trip time, e.g. for c = 343.2m/s and 𝑙 𝑢 = 10cm: 𝑡 𝑡𝑜𝑓 ≈ 0.3ms ➔ 𝑓 ≈ 3.3kHz (for separate emitters and receivers) 𝑡 𝑡𝑜𝑓 ≈ 0.6ms ➔ 𝑓 ≈ 1.6kHz (for co-localized emitters and receivers)

Accuracy

Depends on the constancy of the velocity of sound Needs to equip target?

Target is preferably equipped with ultrasonic emitters

Degrees of freedom (DoF)

-Distance measurement (1DoF) -6DoF pose calculation based on an arrangement of sensors

Implementation

Requires optimized target design to allow reconstructing the target pose from the distance measurements if using co-localized sensors.

Occlusion sensitive

Yes Price Low cost

Strengths (✓) / Weaknesses (✗)

✓: Elementary sensors are simple, low cost and relatively small ✓: Not affected by color or other visual characteristics ✓: Longlasting ✗: Sensitive to temperature, pressure and humidity which affects the velocity of sound thus the accuracy of measured distances ✗: Sequential triple emission of sound signals and speed of sound in air limit the update rate ✗: Signal losses energy with the traveled distance, which limits the measuring range

Applications

Medical imaging, parking systems of cars, liquid level detection, robotics

It is worth noting that it is also possible to use classical ultrasonic sensors composed of co-localized emitters and receivers. This solutions appears however less interesting here.

Indeed, in this case the time of ight t tof will not represent the time required for the acoustic wave to travel from the emitter to the receiver but the time required to travel from the emitter to the target on which the ultrasonic wave is reected plus the time required for this wave to travel back to the receiver, i.e. l = (ct tof )/2. As a consequence, the acquisition frequency is divided by a factor of 2. Also, it is required either to use dierent frequencies for each sensor or to separate the sensor/reecting surfaces pairs in order to avoid cross talk between the dierent sensors. Finally, the geometry of the target must be precisely dimensioned and manufactured so that the 3D or 6D pose of the target can be computed from the dierent measurements which are potentially coupled and which can vary non-linearly with the elementary target movements (e.g. a translation in a given direction or a rotation around a given axis).

Phase-shift method

Another strategy allowing to calculate the distance between an ultrasonic sensor and a target consists in measuring the phase-shift between a reference signal produced by the emitter and the same signal reected by the target (see Fig. [START_REF] Rolland | A Survey of Tracking Technology for Virtual Environments[END_REF]).

Contrary to the TOF technique which relies on emitted pulses, here a continuous signal is being measured to determine the phase dierence, allowing to obtain high update rates [START_REF] Rolland | A Survey of Tracking Technology for Virtual Environments[END_REF]. On the other hand, the relative motion between two measurements will be limited by the size of the wavelength of the signal. Furthermore, cumulative errors appear during the measuring process.

Generally speaking, this method is more accurate, however it requires complex hardware able to measure the phase-shift [START_REF] Gueuning | Accurate distance measurement by an autonomous ultrasonic system combining timeof-ight and phase-shift methods[END_REF]. Also, as for TOF sensors using co-localized emitters and receivers, this solution allows only to measure the distance between a sensor and a surface, not the distance between the sensor and a specic point of the target. As emphasized in the previous paragraph, it is then complex to infer the conguration of the target from such measurements. Table 4.5 provides representative characteristics of the phase-shift approach based on on ultrasonic sensors.

Table 4.5: Phase-shift distance measurement representative performances based on ultrasonic sensors [START_REF] Gueuning | Accurate distance measurement by an autonomous ultrasonic system combining timeof-ight and phase-shift methods[END_REF], Rolland et al., 1999, S. Huang et al., 2002] Sensor type Ultrasonic

Measured variable

Phase shift

Physical phenomenon

Acoustic pulse propagation Weight / Size Lightweight / Diameter in the order of 1cm Measuring range 4mm to 1500mm

Working frequency

Since a continuous signal is being measured, higher sample rates can be obtained

Accuracy

Higher accuracy than employing TOF technique Needs to equip user/env Not required

Degrees of freedom (DoF)

-Distance measurement possible (1DoF) -6DoF pose calculation based on a sensor array is possible

Implementation

-Requires complex hardware to measure the phase -Requires optimized design of the target to allow reconstructing the target pose from the distance measurements

Occlusion sensitive

Yes, ultrasonic waves are reflected on obstacles.

Price

Low cost

Strengths(✓) /Weaknesses (✗)

✓: Simple, cheap and relatively small ✓: Not affected by color or other visual characteristics ✓: Longlasting ✓: More accurate than TOF technique ✓: Higher sample rates than with TOF can be attained ✗: Sensitive to temperature, pressure and humidity which affect the propagation of the sound thus the accuracy of measured distances ✗: Signal losses energy with the traveled distance, which limits the measuring range ✗: Error cumulation due to relative distance measurements ✗: Range of measurement limited by the wavelength

Conclusion

Representative performances attainable with ultrasonic sensors were presented in tables 4.4 and 4.5. Considering the design drivers for an IC haptic interface dened in section 4.4, we conclude that ultrasonic sensors are not adapted to this application for several reasons explained in the following lines.

First of all, the implementation of a 6DoF tracker based on ultrasonic sensors would occupy an important volume, as these sensors are relatively cumbersome. It would not be possible to integrate several sensors necessary for a 6DoF measurement in a volume of few centimeters. As an example, using 3 emitters and 3 receivers as shown in gure 4.14 would require a handle with a diameter of a least 2cm if the emitters are about 1cm large, hence an inner volume of the end-eector in the order of 3cm as the range of motion of the handle is equal to ±0.5cm. The minimum distance of measurement of such sensors being 2cm, they should be placed on a 7cm diameter sphere. The receiver's size being also about 1cm, the resulting end-eector diameter would be at least 9cm, probably without taking into account integration constraints. This is much more than what is acceptable for a small haptic interface like the Skills robot.

Also, the reported measuring ranges are not adapted to our application (few millimeters to several centimeters). On the other hand, an accuracy below 1mm can be obtained by combining TOF and phase shift techniques [START_REF] Gueuning | Accurate distance measurement by an autonomous ultrasonic system combining timeof-ight and phase-shift methods[END_REF]. Still 0.1mm as required here is challenging. Furthermore phase-shift technique is limited by the wavelength size.

Finally, it is dicult to ensure that the working frequency of ultrasonic sensors, which is imposed by the distance separating the sensor from the target and by the speed of sound in the physical medium between them, will be compatible with what is required in a haptic control loop (1kHz). Sampling rate can be improved by employing the phase-shift approach, however ultrasonic waves remain inuenced by the enviromental perturbations as temperature, pressure, humidity and unwanted obstacles. Even if a single measurement can be made at a very high frequency at a short distance (e.g. 17kHz for non-colocated emitters and receivers separated by a distance of 2cm, i.e. the minimum distance of measurement for such sensors), this frequency will quickly drop with the distance and the number of DoFs as the dierent targets have to be acquired sequentially. The sampling rate can be improved employing the phase-shift approach. However in both cases ultrasonic waves remain inuenced by the environmental perturbations such as temperature, pressure, humidity and unwanted obstacles.

By magnetic eld

The principle of operation of an electromagnetic sensor consists in measuring the local magnetic eld produced by an emitter in the sensor's surroundings. Even if the magnetic eld of the Earth can be employed as a reference, such measurement would not be accurate enough in practice. For this reason, it is necessary to use an emitter to create the reference magnetic eld for measurement purposes.

This principle can be used to design 6DoF contactless sensors. The most important points related to the 6DoF tracking of a target based on magnetic elds are explained in [START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF] and will be presented in the following section.

6DoF magnetic induction based tracking

As shown in gure 4.16, when a current ows through a wire, a magnetic eld is created (if such wire is shaped in order to become a coil with several loops, the intensity of the resulting magnetic eld will be more concentrated and stronger than with a single loop).

Magnetic field

Magnetic field vector at the center of the coil Wire or coil It is worth noting that the magnetic eld vector vary in space both in direction and magnitude. At the center of the wire/coil, the magnetic eld vector B is normal to the coil and its magnitude is proportional to the eld's strength H. The relationship between B and H is given in (4.6), where µ 0 is the magnetic constant.

B = µ 0 H (4.6)
Outside the wire/coil axis and at a distance R from its center, the magnetic eld vector B is given by the equation (4.7).

B = µ 0 M 4πR 3 (2a R cos ϕ + a ϕ sin ϕ ) (4.7)
where M = N Iπb 2 (with N the number of loops of the coil, I the current owing through it and b its radius) is the magnetic dipole (assuming R b, the coil can be approximated as a magnetic dipole), R is the distance between the center of the coil and the point of interest, ϕ is the angle between the normal to the coil and a vector linking the coil center to the point of interest, a R and a ϕ are the radial and tangential unit vectors.

All these parameters are illustrated in gure 4.17. .17: Magnetic eld density vector near the coil (adapted from [START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF]).

Motion tracking based on the electromagnetic principle relies on the phenomenon of coupling, i.e. if a second coil (used as sensor) is inserted in the reference magnetic eld produced by the coil of gure 4.17 (used as a source), a current is generated in the former.

The amplitude of this signal being function of the reference magnetic eld's local intensity and direction (known from Eq. (4.7)) as well as of the relative orientation between both coils, it is possible to infer information on their relative conguration from the measured current.

Of course, a single source/sensor pair is not sucient to compute a 6DoF conguration.

To determine the position and orientation of a target in space, a magnetic tracking system employs in practice three orthogonal active coils on the source side and three orthogonal passive coils organized in a similar but usually smaller conguration on the target. A changing magnetic eld is sequentially generated in each coil of the source. These signals generate electric currents in the passive coils located on the target. The measurement of these currents nally allows to estimate the 6DoF relative conguration between the source and the sensor (see Fig. 4.18). Figure 4.18: 6DoF tracking principle based on magnetic eld measurements (adapted from [START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF]).

Conclusion

Even though a magnetic tracking system is able to directly measure the pose of a target without contact, their bandwidth and accuracy do not meet the dened design drivers for an IC haptic interface. Furthermore, they are mainly wired (inconvenient for free space movements) and magnetic sensors measurements are perturbed by metal parts which are typically part of a robot.

By optics

Several types of optical sensors, usually used for 6DoF measurement in VR and/or robotics, can be envisaged for the tracking of the handle of an IC-HI. Their principle of operation and respective merits will be introduced below.

Motion capture system

Motion capture (MOCAP) is regularly employed in several application domains, e.g. computer animation, biomechanics, robotics, cinema, video games, anthropology etc.

Three main types of optical motion tracking systems exist, based on the following paradigms [START_REF] Field | Human motion capture sensors and analysis in robotics[END_REF].

MOCAP with passive markers. Here at least two xed cameras are used to compute, by triangulation, the 3D position of one or more passive markers placed on the target.

Provided the relative position of at least three targets is xed, it is possible to reconstruct the 6D pose information of the target. IR lighting and high-speed IR cameras are usually used to avoid visual pollution, e.g. visible light. The markers are also usually coated with a retroreective tape or painting to increase the image's contrast. With such systems, tracking frequencies of up to 2kHz can be obtained.

Ono main advantage of this solution in the context of human MOCAP is that the target, in this case the user, is not weighted with batteries or cables. Its main disadvantage is related to occlusions. As soon as a target cannot be seen by at least two camera, its position cannot be computed. Occlusion problems can be overcome with the use of more than two cameras and/or supplementary markers, however it augments the processing time. Such system also suers from non-portability and limited workspace. Figure 4.20 shows a Vicon motion capture system employing passive markers. This system is used in conjunction with a humanoid robot aiming to match the user poses in real time.

When considering the tracking of the handle of an IC-HI, the occlusion problem vanishes. Indeed, it can be hypothetized that the design of the system will ensure that the targets are always in front of the cameras, all the more that the range of motion of the handle is limited. However new disadvantages appear. First, the size of the targets, usually in the range of 2mm to 1cm, would result in a cumbersome handle. Second, the integration of lighting systems and cameras in the robot's end-eector would make it large and complex. Finally, the minimum range of measurement, usually in the order of few tens of centimeters, is not adapted in our case. Even if it could be reduced with a dedicated design and optics with shorter focal lengths, it would probably remain around at least a few centimeters. Globally, this solution does not seem very well suited for the local tracking of the handle of an IC-HI.

Cameras

Markers Figure 4.20: Vicon motion capture system (adapted from [START_REF] Shon | Towards a Real-Time Bayesian Imitation System for a Humanoid Robot[END_REF]).

MOCAP with active markers. Here the markers are infrared emitting diodes (IRED) acting as light sources. Their light is usually multiplexed and as a result the frequency of the acquisition is divided by the number of sources to detect. Even though this solution has the advantage that each light source can be individually identied, this approach limits the measurement frequency.

Within the context of human MOCAP, this method has the advantage over the previous one that, since it employs active markers, the measurement area is theoretically higher than with passive ones. In this case however, the user should be equipped with batteries and wires allowing the light sources to work, which contribute to impede motion.

When considering the tracking of the handle of an IC-HI, this is no more a disadvantage since the handle can be equipped with a small battery locally supplying power to the IREDs which are usually small enough to be integrated on the device. However, the problem remains on the side of the robot, with cameras which will require a large and complex end-eector, even if in this case the problem is a little less acute as the IR lightning system is no more required.

Markerless MOCAP. This paradigm represents an active area of research and employs only one set of camera(s) from one angle of view without requiring to mount any type of markers on the tracked object. This approach relies upon image segmen-tation techniques to nd human posture which may be matched to a human template [START_REF] Sigal | HumanEva: Synchronized Video and Motion Capture Dataset and Baseline Algorithm for Evaluation of Articulated Human Motion[END_REF]. Other common approaches employ background scene substraction techniques to extract a silhouette as in [START_REF] Li | Expandable Data-Driven Graphical Modeling of Human Actions Based on Salient Postures[END_REF] as well as learning algorithms as in [START_REF] Elgammal | Tracking people on a torus[END_REF]. These techniques are noisy, generally not real-time and are highly sensitive to lightning conditions. They do not seem well suited for the tracking of the handle of an IC-HI. [START_REF] Field | Human motion capture sensors and analysis in robotics[END_REF].

Sensor type Motion capture

Measured variable

Targets positions Physical phenomenon (Emitted or reflected) IR light intensity measurement Weight / Size

Cumbersome (requires at least two cameras)

Measuring range

Minimum distance of measurement in the order of few centimeters for a dedicated design

Working frequency

Image capture up to 2kHz. With active markers the camera speed is divided by the number of markers to detect. Precision < 1mm

Target instrumentation

Yes (only the targets and their supports with passive markers, with additional batteries and cables with active markers) Degrees of freedom (DoF) 6DoF pose calculation possible

Occlusion sensitive

Yes in the context of human MOCAP, not for the tracking of the handle of an IC-HI, provided a specific design Price Expensive The camera sensor is usually made of high resolution linear discrete photodiodes, commonly a CCD (charged-coupled device) or a CMOS (complementary metal-oxide semiconductor) row. These systems provide a working frequency higher than 1kHz and an accuracy below < 10µm [START_REF] Hatzfeld | Engineering Haptic Devices: A Beginner's Guide[END_REF]. However, compared to other optical sensors, this technique remains expensive as a detection row with a sucient resolution highly impacts its cost. While very precise and having a high bandwidth, this technology does not seem very well suited for the tracking of the handle of an IC-HI. Indeed laser triangulation only provides 1DoF information. In order to get the 6DoF pose of the handle, at least 6 similar systems would be required, hence a very large and expensive system. Also, as was explained in the section related to ultrasonic sensors, the handle would have to be properly designed in order to ensure a proper reection of the dierent lasers without cross-talk nor a too complex transformation matrix between the sensor's measurement and the handle pose.

Strengths

Laser time of ight

The distance to an object can also be measured using an optical distance sensor. A diode or laser serves as a light source and illuminates the distant object, and a photodiode, CCD or CMOS sensor, placed either close to the emitter or on the target, is used to detect this light signal. The TOF measurement principle is then used in the same way as with an ultrasonic sensor, except that here the signal of interest is light instead of sound.

Laser rangenders belong to this category of sensors allowing to measure a distance by TOF with a light source. In such systems, the sensor is just beside the illumination system, and the target does not need any equipment. However, they are usually relatively cumbersome and tted to medium (i.e. few meters) to long range (i.e. few hundreds of meters) 1DoF distance measurement in the eld of construction and public works. They do not seem adapted for the measurement of short distance 6DoF tracking of the handle of an IC-HI and will not be further discussed here.

It is worth noting however, that very compact and close range ToF sensors were recently announced. An interesting technology based on the ight time of an infrared wave for short-range measurement is the ST microeletronics VL6180 sensor which reference information can be found in [ST Microelectronics, 2016]. Unfortunately, this sensor suers from a low accuracy (measurement noise up to 2mm between 0 and 100mm). It is also sensitive to temperature (up to 15mm drift) and voltage (up to 5mm). This low accuracy is prohibitive for precise handle tracking. [START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF]). Table 4.9 provides representative characteristics of 3D imaging systems based on light pattern projection.

The present strategy can be classied as part of the outside-in paradigm which Table 4.9: Light pattern projection representative performances [Geng, 2011].

Sensor type

Camera

Measured variable

Distance (3D points)

Physical phenomenon

Light projection Weight / Size

Relatively big (requires one projector and one camera in a dedicated room)

Measuring range

Limited by the energy of light projection

Working frequency

Around 30 FPS + image post-processing time Reference Target Figure 4.24: Outside-in paradigm (adapted from [START_REF] Rolland | A Survey of Tracking Technology for Virtual Environments[END_REF]).

Accuracy

It has the advantage of directly allowing to estimate the 6DoF pose of an object, without any target instrumentation. However, this technique requires a light source allowing the projection of a pattern on the target, making the sensor cumbersome. An important computer processing capacity is also required, and even so the acquisition frequency remains too low for our application.

Videometric principle

This principle, applied for example in the eld of VR and AR, consists in using several cameras placed on the target, e.g. the head of a user, to take pictures of the surrounding environment, e.g. the ceiling panels, which are equipped with reference patterns. Thanks to the 2D projections of the patterns on the sensors, it is possible to dene a vector going from the sensor to a specic feature of each pattern. The position and orientation of the target can then be calculated using at least three vectors constructed from the sensor(s)

to the features (see Fig. 4.25).

Figure 4.25: Videometric principle (adapted from [START_REF] Rolland | A Survey of Tracking Technology for Virtual Environments[END_REF]).

This approach is part of the inside-out paradigm, in which the sensor is mounted on the target and the emitters are on the reference as shown in gure 4.26.

Target Reference Figure 4.26: Inside-out paradigm (adapted from [START_REF] Rolland | A Survey of Tracking Technology for Virtual Environments[END_REF]).

This approach has reported usage in [START_REF] Janin | Videometric head tracker for augmented reality applications[END_REF] for head tracking in augmented reality applications. A similar system employing lateral-eect photodiodes (LEPDs) that looked upward at a regular array of infrared LEDs installed in precisely machined ceiling panels was reported in [START_REF] Azuma | Space Resection by Collinearity: Mathematics Behind the Optical Ceiling Head-Tracker[END_REF]. In this case, the user is weighted with acquisition and communication electronics. A more recent development applying the inside-out paradigm has been reported in [START_REF] Welch | High-Performance Wide-Area Optical Tracking: The HiBall Tracking System[END_REF] where the HiBall tracking system is described (see Fig. Table 4.10: Representative characteristics and performances of reported videometric tracking systems [START_REF] Janin | Videometric head tracker for augmented reality applications[END_REF], Welch et al., 2001].

Sensor type Camera Measured variable

Position and orientation

Physical phenomenon

Image acquisition Weight / Size

Depends on the mounted sensors, e.g.300g for HiBall

Measuring range

Working volume depends on the number of landmarks, e.g. room of 4.5m × 8.5m for the HiBall system ensuring reported absolute error Working frequency ≈ 2kHz, e.g. HiBall Absolute error < 0.5mm and 0.03°, e.g. HiBall

Target instrumentation

Yes Degrees of freedom (DoF) 6DoF pose calculation possible Occlusion sensitive Yes Price Expensive

Strengths (✓) / Weaknesses (✗)

✓: Current systems are less cumbersome ✓: Workspace can be as large as required depending on the amount of installed landmarks ✗: Heavy sensors have to be mounted on the target Applications Object tracking in virtual and augmented reality

Depth cameras

In its simplest implementation, a depth camera is a multiple pixels range (distance)

sensor. Range measurement can be accomplished by means of several physical principles.

As an example, a type of range sensor known as LIDAR (for Light Imaging Detection And

Ranging or for LIght and raDAR) estimates range (distance or depth) by measuring the time-of-ight (TOF) of collimated laser beams illuminating a target (the reected light being detected by a purposely arranged photodetector). LIDAR technology requires to be combined with some sort of scanning in order to obtain several horizontal and vertical depth measurements, e.g. by employing rotating mirrors (see Fig. 4.28a). However eld of view and resolution are limited.

Another approach consists in emitting a light that will spread on the scene of interest, that will be then reected back and that will be nally imaged onto a two-dimensional array of photodetectors (Flash LIDAR depth camera, see Fig. This technology relies on two measurement principles, 1) direct measure of the time taken for a light pulse to travel from the device and to come back after reection on the target (pulsed-light cameras) and 2) deduction of the travel time from a measure of the phase dierence between the emitted and received signals (continuous-wave modulated-light cameras). Tables 4.11,4.12 and 4.13 show that this kind of sensors is not adapted for our application. The measuring range is too large, and the accuracy and acquisition frequency are limited. They will not be further discussed in this document.

Applications

Collision avoidance, adaptive cruise control, surveillance, day-nightrain-fog imaging, automated rendezvous and docking in space, unmaned ground/air vehicles Table 4.13: Continuous-wave modulated-light cameras representative performances [START_REF] Horaud | An overview of depth cameras and range scanners based on time-of-ight technologies[END_REF][START_REF] Sony | Sony Depth Sensing Solutions[END_REF]. Zentrum für Luft-und Raumfahrt in German) [Hirzinger, 1999], the SPACE MOUSE is a 3D-input device used for CAD and robot control. It employs an arrangement of 6 onedimensional PSDs, slits and light emitting diodes (LEDs) to measure the displacement of a handle in a small workspace (see Fig. Developed in the late 90s [Berkelman, 1999], the Maglev is a tool-based interaction haptic interface (see Fig. The Maglev haptic interface provides the following characteristics:

Sensor type

• workspace: ±12.5mm (translation) and ±7.5 • (rotation),

• working frequency: 1.45kHz (max) and

• resolution: 5 -10µm.

Such technologies appear very well suited for our application. However, in their current implementation, they are still too large and would require a complete redesign before they can be integrated in an IC-HI for the purpose of tracking the handle without contact.

Conclusion

Based on the performances of the explored tracking systems, the following conclusions arised.

The range of tracking systems based on optical principles is very varied. Most of them nd their origins and applications in VR/AR or industry. The former are well suited for human body tracking or environment reconstruction but their range of measurement is often too large, and their acquisition frequency and accuracy too low for the tracking of the handle of an IC-HI. On the contrary, industry-oriented sensors require high accuracy and acquisition frequency. However, existing systems are limited to 1 DoF measurement and the design of a 6DoF tracker would result in a complex, expensive and cumbersome device

The most interesting approach remains the triangulation principle based on simple optical emitter/detector pairs, in particular IRED/PSD pairs with slits. This solution is compact and can work at high frequencies since PSDs are analog sensors.

Global conclusion on existing motion tracking systems

None of the existing systems appears to be well adapted for the tracking of the handle of an IC-HI. As a consequence, we decided to develop a non-contact tracking system that complies with the design drivers of an IC-HI from scratch. The most promising approach being the triangulation principle based on simple 1D or 2D emitter/detector pairs, we rst performed a comprehensive review of such sensors, in order to learn on their principle, characteristics, performances as wells as on their respective advantages and disadvantages.

This review is presented in the following paragraph.

4.6 Non-contact displacement or distance sensors for the design of an IC-HI tracking system

Introduction

The study of existing tracking systems presented in section 4.5 has shown that none of them complies with the design drivers dened in section 4.4. This observation led to the conclusion that the design of a new tracking system for IC-HIs was necessary. Our analysis also led us to favor a design based on the combination of several 1 or 2 DoFs elementary position or distance sensors to get the 6DoF pose of the handle.

A similar approach was used in [Diallo, 2014]. A prototype that computes the 6DoF pose of a handle without contact was developed using elementary displacement sensors.

This system made use of three linear optical sensors (mounted on a receptacle) to measure the position of the spots produced by thin slit oriented perpendicularly to the sensors and sequentially illuminated by three IR light sources mounted on the handle. This system allows to compute the 3D position of each source based on planes intersections. The 6DoF conguration of the handle is then easily calculated from the positions of the three sources (see appendix B for more details). Despite its limitations which do not allow to t our requirements (it was quite cumbersome and its acquisition frequency was <300Hz), this prototype had a suitable workspace and a high precision (10 -1 mm). It inspired thus our work which was oriented towards the development of a similar system, however improving its performances. To this end it is necessary to nd faster, more precise and smaller elementary sensors.

To allow for an informed choice of these sensors, it is of fundamental importance to investigate the characteristics of the dierent available sensor technologies. Our ultimate goal is to allow for a quick and precise calculation of the 6DoF pose of a handle without contact. We dened the associated design drivers in section 4.4, it is however dicult to translate these design drivers into requirements for each elementary sensor, as we do not know their arrangement in space at the beginning of the design process. Still, in order to guide the sensor's comparison, we will use as a rst approximation the same design drivers as for the whole device, i.e. a range of measurement of at least 10mm (in order to cope with the user's and robot's dynamics), with a lower range of measurement as close as possible to 1mm (in order to allow for an as compact as possible design, without having to place the sensors at a longer distance from the handle), an accuracy of 0.1mm and an acquisition frequency around 1kHz. All these sensors should be studied principally in terms of these design drivers, i.e. measuring range, working frequency, precision and of course size.

The following sections aim to provide a review of existing elementary sensor technologies potentially interesting to our application, e.g. ultrasonic, capacitive, magnetic, inertial as well as optical sensors. The working principle and characteristics of each type of sensor will be provided and their pertinence evaluated. 4.30: (a) Reected waves generated by an ultrasonic transducer (adapted from [START_REF] Hatzfeld | Engineering Haptic Devices: A Beginner's Guide[END_REF]) and (b) Commercial ultrasonic sensor.

These transducers employ therefore piezoelectric materials to convert an electrical current into mechanical oscillations (emitter) and to convert oscillations created by a reected wave into an electrical current (receiver). This way, ultrasonic transducers allow to perform presence detection or distance measurements, the later being achieved either by evaluating the time of ight (TOF) or by determining the phase shift (dierence)

between the emitted and received signals (see sections 4.5.2.1 and 4.5.2.2).

Numerous ultrasonic ranging sensors are available on the market (see Fig. 4.30b for an example). Most of them employ the TOF principle to provide distance measurements.

Table 4.14 shows representative characteristics of ultrasonic rangenders issued from the MaxBotix Inc. catalogue, which is one of the main manufacturers of these sensors, located in the state of Minnesota, U.S.A. The rest of the characteristics are issued from other sources [START_REF] Gueuning | Accurate distance measurement by an autonomous ultrasonic system combining timeof-ight and phase-shift methods[END_REF], [START_REF] Rolland | A Survey of Tracking Technology for Virtual Environments[END_REF], [START_REF] Hatzfeld | Engineering Haptic Devices: A Beginner's Guide[END_REF].

Table 4.14: Ultrasonic rangender representative characteristics [START_REF] Gueuning | Accurate distance measurement by an autonomous ultrasonic system combining timeof-ight and phase-shift methods[END_REF], Rolland et al., 1999, Hatzfeld and Kern, 2009[START_REF] Maxbotix | Innovative ultrasonic sensors[END_REF]. Regarding the design of an IC-HI tracking system, interesting acquisition rates can be attained at close distances (> 1kHz). However, these sensors suer from several prohibitive disadvantages. When comparing their characteristics with the specications of an IC-HI tracking system as dened in section 4.4.3 it can be observed that:

Sensor type

Ultrasonic rangefinder

Measured variable

• The minimal reported measuring range (15cm) is too big.

• The reported order of magnitude for accuracy do not comply with the searched value (< 10 -1 mm).

• Finally, using ultrasonic rangenders in order to calculate the 6DoF pose of a target would require a cumbersome arrangement and would provide low accuracy pose measurements.

In conclusion, despite the interesting characteristics of this technology, ultrasonic rangenders are not adapted to be employed in an IC-HI tracking module. near each other, separated by a non-conductive substance (dielectric) [START_REF] Terzic | Capacitive Sensing Technology[END_REF].

Examples of dielectric materials are air, ceramic or fuel, just to mention few of them.

When the circuit from gure 4.31 is closed and thus a voltage is applied across the terminals of the capacitor, the electrodes will start storing energy until attaining the same voltage as the source.

Resistor (𝑅𝑐) Capacitor (𝐶) Battery +𝑄 -𝑄 Figure 4.31: Capacitor principle [Terzic et al., 2012].

The time required to charge a capacitor is determined by the time constant τ C = RcC, where Rc is the resistance (in ohms, Ω) of a resistor connected in series with the capacitor which capacitance (in farads, F) is denoted C. Such time represents how long it takes to a capacitor to store 63% of its total capacity. The stored energy will then remain unless it is consumed by another component.

Equations (4.8) and (4.9) formalize the aforementioned relationships. In (4.8) Q is the charge of the capacitor (in Coulomb, C), C its capacitance (in farads, F ) and V the voltage (in volts, V ).

Q = CV (4.8) C = E 0 E R A D (4.9)
In (4.9) E 0 represents the dielectric permittivity of vacuum (which is a constant equal to 8.85.10 -12 F/m), E R is the relative permittivity of the material placed between the plates (as an example, for the air E R = 1), A is the area of the plates (expressed in square meters, m 2 ) and D is the distance (in meters, m) between them. From these equations, it can be seen that the charge Q is inuenced by the distance between the plates. By measuring Q (either through measuring the current owing through it or the voltage between its electrodes), it is then possible to infer this distance.

In practice, capacitive sensing technologies allow to obtain either proximity or displacement information from an approaching object. In the present case, our interest is focused on displacement capacitive sensors.

A displacement capacitive sensor can be modeled by two parallel plates where one of them represents the sensor and the other one the object of interest (target). Such devices are used to measure the relative displacement between these two parallel plates (see Fig.

Conclusion

Capacitive displacement sensors provide highly interesting characteristics for high resolution and bandwidth tracking systems. However this technology is not of great interest for the intended application (development of the tracking system of an IC-HI) since measuring ranges are very small. Furthermore, commercially available sensors are usually cylindrical and of relatively large sizes. As a consequence an eventual arrangement of several probes would become cumbersome. In conclusion, displacement capacitive sensors are not adapted to our case.

Magnetic eld sensors

Magnetic sensors are very varied and employ many aspects of physics and electronics.

They can be divided in two categories [START_REF] Lenz | Magnetic sensors and their applications[END_REF]: sensors that measure the total magnetic eld amplitude and sensors that allow measuring all its vector components. Common technologies used in both cases are shown in gure 4.34. Some of their advantages are stability and low cost. Furthermore they are a very simple, reliable and maintenance free.

Vector magnetometers

Scalar magnetometers (Induction) Figure 4.34: Common types of magnetic sensors and their estimated sensitivity [START_REF] Lenz | Magnetic sensors and their applications[END_REF].

A review of modern magnetic eld sensors [Tumanski, 2013] has concluded that among these sensors four main types of technologies are dominating: SQUID sensors (for very small magnetic elds), ux-gate sensors (for small magnetic elds), MR sensors (for medium values) and Hall eect sensors (for high values). What is important is then the range of measured magnetic eld, in particular the smallest measurable value which has a direct inuence on the sensor's cost (e.g. AMR sensors, which are a particular type of MR sensors, are cheaper than SQUIDs). The principle and performances of these four types of sensors will be discussed in the following sections.

SQUID sensors

The superconducting quantum interference devices (SQUIDs) work based on the interactions between electric currents and magnetic elds observed when certain materials are cooled below what is called the superconducting transition temperature. This means that at these temperatures these materials show superconductive properties, in particular zero electrical resistance. These transducers convert the magnetic ux threading the SQUID loop into a voltage across the device [START_REF] Drung | Highly Sensitive and Easy-to-Use SQUID Sensors[END_REF]. In practice, it consists in a superconducting ring with one or two Josephson junctions (see Fig.4.35). Two types of SQUIDs can be distinguished: direct current (dc) and radio frequency, with two and one Josephson junctions respectively. The later are less expensive to produce but less sensitive.

Magnetic field

Superconductor

Josephson junction SQUID sensors are the most sensitive of all sensors for measuring a magnetic eld at low frequencies (< 1Hz) [START_REF] Lenz | Magnetic sensors and their applications[END_REF]. They are employed to measure extremely small magnetic eld changes. Most of the SQUID sensors are integrated in biomagnetic systems [START_REF] Clarke | Introduction[END_REF]], e.g. in a magnetoencephalography system which is often installed in a magnetically-shielded room since the brain signals are very week (on the order of few femtotesla). Another example is magnetocardiography which consists on a noninvasive characterization of local magnetic activity of the heart muscle that is generated by currents. Such technique allows to study heart disorders. Other techniques include liver susceptometry (to monitor the accumulation of excess iron in the human liver) and gastro-magnetometry (ingested magnetic markers that are tracked through the gastro-intestinal tract).

SQUID sensors seem to be very specialized sensors. They are supplied by only few manufacturers in the world. Supracon R for example, located in Germany, is one of them.

Their portfolio comprises current sensors, magnetometers and gradiometers (gradient measurement).

Applications

Biomagnetic applications as measurement of magnetic fields emitted by the brain and heart or tracking of magnetic markers in the digestive system.

Fluxgate magnetometers

A uxgate magnetometer is composed of a ferromagnetic material wound with two coils (a drive and a sensor coil) [START_REF] Lenz | Magnetic sensors and their applications[END_REF]. It uses magnetic induction and the property of all ferromagnetic materials to become saturated when exposed to high magnetic elds, i.e. when the applied magnetic eld cannot further increase the magnetization of the material. For example, if a large sinusoidal current is applied in the drive coil, the core is magnetized up to saturation once each half-cycle. When saturation has been reached, the reluctance (opposition to magnetic ux) of the core to any external magnetic eld being measured becomes greater, avoiding any magnetic eld to pass through the core. When the core goes out of saturation, the magnetic ux of the incoming magnetic eld is attracted to the core and detected by the sense coil. The sensor winding

Magnetoristive magnetometers

Magnetoresistive magnetometers employ a change in resistance ∆R provocated by an external magnetic eld [START_REF] Lenz | Magnetic sensors and their applications[END_REF]. While there exist several magnetoresistive eects [Tumanski, 2013], only three main eects are commonly used:

• Anisotropic magnetoresistive (AMR) eect, as was rst observed by William Thomson in 1857. The resistivity of ferromagnetic materials depends on the angle between the direction of an electric current and the orientation of the applied magnetization [START_REF] Jogschies | Recent Developments of Magnetoresistive Sensors for Industrial Applications[END_REF]. This can be represented by a Hunt element in which a owing current I and a magnetization vector M form the angle α. A magnetic eld H y coupled into the sensor material will generate a change on the resistivity of the stripe, which is veried by current measurement (see Fig. • Giant magnetoresistive (GMR) eect, discovered in 1988 [START_REF] Jogschies | Recent Developments of Magnetoresistive Sensors for Industrial Applications[END_REF]. It was given this name since changes in magnetoresistance were larger than in AMR. GMR sensors consist in a four layer structure composed of two thin ferromagnets separated by a conductor. The fourth layer is an antiferromagnet which inhibits the rotation of one of the ferromagnetic layers [START_REF] Lenz | Magnetic sensors and their applications[END_REF]].

• Introduced in 1995 [START_REF] Lenz | Magnetic sensors and their applications[END_REF], Magnetic tunnel junction (MTJ) sensors have a structure similar to that of GMR sensors. However the two ferromagnets are separated by an intervening layer which in this case is an insulator. In MTJ, conduction occurs by tunneling of the electrons through the insulator.

Conclusion

Sensors measuring the magnetic ux density in a magnetic eld oer a wide variety of interesting options according to the targeted application. In previous sections, representative characteristics of SQUID sensors, uxgate magnetometers, magnetoresistive magnetometers as well as hall-eect sensors were explored. The following paragraphs will provide elements of conclusion regarding the intended application: the development of an IC-HI tracking system. SQUID sensors are very specialized and expensive sensors supplied by only few manufacturers. It was reported that they work at very low temperatures and low frequencies (< 1Hz). These factors make that this type of sensors won't be further explored regarding the intended application.

Fluxgate magnetometers and Hall-eect sensors oer interesting characteristics in terms of size and working frequency. However, since accuracy and resolution are provided in terms of magnetic ux density units (either Tesla or Gauss), it is dicult to infer for the accuracy of position measurements. A test bench for one of these sensors would have to be built in order to be able to determine an order of magnitude of the attainable position accuracy.

Finally, commercial AMR technology oers angular and position sensors with interesting reported accuracy and repeatability. However, the reported measuring ranges in the case of position sensors are too low, i.e. in the order of few millimeters.

It appears from this study that, among the proposed sensors, only Fluxgate magnetometers and Hall-eect sensors could potentially be used to design a 6DoF sensor that ts our application. To do so, an arrangement of the discussed sensors could be mounted on a target evolving in a magnetic eld suciently big to cover the desired workspace. This solution would however require a prototype as the sensors' datasheets do not directly inform on the attainable precision. In all cases, these sensors would remain sensitive to disturbances being originated from ferromagnetic and metallic elements present in the vicinity of the target. They would also be disturbed by the magnetic elds generated by the motors of the nearby haptic interface. As a consequence, none of the above reported magnetic eld sensors would comply with the design drivers of an IC-HI tracking system. 4.6.5 Inertial sensors 4.6.5.1 Principle and characteristics

The 6DoF pose of an object can also be reconstructed by employing inertial measurements [START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF]. Commercial inertial measurement units (IMUs) have been largely studied since it represents a cost-eective technology in application cases where optical technologies are not adapted [START_REF] Filippeschi | Survey of Motion Tracking Methods Based on Inertial Sensors: A Focus on Upper Limb Human Motion[END_REF]. Inertial measurement units clockwise [Shamir, 2006]. If the system is static, the two beams travel through the same optical path and return in phase to their origin. If the system turns clockwise with an angular velocity Ω, the origin turns with it. As a consequence the beam which is rotating clockwise will travel a longer distance to reach the origin than the one traveling counter-clockwise and a phase shift ∆φ will be generated (see Fig.4.43b).

Such dierence in phase can be measured by means of an interferometer (an instrument that merges two or more sources of light to create an interference pattern that can be measured and analyzed).

Gyroscopes based on a vibrating mass are generally based on micro-electro-mechanical systems (MEMS). Their working principle consists in a vibrating mass that is aected by the Coriolis acceleration caused by the rotation (see Fig.4.43c). This results in secondary vibrations that are perpendicular to the primary ones and to the angular velocity vector. By measuring the secondary vibrations, it is possible to determine the angular velocity [START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF].

• Accelerometers for the measurement of linear accelerations. An accelerometer consists in a mass m connected to a rigid housing by means of springs with stiness k, the whole being aected by the damping d (see Fig.4.44). When the housing is accelerated, it creates a tension on the spring as the mass does not immediately follow it. This system can be modeled as a second order mass-spring-damper system (see Eq. • Magnetometers to measure the orientation relative to the Earth's magnetic eld.

The principle of a magnetic sensor won't be described here since the most common types of such sensors have already been described in section 4.6.4. The orientation with reference to a magnetic eld can be obtained thanks to the magnetoresistive eect (see section 4.6.4.3).

An IMU s usually composed of a 3-axis gyroscope, a 3-axis accelerometer and a 3axis magnetometer whose data are sent to a computer to calculate the global speed and position, given a known initial speed and position [START_REF] Desa | Study of inertial measurement unit sensor[END_REF]. To illustrate this, gure 4.45 shows the basic principle of inertial motion tracking. Even if IMUs represent an interesting approach which is insensitive to occlusions, their size and working frequency do not comply with the targeted applications.

Also, they natively give absolute position and orientation information. In the perspective of the development of an IC-HI tracking system, it is necessary to determine the relative handle/robot conguration. With an IMU this calculation would require to combine the IMU data with the robot's conguration obtained by forward kinematics. As a consequence, the measurement errors coming from each data source would cumulate.

By precisely knowing the initial position of the handle, the data could be merged using a Kalman lter to increase the accuracy of the system. However working frequencies for small sizes IMUs remain insucient.

Optical sensors

Optical sensors also known as photodetectors are devices that convert light rays into an electrical signal [Dhiraj, 2012]. These type of sensors nd applications in physics, chemistry, biology, medicine, telecommunications, instrumentation, photolithography on semiconductor chips, particle detection as well as object tracking etc. [Haus, 2012].

While it was shown in section 4.5.4 that no existing 6DoF optical tracker ts our requirements (laser triangulation systems presented in section 4.5.4.2 for example are too cumbersome while photodiodes arrangements found in the Maglev haptic interface presented in section 4.5.4.7 are complex and bulky), it seems that using optical sensors for object tracking, which is of main interest for the present work, remains interesting.

In fact, despite dierent specications which led for the SPACE MOUSE presented in section 4.5.4.7 to an insucient workspace, and despite integration and ne-tuning issues in the 6DoF contactless sensor presented in appendix B, which led to an insucient bandwidth, specically designed arrangements of photodetectors still have the potential to t our requirements. Elementary sensors can indeed have a high resolution, a range of measurement compliant with our application and an acquisition frequency potentially higher than in previous examples. The question is then about the optimal choice of such elementary sensors that could be integrated in a compact manner to get a tracker fully compatible with our design drivers.

Photodetectors (or light sensors) can be divided, based on their operating principle, in three major categories [START_REF] Hamamatsu | Photomultiplier Tubes, Basics and Applications[END_REF]:

• external photoelectric eect sensors, like photomultipliers, which principle of operation will be explained below,

• internal photoelectric photodetectors which can be further divided into photoconductive types like photoresistors (which are characterized by an increase of their electrical conductivity when they are exposed to light) and photovoltaic types like photodiodes (which generate a voltage upon exposure to light), both featuring a high sensitivity and a miniature size [START_REF] Hamamatsu | Photomultiplier Tubes, Basics and Applications[END_REF], and

• thermal types (not studied here since temperature is not a metric of interest).

According to our research, the most interesting sensors in the rst category are photomultipliers and in the second case PhotoDiode Arrays (PDAs), Charge Coupled Device (CCD), Complementary Metal-Oxide Semiconductor (CMOS) and Position Sensitive Detectors (PSDs). Each of these sensors will be presented in detail below. Several elds of applications are reported for such devices [START_REF] Hamamatsu | Photomultiplier Tubes, Basics and Applications[END_REF]: spectrophotometry, medical equipment, biotechnology, high-energy physics experiments, environmental measurement, radiation monitors, industrial measurements, aerospace applications, and mass spectrometry etc. Even though these sensors provide a high frequency response (8.7 -111MHz according to [START_REF] Hamamatsu | si photodiodes in Opto-semiconductor Handbook[END_REF]), they require high operating voltages (500 -3000V applied across the anode and cathode) and are complex to use (they require a voltage divider circuit) [START_REF] Hamamatsu | Photomultiplier Tubes, Basics and Applications[END_REF]. Furthermore, as shown in 4.47b which illustrates samples of photomultipliers manufactured by Hamamatsu, they can attain relatively important sizes (13 -127mm diameters [START_REF] Hamamatsu | si photodiodes in Opto-semiconductor Handbook[END_REF]).

Photodiode arrays

Before introducing these sensors, a brief description of the working principle of a photodiode will be provided.

4.6.6.2.1 Photodiodes Photodiodes are sensors that generate an electrical signal (current or voltage) when a P-N junction is irradiated by light photons.

In a N-type semiconductor the number of free electrons is superior to the number of holes (positive charges), meanwhile in an P-type semiconductor the number of holes is superior to the number of free electrons. When both are combined, the region located at the P-N junction, called the depletion layer, acts as an insulating region (see Fig. Unlike diodes, the P-N junction of photodiodes is made with a light-sensitive semiconductor. Depending on the material, the junction will be sensible to several ranges of wavelengths [Arbind, 2017]:

+ + + ----- ----- - --- ----- ----- + + + + + + + -- - -- -- -- - --
• from 190 to 1100nm for Silicon,

• from 400 to 1700nm for Germanium,

• from 800 to 2600nm for Indium Gallium Arsenide and

• from 1000 to 3500nm for Lead Sulphide.

These components are usually encapsulated in a package with a window allowing the light to enter into the P-N junction (see Fig. Since the mid 60s, a combination of either P-N or P-N-P junctions have been employed

for the conversion of light into an electronic signal [START_REF] Titus | Cmos photodetectors[END_REF]. Research works not only focused on the conversion part but also on how to retrieve these signals from the arrays of pixels. During the 70s CMOS sensors lost popularity in comparison to CCDs, since the later provided a more interesting ll factor (ratio of light-sensitive surface to entire pixel surface). CMOS require in fact transistors at each pixel. Also, noise in CCD was considerably less than in CMOS imagers. Finally in the early 90s, improvements in CMOS manufacturing technology and a demand to decrease power consumption for devices employing batteries made CMOS to regain interest as a viable imaging device.

CMOS arrays can make use of two types of pixel circuits:

• Passive pixel sensors (PPS) which were employed in the rst CMOS imagers: these sensors are based on photodiodes without internal amplication stage. They only contain a transistor allowing to connect the elementary sensor (photodiode) to the readout structure (see Fig. 4.54b). These sensors suered from low sensitivity (amount of generated charge in function of the received light) and high noise.

• Active pixel sensors (APS): contrary to PPS, APS can contain several transistors per pixel and an amplication stage (see Fig. 4.54c). Such combination is known for improving the performance of the pixel, e.g. the power dissipation of a pixel is lower than in CCDs since each amplier is activated during readout.

CMOS sensors are commercially available (see Fig. 4.55). Table 4.23 resumes representative characteristics of some of these sensors. The presented characteristics are issued from ON Semiconductors catalogue.

NOIL2SM1300A CMOS high speed sensor from ON Semiconductors 4.56). This phenomenon is called lateral photo-eect [Woltring, 1975].

Figure 4.56: Schematic view of a one-dimensional PSD (adapted from [START_REF] Hamamatsu | si photodiodes in Opto-semiconductor Handbook[END_REF]).

The relation between the location of the incident light and the occurring photocurrents is given by (4.11), where Lx is the length of the photosensitive area and X A the distance from the electrical center of the PSD to the light input position.

I X 2 -I X 1 I X 1 + I X 2 = 2X A Lx

Conclusion

The working principle and characteristics of several optical elementary sensors, able to provide displacement and position information, were presented in the present section.

Photomultipliers where quickly discarded as they are complex to use and cumbersome.

Remained on one hand multichannel sensors such as photodiodes arrays, CCD and CMOS sensors, and on the other hand PSDs, which consist in a large photodiode able to provide the analog coordinates of a spot of light.

Multichannel optical sensors are compact and provide interesting characteristics in terms of resolution, i.e. the size of their pixels is in the order of few µm. On the other hand, these sensors behave basically as a camera and in general one measurement requires reading all the pixels of the imager. This has the disadvantage of an important acquisition time: each pixel requires a minimum time for its stored charge to be converted into an electrical signal, then this electrical signal needs to be converted in to a digital one and nally it is necessary to add the time needed for image processing in order to obtain the information of interest, i.e. the position of the incident light spot. With a number of pixels ranging from 128 (in the case of PDAs) to ≈ 6, 630, 000 (in the case of large CMOS), this considerably slows down the attainable sampling rate. Based on the explored catalogues, full image sampling rates remains limited to between 1Hz and ≈ 800Hz. This rate remains below our requirements to have a control loop working at a frequency higher than 1kHz.

Furthermore, these sensors are relatively complex to use.

In this context, PSDs represent a very interesting option. They remain compact sensors and provide interesting characteristics in terms of acquisition frequency (100kHz -1MHz) and position errors (10µm -150µm). These analog sensors are also very simpleto-use, e.g. in a 1D PSD the position of the center of gravity of a light spot can be determined by directly measuring two photocurrents and making only three operations (two additions and one division).

Global conclusion on elementary sensors for IC-HI tracking systems

The working principle of several types of elementary sensors, in particular ultrasonic, capacitive, magnetic, inertial and optical sensors able to provide distance and/or displacement information, were presented from sections 4.6.2 to 4.6.6, along with their technical characteristics (issued from the catalogs of important sensor suppliers). Having rst described in a simplied and easy to understand yet non-exhaustive manner their working principle allowed to better interpret the technical aspects provided by manufacturers.

The presented study allowed to position the suitability of current commercially available technologies in reference to the design drivers of an IC-HI tracking system of type CT-HI.

After a thorough study of the available sensing technologies and inspired by the system developed in [Diallo, 2014] (see Appendix B) we chose to focus on linear PSDs for the targeted application. PSDs have proven to be an adapted technological solution in the case of non-contact tracking systems (see section 4.5.4.7). Motivated by the simplicity and potential low cost of the light source, slit and linear optical sensor arrangement, a linear PSD was chosen for the development of our IC-HI tracking system.

Modeling and experimental characterization of a 1DoF non-contact displacement sensor

As stated at the beginning of this chapter, the global aim of the current study is the development of a 6DoF tracking system that can be used to eciently measure the conguration of the handle of an IC-HI. To this end, we rst derived important design drivers for such a system. Then the literature on tracking systems and non-contact sensing technologies was studied and their performances were compared to the dened design criteria. We concluded from this study that a custom designed measurement system based on optical elementary sensors was the most promising solution for the intended application.

We more specically focused our attention on a system which will be denoted here Its principle of operation is the following: the angle θ between the normal to the sensor and the line going from the source to the slit is deduced from the position X of the image of the source on the sensor, provided the distance h between the sensor and the slit is known. In space, this angle denes a plane. The position of the source can easily be obtained by repeating this operation for three dierent slits, the source being at the intersection of the three planes (see Appendix B for details).

While simple in theory, this principle requires however in practice an ecient model able to predict the angle θ from the distance X. The rst step towards the development of such an inverse model is to better understand the behavior of the system, which requires the development of a realistic geometric and radiometric modeling of the source, slit and sensor. The aim of the following is to present such a direct model able to estimate X from θ, as well as its experimental validation.

Basic concepts of radiometry

Light sources can emit energy in a wide range of wavelengths, only some of them being visible. Indeed, the spectrum of radiant energy waves that we call light ranges approximately from 380nm to 770nm. Wavelengths shorter (ultra violet) or longer (infrared) than these do not produce a visual response in the eye [Ryer, 1997]. As a consequence, depending on the wavelengths of interest, the measurement of the propagated energy in the electromagnetic waves radiated by light sources can use two approaches: the photometric approach, which refers only to the part of the radiant power produced by the source that is perceived by the human eye as light, and the radiometric approach, which is more general as it takes into account the entire radiant power produced by the source.

In the present application, in order to ensure the best possible sensitivity to handle movements, it is important that the sensor is not perturbed by external conditions, especially ambient light. Therefore, and after a careful analysis of the available sensors and light sources, we decided to rely on components working in the infrared spectrum (>770nm). The attention being given to these wavelengths, in particular in quantifying the power emitted by an infrared emitting diode (IRED), we will deal here with the radiometric approach.

It is worth noting that the sensor, as shown on gure 4.58, will not see the entire light emitted by the source, but only the part of it that:

• passes through the slit and

• illuminates the active area of the sensor.

As a consequence, we will not consider here the radiant power or radiant ux Φ representing the total power (light) radiated by the source, but only the part of it which illuminates the active area of the sensor. Therefore we will use the notion of radiant intensity, denoted here as I e , which refers to the energy radiated by the source into the unit solid angle in a unit of time. This is the power per unit solid angle and it is typically given in mW/sr by IRED's constructors.

The computation of the total emitted power on the active area of the sensor requires to know the corresponding solid angle. Here we will consider that the illuminated sensor surface, as seen from the source, can be modeled as a rectangular plate (a rectangular slit is easy to manufacture and most measuring devices themselves have a rectangular window or sensitive surface [Khadjavi, 1968]) of size a×b (area ab) at a distance d from the source.

Taking the center of the plate as a reference (i.e. considering only the conguration where the vector normal to the plate surface starting at the plate center points to the source, which means that the plate surface is perpendicular to the line of sight [START_REF] Mathar | [END_REF]), the associated solid angle is given by (4.12).

Ω(a, b, d) = 4 arccos 1 + α 2 + β 2 (1 + α 2 )(1 + β 2 ) (4.12) With α = a/(2d) and β = b/(2d).

The presented concepts will be used in the following sections to establish a model of the response of an ERS system.

IRED-PSD slit-based system

The light beam shape generated by this ERS system is similar to a pyramid of rectangular base. As it can be observed in gure 4.60, only a part of its base intersects with the PSD photosensitive area. This intersection represents the light spot A P SD . The associated light beam is called here PSD light beam (PLB). In the present case we suppose that the position X A corresponds to the geometrical center of the light spot A P SD . As the IRED translates in space, the shape of the PLB varies. These variations let us identify other geometrical elements illustrated in gure 4.61. The amount of solid angle contained in the PLB can then be estimated using (4.12).

PSD

Photocurrent calculation

The generated photocurrent of an isotropic IRED can be calculated using: where, P psd represents the power received on the PSD photosensitive area (in watt, W), S is the photoresponsivity (a conversion factor of power into current which is given by the PSD constructor in A/W) and I D stands for the PSD dark current (in A).

I
In the very right part of (4.13), Ω is the PSD light beam (PLB) corresponding solide angle and I e is the radiant intensity (in W/sr), function of I F which is the forward current owing through the IRED (in A).

IREDs are in practice non-isotropic light sources. This means that depending on the view angle γ in reference to the IRED central axis, the emitted power will vary according to a certain prole (see Fig.4.62). This variation is regulated by the relative radiant intensity denoted I e Rel . In order to take this power variation into account, we can add the relative radiant intensity I e Rel (γ) to (4.13) as shown in (4.14).

IRED axis

Half-intensity emission cone

𝐼 𝑒 𝑅𝑒𝑙 -Relative It is worth noting that, as can be seen from the left part of the gure 4.62, an IRED emits a light that is sucient to be seen by the sensor only in a certain cone. As in the case of an IC-HI there can momentarily be an important angular oset between the handle and the end-eector of the robot when the former is manipulated by the user, it is important that the IRED (which is mounted on the handle) has the largest possible half-intensity emission cone so that it continues to illuminate the sensor even for large angulations of the handle relative to the end eector (on which the sensor is mounted).

After a careful review of the manufacturers' catalogues, we selected for our study an IRED CQY36N from VISHAY.

Equation (4.14) assumes that the relative radiant intensity for a given value of γ is representative of the I e Rel distribution inside the solid angle contained in the PLB. This assumption can be considered as valid as long as the slit width is small. This constraint will guide our design.

In order to ease the calculation of the aforementioned geometrical elements, a simulator of the ERS system was developed using Matlab (see Fig.

Experimental results

In order to be able to evaluate complex cases, e.g. an arrangement of several ERS systems, the elementary sensor model should provide a response as close as possible to that of the real components. To validate the pertinence of the proposed model, a test bench of a single ERS system was built and rst experiments were performed. In the following paragraphs the test bench description, performed experiments and results are presented.

ERS Test Bench

The test bench is composed of two sub-assemblies which are denoted here as the Emitter Sub-Assembly (EmSA) and Receptor Sub-Assembly (ReSA). The EmSA can translate in three orthogonal axes, meanwhile the ReSA is static (see Fig. Both sub-assemblies were mounted parallel to each other on a precision table. Their initial relative positioning is adjusted using a plastic tube of known length that denes a perpendicular distance of 32mm between the IRED chip and the PSD surface (see

Experiment 1: Description and Results

The proposed experiment aims to compare the calculated value of the light spot position X A with the real one. The IRED chip is positioned at a distance of d A = 15mm, which remains constant, from the PSD surface and the slit at a distance of d B = 7.5mm from the same surface. The IRED is translated, with its central axis normal to the PSD surface, along the PSD x P SD axis (see Fig.4.69). This conguration would make that the displacement of the IRED is almost equivalent to that of the light spot.

The displacement interval ranged from -5.5 to 5.5mm, with a step of 0.5mm, providing a total of 23 samples of I X1 and I X2 . This range guaranties that the light spot remains geometrically inside the photosensitive area. It is worth noting that the light spot position is measured using a specic part of the photosensitive area. For a PSD which photosensitive area length is Lx ≤ 12mm, the recommended useful area length is only Lx × 0.75. This corresponds to a value of 9mm for the PSD S3932, i.e. 4.5mm on each side of the photosensitive area. It can interestingly be observed that this area corresponds with a range where |ε| is low. Indeed it can be seen that the average error |ε avg | remains low for -4mm < x P SD < 4mm, i.e. |ε avg | ≈ 0.1332mm. On the contrary, it is observed that |ε| rises as the light spot approaches the ends of the photosensitive area. The calculated values of I O preserve a similar order of magnitude in comparison to the measured values. However, the curve proles are dierent. A possible explanation is that the theoretical value of I e Rel given in the datasheet diers from that of the real IRED's behavior. This hypothesis was tested in a second experiment reported in [START_REF] De | [END_REF]. The obtained results better t experimental data but some differences remain. Also, the procedure is too specic and cannot be a viable solution on the context of a generic development. Fortunately, the results plotted in 4.71 are sucient to estimate the envelope of the useful domain. This can be explained by the fact that at long distances the radiant intensity distribution inside the light beam is relatively homogeneous, while at closer distances this is no more the case. To cope with this issue, the inhomogeneity of the radiant intensity should be taken into account in the sensor model.

Conclusion

IC-HI devices require high performances short range non-contact tracking systems to measure the conguration of the tool relative to the robot's end-eector. After a thorough study of the technological solutions that could potentially solve this problem, ERS systems associating an IRED and a linear PSD appeared to be the most suitable solution therefore, allowing a very simple yet ecient implementation of such sensors.

To validate their interest and performances, a mathematical model and experimental characterization of such system was proposed. Radiometry concepts and geometrical elements of the ERS system were detailed in order to calculate the position of the light spot's center of gravity and the amount of radiant ux being received by the photodetector.

Elements of conversion of power into photocurrent were also given and a test bench of a single ERS system was built and tested in two displacement tasks.

The similarity found between the calculated positions X A and the measured values is particularly promising and the proposed displacement model worked particularly well at long distances. At shorter distances, however, we observe more dierence between the model and the experimental data. To improve these results, the ERS model should be improved, e.g. by better determining the position of the center of gravity of the light beam, taking into account the radiant intensity distribution inside it.

On the other hand, the evaluation of the total light intensity received by the PSD seems sucient in practice to estimate at what distances the IRED could saturate or not suciently illuminate the PSD.

It is worth noting that the use of our test bench requires long and tedious manual manipulations to change the position of the light source and report the results in tables.

Another point of improvement would be to build an automated test bench to extend the case study range.

Chapter conclusion

The present chapter provided a contribution to the design of a 6DoF contactless tracking system for an IC-HI allowing tool interaction.

We rst showed that, while sharing several requirements with general VR trackers (e.g. robust 6 DoF tracking at a high frequency), an IC-HI tracking system has also specic design drivers. As an example, while VR trackers raise the major challenge of non-invasive position measurement of dierent body parts in an unlimited workspace, usually using external sensors, a local tracking system is better suited for the later which requires only a small workspace with however a higher accuracy. Also, a tool-based IC-HI tolerates that the target is equipped with sensor parts (i.e. emitters or receptors). These considerations allowed us introduce the design drivers of an IC-HI device (required measuring range, working frequency, precision and size).

Then we made a thorough review of the technological solutions that could t these requirements. We rst considered existing integrated tracking systems and showed that none of them is suitable o the shelf. As a consequence, we proposed to develop a custom designed solution. To this end, elementary sensors were presented in terms of their working principle and technical characteristics. Conclusions for each type of technology were given with a particular focus on their ability to comply with the searched values of the design drivers. Emitter-Receptor-Slit (ERS) system composed of an IRED illuminating a linear PSD through a thin and narrow slit appeared to be the most suitable solution therefore.

Thus we developed a mathematical model of such an ERS and made its preliminary characterization using an experimental test bench. Our results proved that our model allows to eciently predict both the position of the light spot and the total generated photocurrent. While it would still be interesting to extend the characterization of such 1DoF sensor, we can conclude that such ERS system is a promising solution for the construction of a 6DoF IC-HI tracking module.

General Conclusion and Perspectives

General Conclusion

Force feedback interfaces are robotic systems allowing natural motion interactions with virtual or remote environments. They are employed in several domains such as remote handling, manufacturing, entertainment, education, medicine and rehabilitation, just to mention the most popular. In virtual reality applications, the user typically holds a handle that is mechanically linked to the end-eector of the robot. This link has a non-negligible inuence since the presence of the robot can be felt even in free space, decreasing the realism of the interaction.

Intermittent contact haptic interfaces are a promising technological development aiming to cope with this issue. These interfaces track and closely follow (without contact) the user movements in free space and come to his/her contact only when force feedback is required. This way IC haptic interfaces aim to provide more realistic interactions with virtual environments.

Their design and objective evaluation are however particularly complex and there are still challenges to be met. It was then considered important to focus our research in three directions:

1. evaluation of the benets of the IC paradigm compared to classical haptic interfaces: this research was based on the use of an existing 2DoF device providing nger interactions, 2. improvement of the performances of IC haptic interfaces for force rendering at high speeds: this activity was supported by the same 2DoF device, and 3. the extension of the IC paradigm to provide tool-based interactions in 6DoF: this development relied on a 1DoF prototype.

The main results of our work are the following.

The evaluation of the benets of the IC paradigm was performed through three experiments: stiness identication, target pointing and blind obstacle detection. Two kinds of criteria were taken into account for comparing IC and classical haptic interfaces: on one hand quantitative data informing on the quality of the force rendering and on the other hand qualitative elements allowing to take into account the perception of the users. This research was based on the use of an existing 2DoF device providing nger interactions.

The performed psychophysical tests showed that human operators managed to perform the proposed elementary virtual reality tasks with an IC device as eciently as with a CC device. This is particularly encouraging taking into account that learning to manipulate the IC interface was not straightforward.

The same IC device was also tested under a dierent free space to contact transition strategy intended to improve its performances, and in particular to enlarge its capability to approach virtual objects at high speeds. Indeed it was found that the quality of the force rendering relies on an adequate free space to contact transition at adapted speeds, then on the ability of the device to display mechanical properties corresponding to dierent virtual objects. The former is of a particular importance since the interface should be completely stabilized when the user touches it, giving the impression to touch a static object. With the existing control schemes however, this is the case only at relatively low speeds. The new solution we proposed is intended to cope with this issue. In this approach, we exploit the time taken just before contact by the nger to travel the existing gap between the user's nger and the IC end-eector to apply a purely dissipative force on the device. This way the kinetic energy of the robot is reduced before the user's nger touches it and the user encounters a quasistatic interface. The stabilization stage avoids transmitting to the user unexpected jerks. The experiments performed to validate this approach showed that the contact sensation was perceived as more natural with the new control scheme at high speeds (0.4m/s in the present work). Furthermore, the visuo-haptic delay remained lower than 40ms, i.e. it was imperceptible.

Finally, the main design specications (range of measurement, accuracy, size and working frequency) of the tracking system of a 6DoF IC haptic interface aiming to provide tool interactions were explained. Available tracking systems and non-contact sensing technologies were explored and their pertinence regarding the targeted application (development of a 6DoF IC traking system) was discussed. Finally, a 1DoF IC tracking sensor (called ERS system which stands for Emitter-Receptor-Slit) based on a linear position sensitive detector, a slit and an infrared LED was introduced and modeled. Preliminary measurements allowed us to validate this model and to conclude that such ERS system is a promising solution for the construction of a 6DoF IC-HI tracking module.

Short Term Perspectives

The short term perspectives provided here concern the development of the 6DoF IC interface tracking system. These perspectives are:

• To develop an automated test bench for the 1DoF IC tracking system in order to exhaustively characterize its response, i.e. correlate the displacements of the light source with the sensor position measurements and the total generated photocurrent.

• To employ the existing ERS simulator to nd a direct model (i.e. allowing to compute the response of the sensor knowing the position of the source) that is the closest possible to the real behavior of the system.

• To inverse this relation in order to get a useful inverse model allowing to compute the equation of the plane in which the source lies based on the generated photocurrents of the sensor.

• To simulate a sensor composed of n ERS systems in order to nd a pertinent arrangement allowing to obtain a transformation matrix connecting the sensor readings to the coordinates of a 3D point or directly to a 6DoF information.

• To perform simulations to optimize the sensing space based on the targeted volume.

• To perform the housing design and electronic integration of sensors as well as light sources on a handle.

• To perform its integration on the end-eector of a robot.

• To design the tracking control strategy in 3DoF and 6DoF.

Long Term Perspectives

The long term perspectives assume the existence of a 6DoF tracking system. The proposed perspectives are the following:

• To develop a 3DoF force feedback system with embedded 3DoF tracking system.

• To develop of a 6DoF force feedback system able to track and constraint the tool in 6DoF.

• To perform its integration on the end-eector of a robot.

• To design the free space to contact control strategy in 3DoF and 6DoF.

• To perform psychophysical evaluations as detailed in the present report but employing a robot with low mechanical transparency.

In practice, the three angular sensors (slit/sensor pairs) are arranged on a disk of radius R at 120deg (2π/3) from each other (see Fig.B.3). Their position vector is denoted here P i , the center of the circle being assumed as the origin (0, 0). Based on these resources the vectors v i are dened as follows:

v i = v cos(γ i ) + (u i ∧ v) sin(γ i ) (B.
3)

The equations of the planes corresponding to the angular sensors i containing the points P i are: In order to nd the position of the IR light source, which is the intersection between these planes, it is required to solve the following equations system:    sin(γ 1 ) 0 cos(γ 1 ) sin(7π/6) sin(γ 2 ) -cos(7π/6) sin(γ 2 ) cos(γ 2 ) sin(11π/6) sin(γ 3 ) -cos(11π/6) sin(γ 3 ) cos( γ This solution is more compact. However, the 6DoF pose of the target can only be calculated upon completion of the computation of the three points. As a consequence, the acquisition frequency is only a third of the previous approach. Still, if the bandwidth of the 3D acquisition system is high enough, the position of three points can be computed suciently fast.

The later approach being much more compact, it was employed for the development of the prototype.

Assuming that the three IR light sources attached to the handle form an equilateral triangle whose vertices are denoted A, B and C, the position of the handle can be dened as the center of the triangle located at the point G dened as:

X G = (X A + X B + X C )/3 Y G = (Y A + Y B + Y C )/3 Z G = (Z A + Z B + Z C )/3 (B.8)
This triangle lies in a plane whose normal vector can be denoted as t. The following identities are then veried:

GA • t = 0, GB • t = 0 and GC • t = 0 (B.9)

Thus the components [t x , t y , t z ] of vector t can be found by solving the following equations system:

   X A -X G Y A -Y G Z A -Z G X B -X G Y B -Y G Z B -Z G X C -X G Y C -Y C Z C -Z G       t x t y t z    =    0 0 0    (B.10)
Then, once normalized, the vector t norm = t/|t| can be used as one of the orientation vectors of the handle, i.e. as one of the columns of its transformation matrix T handle , for example the last one a handle which is usually associated with the vector normal to the body of reference. It can be completed with the unit vector GA/|GA|, which has the advantage of being perpendicular to t and can thus be used as another column of T handle , for example the rst one s handle . The second column n handle can be easily obtained as the crossproduct between a handle and s handle .

The handle transformation matrix is then obtained as:

T handle = s handle n handle a handle [X G , Y G , Z G ] T 0 0 0 1 = GA/|GA| t/|t| ∧ GA/|GA| t/|t| [X G , Y G , Z G ] T 0 0 0 1 (B.11)

B.4 Prototype main characteristics

The developed prototype of the tracking system, whose nal design is still condential and cannot be shown here, employs three linear arrays of photodiodes (ref. MLX75306) mounted on a disk in order to measure the intensity of the light emitted by three IR light sources mounted on a pen-like target and ltered by three masks which are perpendicular to the sensors. The current characteristics of the prototype are the following:

• System working frequency: < 300Hz,

• Precision: < 10 -1 mm and

• Workspace: ±10mm.

  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Virtual reality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Sense of touch and haptic feedback . . . . . . . . . . . . . . . . 6 1.4 Force feedback devices application examples . . . . . . . . . . 8 1.5 Commercially available force feedback interfaces . . . . . . . . 10 1.6 Limitations of existing haptic interfaces . . . . . . . . . . . . . 14 1.7 Intermittent-contact paradigm . . . . . . . . . . . . . . . . . . . 15 1.8 Proposed research . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Figure 1 . 3 :

 13 Figure 1.3: First developed and patented VR system.

Figure 1 . 6 :Figure 1

 161 Figure 1.6: Commercial HMDs.

  Figure 1.10:

  Figure 1.11: Examples of common commercial force feedback interfaces.

Figure 1

 1 Figure 1.12: Encountered-type haptic interfaces functioning principle.

  Figure1.13: Virtual haptic space representation (adapted from[START_REF] Tachi | A construction method of virtual haptic space[END_REF]).

Fig. 1 .

 1 Fig.1.15a) and a specically designed contact module for nger interaction (see Fig.1.15b), together accounting for the necessary number of DoF to place a local surface patch any-

Figure 1

 1 Figure 1.15: Multiple nger ET-HI (adapted from[START_REF] Yokokohji | Design and path planning of an encountered-type haptic display for multiple ngertip contacts based on the observation of human grasping behavior[END_REF]).

Figure 1

 1 Figure1.16: Path-planning issue in ET-HIs (adapted from[START_REF] Yokokohji | Path planning for encountered-type haptic devices that render multiple objects in 3d space[END_REF]).

Figure 1 .

 1 Figure 1.18: Close-tracking-type haptic interfaces functioning principle.

Figure 1

 1 Figure1.19: Surface display (adapted from[START_REF] Hirota | Development of surface display[END_REF]).

  Fig.1.20c). A force sensor placed between the ring and the tip of the arm allows then to measure the force applied by the arm on the ngertip.

  Figure1.21: 2DoF CT-HI system from[Gonzalez, 2015].

Figure 1

 1 Figure 1.23: Two nger dexterous CT-HI (adapted from[START_REF] Chabrier | Design and experimental evaluation of an infrared instrumentation for haptic interfaces[END_REF]).

Figure 2 . 2 :

 22 Figure 2.2: Assignment of experiments.

Figure 2 . 3 :

 23 Figure 2.3: 2DoF robot employed for experiments.

  2.4b). It is composed of a thimble that mechanically links the user's nger to the robot. Its internal cup can be replaced with another one of a dierent inner diameter according to the user's nger's size (ve dierent cups ranging from 15 to 19mm were proposed). In order to avoid nger twisting during manipulations, each cup can freely rotate around the distal phalanx axis. (a) IC end-effector (b) CC end-effector

Figure 2 . 4 :

 24 Figure 2.4: Employed end-eectors.

Figure 2 Figure 2

 22 Figure 2.5: VE main elements.

Figure 2 .

 2 Figure 2.7: User's nger and ring representation in the robot's reference frame R 0 .

Figure 2

 2 Figure 2.9: Spring-damper coupling between the ring avatar and the virtual wall.

Figure 2 .

 2 Figure 2.10: Smooth transition-based control block diagram.

Figure 2 .

 2 Figure 2.11: CC force rendering control block diagram.

•

  Did you nd that the interface was tiring to use?

Figure 2 .

 2 Figure 2.13 shows a top view diagram indicating the relative distribution of the dierent mentioned elements.

Figure 2 .

 2 Figure 2.13: Experimental setup top view diagram.

Figure 2 .Figure 2 .

 22 Figure 2.14: Experimenter graphical user interface.

  (a) Please go to the home/starting position (b) O.k.! Let's move back to the starting position 2. The experimenter activates the data recording and invites the participant to perform the VR task. Examples of employed phrases were: (a) 1, 2, 3, Go! (b) 1, 2, 3, Let's go! 3. Once that the participant had accomplished the task, a small break of 10s was given to him/her . At the same time the experimenter stopped recording data. During this break he/she was free to keep his/her nger inside the robot's end-eector or put it aside. Examples of employed phrases were: (a) O.k.! Time for a break. You can put your arm aside if you wish (b) O.k. break! (c) Small rest!

Figure 2 .

 2 Figure 2.17: Elements of a boxplot.

Figure 2 .

 2 Figure 2.18: Stiness identication VE.

Figure 2 .•

 2 Figure 2.19: Stiness identication experiment remote control

Figure 2 .Figure 2 .

 22 Figure 2.21: Stiness identication visual aids.

Figure 2 .

 2 Figure 2.24 shows the boxplot that allows to compare the behavior of the dierent samples in each case. It can be noticed that the data were grouped according to the condition (CC and IC) and according to the reference stiness. Here each point represents the mean of the three trials performed by each user at each K ref value. Several observations can be made based on this resource.

Figure 2 .

 2 Figure 2.24: Dierence D S vs reference stiness K ref boxplot.

  The measured perception P e for this experiment is shown in gure 2.25. The chart shows the measured perception and the ideal value is highlighted by a dotted line. Based on this resource it can be noticed that the perception of participants of low K ref values (Q1) was better in the CC condition. On the other hand no particular dierence was observed in the perception of high K ref values (Q2). It can be also noticed that the participants found the CC interface easier (Q3) and less tiring to use (Q4).

Q1:Figure 2 .

 2 Figure 2.25: Measured perception for 10 subjects for the stiness identication task.

Figure 2

 2 Figure 2.26: Target pointing VE.

  agree• Q2.Were you able to reach the target rapidly? agree • Q4.Did you nd that the interface was tiring to use?

Figure 2 .Figure 2 .

 22 Figure 2.27: Target pointing experiment blocks.

Figure 2 .

 2 Figure 2.29 shows the boxplot that allows to compare the dierent IP s at each ID for both haptic interfaces. It can be noticed that the data set was grouped according to the condition (CC and IC) and according to the index of diculty ID. Each data point represents the mean of trials of each subject at each level of diculty.

Figure 2 .

 2 Figure 2.29: Index of performance IP vs. index of diculty ID boxplot.

  Figure 2.30: Measured perception for 8 subjects for the target pointing task.

Figure 2 .

 2 Figure 2.31: Blind obstacle detection VE.

  agree• Q2.Did you manage to not press too hard on the obstacle? agree • Q3.Did you rapidly stop as soon as the obstacle was detected? agree • Q4.Did you nd the interface easy to use? agree • Q5.Did you nd that the interface was tiring to use? procedure During each trial, the user was instructed to move his/her nger avatar along a vertical line (index nger inside the robot's end-eector) until he/she encounters a horizontal wall (obstacle, invisible to the user) which was positioned at an unknown variable distance from the bottom of the VE. No particular instructions were given regarding the speed of the movement.

Figure 2 .

 2 Figure 2.32: Blind obstacle detection experiment blocks.

Figure 2 .

 2 Figure 2.33: Target pointing procedure stages.

Figure 2 .

 2 Figure 2.34: End eector's speed v r vs. obstacle's position x obs boxplot.

Figure 2 .

 2 Figure 2.35: Time in contact with the obstacle t cont vs. obstacle's position x obs boxplot.

Figure 2 .

 2 Figure 2.36: Maximum estimated force during contact F emax vs. obstacle's position x obs boxplot.

Q2:Figure 2 .

 2 Figure 2.37: Measured perception for 7 subjects for the blind obstacle detection task.

  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.2 Smooth transition-based control . . . . . . . . . . . . . . . . . 75 3.3 Oset transition-based control . . . . . . . . . . . . . . . . . . . 76 3.4 Preliminary comparison of control strategies . . . . . . . . . . 80 3.5 User-test-based comparison of control strategies . . . . . . . . 85 3.6 Chapter conclusions and perspectives . . . . . . . . . . . . . . 99

Figure 3 . 2 :

 32 Figure 3.2: Smooth transition-based control illustration.

  (3.1)) with B d being the dissipation gain. When | Ẋr/0 | < v th the VO state becomes active.

F

  d = -Ẋr/0 B d n (3.1)

Figure 3 . 3 :

 33 Figure 3.3: Finite State Machine governing the proposed control law.

Figure 3 . 4 :

 34 Figure 3.4: Approaching phase of the oset transition-based control.

  3.5).The oset transition-based control block diagram is shown in gure 3.6. Here the KVM block computes the interaction force based on the modied Kelvin-Voigt model.The block f (•) provides the estimation of the robot's end-eector speed Ẋr/0 and relative distances d r/ε and d f /e,ε according to the active state. Here d f /e,ε means that β will be function either of d f /e or d f /ε , according to the active state.

Figure 3 . 6 :

 36 Figure 3.6: Oset transition-based control block diagram.

Figure 3 Figure 3

 33 Figure 3.7: Typical encounter with a vertical virtual wall at a low speed in condition VO-A.

Figure 3 Figure 3 .

 33 Figure 3.9: Typical encounter with a vertical virtual wall at a high speed in condition VO-A.

Figure 3 .

 3 Figure 3.11: Virtual environment employed for the tapping test.

Figure 3 .

 3 Figure 3.13: Main elements of the experimental setup (picture).

Figure 3 .

 3 Figure 3.14: Main elements of the experimental setup (top view diagram).

•Figure 3 .

 3 Figure 3.15: Experimental procedure stages and representative times.

  3.16).

Figure 3 .

 3 Figure 3.16: User's hand expected positioning during manipulations.

  (a) Please go to the starting line (b) O.k.! Let's move back to the starting line 2. The experimenter activated the data recording and invited the participant to perform the VR task (to tap on the left vertical wall of the VE). Examples of employed phrases were:

Figure 3 .

 3 Figure3.17: Scheme of a typical experiment in a case 2 structure.

Figure 3 .

 3 Figure 3.18: Elements of a boxplot.

Figure 3 .Figure 3 .

 33 Figure 3.19 illustrates the boxplot corresponding to the speed of the ring when it encountered the VO (v r (t r/vo )). It can be observed that the movements were performed

Figure 3 .

 3 Figure 3.20: Speed of the ring at time t f /r .

Figure 3 .Figure 3 .

 33 Figure 3.21 resumes the retrieved amplitudes d max of the rst rebound of the ring against the wall. This value should be as small as possible to reduce unnatural perceived

Figure 3 .

 3 Figure 3.23: : Survey scores.

Figure 4

 4 Figure 4.1: IC interface using tool-based interaction paradigm with local tracking system.

Figure 4 . 2 :

 42 Figure 4.2: External tracking approach, based on a camera motion capture system, and associated errors.

Figure 4 . 3 :

 43 Figure 4.3: Hybrid tracking approach, combining data from motion capture tracking system and robot joint sensors, and associated errors.

Figure 4 . 4 :

 44 Figure 4.4: Equipped end-eector employed as a local tracking system and associated errors.

4. 4

 4 Design drivers of an IC haptic interface tracking system 4.4.1 General considerations

Figure 4 . 7 :

 47 Figure 4.7: Tracking error vector between the handle and the IC haptic interface.

Figure 4 .

 4 Figure 4.8: 1DoF IC interface control block diagram.

Figure 4 . 9 :Figure 4 .

 494 Figure 4.9: Maximal tracking error abacus for dierent values of K p and K d .

  in robotics and in VR applications. Its goal is to open a discussion towards the choice of tracking systems possibly suiting the development of an IC handle tracking system. The question is then what kind of sensing technologies/approaches are compatible with the targeted application? A comprehensive taxonomy of existing tracking methods is shown in gure 4.11. The most promising will be discussed in the following paragraphs.

Figure 4 .

 4 Figure 4.11: User motion tracking methods (taken from[START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF]).

  Figure 4.12: Mechanical linkage tracking paradigm (adapted from[START_REF] Rolland | A Survey of Tracking Technology for Virtual Environments[END_REF]).

lFigure 4 .

 4 Figure 4.13: Calculation of the position of a point based on ultrasonic distance measurements.

Figure 4 .

 4 Figure 4.14: Ultrasonic sensor arrangement paradigm to estimate the complete pose of a target (adapted from[START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF]).

Figure 4 .

 4 Figure 4.15: Phase-shift distance measurement principle (inspired from[START_REF] Rolland | A Survey of Tracking Technology for Virtual Environments[END_REF]).

Figure 4 .

 4 Figure 4.16: Magnetic eld of a simplied coil (adapted from[START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF]).

  Figure 4.17: Magnetic eld density vector near the coil (adapted from[START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF]).

Figure 4 .

 4 Figure 4.21: Laser triangulation principle (adapted from[START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF]).

  parts, e.g. parts with surfaces easily damaged, inspection of dynamic materials, e.g. monitoring the dimensions of a tire while rotating at high speed, monitoring vibrations, close control loop of pouring of molten metal Optical triangulation is employed as general measuring principle.

Figure 4 .

 4 Figure 4.22: Sample diagram of triangulation based laser sensor from Micro-Epsilon (adapted from [Micro-Epsilon, 2018]).

  4.5.4.4 Light pattern projectionThe light pattern projection principle consists in illuminating an object of known geometry with a known pattern of light and taking a picture of this object. Its conguration is then computed by matching this image with a model of the illuminated object. A simple pattern consists in parallel stripes projected onto the object of interest. A camera, which is displaced by a certain triangulation angle, perceives the same stripes as curves running along the surface of the object. With the use of mathematical algorithms, the three-dimensional shape of the object can be determined (seeFig.4.23).

Figure 4 .

 4 Figure 4.23: Pattern projection principle (adapted from[START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF]).

  3D imaging systems may have different accuracies in different (𝑥,𝑦,𝑧) directions because of the inherent design properties of the systems Target Does not require target instrumentation ✗: Bandwidth decreased because of image post-processing times ✗: Cumbersome and requires a controlled environment Applications 3D Facial recognition, 3D dental imaging, 3D imaging techniques for plastic surgery, 3D model of ear impression for custom hearing aid, imaging for reverse engineering consists on the employ of video cameras placed on a reference and that record features of the target (see Fig.4.24).

  4.27a). HiBall was designed as a single, rigid, hollow ball having dodecahedral symmetry, with lenses in the upper six faces and LEDs on the insides of the opposing six lower faces (seeFig.4.27b). This system shows remarkable improvements in terms of size and weight. Despite this, this system remains unfortunately too large and heavy for our application. Also, its accuracy is insucient for the precise tracking of the handle of an IC-HI. Representative characteristics of reported videometric tracking systems are provided in Table4.10. a) HiBall tracking system b) HiBall

Figure 4 .

 4 Figure 4.27: HiBall tracking system[START_REF] Welch | High-Performance Wide-Area Optical Tracking: The HiBall Tracking System[END_REF]).

  4.28b). b) DragonEye 3D Flash LIDAR Space Camera (by Advanced Scientific Concepts Inc.) a) VLP-16 LIDAR range scanner (by Velodyne)

Figure 4

 4 Figure 4.28:

  4.5.4.7 Systems employing PSDsMost of the aforementioned techniques were developed for applications outside the eld of haptics. A couple of tracking systems specically developed for contactless measurement of the 6DoF conguration of the handle of manual human-machine interfaces were also identied in literature. The systems in question are the SPACE MOUSE and the Maglev haptic interface which will be described in the following paragraphs. Both employ position sensitive detectors (PSDs) to obtain non-contact 6DoF displacement information. These sensors are basically large photodiodes providing 1D or 2D coordinates of a spot light hitting their active surface.Developed in the mid-80s by the German Aerospace Center (known as DLR or Deutsches

  4.29a). The inner moving ring is composed of the LEDs and slits. Each slit faces a 1D PSD which is perpendicularly oriented. Although not shown in gure 4.29a, the ring with PSDs is xed inside the outer part and connected via springs with the inner ring. The springs bring the inner ring back to an initial position when no forces are applied.

FlotorFigure 4 .

 4 Figure 4.29: 6DoF sensors employing emitter/detector pairs based on PSDs.

  and characteristics Ultrasonic sensors generate high frequency acoustic waves (> 20kHz) that can travel and be reected by an obstacle (see Fig.4.30a). Ultrasonic transducer Obstacle a) Ultrasonic sensor principle b) HRUSB-MaxSonar® -EZ TM Series from MaxBotix Inc.

Figure

  Figure 4.30: (a) Reected waves generated by an ultrasonic transducer (adapted from

-

  Imposed by the pulse trip time, e.g. for c = 343.2m/s, 𝑙 = 10cm: 𝑡 𝑡𝑜𝑓 ≈ 0.3ms ➔ 𝑓 ≈ 3.3kHz (for separate emitters and receivers) 𝑡 𝑡𝑜𝑓 ≈ 0.6ms ➔ 𝑓 ≈ 1.6kHz (for co-localized emitters and receivers) -If phase-shift method, higher sample rates can be obtained since continuous signals are being measured Accuracy Repeatability Resolution -Minimum measurement accuracy possible in transversal direction is 𝜆/2 (depends on the frequency used and the density of the medium, e.g. air) e.g. for an ultrasonic wave of 𝑓 = 40kHz traveling in air at a speed 𝑐 = 343.2m/s we obtain 𝜆 = 8.5mm thus an accuracy of 4.25mm -Some tenths of the ultrasonic wave -1 -25.4 mmNeeds to equip target?-Yes (if separate emitters and receivers) -No (if co-localized emitters and receivers) Simple, cheap and relatively small. ✓: Not affected by color or other visual characteristics ✓: Longlasting ✗: Sensitive to temperature, pressure and humidity which affect the velocity of sound and thus the accuracy of measured distances ✗: Signal losses energy with the traveled distance, which limits the measuring rangeApplicationsParking systems of cars, liquid level detection, robotics

  in two parallel conductive plates (electrodes) placed face to face

Figure 4 .

 4 Figure 4.32: Capacitive sensor principle [MicroSense, 2018].

Figure 4 .

 4 Figure 4.33: High resolution non-contact capacitive position sensor 8810 from MicroSense.

Figure 4 .

 4 Figure 4.35: DC SQUID simplied diagram.

Figure 4 .

 4 36 shows some examples.

Figure 4 .

 4 Figure 4.36: Commercial SQUID sensors from Supracon R .

Figure 4 .

 4 Figure 4.39: Hunt element (adapted from [TE Connectivity Sensors, 2018a]).

Figure 4 .

 4 Figure 4.40, shows commercially available angular and position AMR sensors from the Swiss company TE Connectivity. For simplication purposes, only AMR sensors characteristics will be presented here.Table 4.18 provides representative characteristics

  (4.10)), where the product ma represents the force acting on the mass. mẍ + d ẋ + kx = ma

  Figure 4.44: Accelerometer principle (taken from[START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF]

Figure 4 .

 4 Figure 4.45: Position measurement based on inertial sensors (taken from[START_REF] Mihelj | Virtual Reality Technology and Applications[END_REF]).

  Photomultipliers are sensors that work based on the external photoelectric eect which states that when light (with sucient energy) hits a metal plate, photoelectrons are released from the surface of the material. An example of a photomultiplier diagram is shown in gure 4.47a. Such arrangement (typically build in a vacuum glass tube)shows how the incoming light gets amplied (based on the external photoelectric eect) when hitting several additional electrodes (dynodes). Such avalanche eect leads to a current amplication converted into a voltage thanks to resistors. The voltage obtained is proportional to the incoming light intensity on the photocathode.

Figure 4 .

 4 Figure 4.47: Photomultiplier diagram and commercial samples.

  4.48).The association of these two types of materials represents one of the most common semiconductor devices, a diode. This junction allows the passage of current only in one direction if a positive voltage (forward bias) is applied on the ends of the P-N junction, i.e. the diode is acting as a closed switch (seeFig.4.49a). On the contrary, if the applied voltage is inverted (reverse bias), the P-N junction will act as an open switch (seeFig.4.49b).

Figure 4 .

 4 Figure 4.48: Main elements of a P-N junction.

Figure 4 .

 4 Figure 4.49: Forward and reverse bias of a P-N junction.

  4.50a). The symbol of a photodiode is shown in gure 4.50b. Anode (+) Catode (-) (a) SD5421-002 Photodiode p-i-n from Honeywell (b) Photodiode symbol

Figure 4 .

 4 Figure 4.50: Photodiode sensor.

Figure 4 .

 4 Figure 4.53: Charged coupled device sensor. (a) adapted from [Alfaraj, 2017].

  Photodiode

Figure 4 .

 4 Figure 4.54: CMOS image sensor oorplan and common pixel types. (a) adapted from[START_REF] Bigas | Review of cmos image sensors[END_REF].

Figure 4 .

 4 Figure 4.55: Commercial CMOS imager.

  photosensitive area, the light incident on the detector is converted into an electrical current (photocurrent) that is divided between the contacts in proportion to the resistance of the active layer (seeFig.4.56). This phenomenon is called lateral photo-eect[Woltring, 1975].

  used in non-contact distance measurement systems using the triangulation principle for various height and vibration measurements. They are commercially available either in 1D (see Fig.4.57a) or in 2D (see Fig.4.57b) formats. (b) S5991-01 2D PSD from Hamamatsu (a) S3932 1D PSD from Hamamatsu

Figure 4 .

 4 Figure 4.57: Commercial 1D and 2D PSDs.

  Photosensitive area𝑋

Figure 4 .

 4 Figure 4.58: Emitter-Receptor-Slit principle.

Figure 4 .

 4 Figure 4.60: Light beam shaped by the slit (left) and its subsection illuminating the PSD active area (right).

Figure 4 .

 4 Photosensitive area

  O = P psd S + I D = ΩI e (I F )S + I D (4.13)

Figure 4 .

 4 Figure 4.62: Relative radiant intensity prole for IRED CQY36N (left) and IRED half-intensity emission cone (right). At a view angle γ = ϕ, the emitted power corresponds to half of the total radiant intensity I e .

  4.63). The ERS simulator allows to calculate the response for any number of ERS arbitrarily positioned and oriented in space.z (mm)

Figure 4 .

 4 Figure 4.63: Single (left) and 6 ERS (right) congurations simulation.

  4.64).

Figure 4 .

 4 Figure 4.64: ERS test bench main elements

Figure 4 .

 4 Figure 4.65: Emitter Sub-Assembly's main elements. From left to right, from top to bottom: an IRED CQY36N from VISHAY. A ROCHPROFIL displacement indicator of 0.01mm resolution allowing to measure translations on each axis. The rotation axis that hosts the IRED support and which rotation axis is coincident with the IRED's chip. The IRED support that can be rotated around the IRED's central axis by steps of 45 • . A goniometer allows to quantify the rotation on the vertical axis. Finally the complete Emitter Sub-Assembly.

Figure 4 .

 4 Figure 4.66: Receptor Sub-Assembly main elements. From left to right, from top to bottom: one-dimensional PSD S3932 by HAMAMATSU. A 0.16mm thick dark steel mask, containing a slit that can be mounted on the PSD support. The slit width equals 0.4mm and it is oriented perpendicular to the PSD photosensitive area, dividing it into two halves. Aluminum shims of 2.5mm height allow to position the slit at a distance d B from the PSD surface. A PSD support specially designed to host the one-dimensional PSD S3932. Finally the complete Receptor Sub-Assembly

Figure 4 .

 4 Figure 4.67: Shim of 2.5mm height containing a 1mm thick OptoliteTM infrared lter made by Instrument Plastics.

Fig. 4 .

 4 Fig.4.68).

Figure 4 .

 4 Figure 4.68: Positioning at the zero reference by means of the centering tube. At this position the IRED central axis is coincident with the center of the photosensitive area of the PSD.

Figure 4 .

 4 Figure 4.69: PSD reference frame seen by the IRED. The frame has its origin at the geometrical center of the photosensitive area and the x P SD axis is parallel to it.

Figure 4 .

 4 Figure 4.70 shows the resulting X A position for the proposed experiment. It can be observed that the calculated and measured values are very similar, however there

Figure 4 .

 4 Figure 4.70: Comparison of the calculated and measured values of the position X A of the light spot on the sensor. When the IRED translates in the positive direction of x P SD , the light spot moves in the opposite direction and vice versa.

Figure 4 .

 4 Figure 4.71 shows the amount of generated photocurrent I O for this experiment. The calculated values of I O preserve a similar order of magnitude in comparison to

Figure 4 .

 4 Figure 4.71: Calculated and measured values of the total photocurrent I O generated by the sensor.

Figure 4 .

 4 Figure 4.72: Comparison of the calculated and measured values of the position X A of the light spot for dierent values of the distance d A between the IRED and the sensor.

  The total generated photocurrents corresponding to the same four values of d A are shown in Fig.4.73. This conrms that despite the dierence of photocurrent proles, the order magnitude of theoretical photocurrent I O remains close to the measured values. This result allows to conclude that our model is sucient to estimate at what distances the IRED could saturate or not suciently illuminate the PSD.

Figure 4 .

 4 Figure 4.73: Calculated and measured values of the total photocurrent I 0 generated by the sensor for dierent values of the distance d A between the IRED and the sensor.

Figure B. 3 :

 3 Figure B.3: Placement of the angular sensors on the circular base.

Figure B. 4 :

 4 Figure B.4: Representation of vectors in space.

P 1

 1 : sin(γ 1 )X + cos(γ 1 )Z = d 1 withd 1 = R sin(γ 1 ) (B.4) P 2 : sin(7π/6) sin(γ 2 )X -cos(7π/6) sin(γ 2 )Y + cos(γ 2 )Z = d 2 with d 2 = R sin(γ 2 )[cos(2π/3) sin(7π/6) -sin(2π/3) cos(7π/6)] (B.5) P 3 : sin(11π/6) sin(γ 3 )X -cos(11π/6) sin(γ 3 )Y + cos(γ 3 )Z = d 3 withd 3 = R sin(γ 3 )[cos(4π/3) sin(11π/6) -sin(4π/3) cos(11π/6)] (B.6)

Figure B. 6 :

 6 Figure B.6: Alternated employ of a 3D sensor, maximizing the compactness.

  .14 Main elements of the experimental setup (top view diagram). . . . . . . . . 3.15 Experimental procedure stages and representative times. . . . . . . . . . . 3.16 User's hand expected positioning during manipulations. . . . . . . . . . . .

	Introduction
	Classical force feedback interfaces, also called here classical-contact haptic interfaces
	(CC-HIs), are robotic systems allowing natural motion interactions with virtual or re-
	mote environments. They are used in several domains such as design, manufacturing,

Introduction xxi Moving away from the virtual object. . . . . . . . . . . . . . . . . . . . . . 3.6 Oset transition-based control block diagram. . . . . . . . . . . . . . . . . 3.7 Typical encounter with a vertical virtual wall at a low speed in condition VO-A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Typical encounter with a vertical virtual wall at a low speed in condition VO-B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Typical encounter with a vertical virtual wall at a high speed in condition VO-A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10 Typical encounter with a vertical virtual wall at a high speed in condition VO-B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11 Virtual environment employed for the tapping test. . . . . . . . . . . . . . 3.12 Finger avatar location in VO-B approach. . . . . . . . . . . . . . . . . . . 3.13 Main elements of the experimental setup (picture). . . . . . . . . . . . . . 33.17 Scheme of a typical experiment in a case 2 structure. . . . . . . . . . . . . 3.18 Elements of a boxplot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.19 Speed of the ring at time t r/vo . . . . . . . . . . . . . . . . . . . . . . . . . . assembly, scientic visualization, entertainment, education, medicine, space, rehabilitation, micromanipulation and molecular biology. In all cases, they should provide adequate kinesthetic (force) feedback, contributing to enhance the sense of presence in the virtual environment.

Table 1 .

 1 1: Characteristics of commercial force feedback interfaces. Here the Ø (diameter)

Table 2 .2: Experiments calendar. Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 IC Stiffness IC Contact CC Pointing CC Stiffness CC Contact IC Pointing

 2

	S1 to S5	S11 to S15 S21 to S25	S1 to S5	S11 to S15 S21 to S25

IC Pointing CC Stiffness CC Contact CC Pointing IC Stiffness IC Contact

	S6 to S10 S16 to S20 S26 to S30	S6 to S10 S16 to S20 S26 to S30

  2.8).

	Ring	Real world	Virtual world	𝑥 𝑒
	(End-effector)
			𝑑 𝑓/𝑒
	User's		Finger
	finger	𝑿 𝑓/0	avatar	𝑑
	𝑿 𝑟/0		Ring avatar
		𝐙 𝑡 𝑐𝑎𝑟𝑡
			𝑑 𝑟/𝑒

𝛽

Figure

2

.8: Spring-damper coupling between the center of the ring and the nger. Here the nger and ring avatars are approaching a VO located at x e and are respectively located at a distance d f /e and d r/e from it. In this gure, the impedance Z tcart is represented in the Cartesian space. It is linked to the joint space impedance Z t dened in equation

(2.3)

by the relation

Table Experimenter

 Experimenter

		Remote
		control
			Screen
		Wall
	Table	Robot	Wall	Supervision computer

Table Figure 2

 Figure .20: Stiness identication experimental setup.

  The corresponding ID values for each (A,W ) combination are shown in table2.3.

Table 2 .

 2 3: Index of diculty ID for each (A, W ) combination.

	Level

Combination A (cm) W (cm) ID (bits)

•

  VO state: in this state the VO properties (the same as implemented in the original control law) are displayed.

	Transparent state	𝑑 𝑟/𝑒 < 0	Braking state
			ሶ 𝑿 𝑟/0 < 𝑣 𝑡ℎ
	𝑑 𝑟/𝑒 > 𝑑 𝛽
			VO state

  𝝉 𝒕 = 𝐙 𝐭 . 𝛽 𝑚𝑖𝑛 . 𝛜 𝒒 𝝉 𝒕 = 𝐙 𝐭 . 𝛽 𝑚𝑖𝑛 . 𝛜 𝒒

	Transparent state	Braking state		Transition		VO state
	𝑑 𝑓/𝑒 𝑥 𝑒	𝑥 𝑒		𝑥 𝑒	𝑥 𝜀	𝑑 𝑓/𝜀	𝑥 𝑒	𝑥 𝜀	𝑑 𝑟/𝜀
	𝑑 𝛽	𝑑 𝑟/𝑒
	1	2			3			4
				𝜀
	𝑖𝑓 𝑑 𝑓/𝑒 > 0	𝑖𝑓 𝑑 𝑟/𝑒 ≤ 0		𝑖𝑓 ሶ 𝑋 𝑟/0 ≈ 0		𝑖𝑓𝑑 𝑟/𝜀 ≤ 0 (𝑑 𝑟/𝑒 ≤ -𝜀)
	Regulated tracking reference torque	Additional bilateral damping force	Wall offset		Contact
	𝝉 𝒕 = 𝐙 𝐭 𝛽𝛜 𝒒	𝝉 𝒕 = 𝐙 𝐭 . 𝛽 𝑚𝑖𝑛 . 𝛜 𝒒
		𝑭 𝐝 = -ሶ 𝑋 𝑟/0 𝐁 𝐝 𝒏	New wall position	𝑖𝑓 𝑑 𝑟/𝜀 < 0 & ሶ 𝑋 𝑟/0 > 0
				𝑥 𝜀 = 𝑥 𝑒 + 𝜀		𝑭 𝐞 = -𝑑 𝑟/𝜀 𝐊 𝐞 + 𝐁 𝐞 𝑠 𝒏
				(used for contact		𝑖𝑓 𝑑 𝑟/𝜀 < 0 & ሶ 𝑋 𝑟/0 < 0
				AND tracking)		𝑭 𝐞 = -𝑑 𝑟/𝜀 𝐊 𝐞 𝒏
							𝑒𝑙𝑠𝑒
							𝑭 𝐞 = 0
	Ring avatar	Finger avatar	Virtual object (wall)

  𝑖𝑓 𝑑 𝑓/𝜀 > 𝑑 𝛽 𝑖𝑓 𝑑 𝑟/𝑒 > 𝑑 𝛽

				VO state				Transparent state
				𝑥 𝑒	𝑥 𝜀							𝑥 𝑒	𝑥 𝜀
				𝑑 𝑓/𝜀						𝑑 𝑟/𝑒
					𝑑 𝛽							𝑑 𝛽
						5							6
			Moving away from virtual object				Free space
	+ -𝑿 𝑓/𝑟 0	𝛽 𝑑 𝑓/𝑒,𝜀	𝝐 𝒙	𝝉 𝒕 = 𝐙 𝐭 𝛽𝛜 𝒒 𝐉 -1 (𝒒)	𝝐 𝒒	𝐊 𝑡 + 𝐁 𝑡 𝑠	𝝉 𝑡 + 𝝉 𝑒	+ +	𝝉 ℎ 𝝉 𝒕 = 𝐙 𝐭 𝛽𝛜 𝝉 𝐝 𝝉 +	Human Operator Robot 𝑿 𝑟/0	-+	𝑿 𝑓/0
								𝐉 𝐓 (𝒒)	𝑭 𝒅		𝐁 𝑑	-ሶ 𝑿 𝑟/0
								𝐉 𝐓 (𝒒)	𝑭 𝑒	KVM	𝑑 𝑟/𝜀	𝑓(•)

𝒒 Figure 3.5: Moving away from the virtual object. When any of the distances d f /ε or d f / is bigger than a distance d β , in reference to x ε or x e respectively, β = 1.

Table Participant Table Experimenter WallTable Haptic interface Screen

 ParticipantExperimenterHapticScreen

Table 3 .

 3 2: Mean and standard deviation for t vr≈0 and ε.

	mean (std)	𝒕 𝒗 𝒓 ≈𝟎 (ms)	𝛆 (mm)
	Low speed	3.38 (2.90)	0.45(0.28)
	High speed	13.55 (1.97)	2.21(0.37)

Table 4 .

 4 1: Human hand speeds and accelerations in VR applications. Values taken from (

Table 4 .

 4 2: Skills haptic interface main characteristics.

	Parameter	Value
	Peak translational effort: 𝐹 𝑝𝑘	25N
	Apparent mass: 𝑚	0.460kg
	Robot link length: 𝑙 𝑟	0.300m
	The block diagram of the simulated robot (implemented in Matlab Simulink) is shown
	in gure 4.8. The simulation takes as a set point the human's hand position x

h . The tracking error X is calculated by subtracting the sensed position of the robot x * r from

  Angular acceleration ω allows to calculate the angular position θ which is nally used to compute the robot's position x r . The position of the robot is sensed with a delay of 2ms in order to take into account the haptic loop servo rate and other delays.

			𝜖 𝑋
	𝑥 ℎ	+ -	𝑥 ℎ -𝑥 𝑟 *	1 𝑙 𝑟	𝜃 ℎ -𝜃 𝑟 *	PD	𝜏	𝜏 𝑠	1 𝑚𝑙 𝑟 2	ሶ 𝜔	1 𝑠 2	𝜃	𝑙 𝑟	𝑥 𝑟
		𝑥 𝑟 *					Sensor

Table 4 .

 4 3: IC tracking system design specications.Localization of objects or persons is a common problem faced in several elds of applications. For instance, it is necessary to localize airplanes for air trac control. It can also be interesting to localize a person which mobile phone has a GPS or to propose him/her location based services or to localize an object in space thanks to the information provided by several cameras observing the scene. Each application may need one or more sensing technologies which data are employed to determine the information of interest.

	IC end-effector design drivers	Value
	Minimum distance of measurement	1mm
	Range of measurement	≥ 1cm*
	Working frequency	1kHz
	Position/orientation accuracy	< 10 -1 mm/1°*
	i.e. an inner spherical volume of diameter 𝑑 = 𝜖 𝑋 1cm + handle diameter 1.5cm
	4.5 Review of common motion tracking systems

Table 4 .

 4 7 summarizes representative performances of systems employing both types of markers (markerless techniques being out of the interest of the present work).

Table 4

 4

	.7:	Representative	performances	of	tracking	systems	employing	markers

Table 4 .

 4 8 provides representative characteristics of triangulation based laser sensors, manufactured by the company Micro-Epsilon, and gure 4.22 shows a representative diagram of these sensors.

Table 4 .

 4 8: Laser sensor (triangulation) representative performances[Micro-Epsilon, 2018].

	Sensor type	Laser sensor (triangulation)
	Measured variable	Displacement, distance and thickness
	Physical phenomenon	Light reflection
	Size	[46 × 20 × 30mm] -[200 × 48 × 83mm]
	Measuring range	2mm -1000mm
	Working frequency	2kHz -100kHz
	Resolution	0.2𝜇m -100𝜇m
	Target instrumentation	No
	Degrees of freedom (DoF)	1DoF
	Occlusion sensitive	Yes
	Price	Expensive

Table 4 .

 4 11: LIDAR range scanner representative performances[START_REF] Velodyne | Products[END_REF].

	Sensor type	LIDAR
	Measured variable	Time of flight
	Physical phenomenon	Laser effect
	Weight / Size	590g -12.7Kg / [7 × 9 ]cm to [18 × 28]cm
	Measuring range	Up to 120m
	Working frequency	600,000 to 2,200,000 points per second Rotation rate between 5 to 20Hz
	Accuracy / Resolution	Range accuracy between ±2cm to ±3cm / Vertical resolution between 0.33°and 2°T
	arget instrumentation	Not necessary
	Degrees of freedom (DoF)	1DoF since it acquires distance measurements
	Installation	Requires to be mounted
	Occlusion sensitive	Yes
		✓: Large measurement ranges
	Strengths (✓) / Weaknesses (✗)	✗: Cumbersome ✗: Limited vertical field of view
		✗: Low range accuracy regarding the design of an IC-HI
	Applications	Car security, autonomous trucking, drones, robotics

Table 4 .

 4 12: 3D ash LIDAR cameras representative performances[START_REF] Horaud | An overview of depth cameras and range scanners based on time-of-ight technologies[END_REF]

	Advanced Scientic Concepts Inc., 2018].
	Sensor type	3D Flash LIDAR camera
	Measured variable	Time of flight
	Physical phenomenon	Reflection of light pulses
	Size	[11 × 11,2 × 12,1cm] -[14 × 20,6 × 16,5cm]
	Measuring range	7m-1100m
	Working frequency	Between 10 -450 Frames per second (FPS)
	Resolution	[128 × 128] to [1280 × 1024] pixels
	Target instrumentation	Not required
	Degrees of freedom (DoF)	Provides point cloud of depth measurements
	Occlusion sensitive	Yes
	Price	Expensive
		✓: Can perform outdoors, under adverse conditions
		✓: Target does not require to be equipped
	Strengths (✓) / Weaknesses (✗)	✗: Cumbersome
		✗: Measuring range too big
		✗: Low working frequency

  4.6.2.2 ConclusionUltrasonic rangenders are relatively simple and cheap sensors employed in applications as parking systems of cars, liquid level detection and robotics among others.

Table 4 .

 4 15: Capacitive displacement sensors representative performances [MicroSense, 2018, RS Components, 2018].

	Sensor type	Capacitive
	Measured variable	Current or voltage
	Physical phenomenon	Change of capacitance
	Size	Probe diameters between 0.5mm and 10mm
	Measuring range	Between ±10μm to ±1000μm
	Working frequency	-Up to 100kHz for active sensors -Up to 20kHz for passive sensors
	Resolution	< 1nm
	Needs to equip target?	No
	Degrees of freedom (DoF)	1DoF (small displacements)
	Occlusion sensitive	Yes: the presence of other targets will impact the measured capacitance.
	Price	Expensive
		✓: High resolution and bandwidth
		✗: Dirty particules on the sensor can affect the measurement
		✗: Highly dependent on the permitivity of the medium between the
		plates, e.g. it can be strongly influenced by dust or humidity
		✗: Small measurement ranges
	Strengths (✓) / Weaknesses (✗)	Passive ✓: Flexibility in probe configuration, stability and lower costs
		✗: Cable length restrictions (3 -7m)
		Active
		✓: Do not depend on a cable length
		✓: Work at higher frequencies
		✗: Less flexible and higher costs
		Positioning, run out measurement, autofocus and nulling, distance and
	Applications	displacement measurement, thicknes and vibration measurements,
		contact detection

Table 4 .

 4 16: Representative performances of SQUID sensors.

	Sensor type	SQUID
	Measured variable	Current, magnetic field
	Physical phenomenon	Superconducting ring with one or two Josephson junctions
	Size	Chip size: 2.5 × 2.5 mm 2 to 4 × 4 mm 2
	Measuring range	Not reported
	Working frequency	< 1Hz
	Accuracy / Resolution	Not reported
	Needs to equip target?	No
	Degrees of freedom (DoF)	Not reported
	Occlusion sensitive	Not reported
	Price	Expensive
	Strengths (✓) / Weaknesses (✗)	✓: Provides the highest available sensitivity ✗: Expensive

Table 4 .

 4 18 provides representative characteristics issued from the TE Connectivity catalogue.

Table 4 .

 4 20: Representative characteristics of IMUs[START_REF] Honeywell | Inertial Measurement Units[END_REF][START_REF] Xsens | XSens Products[END_REF]

	Filippeschi et al., 2017]
	Sensor type	Inertial measurement unit (IMU)
	Measured variable	Angle/Position
	Physical phenomenon	Gyroscope effect, Acceleration
	Size	[13.2 × 13.2]mm -[130 × 135 × 66]mm
	Measuring range	Angular speed: ±75 -±2000deg/s Acceleration: ±6 -20g
	Working frequency	100-2000Hz
	Resolution	Angular speed: 1 -40mdeg/s Acceleration: in the order of 0.01m/s 2
	Needs to equip target?	Yes: sensor moves with the target to generate data
	Degrees of freedom (DoF)	6DoF measurements
	Occlusion sensitive	No
	Price	Relatively cheap
		✓: Low power consumption
	Strengths (✓) / Weaknesses (✗)	✓: Small size
		✗: Suffer from drift error due to integration of acceleration
		Activation or airbags, biomechanical applications for human activity
	Applications	recognition, in cameras for image stabilization, human-robot interaction,
		vibration control, missile guidance.
	filippeschi_survey_2017
	4.6.5.2 Conclusion

Table 4 .

 4 22: Representative characteristics of CCDs.

	Sensor type	CCD
	Measured variable	Light intensity
	Physical phenomenon	Conversion of light into electric current (MOSCAP pixel)
	Size	[20 × 30 × 4]mm -[59 × 48 × 7]mm
	Measuring range	Wavelength: 400 -1000nm Array dimensions: [512 × 512]pixels -[8304 × 6220]pixels
	Working frequency	1-20 fps (frames per second)
	Resolution	Pixel size: 5.4 × 5.4 μm -24 × 24 μm
	Needs to equip target?	Yes, target should provide any detectable light source
	Degrees of freedom (DoF)	2DoF, 6DoF possible employing a sensor arrangement
	Occlusion sensitive	Yes
	Price	Relatively expensive
		✓: Compact
		✓: Mature technology
	Strengths (✓) / Weaknesses (✗)

✗: Important power consumption ✗: Low noise ✗: Needs external analog-to-digital converter

Applications

Machine vision, UV-VIS-IR spectroscopy, digital oscilloscopes, scientific imaging

Table 4 .

 4 23: Representative characteristics of CMOS imagers.

	Sensor

type CMOS Measured variable Light intensity Physical phenomenon Conversion

	Measuring range	Wavelength: 400 -1000nm Array dimensions: [640 × 480]pixels -[2210 × 3002]pixels
	Working frequency	5 -815 fps (frames per second)
	Resolution	Pixel size: 3 × 3 μm -14 × 14 μm
	Needs to equip target?	Yes, target should provide any detectable light source
	Degrees of freedom (DoF)	2DoF, 6DoF possible employing a sensor arrangement
	Occlusion sensitive	Yes
	Price	Relatively cheap
		✓: Individual pixel readout
		✓: Low power consumption
	Strengths (✓) / Weaknesses (✗)	✓: Cheaper than CCDs

of light into electric current (PPS or APS pixels) Size

[11.5 × 11.5 × 1.4]

mm -[36 × 31 × 6.8]mm ✓: Faster than CCDs ✗: Face lower fill factor than CCDs ✗: Less sensitive than CCDs Applications Space, automotive, medical, digital photography, machine vision, motion monitoring, security, barcode scanning.

Table 4 .

 4 24 provides representative characteristics of commercially available PSDs. The provided characteristics were issued from Hamamatsu catalogue.

Table 4 .

 4 24: Representative characteristics of PSDs.

	Sensor type	Position sensitive detector (PSD)
	Measured variable	Generated photocurrent
	Physical phenomenon	Conversion of light into electric current (lateral photo-effect)
		Package size:
	Size	1D: 4.1 × 4.8 × 1.8 mm to 55 × 5 × 2.5 mm
		2D: 8.8 × 10.6 × 1.2 mm to 28 × 28 × 5 mm
		Wavelength: 320nm -1100nm
	Measuring range	Photosensitive area size: 1D: 2 to 37mm
		2D: [4 × 4]mm to [12 × 12]mm
	Working frequency	100kHz -1MHz
	Error / Resolution	1D, 2D Position error: 10μm -150μm / 2D Resolution: 0.4mm -1mm
	Needs to equip target?	Yes, target should provide any detectable light source
	Degrees of freedom (DoF)	1DoF, 2DoF, 6DoF (employing a sensor arrangement)
	Occlusion sensitive	Yes
	Price	Relatively cheap
	Strengths (✓) / Weaknesses (✗)

✓: Compact ✓: High speed ✓: Simple to use ✗: Require precise current measurement equipment

Applications

Non-contact distance measurement, e.g. height and vibration measurements.

Acknowledgments

I wish to express my deepest gratitude to my supervisors who gave me the opportunity to undertake this project.

The research work for this doctoral thesis was conducted at the Laboratoire de Robo-The funding for this project was made possible by the Commissariat à l'énergie atomique et aux énergies alternatives de Saclay (CEA, the French Alternative Energies and Atomic Energy Commision, Center of Saclay) under the scope of a Contrat de Formation par la Recherche grant (CFR, Research Training Contract).

Amongst the numerous individuals and institutions, I would like to express my profound gratitude to the following:

• Marie-Aude Vitrani and Guillame Morel, for giving me the opportunity to be part of the Assistance to Gesture with Applications to THErapy (AGATHE) team at ISIR as a Research Engineer and for welcoming me during my PhD,

Introduction

Until now, we have seen that an IC haptic system is composed of three main elements:

• the tracking system able to compute the user's conguration,

• the force feedback system which constraints the user when a virtual object (VO) is being touched and • a control law that manages close following in free space, force feedback at contact and the transitions between these two modes. From our experience, a tracking accuracy of about 0.1mm as in [Gonzalez, 2015] and 1 • as in [Chabrier, 2018] is sucient to ensure an ecient control. 4.4.2.3.2 Minimum distance of measurement In order be able to precisely control the free space to contact and contact to free space transitions, the tracking of the handle should be ensured for any handle position within the end-eector, up to the situation where it encounters the IC interface, i.e. even when d handle/robot = 0. It is worth noting however that, in such a system, the sensors are usually hidden behind small diaphragms protecting them from direct contacts against the tracked object (nger or handle). In existing systems, the thickness of the protecting contact surface varies from 0.5mm in [Chabrier, 2018] (metallic end-eector) to about 1mm in [Gonzalez, 2015] (plastic endeector), the minimum distance between the sensors and the tracked object varying between 0.75 and 1.25mm (due to integration constraints). We will use here a similar value as design driver, i.e. 1mm. 4.4.2.3.3 Maximal range of measurement The goal of the IC interface tracking system is to provide the conguration of the tool (in 3DoF or 6DoF) to the robot so that it can follow it, i.e. to maintain the center of the IC interface inner volume as close as possible to the handle.

In practice however, perfect following of the handle is almost impossible. Indeed the data from the tracking system's unitary sensors need rst to be ltered and treated

Several magnetic tracking systems are commercially available (see Fig.4.19). As an example, the representative performances of magnetic trackers manufactured by the company Polhemus are provided in table 4.6. Such magnetic sensors are usually considered as small and light. This is true in the eld of VR and motion tracking, however not regarding our requirements. First of all, sensors are mainly wired (inconvenient for pure free movements). Furthermore, their acquisition bandwidth is limited by the sequential nature of the excitation of the source's coil, all the more that in practice, the magnetic eld in a source's coil must dissipate completely before a magnetic eld can be generated in the next coil. Also, their precision decreases with the magnetic eld's amplitude hence with the distance from the source. Last but not least, the magnetic eld is perturbed in the presence of ferromagnetic materials in the workspace, which is prohibitive when considering their association with a haptic interface.

FASTRAK® 6DoF Motion tracker

is driven by a current induced by the passing magnetic eld. The voltage at this coil is then measured to nd the eld [Primdahl, 1979]. This principle is illustrated in gure 4.37.

Drive coil Sense coil

Sense coil

Out of saturation

In saturation

External flux passes through the core Flux is pushed out of the core Drive coil

Figure 4.37: Fluxgate magnetometer operating operating principle (adapted from [START_REF] Lenz | Magnetic sensors and their applications[END_REF]).

Fluxgate magnetometers are able to directly measure the vector components of the magnetic eld with high accuracy [Primdahl, 1979]. 4.17: Fluxgate sensor representative characteristics ( [Tumanski, 2013, Keller, 2018, Texas Instruments, 2018]).

Sensor type

Fluxgate magnetometer

Measured variable

Intensity and orientation of magnetic field

Physical phenomenon

Magnetic induction and saturation of a ferromagnetic material Size

From

Sensor type

Magnetoresistive magnetometers

Measured variable

Angle/Position

Physical phenomenon

Change in resistance caused by external magnetic field Size

In the order of a 5mm × 5mm × 2mm package Measuring range 1 -5mm

Working frequency

Not reported Accuracy Repeatability 0.1deg / 10 to 50μm 0.1deg

Needs to equip target?

Yes, these sensors could be mounted on the target evolving in Hall sensors are the most popular magnetic sensors on the market. They are based on the hall eect, which is a physical phenomenon that was discovered more than 100 years ago ( 1879) by Edwin H. Hall [START_REF] Lenz | Magnetic sensors and their applications[END_REF]].

In the absence of a magnetic eld, the current owing through a plate of a conductive material follows a regular path. However when this material is put under the inuence of a strong magnetic eld perpendicular to it, the current ow is deviated [Tumanski, 2013] as the electrons moving through the magnetic eld experience a force, known as Lorentz force, which is perpendicular to the direction of motion and to the direction of the magnetic eld. As a result, a voltage dierence, known as Hall voltage, is created (see Fig.4.41).

This voltage allows then to determine the intensity of the magnetic eld since the amount of current owing through the material is known.

Absence of magnetic field

Current Table 4.19: Hall-eect sensor representative characteristics [Honeywell, 2018c].

Sensor type

Hall-effect sensor Measured variable

Magnetic field intensity Physical phenomenon

Hall effect Size

In the order of 4mm × 1. • Gyroscopes for the measurement of angular velocities. Three major categories are distinguished [START_REF] Passaro | Gyroscope Technology and Applications: A Review in the Industrial Perspective[END_REF]: mechanical, optical and vibrating-mass based gyroscopes.

Mechanical gyroscopes are usually composed of a spinning wheel that is linked to a basis through two gimbals (see Fig.4.43a). Provided the wheel is rotated at a high angular speed, it will tend to keep its axis at a constant orientation despite any rotation of the basis due to the conservation of its angular momentum (a mass that is rotating at high angular speeds conserves its angular momentum if no external moments act on it) [START_REF] Passaro | Gyroscope Technology and Applications: A Review in the Industrial Perspective[END_REF]. The axis of rotation of the wheel (whose orientation is constant is space) being used as a reference, it is possible to measure the orientation of the basis by using joint sensors in the gimbals. However since these elements are mechanically linked, they are subject to friction, which causes a drift in the direction of the wheel axis with time. Commercial photodiodes are available in the market (see Fig.4.51b). They can also be found under the name of linear optical arrays.

Spin axis

Gimbal

Model of a emitter-receptor-slit sensor

When a slit is placed in the eld of view of a light source, the light passing through it builds a light beam and its shape is mainly determined by the slit geometry. When the light beam hits the photosensitive area of the receptor, a certain amount of power is transmitted to it (see Fig. The received power does not only depend on the geometry of the light beam but as well on the characteristics of the light source and the irradiated portion of the receptor's photosensitive area. In the following subsections we will present the characteristics of the light beam formed by an ERS system that uses one IRED (emitter) and one linear PSD (receptor).

We are interested here in modeling the response of the ERS system in order to predict two outputs:

• the position of the light spot X A (see Fig. 4.56): our aim is to get a relationship between the position of the source and X A that can be inverted in the future to compute the angle θ of the plane in which the source lies from the measurement X A , and

• the total generated photocurrent I O = I X 1 + I X 2 : this data is useful to compute the theoretical limits of the workspace in which the source can move. In practice,

we intend to use this information to check for each position of the source if the sensor is not insuciently illuminated (in this case the signal/noise ratio would be insucient) nor saturated. Indeed even if the position X A can still be computed from θ in such cases, the sensor will not be useful in practice as X A will not be exploitable for the calculation of θ.

It will however be required therefore to invert the relationship between the position of the source and the position of the spot. Our aim in the future is to do so in order to allow computing the equation of the plane, in which the source lies, from the sensor's response.

This will give the opportunity to compute the 3D position of a source (assumed to be punctual) by repeating this operation with three dierent ERS systems, the source being at the intersection of the three planes. By doing so for at least 3 IREDs mounted on the handle, it will be possible to get the later's full conguration in space.

The second part of our model (allowing to compute the theoretical limits of the workspace in which the source can move) will be particularly useful when designing and optimizing such a 3DoF or 6DoF sensor as it will allow to verify that for any possible handle conguration no sensor is insuciently illuminated nor saturated.

Author's publications As described in [Gonzalez, 2015], it is equipped with a CT-HI, or IC-HI, ring-like endeector. This ring has an inner diameter of 24mm, which allows a gap between a mediumsized index nger and the ring which is sucient to track and follow this nger at medium speeds (i.

Proximity sensors Diaphragms

Figure A.2: Ring-like CT-HI end-eector (picture from [Gonzalez, 2015]).

ATMega328P microcontrollers retrieve and send proximity sensor measurements to the haptic interface controller trough a fast serial bus at a rate of 400kbps. Estimation of the nger's location is computed as the center of the polygon build from the measurements (see Fig.A.3). CEA, LIST has developed a 6DoF tracking system prototype in 2014 [Diallo, 2014].

Ring

This system is composed of three 3DoF elements each composed of 3 elementary 1DoF sensors. Indeed an ecient solution to obtain the 6DoF pose of a target, in this case a handle, is to compute the position of at least three points laying on it, as usually done in IR based motion capture systems.

In the following sections we will present its principle of operation. We will rst introduce the 1DoF sensor, then the concept of 3DoF sensors. Then the principle of the 6DoF tracking system will be explained. Finally technical specications of the developed prototype will be provided.

B.1 1DoF Sensors

To design a multi-DoF position sensor, it was proposed in [Diallo, 2014]

B.3 6DoF Tracking system

As previously explained, it is possible to obtain the 6DoF pose of a target from the position of at least three points located on it. The pose of the handle can thus be obtained with an arrangement of at least three 3D sensors.

Two solutions can be envisaged therefore:

• It is possible to use 3 independent 3D sensors to compute the Cartesian coordinates of three points laying on the target (see Fig.B.5). This strategy has the advantage of allowing a simultaneous computation of the three points in space, which maximizes the acquisition frequency. It requires however to employ nine slit/sensor pairs, which makes the entire system more cumbersome, which is not desired. • Another approach consists in calculating the three targets poses alternatively, i.e. to employ only one 3D sensor that will provide the 3D coordinates of each light source one after another (see Fig.B.6).