Oliver Brdiczka

James L Crowley

Patrick Reignier

Learning Situation Models in a Smart Home

Keywords: Human-centered computing, Context-Awareness, Situation modeling, Machine learning, Situation split

This article addresses the problem of learning situation models for providing context-aware services. Context for modeling human behavior in a smart environment is represented by a situation model describing environment, users and their activities. A framework for acquiring and evolving different layers of a situation model in a smart environment is proposed. Different learning methods are presented as part of this framework: role detection per entity, unsupervised extraction of situations from multimodal data, supervised learning of situation representations, and the evolution of a predefined situation model with feedback. The situation model serves as frame and support for the different methods, permitting to stay in an intuitive declarative framework. The proposed methods have been integrated into a whole system for smart home environment. The implementation is detailed and two evaluations are conducted in the smart home environment. The obtained results validate the proposed approach.

I. INTRODUCTION

Smart environments have enabled the computer observation of human (inter)action within the environment. Computerized spaces and their devices require situational information, i.e. context [START_REF] Dey | Understanding and using context[END_REF], to respond correctly to human activity. In order to become contextaware, computer systems must thus maintain a model describing the environment, its occupants and their activities. Situations are semantic abstractions from lowlevel contextual cues that can be used for constructing such a model of the scene. The situation model [START_REF] Crowley | Perceptual components for context aware computing[END_REF] and the underlying concepts are motivated by models of human perception of behavior in the environment. Human behavior is described by a finite number of states, called situations. These situations are characterized by entities playing particular roles and being in relation within the environment. Perceptual information from the different sensors in the environment is associated to the situations, roles and relations. The different situations Oliver Brdiczka is with Telecooperation Group at TU Darmstadt, Germany. Email: brdiczka@tk.informatik.tu-darmstadt. de James L. Crowley are connected within a network. A path in this network (called script) describes behavior in the scene. System services to provide are associated to the different situations in the network. Figure 1 gives a simple example of a situation model for a lecture room. The situations "empty", "lecture" and "audience" are characterized by the roles "lecturer" and "audience" as well as the relation "notSameAs". System services can then be associated to the situations (e.g. service "switch on projector" to situation "lecture"). This article proposes a framework for learning situation models. The objective is to build up and evolve a context model for providing context-aware services in a smart environment. The proposed framework consists of different machine learning methods that acquire and adapt a situation model with different levels of supervision. The approach has been implemented and evaluated in the smart home environment of the PRIMA research group. Human behavior evolves over time. New activities and scenarios emerge in a smart environment, others disappear. New services must be integrated into the environment, while obsolete services should be deleted. A fixed context model is thus not sufficient. Experts can construct and adapt context models according to changing needs of users and application. However, experts are expensive and not always available. Moreover, the environment's intelligence lies in its ability to adapt its operation to accommodate the users. The research challenge is thus to develop machine learning methods for this process, making it possible to automatically acquire and evolve context models reflecting user behavior and needs in a smart environment (Figure 3). Intelligibility [START_REF] Bellotti | Intelligibility and accountability: Human considerations in context-aware systems[END_REF] of the employed context model and the reasoning process is essential in order to permit the users to trust the system.

The proposed approach addresses the problem by providing an intelligible framework for acquiring and evolving an intuitive, comprehensible context model of the scene, the situation model. The methods proposed as part of this framework acquire different layers of the situation model, with different levels of supervision (Figure 3). The situation model serves as frame and support for the different learning methods, permitting to stay in an intuitive declarative framework. First, roles are learned and detected using support vector machines Fig. 3. Bottom-up acquisition and evolution of a context model using an automatic framework based on collected data labeled by an expert [START_REF] Brdiczka | Learning individual roles from video in a smart home[END_REF]. Situations are then extracted in an unsupervised manner from observation data using the Jeffrey divergence between sliding histograms [START_REF] Brdiczka | Unsupervised segmentation of meeting configurations and activities using speech activity detection[END_REF]. The extracted situation segments can then be used to learn situation labels with user or expert input [START_REF] Brdiczka | Automatic acquisition of context models and its application to video surveillance[END_REF]. The resulting situation model can finally be evolved according to user feedback using the situation split [START_REF] Brdiczka | Supervised learning of an abstract context model for an intelligent environment[END_REF].

III. IMPLEMENTATION

In this section, we describe our current implementation. The implementation is based on a 3D tracking system that creates and tracks targets in our smart home environment. The extracted target are used to detect individual roles per entity (subsection III-B). Using the role values of several entities, observations are generated that are the input for unsupervised situation extraction. The results of the extraction are used for supervised situation learning. The learned situation model is then the basis for the integration of user preferences, i.e. associating and changing services.

A. Smart Home Environment: 3D tracker, microphone array and head set microphones

The experiments described in the following sections are performed in our laboratory mockup of a living room environment in a smart home. The smart room is equipped with a wide-angle camera (Figure 4) plus two other normal cameras mounted in the corners of the room. A microphone array mounted against the wall of the smart environment is used for noise detection. The speech of people in the scene is recorded using head set microphones.

Fig. 4. The Smart Room environment as seen by the wide angle camera A 3D video tracking system [START_REF] Biosca-Ferrer | A visual service for distributed environments: a bayesian 3d person tracker[END_REF] detects and tracks entities (people) in the scene in real-time using multiple cameras (Figure 5). The tracker itself is an instance of basic Bayesian reasoning combining tracking results from several 2D trackers [START_REF] Caporossi | Robust visual tracking from dynamic control of processing[END_REF] running on the video images of each camera. Each couple camera-detector is running on a dedicated processor. All interprocess communication is managed with an object oriented middleware for service connection [START_REF] Emonet | O3miscid: an object oriented opensource middleware for service connection, introspection and discovery[END_REF]. The output of the 3D tracker are the position (x, y, z) of each detected target as well as the corresponding covariance matrix (3x3 matrix describing the form of the bounding ellipsoid of the target). Additionally, a velocity vector ! v can be calculated for each target. The microphone array is used for noise detection. Based on the energy of the audio streams, we determine whether there is noise in the environment or not (e.g. movement of objects on the table). A real-time speech activity detector [START_REF] Brdiczka | Unsupervised segmentation of meeting configurations and activities using speech activity detection[END_REF] analyzes the audio stream of each head set microphone and determines whether the corresponding person speaks or not.

The association of the audio streams (microphone number) to the corresponding entity (target) generated by the 3D tracker is done at the beginning of each recording by a supervisor.

Ambient sound, speech detection and 3D tracking are synchronized. As the audio events have a much higher frame rate (62.5 Hz) than video (up to 25 Hz), we add sound events (no sound, speech, noise) to each video frame (of each entity).

B. Role Detection per Entity

Role detection is conducted per entity (person) and for each observation frame. The input are the extracted properties of each target (position (x, y, z), 3x3 covariance matrix and speed | ! v |) provided by the 3D tracking system. The output is one of the role labels (Figure 8 bottom). The role detection process consists of 3 parts (Figure 6). The first part is based on support vector machines (SVMs). A first approach used only SVMs as a black box learning method, without considering specific target properties. From first results obtained in our smart home environment [START_REF] Brdiczka | Learning individual roles from video in a smart home[END_REF], we concluded that, in order to optimize role recognition, we need to reduce the number of classes as well as the target properties used for classification. Additional classes are determined by using specific target properties (speed, interaction distance) and expert knowledge (see parts 2 and 3 of the role detection process).

The first part of the process (Figure 6 left) takes the covariance matrix values of each target as input. Trained SVMs detect, based on these covariance values, the basic individual roles "sitting", "standing" and "lying down" (Figure 7). The third part of the process (Figure 6 right) uses the position (x, y, z) of each target to calculate the distance to an interaction object. In our smart environment, we are interested in the interaction with a table at a known position (white table in Figure 4). So we calculate the distance d between the target and the table in the environment. If this distance is approaching zero (or below zero), the target is interacting with the table. Fig. 8. Schema describing the combination of basic individual role, speed and distance values to roles (blue arrows refer to "no interaction distance with table", red arrows refer to "interaction distance with table ")

The results of the different parts of the detection process are combined to roles following the schema in Figure 8.

Based on role detection results as well as the ambient sound and speech detection, we derive multimodal observation codes for each entity created and tracked by the 3D tracking system. 12 individual role values (Figure 8 bottom) are derived for each entity by the role detection process. Further, the ambient sound detector indicates whether there is noise in the environment or not. The speech activity detector determines whether the concerned entity is speaking or not. This multimodal information is fused to 53 observation codes for each As we can have several persons involved in a situation, multimodal observations of several entities are fused by combining the individual observation codes (Figure 9). The idea is to attribute a code to the combination of two multimodal entity observation codes (without considering their order). The resulting observation code fuses the observation codes of two (or more) entities. In order to fuse the observation codes of more than two entities, the fusion can be applied several times, fusing successively all entities.

IV. EXPERIMENTAL EVALUATION AND RESULTS

In this section, we detail the experimental evaluations that have been conducted as well as the obtained results. We did 2 different evaluations (Figure 10). The aim of Evaluation A was to investigate the quality of one-person and multi-person situation learning and recognition using the proposed framework. Therefore, we recorded several small scenarios showing different situations like "presentation" or "siesta". The recordings have been segmented automatically and the situations have been learned using the methods of the framework. We evaluate the recognition of the one-person and multiperson situations in the scenarios with and without automatic presegmention. The aim of Evaluation B was to show and validate the combination of the three methods: unsupervised situation extraction, supervised situation learning and integration of user preferences. Therefore, we recorded 3 long scenarios showing several situations like "aperitif", "playing game" or "presentation". The recordings have first been automatically segmented. Then, the extracted segments have been labeled and the situations have been learned. Finally, the learned situation model has been evolved with user feedback. We evaluate the recognition of the labeled as well as the added situation (via situation split).

A. Evaluation A Fig. 11. One person situations "individual work" and "siesta" (left side) and multi-person situations "introduction", "aperitif", "presentation" and "game"

In this subsection, we aim at investigating the quality of one-person and multi-person situation learning and recognition. Therefore, we made three different recordings of each of the following situations: "siesta", "an individual working", "aperitif", "introduction/address of welcome", "presentation", and "playing a game". "Introduction/address of welcome", "aperitif", "presentation" and "playing a game" involved two persons, while "siesta" and "individual work" concerned only one person. The role detection values have been generated as described in subsection III-B. The sequences designated for learning are presegmented, i.e. only the segment containing the pure situation is used for learning. This means that, for recordings containing only one situation, disturbances at the beginning and at the end of the recording are automatically removed (see Figure 12 for an example). The supervised learning scheme [START_REF] Brdiczka | Automatic acquisition of context models and its application to video surveillance[END_REF] is then used for learning the situation representations from the sequences. We adopt left-right hidden Markov models as unique learner class for the situations. Fig. 12. Extracted segments for situation recordings "Aperitif 1", "Aperitif 2", "Aperitif 3". Segments at the beginning and at the end of the recordings will be removed automatically First, we did an evaluation on the situation detection for one person only (role detection value between 0 and 52). Situation recordings involving 2 people gave thus two one-person sequences. We did a 3-fold crossvalidation, taking two third of the sequences as input for supervised learning and the remaining third of the sequences as basis for recognition. Table I shows the results. The presegmentation improves the recognition results for the one-person recording sequences. In particular, "aperitif" and "game" can correctly be distinguished, while some wrong detections between "introduction" and "presenter" persist.

Additionally, we did an evaluation on the situation detection for two-person situations. Therefore, multiperson observation codes have been generated from the individual role detection values. We did again a 3fold cross-validation on the situation recognition after supervised situation learning of the given observation sequences. Table II shows the results. The presegmentation also improves the recognition results for the twoperson recordings. As for the one-person situation detection, situations "aperitif" and "game" can correctly be distinguished with presegmentation. The two-person observation fusion further eliminates wrong detections between "aperitif" and "game", resulting in a correct situation recognition rate of 100 % (Table II). The obtained results indicate that multi-person observation and presegmentation of observation streams is beneficial when learning and recognizing situations.

B. Evaluation B

In this subsection, we intend to show and validate the combination of the three methods: unsupervised situation extraction, supervised situation learning and integration of user preferences. Therefore, we evaluated the integral approach on 3 scenarios recorded in our smart home environment. The scenarios involved up to 2 persons doing different activities (situations: "introduction/address of welcome", "presentation", "aperitif", "playing a game", "siesta"{1 person}) in the environment. The role detection values have been generated as described in subsection III-B using 3D tracker as well as noise and speech detection (head set microphones).

The role detection values have then been fused to multiperson observations. The first step of our proposed approach is to create the initial situation model. We extract the situations from the sensor perceptions, i.e. the observations generated for the targets in the scene using our automatic segmentor [START_REF] Brdiczka | Unsupervised segmentation of meeting configurations and activities using speech activity detection[END_REF]. The automatically extracted segments and the ground truth for the scenarios are depicted in Figure 13. The overall segmentation exactitude Q [START_REF] Zhang | Multimodal group action clustering in meetings[END_REF] is best for scenario 2. This can be explained by the fact that the algorithm has difficulties to distinguish ground truth segments "game" and "aperitif". In scenario 1 and scenario 3, "game" and "aperitif" are detected as one segment. Because in scenario 2, "playing game" and "aperitif" are separated by "presentation", these segments can be correctly detected. Recognition rate of situations "introduction", "presentation", "group activity" (="aperitif" or "game") and "siesta" for different recognition window sizes

The supervised learning scheme [START_REF] Brdiczka | Automatic acquisition of context models and its application to video surveillance[END_REF] is applied on the detected segments. As expert knowledge, we inject the situation split scheme of [START_REF] Brdiczka | Supervised learning of an abstract context model for an intelligent environment[END_REF]). The learned situation representation for "group activity" (here: a HMM) is erased and two distinct situation representations (here: HMMs) for "aperitif" and "game" are learned. The observations necessary to learn these situations are taken around the time points when the user gave the corresponding feedback. The size of the observation window used for learning the new sub-situations can be varied. The situation recognition rates for different learning window sizes are depicted in Figure 15. We used a window size of 250 observations for recognition (i.e. 10 seconds of observation time with a frame rate of 250 frames/sec). The curve indicates that a larger learning window size does not always result in a better recognition rate. The total situation recognition rate can even drop with a larger learning window size. This is due to the fact that the best recognition results are obtained when the learning window contains a maximum of observation data being characteristic for the concerned situation and a minimum of "foreign" observations, i.e. wrong detections or observations corresponding to other situations. The resulting situation recognition curve tends upwards, but it contains local peaks corresponding to a learning window size with a good tradeoff between characteristic and foreign observations. For our scenario recordings, such a local peak is at a learning window size of 400, i.e. 400 observations around the feedback time points to learn "aperitif" and "game". The obtained results of the 3-fold cross validation for recognition window size 250 are detailed in Table IV. Recognition rate of situations "introduction", "presentation", "aperitif", "game" (after split) and "siesta" for different learning window sizes. The curve is for 250 observations (recognition window size) V. CONCLUSIONS Although the obtained results are encouraging, the realization of a smart home anticipating the needs and preferences of the user is still far away. First products that a user could buy in his local computer store and install himself are not mature enough. First, the sensors necessary for a reliable sensing of user activities are still too invasive. Multiple cameras, microphones or other sensors must be installed and calibrated in the home. These are still not auto-installing and not easy to use. Second, even though our results are encouraging, the error rates are still too high. Further improvements in detection and learning algorithms are necessary in order to provide a reliable system that could be accepted by a user in his daily life. One way to alleviate this is to provide explanations. When errors occur (and corresponding system explanations are good), the user could understand and correct wrong system perceptions and reasoning himself.

Fig. 1 .

 1 Fig. 1. Example of a simple situation model for a lecture room. Empty, Audience and Lecture are the available situations. Lecturer, Audience are the available roles and NotSameAs the available relation

Fig. 2 .

 2 Fig. 2. Top-down manual specification and implementation of a context model

Fig. 5 .

 5 Fig. 5. 3D video tracking system fusing information of 3 2D trackers to a 3D representation

Fig. 6 .

 6 Fig. 6. Role detection process: SVMs (left), Target Speed (middle), Distance to Interaction Object (right)

Fig. 7 .

 7 Fig. 7. Basic individual roles "standing", "lying down" and "sitting" detected by the SVMs

  entity. Codes 1-13 (12 role values + 1 error code) are based on the role detection process. These 13 codes are combined with ambient sound detection (codes 27-39 and 40-52) and speech detection per entity (codes 14-26 and 40-52). As ambient sound and speech detection return binary values, 2 2 ⇤ 13 = 52 different code values are necessary to represent role, ambient sound and speech detection. If we add an observation code value for a non-existing entity (code 0), we get 53 different observation code values.

1 i=0 {(max code + 1 )

 11 Fusion algorithm Input: (a, b), 0  a, b  max code Step 1: if (a > b) {exchange(a, b)}, Step 2: code = P a i} + (b a).

Fig. 9 .

 9 Fig. 9. Fusion algorithm combining the multimodal observation values (a, b) of two entities. For max code = 52, the resulting codes are between 0 and 1430

Fig. 10 .

 10 Fig. 10. Different parts of the implementation and their evaluation: role detection per entity, unsupervised situation extraction, supervised situation learning and integration of user preferences

Fig. 13 .

 13 Fig. 13. Extracted situation segments and the corresponding ground truth for scenario 1 (Q = 0.68), scenario 2 (Q = 0.95), scenario 3 (Q = 0.74)

Fig. 14.

  Fig. 14.Recognition rate of situations "introduction", "presentation", "group activity" (="aperitif" or "game") and "siesta" for different recognition window sizes

Fig

  Fig. 15.Recognition rate of situations "introduction", "presentation", "aperitif", "game" (after split) and "siesta" for different learning window sizes. The curve is for 250 observations (recognition window size)

TABLE IV CONFUSION

 IV MATRIX AND INFORMATION RETRIEVAL STATISTICS FOR EACH SITUATION (OBSERVATION WINDOW SIZE=250) AFTER THE SPLIT OF "GROUP ACTIVITY". THE WINDOW SIZE FOR LEARNING THE NEW SUB-SITUATIONS IS 400. THE OVERALL SITUATION RECOGNITION RATE IS 81.86 %

situation labels: "introduction", "presentation", "group activity" (="aperitif" or "game"), "siesta". We will adopt left-right hidden Markov models as unique learner class for the situations. To evaluate, we did 3-fold crossvalidation, taking the detected segments + expert labels of 2 scenarios as input for learning and the third scenario as basis for recognition. As our system should be as responsive as possible, we evaluated different window sizes used for recognition. The obtained situation recognition rates are depicted in Figure 14. If we limit the observation time provided for recognition to 10 seconds (i.e. 250 frames with a frame rate of 25 frames/sec), we get a recognition rate of 88.58 % (Table III). The recognition rate of "siesta" is poor due to the fact that in two of the three scenario recordings wrong targets have been created and detected when a person lay down on the couch, resulting in a disturbance of the existing target properties. We have now learned an initial situation model with the situations "introduction", "group activity", "presentation" and "siesta". In order to integrate user preferences into this model, a user can give feedback to our system. The feedback is recorded and associated to the particular frame when it has been given. The initially learned model is then adapted according to this feedback. For our scenarios, we want to integrate the following services:


Eric Vezzoli
email: eric.vezzoli@ed.univ-lille1.fr

Michel Amberg
email: michel.amberg@univ-lille1.fr

Frédéric Giraud
email: frederic.giraud@polytech-lille.fr

Betty Lemaire-Semail

Electrovibration modeling analysis

Keywords: Electrovibration, Electrostatic Force, Modeling, Haptic, Tactile, Friction

Electrostatic attraction may be used to modulate the apparent friction coefficient between two surfaces. Applied to the human finger and a polarized interface, the principle can modify the user perception of the interface surface. In this paper, the different steps towards the modeling of the electrovibration phenomenon are developed. An investigation on the current modeling will be carried out, with a focus on the temporal evolution and frequency dependence of the stimulus. Thus, an improvement of the modeling will be proposed to take into account this major effect, and then, it will be checked with an experimental set-up and compared with literature results.

Introduction

The last few years have seen an increasing interest for haptic stimulation and simulation. Different technologies are available to provide a tactile feedback to a user by modifying his perception of a surface. In particular, it is possible to control the friction between a surface and a finger thanks to squeeze film effect or to electrovibration. This study is focused on the electrovibration effect: the modulation of the perceived friction coefficient due to the induced electrostatic force between a finger and a high voltage supplied plate [START_REF] Bau | TeslaTouch: electrovibration for touch surfaces[END_REF]. The effect is known since the mid fifties [START_REF] Mallinckrodt | Perception by the Skin of Electrically Induced Vibrations[END_REF], but the interest has raised only recently. Firstly, spatial division of electrode was developed to provide precise and complex stimulus pattern of conductive pads, but this solution suffered from its complexity and turned out difficult to apply [START_REF] Meyer | Fingertip Friction Modulation due to Electrostatic Attraction[END_REF]. Recently, electrovibration took advantage of technological improvements of fingertip's position sensor based on optical or resistive solutions. The possibility to track precisely the position of the finger leads to fine gratings simulation thanks to spatial-stimulus relation. With spatiotemporal transformation, the stimulator itself becomes easier to manufacture and it becomes possible to produce tactile feedback on transparent surfaces [START_REF] Bau | TeslaTouch: electrovibration for touch surfaces[END_REF] or merge it with another tactile stimulation technique [START_REF] Giraud | Merging two tactile stimulation principles: electrovibration and Squeeze Film Effect[END_REF].

If the efficiency of the process to provide successful tactile feedback is clear, the physical modeling of the phenomenon involving the finger is not yet satisfactory. The aim of this paper is to investigate on the modeling proposed in the literature and to suggest a modification to take into account the frequency dependence of the effect. The work is organized as follows: first the experimental set up is presented, with a description of the working principle of the technology. Second, the electrostatic force applied on a finger will be described, and the different parameters included in the modeling will be discussed. Finally, a new modeling is proposed and the simulation results obtained will be compared with the experimental ones.

2

Electrostatic force analysis Electrovibration modifies the lateral force felt by the finger in motion by a modulation of the normal force. The modulation is due to electrostatic force and appears between the finger and the polarized surface (see Fig. 1.a). The experimental set-up developed and detailed in this paper is able to detect these forces.

To measure the normal and lateral force felt by the finger, a tribometer has been developed, (see Fig. 1.b). Past measurements indicate a value around 100 mN of the induced electrostatic force [START_REF] Giraud | Merging two tactile stimulation principles: electrovibration and Squeeze Film Effect[END_REF]. A high-bandwidth sensor is needed to measure this force due to its fast varying nature. A measurement of the normal force is also required. To achieve this goal, a force sensor (9217A, KISTLER, France) is used for the normal force measurements. On top of that, a floating table equipped with a force sensor (FSG, Honywell, USA) coupled with a conditioner (max4209H, Maxim Integrated, USA) is mounted to ensure a fast acquisition of the lateral force.

To acquire the data, an oscilloscope (3014B, Tektronix, USA) is used providing both the acquisition and a visual feedback for the users. A waveform generator (33120A, Agilent, USA) provides waveforms to the high voltage amplifier supplying the tactile plate. The data are acquired and elaborated in a post-process. To provide electrostatic stimulation to the finger, an aluminum plate covered with a plastic insulator film has been used.

Electrostatic force expression

A finger approaching an electric field experiences an induced polarization. The polarized material interacts with an electric field generated by the electrode due to Coulomb interaction. The amplitude of this interaction is small, but is comparable with the amplitude of touchsensing action [START_REF] Giraud | Merging two tactile stimulation principles: electrovibration and Squeeze Film Effect[END_REF]. A model of the phenomenon is deduced in [START_REF] Kaczmarek | Polarity Effect in Electrovibration for Tactile Display[END_REF], the expression of the electrostatic force, 𝑓 ' , is the following:

𝑓 ' = 𝜀 + 𝐴 𝑣 . 2 𝑇 1 𝜀 1 + 𝑇 34 𝜀 34 𝑇 34 + 𝑇 1 (1)
where 𝜀 + is the vacuum permittivity, 𝐴 is the finger contact area, 𝑇 1 and 𝑇 34 are the thicknesses of the insulator and the stratum corneum and 𝜀 1 and 𝜀 34 are the relative permittivities of the insulator and stratum corneum. It may be noted that this expression gives as a result a constant force 𝑓 ' if the applied voltage 𝑣 is constant. Thanks to the experimental setup described in section 2.1, we measured the force between a finger and the polarized plate, while there is no contact between the finger and the plate. In Fig. 2 is reported the normal force measured for a given voltage signal for a floating finger over the polarized plate. We can remark oscillations due to the difficulties to maintain the finger close to the plate without any contact. But the major behavior is in agreement with [START_REF] Bau | TeslaTouch: electrovibration for touch surfaces[END_REF], that is roughly a constant force once the voltage applied is constant. If we assume the force 𝑓 ' is also given by the equation (1) once the finger touches the plate, we may define the tangential force 𝑓 5 as 𝑓 5 = 𝜇 (𝑓 8 + 𝑓 ' ) where 𝑓 8 is the normal force applied by the finger and 𝜇 the dynamic friction coefficient of the plate. An increase of 𝑓 ' would lead to an increase of the lateral force, creating a friction change feeling. Nevertheless, Giraud et al. [START_REF] Giraud | Merging two tactile stimulation principles: electrovibration and Squeeze Film Effect[END_REF] found an exponential reduction of the lateral force for an applied square signal when the finger is sliding on the plate. This phenomenon is unexplained by this static model. Every human tissue exhibits specific electrical characteristics; in this case, it is interesting to investigate the properties of the stratum corneum for its relevant role in the electrovibration force generation. The electrical properties of the stratum corneum were investigated by Yamamoto et al. [START_REF] Yamamoto | Dielectrictric constant and resistivity of epidermal stratum corneum[END_REF]. In their work, the strong frequency dependence of the resistivity and permittivity is highlighted for this biological material due to its intrinsic structural characteristics. In this modeling, the resistivity of deeper tissue is neglected for its low value.

On the basis of this assumption, it is possible to model the interface of the finger and the insulator like in Fig. 3, with 𝑅 34 and 𝐶 34 the resistance and the capacitance of the stratum corneum, 𝐶 1 the capacitance of the insulator and 𝑣 the applied voltage. From electrical circuit theory it comes:

𝑣 34 = 𝑅 34 𝐶 1 𝑠 1 + 𝑅 34 𝐶 34 + 𝐶 1 𝑠 = 𝐶 1 𝐶 1 + 𝐶 34 𝜏𝑠 1 + 𝜏𝑠 𝑣 (2)
where 𝜏 = 𝐶 1 + 𝐶 34 𝑅 34 . For a given material:

𝐶 = 𝜀 + 𝜀 > 𝐴 𝑇 and 𝑅 = 𝜌 𝑇 𝐴 (3)
where 𝜀 > is the material relative permittivity, 𝜌 the material resistivity, 𝐴 the area of the electrode and 𝑇 the material thickness. In this case, a plastic film has been used to insulate the finger from the electrode, leading to 𝐶 1 = 32 pF where 𝜀 1 = 3.35, 𝑇 1 = 90 µm and the contact area between the finger and the plate is estimated as 𝐴 = 1 cm . . For the stratum corneum, 𝐶 34 = 6.9 nF with 𝑇 34 = 200 µm [START_REF] Fruhstorfer | Thickness of the stratum corneum of the volar fingertips[END_REF] and 𝜀 34 = 1560 [START_REF] Yamamoto | Dielectrictric constant and resistivity of epidermal stratum corneum[END_REF]. It is possible to assume 𝐶 34 ≫ 𝐶 1 which leads, using (3), to 𝜏 = 𝐶 34 𝑅 34 = 𝜀 + 𝜀 34 𝜌 34 . In Fig. 4, the frequency dependence of the time constant 𝜏 is represented; the parameters 𝜀 34 and 𝜌 34 were measured in function of the frequency in [START_REF] Yamamoto | Dielectrictric constant and resistivity of epidermal stratum corneum[END_REF]. It may be noticed that there is a strong frequency dependence of this time constant which substantially changes the behavior of (2) from a pure first order high pass filter to a more complex frequency dependence. It may be noted that this approach is valid for a static or moving finger. In addition with the previous phenomenon of frequency dependence, we have to consider in the modeling the charge lost through the stratum corneum. The lost charge is gathered on the surface of the insulator as free surface charge, for this reason it no longer participates to the generation of the force on the finger, and consequently, to the measured force. This happens because the charges on the surface of the insulator are no longer mechanically bounded to the finger and the insulator sustains the induced electrostatic force.

τ constant 𝑣 = 𝑣 ' + 𝑣 1 = 𝑄 34 𝐶 ' + 𝑄 1 𝐶 1 (4)
where 𝑣 ' and 𝑣 1 are the voltages at the terminals of the capacitors 𝐶 ' and 𝐶 1 , and 𝑄 34 and 𝑄 1 are respectively the charge on the stratum corneum and the insulator. The link between the two charges is determined by the rate at which the charge flows through the stratum corneum. The capacitor contributing to the electrostatic force between the finger and the insulator is 𝐶 ' , because it is the only one that has a charge bounded to the finger. Then the effective part of the applied voltage contributing to the force is:

𝑣 ' s = 𝑄 34 𝐶 ' = 𝐶 34 𝑣 34 𝐶 ' = 𝐶 34 𝐶 1 𝐶 34 𝐶 1 + 𝐶 34 𝐶 1 𝐶 1 + 𝐶 34 𝜏𝑠 1 + 𝜏𝑠 𝑣 = 𝜏𝑠 1 + 𝜏𝑠 𝑣 (5)
where ( 2) has been used. It is then possible to recover the effective force acting on the finger by replacing 𝑣 in (1) with 𝑣 ' to take into account the effect described above:

𝑓 ' = 𝜀 + 𝐴 𝑣 ' . 2 𝑇 1 𝜀 1 + 𝑇 3 𝜀 34 𝑇 3 + 𝑇 1 (6)
It has to be noticed that 𝜀 OP has a frequency dependence [START_REF] Yamamoto | Dielectrictric constant and resistivity of epidermal stratum corneum[END_REF] taken into account in this modeling.

Simulated and experimental results

From [START_REF] Yamamoto | Dielectrictric constant and resistivity of epidermal stratum corneum[END_REF], it is possible to predict the time evolution of the lateral force 𝑓 5 for a given applied voltage signal thanks to the relationship 𝑓 5 = 𝜇 (𝑓 8 + 𝑓 ' ). The evolution of the measured lateral force compared to the predicted one is proposed in Fig. 6. The plate is polarized with a trapezium signal from 0 to 1000 V to investigate both the transient and the steady state. The signal is provided by an amplifier (HVA2kV, Ultravolt, USA) with a safety system to avoid any electrical shock and to limit the current to 𝐼 3 = 250 µA detailed in [START_REF] Giraud | Merging two tactile stimulation principles: electrovibration and Squeeze Film Effect[END_REF]. The mechanics of the finger and the measurement system has not been considered in this modeling. 0 0,05 0,1 0,15 0,20 0,25 0,30 0 1 time (s) amplitde (noscale) measured lateral force applied voltage simulated response Fig. 6. Lateral force measured for the finger sliding at constant speed on the polarized plane (blue), in red is reported the modeled electrostatic force acting between the stratum corneum and the insulator.

The reported behavior has been observed on 8 different subjects, both male and female, aged from 22 to 29. Three of them were students and the other five were from the laboratory staff, all of them gave their informed consent to perform the experiment. We can remark a very close behavior between the proposed modeling and the experimental results on the rising steps, however on the discharging parts there is a difference between the modeled and the measured signal. One assumption to explain this phenomenon could be the measurements system that can show relaxation behavior. Nevertheless the modeling is able to take into account the discharge phenomenon of the finger. The absolute value of the measured force varies from 2 to 5 mN whereas the model, for a thickness of the stratum corneum about 0.2 mm, predicts 2.5 mN. The variability of the force can be explained by the variability of the stratum corneum explained in [START_REF] Fruhstorfer | Thickness of the stratum corneum of the volar fingertips[END_REF]. It may be noticed that Giraud et al. [START_REF] Giraud | Merging two tactile stimulation principles: electrovibration and Squeeze Film Effect[END_REF] found a value of the decay of the lateral force, considering the mechanics of the measurements system, of τ = 6 ms for a square signal applied. The calculated value of τ with our modeling, considering their experimental situation, is 7.7 ms. Fig. 7. Comparison of the model with experimental data taken from [START_REF] Meyer | Fingertip Friction Modulation due to Electrostatic Attraction[END_REF] Another way to assess the relevance of this modeling is to compare with the experimental results from Meyer et al. [START_REF] Meyer | Fingertip Friction Modulation due to Electrostatic Attraction[END_REF]. In their paper, the authors investigated the frequency dependence of the electrostatic force from 100 to 10000 Hz. The inferred measured force had a noticeable dispersion between different subjects, but generally exhibited an increasing and a successive saturation for all the measure detailed in their article. The dispersion of the force is well explained by [START_REF] Yamamoto | Dielectrictric constant and resistivity of epidermal stratum corneum[END_REF], considering the variability of the thickness of the stratum corneum in human fingers reported in [START_REF] Fruhstorfer | Thickness of the stratum corneum of the volar fingertips[END_REF]. The proposed model in comparison with one result from [START_REF] Meyer | Fingertip Friction Modulation due to Electrostatic Attraction[END_REF] is reported in Fig. 7. According to the different experimental situations described in the paper, the approximation of 𝜏 = 𝐶 34 𝑅 34 is not valid anymore for the comparable value of 𝐶 1 and 𝐶 34 and, in the shown simulation, we considered 𝜏 = 𝐶 1 + 𝐶 34 𝑅 34 .

Conclusion

In this paper the electrovibration effect has been presented and analyzed on its temporal and frequency behavior. An electrical model has been developed to take into account the frequency dependent electrical parameters of the stratum corneum. Based on this data, the transfer function of the voltage through the stratum corneum has been calculated, and linked to the generated electrostatic force. Then the temporal response of the lateral force to a given signal has been measured and compared with the calculated one. A comparison with literature data has been carried out to assess the validity of the model.

Fig. 1 .

 1 Fig. 1. a) Schematic representation of electrovibration. b) Representation of the measurement system, the finger is moved on the plate by the motor.

Fig. 2 .

 2 Fig. 2. Normal force for the finger suspended near the polarized plate

Fig. 3 .

 3 Fig. 3. Electrical representation of the stratum corneum

Fig. 4 .Fig. 5 .

 45 Fig. 4. 𝜏 constant frequency dependence, 𝜏 = 𝜀 + 𝜀 34 𝜌 34

Fig. 5

 5 illustrates three different moments of the discharge through the stratum corneum. The electrostatic force generated by 𝑣 associated to the first configuration is described by (1), but in the third configuration the electrostatic force between the finger and the polarized plate is 0 for the reason explained before. During the transient period represented by the second case, it is possible to imagine the applied voltage 𝑣, distributed across two different perfect capacitances. These capacitances are 𝐶 ' formed by the case 1, where the charge is still on the finger, and 𝐶 1 in the case 3, where the charge has migrated through the stratum corneum. It gives:

Acknowledgement

This work was founded by the FP7 Marie Curie Initial Training Network PROTOTOUCH, grant agreement No. 317100. The authors would like to thank the IRCICA laboratory for hosting and Clement Nadal for the useful discussion.