Lisheng Kuang

Marco Aggravi

Paolo Robuffo Giordano

Claudio Pacchierotti

Wearable cutaneous device for applying position/location haptic feedback in navigation applications

We present a wearable cutaneous device capable of applying lateral stretch and position/location haptic feedback to the user's skin. It is composed of a 2D Cartesian-like structure able to move a pin on the plane parallel to the skin. The pin houses a small metallic sphere of 8 mm of diameter. The sphere can be either left free to rotate when the pin moves, providing location feedback about its absolute position, or kept fixed, providing skin stretch about its relative displacement. The device weighs 30 g for a workspace of 12×12 mm. This paper presents the device's design and actuation together with a perceptual evaluation of the position/location feedback provided by the device when worn around the forehead, forearm, and hand. Finally, we test the device in a preliminary human navigation task. Results show an average navigation error of 0.26 m, which is comparable to state-of-the-art vibrotactile guidance techniques using two vibrating armbands.

I. INTRODUCTION

Wearable haptic devices have been used in various humanmachine and human-robot interaction applications [START_REF] Pacchierotti | Wearable haptic systems for the fingertip and the hand: taxonomy, review, and perspectives[END_REF], including robotic teleoperation [START_REF] Clark | On the role of wearable haptics for force feedback in teleimpedance control for dual-arm robotic teleoperation[END_REF], rehabilitation [START_REF] Bortone | Serious game and wearable haptic devices for neuro motor rehabilitation of children with cerebral palsy[END_REF], and guidance [START_REF] Kerdegari | Head-mounted sensory augmentation device: comparing haptic and audio modality[END_REF], [START_REF] Scheggi | Cooperative navigation for mixed human-robot teams using haptic feedback[END_REF], [START_REF] Aggravi | Design and evaluation of a wearable haptic device for skin stretch, pressure, and vibrotactile stimuli[END_REF], [START_REF] Aggravi | Evaluation of a predictive approach in steering the human locomotion via haptic feedback[END_REF], [START_REF] Chinello | Design and evaluation of a wearable skin stretch device for haptic guidance[END_REF]. Indeed, using wearable haptics for navigation is promising. In this respect, vibrotactile feedback has been the most popular choice. For example, Kerdegari et al. [START_REF] Kerdegari | Head-mounted sensory augmentation device: comparing haptic and audio modality[END_REF] and Bertram et al. [START_REF] Bertram | Sensory augmentation with distal touch: the tactile helmet project[END_REF] proposed a head-mounted device conveying ultrasonic range information trough vibrations; blindfolded participants navigated a maze with and without the vibrotactile assistance on the helmet. Scheggi et al. [START_REF] Scheggi | Cooperative navigation for mixed human-robot teams using haptic feedback[END_REF] used two vibrotactile bracelets on the left and right forearms to make a user follow a mobile robot while avoiding static and dynamic obstacles. On the other hand, non-vibrotactile haptics is less common for navigation. Examples are the works of Aggravi et al. [START_REF] Aggravi | Design and evaluation of a wearable haptic device for skin stretch, pressure, and vibrotactile stimuli[END_REF], whose haptic device provides skin stretch, pressure, and vibrations for robotic teleoperation and guidance applications; Chinello et al. [START_REF] Chinello | Design and evaluation of a wearable skin stretch device for haptic guidance[END_REF], who designed a skin stretch device for generating guidance stimuli at the palmar, dorsal, ulnar, and radial sides of the arm; and Berning et al. [START_REF] Berning | Proximityhat: a headworn system for subtle sensory augmentation with tactile stimulation[END_REF], who used six pressure actuators around the forehead to convey spatial information for obstacle avoidance. Similarly, Bark et al. [START_REF] Bark | Comparison of skin stretch and vibrotactile stimulation for feedback of proprioceptive information[END_REF] and Stanley et al. [START_REF] Stanley | Evaluation of tactile feedback methods for wrist rotation guidance[END_REF] used skin stretch to provide directional cues, while Spiers et al. [START_REF] Spiers | Design and evaluation of shapechanging haptic interfaces for pedestrian navigation assistance[END_REF] presented a hand-held shape-changing device to represent heading and proximity to targets.

We present a 2-DoF wearable cutaneous device able to provide skin stretch and position/location haptic feedback in a 12×12 mm workspace. Two servomotors move a Cartesianlike structure, actuating a pin housing a small metallic L. Kuang is with Univ Rennes, Inria, CNRS, IRISA -Rennes, France. C. Pacchierotti, P. Robuffo Giordano, and M. Aggravi are with CNRS, Univ Rennes, Inria, IRISA -Rennes, France. E-mail: {lisheng.kuang, marco.aggravi, prg, claudio.pacchierotti}@irisa.fr.

This work has received funding from the Inria Défi project "DORNELL" and the China Scholarship Council No. 201908440309. A metallic sphere either provides position/location feedback or skin stretch in a 12×12 mm workspace. We tested the device at the forehead, forearm, and hand. A video is available as supplemental material and at https://youtu.be/38BHsYCQ6uM. sphere. The sphere can be either left free to rotate when the pin moves, providing location feedback about its absolute position, or kept fixed, providing skin stretch about its relative displacement. The device is worn using an elastic belt that can be easily adapted to many parts of the body. After presenting the mechanical design of the device, we evaluate the effectiveness of using location haptic feedback when the device is worn on the forehead, forearm, and back of the hand. Finally, we test the device in a human navigation task. Users are asked to move along a target trajectory following the cutaneous location/position feedback provided by the device. While the proposed device is also capable of providing skin stretch, we focus our evaluation on position feedback. Wearable devices providing position feedback are quite rare. For example, Rossi et al. [START_REF] Rossi | Happro: a wearable haptic device for proprioceptive feedback[END_REF] developed a 1-D positionfeedback device for the forearm, able to convey proprioceptive information about the aperture of a prosthetic hand, while Provancher et al. [START_REF] Provancher | Contact location display for haptic perception of curvature and object motion[END_REF] developed a 2-D position-feedback device for the fingertip to render the contact location in telemanipulation and virtual reality applications. We present one the first wearable device capable of providing skin stretch and position feedback for guidance.

II. DEVICE DESIGN AND ACTUATION

The CAD assembly of the device is shown in Fig. 1, while a detail of its actuated parts is shown in Fig. 2a. A video of the device is available at https://youtu.be/38BHsYCQ6uM.

A. Mechanism and structure

The cutaneous device is composed of a squared 60×60×30 mm ABS frame housing two linear servomotors that drive two intersecting guides. For our prototype, we used two VS-19 Linear Pico Servomotors (max. stall torque of 60 gf.cm at 3.7 VDC, yielding a theoretuca). A Maestro board (Pololu, USA) is in charge of controlling the motors. At the intersection of the guides, we fixed a cylindrical pin indenting the skin. It has a diameter of 6 mm and a length of 30 mm. A metallic sphere is housed at the end of the pin, in contact with the skin. When the pin moves, the sphere can be either left free to rotate or not. If it rotates freely on the skin, it provides position/location feedback about its absolute position; if it is blocked, it provides skin stretch about its relative motion. The behavior of the sphere, and thus the feedback provided, can be chosen by adjusting how strong the sphere is fastened to the pin. We also explored the possibility of employing a small electromagnet between the pin and the sphere to dynamically change the sphere's behavior without any manual intervention; however, this technique is not used in this work. Finally, a spring on the pin ensures that the sphere is always in contact with the skin, applying a constant pressure throughout the interaction.

B. Wearability

At two opposite sides of the ABS frame, we placed two hooks for fixing an elastic belt. In the following Sections, we evaluate the device around the forehead, forearm, and hand. However, the device can be easily worn in other parts of the body. A thin layer of foam between the frame and the skin ensures a comfortable and firm fastening, enabling the user to focus on the feedback provided by the sphere. Figure 3 shows the device worn by a user. For attaining increased wearability, we can also directly attach the cutaneous device on the skin using a layer of adhesive silicone, without needing the elastic belt. We already used this technique for fixing a much heavier wearable haptic device on the back of a user's hand [START_REF] De Tinguy | Weatavix: Wearable actuated tangibles for virtual reality experiences[END_REF]. This approach enables to attach the device wherever needed, with very little impact on the user's mobility.

III. PERCEPTUAL EVALUATIONS

While research on skin stretch devices is well documented [START_REF] Kanjanapas | Design and analysis of pneumatic 2-dof soft haptic devices for shear display[END_REF], [START_REF] Yoshida | 3-dof wearable, pneumatic haptic device to deliver normal, shear, vibration, and torsion feedback[END_REF], we focus on evaluating the effectiveness of our wearable cutaneous device in providing position/location feedback. We carried out two perceptual experiments. The first one evaluates the differential threshold for the location feedback (see Sec. III-C), while the second one analyses the capability of recognizing different shapes/patterns (see Sec. III-D). In both experiments, we tested the device when worn on the forehead, forearm, and back of the hand. As already discussed in Sec. I, although the device is also capable of providing skin stretch, we focus our evaluation on position/location feedback.

A. Participants

Five subjects participated in the experiments (4 males, 1 females, age 27-34, right-handed). Two of them had previous experience with haptic interfaces. None of the participants reported any deficiencies in their haptic perception abilities. Participants received an information sheet with the experiment details and signed a consent form. The study has been approved by Inria's ethics committee (Saisine 513).

B. Setup

Users were asked to wear the wearable cutaneous device around the considered part of the body (forehead, forearm, or hand) in a comfortable yet firm way (see Sec. II-B for details). A picture of the device being worn is shown in Fig. 3. Then, the experimenter spent around two minutes ensuring that the device was worn correctly and that the end-effector contacted the skin. As the servomotors make some noise when actuated, users were also required to wear a pair of noise-cancelling headphones. Finally, the Maestro board commanding the servomotors was controlled by an external computer through ROS. Standard stimulus (mm)

C. Differential threshold or Just-Noticeable Difference (JND)

The Just-Noticeable Difference (JND) provides information about how different two displacements conveyed with our device need to be so as to be perceived as different. This information is important for correctly controlling the device's output and known the renderable range of information. It also reflects the fact that humans are usually more sensitive to changes in weak stimuli than they are to similar changes in stronger stimuli. E. Weber proposed the proportional law JN D = kI, suggesting that the differential threshold increases with increasing intensity I of the stimulus. Constant k is thus referred to as "Weber's fraction".

In our experiment, subjects were asked to wear the device as indicated in Sec. III-B and shown in Fig. 3. We evaluated the JND for two directions of motion, vertical (y axis in Fig. 3a) and horizontal (x axis in Fig. 3a), using the method of limits adapted for finding JND values [START_REF] Tirmizi | A perceptually-motivated deadband compression approach for cutaneous haptic feedback[END_REF]. Subjects were required to tell the experimenter when the two provided stimuli felt different. We tested the JND at eleven standard/reference stimuli, from 1 mm to 11 mm, with a stepsize of 0.1 mm (the minimum displacement the servomotors can actuate). Fig. 4 show the recorded JND and Weber's fraction for each standard stimuli and considered location. Although further analysis is needed, we can already see that the forehead shows the highest recognition rates, followed by the forearm and the back of the hand, which shows little difference between each other. As expected, Weber fractions k are quite consistent across columns, except for the standard stimulus of 1 mm. We did not report separately the results of the two directions of motion as we did not find any relevant difference between them.

D. Shape recognition

Our second experiment aimed at evaluating the capability of our device in rendering different shapes on the user's skin, once again when worn on the forehead, arm, and hand. As shown in Fig. 2(b)-(f), we considered five shapes: square, equilateral triangle, inverted equilateral triangle, vertical line, and horizontal line. We chose these shapes as they have Fig. 6. Perceptual experiment: shape recognition. Mean and 95% confidence interval of the subjective ratings given by the subjects in the questionnaire, with noncontiguous Likert scale answer. They were asked to evaluate the comfort and effectiveness of wearing the device on the head, arm, and hand.

edges, which are known to be salient features in haptic shape perception [START_REF] Plaisier | Salient features in 3-d haptic shape perception[END_REF], and they could be used for navigation purposes, e.g., to indicate the user to stop, look up, look down, move up/down, move left/right, respectively. The pin moved at a speed of 12 mm/s. Subjects were again asked to wear the device as indicated in Sec. III-B and shown in Fig. 3. They were then given the possibility of trying/feeling each shape once before the beginning of the experiment. After that, subjects were presented with ten sequences of rendering, each sequence contains 15 rendering of shapes in a random order, i.e., each shape was repeated three times. After each sequence, subjects were asked to tell which shape they felt.

Figure 5 shows the results of this experiment for each shape and considered location. Confusion matrices indicate that subjects were able to well recognize the five shapes in all the considered situations. The lowest recognition rate, 62%, was registered when the equilateral triangle was rendered on the forehead, while the highest one, 88%, was registered when the horizontal line was rendered on the back of the forehead. As expected, more complex shapes (square and triangles) were harder to recognize than easier ones (lines).

Immediately after the experiment, participants were asked to fill in a six-item questionnaire using bipolar Likert-type 9-point scales, rating the following assertions: (A1.1) It was comfortable to wear the device on the forehead. (A1.2) It was comfortable to wear the device on the forearm. (A1.3) It was comfortable to wear the device on the hand. (A2.1) It was easy to identify the shapes when the device was worn on the forehead. (A2.2) It was easy to identify the shapes when the device was worn on the forearm. (A2.3) It was easy to identify the shapes when the device was worn on the hand. A score of 9 indicated that the subjects fully agreed with the assertion, while a score of 1 indicated that they completely disagreed with it. Fig. 6 shows the average evaluation of each question. A Friedman test showed a statistically significant difference between the means of the three locations in terms of effectiveness (χ 2 (2) = 7.444, p = 0.024, a = 0.05) but not in terms of comfort (χ 2 (2) = 1.529, p > 0.05, a = 0.05). The Friedman test is the non-parametric equivalent of the more popular repeated-measures ANOVA. The latter is not appropriate here since the dependent variable (i.e., the subjects' answer to the questionnaire) was measured at the ordinal level. Post hoc analysis with Bonferroni adjustments revealed a statistically significant difference in the perceived effectiveness when the device was worn on the forehead vs. forearm (p = 0.034).

In addition to this questionnaire, subjects were also asked which position of the device they preferred. Four out of six preferred when the device was placed on the forehead, one on the back of the hand, and one on the arm.

IV. NAVIGATION USE CASE

After this perceptual evaluation, we tested the effectiveness of the proposed device in a human navigation task.

A. Experimental setup

The navigation was carried out in an indoor 4×5 m room instrumented with twelve optical cameras (Vicon Motion Systems, UK) tracking the motion of the human users in real time. Such tracking system features little latency and it is suitable for the real-time tracking and guidance of human users, as already proven in [START_REF] Aggravi | Decentralized control of a heterogeneous human-robot team for exploration and patrolling[END_REF], [START_REF] Aggravi | Haptic-enabled decentralized control of a heterogeneous human-robot team for search and rescue in partially-known environments[END_REF].

Participants wore the cutaneous device around the forehead in a comfortable yet firm way (see Sec. II-B for details).

To avoid receiving any additional information about the environment, participants were also blindfolded and wearing headphones. We chose to wear the device on the forehead as it showed good performance and was the location most preferred by the subjects in Sec. III. As before, the experimenter spent around two minutes ensuring that the device was worn correctly and that the end-effector contacted the skin. Users were required to wear a pair of noise-cancelling headphones. A computer, carried on a backpack by the user, controlled the device's Maestro board through ROS.

A video of the navigation experiment is available as supplemental material and at https://youtu.be/38BHsYCQ6uM. In the trial shown in the video, the subject does not wear the headphones so as to better show the device.

B. Subjects

Six subjects participated in this navigation experiment (4 males, 2 females, age 27-34, right-handed). Five of them had also participated in the shape recognition experiment. Two of them had previous experience with haptic interfaces. None of the participants reported any deficiencies in their haptic perception abilities.

C. Task and methods

Inspired from our previous work [START_REF] Aggravi | Evaluation of a predictive approach in steering the human locomotion via haptic feedback[END_REF], we considered three target paths, shown in red in Fig. 7. Participants were asked to wear the device on the forehead, keep their head pointed forward, and follow the provided guidance feedback as closely as possible. At the end of the indicated path, subjects were provided with three shape patterns in a randomized order, similarly to what we did in Sec. III-D. The rendering of shapes at the end of the path can convey the user with information about additional tasks to carry, e.g., push a button, open a door, turn a valve. We decided to render the three most complex shapes for this use case, i.e., square, equilateral triangle, or inverted equilateral triangle. The area where subjects were provided with the target shape instead of guidance feedback is shown in light blue in Sec. III-D (an area of 1.4 m radius centered at the end of each path). While subjects knew they were going to receive a shape to identify at some point during the task, they did not know when it would happen. Each participant repeated the combined navigation/recognition task once per path, yielding to 18 navigation trials in total. Recorded paths are depicted in grey in Fig. 7. This task was inspired from industrial training tasks, where operators need to carry out a target movement and then execute a specific action, e.g., pushing a button, pulling a level, turning a knob.

Guidance feedback was conveyed through location/position feedback provided by the cutaneous device, indicating the direction toward the reference target path. Given the similarity between the human locomotion and the simplified kinematics of a unicycle robot [START_REF] Arechavaleta | On the nonholonomic nature of human locomotion[END_REF], and considering that the user is moving forward, it is possible to indicate a desired rotation that would lead him or her to the desired path. This control approach has been described in [START_REF] Wit | Theory of robot control[END_REF] and has been used in [START_REF] Scheggi | Cooperative navigation for mixed human-robot teams using haptic feedback[END_REF], [START_REF] Aggravi | Evaluation of a predictive approach in steering the human locomotion via haptic feedback[END_REF] for human navigation using vibrotactile haptic feedback. In our case, this rotation feedback was delivered through our position/location cutaneous system and it was proportional to the distance of the user from the path: if the person had to turn left, the pin end-effector would move the sphere toward the left, i.e., P (x,y) = [ 6 -α, 6 ] T with 0 ≤ α ≤ 6 proportional to the user error in following the path; conversely, if the person had to turn right, the pin would move toward the right, i.e., P (x,y) = [ 6 + α, 6 ] T .

D. Results

As a measure of performance, we registered the error in following the target path, calculated as the average distance of the user from the path throughout the trial. We compare the performance of our device with a recent vibrotactile haptic guidance technique [START_REF] Aggravi | Evaluation of a predictive approach in steering the human locomotion via haptic feedback[END_REF]. Aggravi et al. [START_REF] Aggravi | Evaluation of a predictive approach in steering the human locomotion via haptic feedback[END_REF] evaluated the use of two vibrotactile armbands, one on each arm, to guide a human user along predefined paths very similar to the ones considered in this work. Each armband was composed of four vibrotactile motors positioned evenly around the arm.

Figure 8 shows the results of the navigation experiment for each path, 1, 2, 3, and for each guidance methods, our position/location feedback technique and the state-of-the-art vibrotactile method of [START_REF] Aggravi | Evaluation of a predictive approach in steering the human locomotion via haptic feedback[END_REF]. Figure 9 shows the recognition rate for the shape provided at the end of the path. Results show that, for all paths, the average walking speed in the navigation is 0.207 m/s, the navigation error was rather small (0.26 m in average) and comparable with that registered by Aggravi et al. [START_REF] Aggravi | Evaluation of a predictive approach in steering the human locomotion via haptic feedback[END_REF]. However, with respect to [START_REF] Aggravi | Evaluation of a predictive approach in steering the human locomotion via haptic feedback[END_REF], here we only use one device. Moreover, it is known that providing sustained vibrations becomes quickly uncomfortable [START_REF] Devigne | Power wheelchair navigation assistance using wearable vibrotactile haptics[END_REF], so other types of feedback might be preferable. Finally, the proposed device can be more easily worn wherever needed, especially in the version using adhesive silicon (see Sec. II-B). All these considerations make the proposed navigation technique and device design rather promising.

V. CONCLUSIONS AND FUTURE WORK

We presented a wearable cutaneous device able to apply 2D skin stretch and position/location haptic feedback on a workspace of 12×12 mm. Two linear servomotors actuate two intersecting guides housing a cylindrical pin at their intersection. By moving the guides, the motors can control the position of the pin within the workspace. At the end of the pin, in contact with the skin, we placed a metallic sphere, which can be either left free to rotate when the pin moves or not. In the first case, the sphere provides location feedback about its absolute position, while in the second case it provides skin stretch about its relative displacement. The device weighs 30 g for an overall encumbrance of 60×60×30 mm. It can be easily worn through an elastic band, similarly to an armband, or using a layer of adhesive silicone, similarly to a gel patch. The device can be embedded in garments or other devices, such as a bike helmet.

This paper presents the device design, its actuation principle, and a series of experiments evaluating the position/location feedback it provides. First, we evaluate the differential threshold of the provided feedback when the device is worn on the forehead, forearm, and hand. The device showed the lowest JND (best performance) when worn on the forehead, but also the two other locations performed rather well, with a Weber fraction around 0.20. Then, we carried out a shape recognition experiment, where subjects were asked to recognize five shapes rendered by the device on the forehead, forearm, and hand. Recognition rates varied between 62% and 86%, well above the chance level. No striking difference between the three locations was observed, although further statistical analysis is needed. As expected, more complex shapes (square and the two triangles) were harder to recognize than simpler shapes (the two lines). Finally, we evaluate the performance of our device in guiding blindfolded users along three predefined paths. Users were asked to wear the device on the forehead and follow its guiding feedback while walking in an instrumented room.

Results show that users were able to follow the indicated paths rather well and that their performance is comparable with that registered in another work on human haptic guidance, where users were guided using two vibrotactile armbands. The results of our experimentation show that the proposed device and feedback is a viable approach for navigation, providing a more comfortable and flexible solution with respect to more popular vibrotactile solutions. Future work will focus on improving the device design: reduce its encumbrance and weight, following the guidelines of [START_REF] Pacchierotti | Wearable haptic systems for the fingertip and the hand: taxonomy, review, and perspectives[END_REF]; improve the actuation system, increasing the device's resolution and workspace; dynamically change the feedback provided between skin stretch and location/position stimuli, adjusting the friction between the sphere and the pin using an electromagnet. Moreover, we want to carry a more extensive experimentation, involving more subjects in a wider range of navigation scenarios (e.g., outdoor) and testing also the skin stretch feedback. Another important variable to consider is the speed is the provided sensation, which might play a role in the perception and recognition of sensations and was not addressed in this work.

Fig. 1 .

 1 Fig.1. Assembly of the 2-DoF wearable cutaneous device. A metallic sphere either provides position/location feedback or skin stretch in a 12×12 mm workspace. We tested the device at the forehead, forearm, and hand. A video is available as supplemental material and at https://youtu.be/38BHsYCQ6uM.

Fig. 2 .

 2 Fig. 2. Actuation principle. (a) The servomotors move two intersecting guides housing a cylindrical pin, that in turn houses a metallic sphere contacting the skin. The maximum displacement of each guide is D = 12 mm. (b)-(f) To evaluate the rendering capabilities of our device, we ask subjects to recognize five different shapes: (b) a square, (c) an equilateral triangle, (d) an inverted triangle, (e) a vertical line, and (f) a horizontal line.

  Device on the hand Fig. 3. The prototype of our wearable cutaneous device worn on the (a) forehead, (b) forearm, and (c) back of the hand.

  forehead (k) forearm (k) back of the hand (k)

  ) forearm (JND) back of the hand (JND) forehead (k) forearm (k) back of the hand (k) JND value (mm) and Weber fraction k

Fig. 4 .

 4 Fig. 4. Perceptual experiment: differential threshold. Results per each standard stimulus and considered location, considering the absolute JND value (mm) and the Weber fraction k.

Fig. 5 .

 5 Perceptual experiment: shape recognition. Confusion matrices showing the recognition rates of five shapes (square, equilateral triangle, inverted equilateral triangle, vertical line, horizontal line) in the three tested location ((a) forehead, (b) forearm, (c) hand).

3 Fig. 7 .

 37 Fig.7. Navigation use case. We considered three target paths (red), inspired from[START_REF] Aggravi | Evaluation of a predictive approach in steering the human locomotion via haptic feedback[END_REF]. Six subjects carried out one navigation trial per path (grey).

Fig. 8 .

 8 Fig.8. Navigation use case. Mean and standard deviation of the error in following the target path for the three paths and two guidance methods: using position feedback provided by our device or vibrotactile feedback provided by two vibrotactile armbands from[START_REF] Aggravi | Evaluation of a predictive approach in steering the human locomotion via haptic feedback[END_REF] (superscript "old").

Fig. 9 .

 9 Fig.9. Navigation use case. Recognition rate for the shape provided at the end of the path. Each shape was provided twice.


. The manuscript evidence

The Prayer of Manasseh is known in CPA from a Horologion Book written in Jerusalem on paper in the year 1187-1188, i.e. manuscript Berlin, Staatsbibliothek, Or. Oct. 1019. It was acquired in 1906 in Cairo from a Syrian dealer. The manuscript preserves a Malkite Horologion that is a translation of the Horologion of the Greek Orthodox Church. [START_REF]A detailed presentation of the manuscript and its content is given in Black[END_REF] The manuscript is well preserved except that few folios are damaged on the external borders and one folio is missing. The text is clearly written and easily legible.

The Prayer of Manasseh is written on folios 93 v -96 r and is preceded by the phrase "Then say the Prayer of King Manasseh" written in Karshuni. Versification is not marked. The Prayer is recited during the service of the Great Compline.

It should be underlined that the Prayer of Manasseh occurs in this manuscript as one of the prayers of the Horologion. There is no evidence that the text was ever copied as a part of the CPA Bible.

Modern edition

The manuscript was published by Black in 1954 with a detailed philological commentary and a translation of all the texts not excerpted from the Bible. 2 In his critical notes, Black compares the lemmata which diverge from the Greek text of with other known versions. In the case of The Prayer of Manasseh, 3 Black collated the CPA text with the Greek text of Codex Alexandrinus (LXX A ) and Codex Turicensis (LXX T ; cf. 11.3), according to the edition of Swete [START_REF] Swete | The Old Testament in Greek[END_REF] and with the text of the modern Greek Horologion (from the edition of 1930) [START_REF] Μεγα | σύμφωνον πρὸς τὴν ἔκδοσιν τῶν Πατριαρχείων τοῦ[END_REF] as well as with the Syriac text of the Prayer of Manasseh published by Wilkins (cf. 11.4). 6

History of research

Black underlined the complexity of the CPA version of the Prayer of Manasseh. The text is closer to the Greek text of the Horologion than to the other Greek versions of the Prayer of Manasseh (cf. 11.3), although some exceptions can be found. He also noticed that, in verses 7, 9 and 10, CPA-Pr Man renders the Syriac text of S 17a6 (cf. 11.4) quite closely and that, in few cases, CPA-Pr Man text would go off on its own.

Relevant variants with Greek and Syriac versions

Verses 7, 9, and 10 are of particular importance for the study of the CPA version of the Prayer of Manasseh. Some other variants throughout the text are peculiar to the CPA version and must be analyzed separately.

In general, CPA-Pr Man is closer to the Syriac version (cf. 11.4) than to the Greek Horologion. It must be remembered first that we have two main versions of this text in Syriac, represented by manuscripts S 10t1 and S 9a1 , [START_REF]For the sigla of OT Peshitta manuscripts, see List of the Old Testament Peshitta Manuscripts[END_REF] which Gutman and van Peursen compared with each other. [START_REF] Gutman | Two Syriac Versions. these three versions. We cannot say for sure that the CPA-Pr Man derives from a Syriac text. The translator could as well have known several versions and tried to merge them into an ecclectic rendition as the presence of the two variants in v. 10 suggests[END_REF] CPA-Pr Man is closer to S 9a1 , which in general reflects the same text as that published by Wilkins. This similarity is especially obvious in verses 9 and 10.

In v. 9a, CPA follows the Syriac text very closely, with the only difference that CPA does not have an equivalent of ܢܝ ܥܝ̈ ܕܐܪܝܡ "so that I can lift up my eyes." No Greek version has an equivalent to this line either. In v. 9b, CPA follows the Syriac, which is not in any Greek version. In v. 10, CPA differs slightly from the Syriac since it omits the phrase ܟܦܝܦ ܐ ܘܐܢܐ "and I am bent". It is possible that CPA originally contained this phrase as a translation of the Syriac ܐܢܐ ܘܟܦܝܦ "and I am bent" and that it was omitted in the sequence ܟܦܝܦ ܘܐܢܐܠ ܟܦܝܬܠ ܘܐܢܐܠ "and I am bound, and I am bent", due to homoeoarchton.

In the beginning of v. 10, CPA follows the Syriac text as well, particularly with the mention of ܠܓܠܠ ܠ ܃ ܠ ܖܫܘܡܝܐ ܠ ܠܪܘܡܝܗܘܢ ܠ ܘܝܖܡܐ ܠ ܃ ܠ ܐܧܝ ܠ ݁ܠܐ ܖܝܬ ܠ ܫܘܐ ܠ ܐܢܐ ܠ ݁ ܘܠܝܬ ܖܛܠܘܡܝ ܠ ܣܘܓܝܐ "and I do not deserve to lift up my face and look at the height of the heaven, on account of the multitude of my sins." This is an exact translation of the second part of the Greek v. 9a, καὶ οὐκ εἰμὶ ἄξιος ἀτενίσαι καὶ ἰδεῖν τὸ ὕψος τοῦ οὐρανοῦ ἀπὸ πλήθους τῶν ἀδικιῶν μου, which is transposed both in CPA and in Syriac. But the end of the sentence corresponds again to the Greek text, where the Syriac has the variant ܕ̈ܪܘܫܥܝ ܐ ܕܡܒܐܫܢܘܬܐ ܐ ܣܘܓܐܐ ܐ ܡܛܠ "because of the multitude of the iniquity of my wicked deeds."

In the last part of v. 10, where the Syriac text inverts the two sentences found in Greek (παρώργισα τὸν θυμόν σου καὶ τὸ πονηρὸν ἐνώπιόν σου ἐποίησα "I provoked your anger and did what was evil before you") and gives the variant of the Greek text of Odes (cf. 16 ; στήσας βδελύγματα καὶ πληθύνας προσοχθίσματα "having set up abominations and having mutiplied objects of wrath"), CPA keeps the Greek order of the text and gives first the equivalent found in the Greek Horologion (μὴ ποιήσας τὸ θέλημά σου, καὶ μὴ φυλάξας τὰ προστάγματά σου "do not do your will, and do not keep your ordinances"), followed by the variant of Odes.

In v. 7, CPA seems closer to the Greek Horologion than to the Syriac version, since it gives the same variant (κατὰ τὸ πλῆθος τῆς χρηστότητός σου "according to the abundance of your compassion") where the Syriac text agrees with the text of the Greek Didascalia (κατὰ τὴν χρηστότητα τῆς ἀγαθωσύνης σου "according to the compassion of your uprightness"). The Greek text of Odes omits this part of the verse entirely.

Differences and relations to others translations

In some cases, CPA has its own variants, some of which are certainly due to scribal error. In vv. 2-3, CPA shows a lack of consistency: first it translates the Greek participles precisely (ὁ ποιήσας "he who makes" translated by ܖܥܒܖ ܠ ,)ܗܖܝܢ but then it uses second person verbs ( ܠ ܣܓܪܬ , ܚܫܒܬ and ܛܒܥܬ "you have held," "you have shut up," and "you have sealed") to translate ὁ πεδήσας "he who has held," ὁ κλείσας "he who has closed," and σφραγισάμενος "he who has sealed." In v. 13, CPA makes two mistakes: instead of translating ἄνες μοι, Κύριε, ἄνες μοι "relieve me, O Lord, relieve me," it reads ܢܦܫܝ ܠܝ "my soul" which has no meaning in this context. Further, it omits the equivalent of Greek μηδὲ εἰς τὸν αἰῶνα μηνίσας τηρήσῃς τὰ κακά μοι "nor be angry forever and retain evil for me." This last omission is certainly due to a homoeoarchton. In v. 15, CPA presents a variant which is hard to explain: ܫܘܦܪܐ ܖܫܘܡܝܐ ܠ ݁ܗܘܢ ܦܪܚܬ ܠ ܘܟܘܠ "the beauty and all the birds of heaven" where LXX has πᾶσα ἡ δύναμις τῶν οὐρανῶν "all the force of heaven." S-Pr Man (cf. 11.4) seems to have excerted a strong influence on CPA-Pr Man despite some textual peculiarities in the latter. Secondarily, the Greek version (cf. 11.2) as represented by the Greek Horologion influenced CPA-Pr Man as well. It is impossible though to establish a direct lineage among

  Version imprimée Capron, Laurent, "11.11 Prayer of Manasseh : Christian Palestinian Aramaic", in: Textual History of the Bible, vol. 2: The Deuterocanonical Scriptures, part 2C, (gen. ed. A. Lange, vol. eds. F. Feder and M. Henze; Leiden: Brill, 2019), 272-274 Version en ligne Capron, Laurent, "11.11 Prayer of Manasseh : Christian Palestinian Aramaic", in: Textual History of the Bible (gen. ed. A. Lange; vol. eds. F. Feder and M. Henze). http://dx.doi.org/10.1163/2452-4107_thb_COM_0211110000 (accès payant en janvier 2022) 11.11. Christian-Palestinian Aramaic Translation 11.11.1


Inès Lacôte

Claudio Pacchierotti

Marie Babel

David Gueorguiev

Maud Marchal

Maud Marchal " Tap Stimulation

"Tap Stimulation": An Alternative To Vibrations To Convey The Apparent Haptic Motion Illusion

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

"Tap Stimulation": An Alternative To Vibrations To Convey The Apparent Haptic Motion Illusion

Inès Lacôte 1 , Claudio Pacchierotti 2 , Marie Babel 1 , Maud Marchal 1,3 , and David Gueorguiev 4

Abstract-Vibrotactile sensations can be used to elicit apparent haptic motion illusions, which consist in using discrete vibration patterns to convey an illusory continuous moving sensation across the skin. However, experiencing prolonged vibrations is also known to increase the cognitive load. This study investigates whether continuous mechanical stimulations, or taps, that are activated in sequence, can also create a convincing illusion of haptic motion across the skin. Moreover, we also test whether an increased curvature of the contact surface impacts the quality of the felt illusion. We conducted a comparative psychophysical experiment enrolling 18 participants showing that the proposed "tap" stimulation was as efficient as a 120 Hz vibrotactile stimulation in conveying the haptic motion illusion. Moreover, results showed that the curvature of the contact surface had little effect on the quality of the sensation. Thus, using continuous mechanical stimulations that do not vibrate can be a good alternative to vibrations for rendering haptic sensations in hand-held devices in a lot of applications including navigation guidance.

I. INTRODUCTION

Tactile stimulations often rely on the use of haptic illusions, as they constitute a major mean of enriching devices and their transmitted messages [START_REF] Lederman | Haptic perception: A tutorial[END_REF], [START_REF] Lederman | Tactile and Haptic Illusions[END_REF] in various applications. One of these illusions is the Apparent Haptic Motion (AHM), which has been a research interest since 1917 [START_REF] Burtt | Tactual illusions of movement[END_REF], [START_REF] Lakatos | Constraints common to apparent motion in visual, tactile, and auditory space[END_REF]. This illusion consists in actuating asynchronously discrete stimulation points on the skin. With proper parameters of time delay and duration, it is possible to convey a sensation of continuous motion along a line delimited by the activation of separated contact points stimulated on the skin [START_REF] Sherrick | Apparent haptic movement[END_REF]. As a 1D or 2D motion [START_REF] Park | Rendering Moving Tactile Stroke on the Palm Using a Sparse 2D Array[END_REF], AHM is an interesting tool to indicate directional cues and provide a sensation of movement in applications such as navigation assistance. Studies demonstrated that the AHM illusion can be very well perceived on different body parts such as the arm [START_REF] Niwa | Determining appropriate parameters to elicit linear and circular apparent motion using vibrotactile cues[END_REF], the hand, and the back [START_REF] Israr | Control space of apparent haptic motion[END_REF], where it was found to convey clear directional cues, when stimulated with vibrotactile actuators. Indeed, in navigation tasks, passive touch is used so that users do not have to search for the information, but instead can keep their attention on the mobility task while passively getting the complementary indications [START_REF] Kammoun | Guiding blind people with haptic feedback[END_REF]. Tactile stimulations have been found to be a great tool to assist navigation, as they are easy to understand and implement [START_REF] Ross | Wearable interfaces for orientation and wayfinding[END_REF], [START_REF] Aggravi | Haptic-enabled decentralized control of a heterogeneous human-robot team for search and rescue in partially-known environments[END_REF], [START_REF] Aggravi | Decentralized control of a heterogeneous human-robot team for exploration and patrolling[END_REF]. The main goal of technologies that rely on vibrotactile feedback is thus to improve the amount of information delivered by the device while staying intuitive, clear, and comfortable through the use of various patterns and stimulation methods for various applications, such as virtual reality or navigation indications. Researchers are precisely investigating these thematics with various technologies such as the small device Buru-Navi3 for navigation guidance [START_REF] Amemiya | Buru-Navi3: behavioral navigations using illusory pulled sensation created by thumb-sized vibrator[END_REF] or embedded vibrations onto mobility assistance devices like powered wheelchairs [START_REF] Devigne | Power Wheelchair Navigation Assistance Using Wearable Vibrotactile Haptics[END_REF] and white canes [START_REF] Gallo | Augmented white cane with multimodal haptic feedback[END_REF]. However, when transmitting complex vibratory messages or combining multiple vibrotactile signals, there is a risk of altering the perception or creating tactile noise referred to as tactile clutter [START_REF] Van Erp | Guidelines for the use of vibro-tactile displays in human computer interaction[END_REF], especially during prolonged use as in navigation tasks. Thus, an interesting research topic is to find whether another way of stimulation could be a viable, informative, and comfortable alternative to vibration when it comes to conveying apparent haptic motion. Based on this assessment, this study aims to compare the state of the art vibrotactile apparent motion with a continuous mechanical stimulation, that will be referred to as "tap" stimulation, which already has been investigated for other applications with pin arrays [START_REF] Seizova-Cajic | Lateral Skin Stretch Influences Direction Judgments of Motion Across the Skin[END_REF], [START_REF] Duvernoy | Electromagnetic Actuator for Tactile Communication[END_REF]. The goal of this paper is to test the robustness of the illusion on multiple curvatures, e.g., for usage on handle-like devices, as the AHM literature mainly focuses on flat surfaces. Gallo et al. [START_REF] Gallo | Augmented white cane with multimodal haptic feedback[END_REF] developed a smart cane integrating technologies that rely on the AHM mechanism, however, they did not study the impact of curvature. Besides, this study aims to compare stimulation modes to understand if vibrations are a main condition for obtaining AHM illusions or if a "tap" stimulation, as that used in haptic communication of people who are deaf-blind [START_REF] Duvernoy | HaptiComm", a Haptic Communicator Device for Deafblind Communication[END_REF], could be one of the viable alternatives we are looking for. To that aim, we propose a study with two main objectives conducted on 18 participants, with the setup presented in Fig. 1. First, we compare the vibratory mode and the "tap" stimulation to convey the apparent haptic motion on the hand. Secondly, we study the impact of bending the contact surface on the perception of the illusion, by using a flexible handrest that we position on five different curvatures. The paper is organized as follows. Section II presents the materials and methods of the user study, Sec. III the results and statistical analysis across the considered conditions, and finally Sec. IV discusses the results and proposes future directions and perspectives.

II. USER STUDY

This study aims to compare the effectiveness of vibratory and continuous mechanical stimulations, referred to as "tap" stimulations, for eliciting an apparent haptic motion illusion. The study has been approved by Inria's ethics committee Fig. 1: A) The experimental setup is composed of 3 electromagnetic actuators placed on a flexible hand-rest, adaptable to various curvatures. The participants answer to questions regarding the illusory effect on a GUI interface located in front of them. The colored dots show the contact points of the actuators on the hand. B) The signals are generated via a controller, then amplified before being played by the custombuilt actuators.

(COERLE Dornell -Saisine 513). Three different contact points on the palm and the middle finger are stimulated to convey the apparent haptic motion illusion either through subsequent vibrations or "taps". Only one type of motor was used to provide both types of stimulations, to keep the experimental set-up as similar as possible between the stimulation modes.

A. Experimental setup

The experimental setup shown in Fig. 1 is composed of three custom actuators inspired by Duvernoy's [START_REF] Duvernoy | Electromagnetic Actuator for Tactile Communication[END_REF], with a coil as a stator and two magnets glued together in their repulsive position as a mover to increase the magnetic field. A representation of the actuators is given in Fig. 2. The actuators are mounted onto a flexible 3D printed hand-rest which is set to 5 different curvatures during the experiment, as shown in Fig. 4. The commands for the three actuators are created via Matlab and then provided through a National Instrument USB-6343 series controller, which sends them to three amplifiers enabling to deliver a 6.5V signal to the motors, corresponding to a force of approximately 0.4 N exerted on the palm and the finger. Fig. 3 presents the superposed force data of five activations of an actuator recorded with a Nano17 force sensor (ATI, USA) at a sampling rate of 5000Hz. The two magnets of the electromagnetic actuators go upward and downward in the center of the coil depending on the electrical tension passing through it. This design enables to implement the two stimulation modes for the study: (i) the vibratory mode and (ii) the Fig. 2: CAD and picture of the custom electromagnetic actuators. The coil structure (dark grey) is 3D printed, and two magnets (light grey) glued in their repulsive position constitute the mover. The designed is inspired by Duvernoy [START_REF] Duvernoy | Electromagnetic Actuator for Tactile Communication[END_REF]. Dimensions are in mm.

"tap" mode. The vibratory mode consists of an oscillation of the magnets at a chosen frequency. This is implemented with the tension signal following a sinusoïdal carrier in a ramp envelop, see Fig. 5a. The second mode, also called "tap" mode, corresponds to a unique upward displacement of the magnets inside the coils, which is maintained during a time period given by the Duration of Signal (DoS), before going back to their resting position, see Fig. 5b. The two modes provide asynchronous stimulations at the same three locations on the hand (see Fig. 1). For both stimulation techniques, overlapping ramp activation of the voice coil actuators are implemented, as illustrated in Fig. 5. The time delay between the actuators, also called Stimuli Onset Asynchony (SOA) and DoS are fixed parameters.

Based on pilot tests and [START_REF] Gallo | Augmented white cane with multimodal haptic feedback[END_REF], which investigated apparent motion for augmenting a walking cane, we set the SOA and the DOS parameters to SOA = 110 ms and DoS = 220 ms in both stimulation conditions. A review of various studies on apparent haptic motion with vibrotactile stimulations [START_REF] Zhao | Intermanual apparent tactile motion on handheld tablets[END_REF] helped determine the vibrating frequency of the motors along with some pilot tests, so as to ensure that frequency and intensity were pleasant for the user. Finally, the vibration frequency was set to 120Hz. A unique maximum intensity of the signal at 6.5V is used during the entire experiment.

B. Experimental design

The experiment is designed so that the stimulations are conveyed along the middle finger to the bottom of the palm and tests several conditions. Besides (i) the two ways of stimulating (vibratory and "tap"), we also consider (ii) five different curvatures of the contact surface (Fig. 4) and (iii) two directions of motion. (ii) The five curvatures are obtained by bending the flexible hand support in which the motors are embedded. The obtained distances between the top and the bottom of the flexible support, as a result of the bending, are respectively 19 (totally flat, Curvature 1 in Fig. 4), 16, 13, 10, and 7 cm (fully curved, Curvature 5 in Fig. 4). The curvatures are chosen to range from the standard flat position to a curvature that resembles the one of a handle or joystick. (iii) The two directions are either proximal or distal along the hand (green towards orange or orange towards green in Fig. 1). They are described to the participants as "upward" and "downward" directions as well as represented on a drawing. The time delay between the actuator activation (SOA) and the duration of the signals (DoS) being constant, the speed of the illusory motion is a fixed parameter. Finally, the signal maximum intensity is given at 6.5V for all stimulations making the signal amplitude also constant.

Globally, the study is organized to test the changing parameters as following. The curvatures are tested one after the other and their presentation order is pseudo-randomized and counterbalanced across participants to avoid habituation or learning effects. For practicality, the two modes (vibrations or "taps") are tested one after the other in a random order on a specific curvature, before the curvature is modified. A testing block is composed of 6 trials of which the only changing parameter is the direction. A block is thus made of only vibratory or only "tap" trials of which three are identical distal stimulations and three are identical proximal signals. Thus, blocks are differentiated by the type of signal that is provided (vibratory or "tap") and by the curvature of the support (curvature from 1 to 5). The order of the six trials is also pseudo-randomized in each block. Moreover, a trial is made of three repetitions of the AHM pattern stimulation, to be sure the participants are able to perceive well the signal before answering

C. Participants

Eighteen persons participated in the experiment, of which eleven were women, between twenty-one and fifty-seven years old, and one was left-handed. Stimulations were delivered on the dominant hand, determined with a questionnaire before the experiment. None of the participants have had trauma on the tested hand that could affect his/her tactile perception. Participants were naive about the objectives and hypotheses of the experiment and had not seen or tried the setup before participating in the study.

D. Experimental procedure

Participants carried out the experiment in a dark room, with a box placed above the setup, so that they could not see the device before or during the experiment. They also wore noise-cancelling headphones to avoid any auditory information about the received stimuli. They received no indication about the number of embedded motors in the setup nor about the number of activated ones, but they were told that the number would not vary within a block. Indications about the global number of stimulations and repetitions were given before the experiment along with the sum-up of the questions participants would face during the test. A Matlab script manages the transmissions of signals to the National Instrument controller card and stores the characteristics of the trials sent as well as the answers to the questions. The presentation order of the five curvatures is given when launching the script for a user.

To begin with, the first curvature is set on the flexible hand-rest. The participants keep the hand in a static position upon the support after the investigator had positioned it correctly on the hand-rest. The correct positioning of the hand is checked throughout the experiment. After each trial, the participants answer two questions about what they perceived: (i) What was the direction of the stimulations ? (ii) Rate the smoothness of the apparent motion generated by this particular trial on a seven-points Likert scale, from 1 (discrete) to 7 (continuous). Here the evaluated parameters are the curvature, the mode of actuation and the direction of the motion. After the sixth trials, corresponding to the end of the block, participants are asked to rate three other perceptual dimensions of their tactile experience during the block: (iii) the ease to answer the up/down question from 1 (very difficult) to 7 (very easy), (iv) the pleasantness of the stimulation 1 (very annoying) to 7 (very pleasant), and finally (v) the fatigue perceived on their stimulated hand from 1 (not tiring at all) to 7 (very tiring). For this second part, the evaluated parameters are the curvature and the mode of actuation. The directions being mixed within a block, it is not evaluated for those questions. This process is repeated for the other mode of stimulation and on the 5 curvatures, which are tested in pseudo-random order.

The data is then processed and organized to create the matrix of interest to study the impact of the curvatures, the difference of perception of the two stimulation modes and the effect of the direction of the pattern. The participants were also able to give free comments and feedback about their sensations and the experiment at the end of their participation to the study.

III. RESULTS

The results showed that whatever the curvature and the signal type, the participants could perfectly sense the direction of the apparent motion, as the median, first and third quartile of scores were all at 100% of success. Thus, the quality of the AHM illusion was assessed by the additional questions to which participants had to answer.

For each of these questions, we performed a Generalized Linear Model (GLM) statistical analysis on the independent variables of our study. For the smoothness score, which was answered after each trial, these variables were the curvature, the mode of stimulation and the direction of the movement. The GLM analysis showed no statistical effect of curvature (p=0.450), nor an effect of the stimulation mode (p=0.484). Only the direction of the stimulation showed a weakly significant effect on the perceived smoothness. To investigate further this effect, we performed a post-hoc statistical analysis that confirmed that the perceived smoothness was significantly different (Mann-Whitney ranked test: U = 135349, p = 0.038) between the two directions of stimulation. Its score was 3.85 ± 1.53 when stimulating distal AHM and 4.05 ± 1.60 for proximal AHM. Interestingly, both stimulation techniques showed an identical perceived level of smoothness that corresponds to a slightly above average perception of smoothness reported in Fig. 6a.

A similar GLM analysis was performed on the answers of the other questions about the pleasantness (Fig. 6b), the ease to answer (Fig. 7a) and the induced fatigue (Fig. 7b). Since these questions were answered after experimental blocks that mixed the two directions of stimulation, we considered solely the stimulation mode and the curvature as independent variables. The GLM analysis only showed a significant effect of the amount of curvature on the fatigue (p=0.009). In the subsequent post-hoc analysis we only found a significant effect of the curvature (Friedman test n = 18, Q(4) = 11.47, p = 0.049) for fatigue results when using "tap" signals. However, the influence of curvature on fatigue was not found significant when stimulating with vibrations (Friedman test n = 18, Q(4) = 5.515, p = 0.24). As a consequence, the "tap" mode was found to be slightly more tiring: Wilcoxon matched-pairs signed rank n = 90, W = -364, p = 0.0018.

IV. DISCUSSION

A. Impact of the hand-rest curvature

An important objective of this paper was to determine whether the curvature of a hand-rest would have significant impact on the perception of the apparent haptic motion on the hand. To better understand the perceptual strength of the apparent motion, we conducted a study to test the illusion with parameters validated by other studies like Gallo et al.'s [START_REF] Gallo | Augmented white cane with multimodal haptic feedback[END_REF] on a hand-rest taking 5 different curvatures. It was decided to use a flat surface as one of the 5 hand-rest positions, to have a reference model that could easily be transposed to the existing literature. Secondly, we tested bending that went until the highest curve of the support, still enabling the magnets to remain in the coil despite of gravity. The palm and the middle finger were chosen to be the stimulated zone because some studies already exist about the AHM on the hand. Moreover, this area being the largest on the hand, it enabled separating the stimulation points to their maximum distance for two reasons: testing the maximum robustness of the illusion with few amount of material and to be free of electromagnetic interference considerations. The study, conducted on 18 participants, tested, between other elements, the clearness and comprehensibility of the direction conveyed on the 5 curvatures. It showed no significant impact of the bending on the perception of the directional cues, neither did it have effect on the perception difficulty, pleasantness of the stimulation or perceived smoothness. An effect was statistically found on the fatigue perceived on the highest curvatures. This might be due to the increasing circularity of the AHM but it is also possible that the sensation was mainly unpleasant because of the uncomfortable wrist position that participants felt was causing fatigue. Overall, the apparent motion illusion was found to generate surprising stable perception across every bending of the contact surface.

B. Comparison of the two modes of stimulation

Besides being widely tested on flat surfaces, experiments on the apparent haptic motion were mainly conducted with vibrations and proved its efficiency. However, vibrations are also known to engender various difficulties when used for an extended period of time, such as sensation of fatigue or tactile noise which can sometimes be confusing. An interesting solution to this issue would be to find an alternative method to the vibration. In this study, we propose a mode of stimulation that does not constantly vibrate and thus compare two modes of activation that are the vibratory stimulations and a continuous mechanical stimuli causing a "tap" stimulation. For every mentioned curvature, participants scored equally on the direction questions. Besides, the "tap" stimulations were found to be as smooth, easy to understand, pleasant as the vibratory mode. Only the fatigue experienced by participants was slightly higher with the "tap" mode, especially for the most curved contact surfaces. However, since the task was easy and participants' fatigue was very low in both modes, this difference might be due to the transient nature of the changes in the "tap" mode. For their free comments, several participants reported that the "taps" were perceived as more delicate stimulations and that their amplitude was felt lower than the vibrations'. As a consequence, some of the participants suggested the vibrations appeared more as alert signals.

C. Impact and applications

The apparent haptic motion and the conclusions of this study represent a crucial point of interest for many applications like navigation indications [START_REF] Amemiya | Buru-Navi3: behavioral navigations using illusory pulled sensation created by thumb-sized vibrator[END_REF], [START_REF] Gallo | Augmented white cane with multimodal haptic feedback[END_REF] ; but it can also answer an increasing and essential need that is the assistance for people who have sensory impairments. Indeed, the prevalence of sensory impairments in the world population is predicted to significantly increase in the following decades [START_REF] Who | Strategic Plan for Vision 2020 : The Right to Sight[END_REF], [START_REF]Ear and Hearing Survey Handbook[END_REF], urging for solutions to augment the independence capabilities of people affected by sensory deficiencies. Moreover, the loss of autonomy and the lessening of communication capabilities are proven to lead to a multitude of other issues, such as depression and psychological disorders [START_REF] Dammeyer | Deafblindness: A review of the literature[END_REF]. Communication and navigation tasks represent the two essential points of interest for people with visual or auditory impairments, because their lessening is the leading cause of isolation and autonomy loss. Research is actively looking for methods and devices to convey indications for navigation and communication through various stimulation modalities such as audio and touch. For example, some systems implement audio descriptions or alerts, like the WeWalk smart cane [START_REF] Kugler | Technologies for the visually impaired[END_REF] ; but it appears that haptic devices are a key solution to inform people without interfering with other engaged sense during the navigation. Haptic devices are investigated such as the smart cane from Gallo et al. [START_REF] Gallo | Augmented white cane with multimodal haptic feedback[END_REF] or smaller devices like the Buru-Navi3 from Amemiya et al. [START_REF] Amemiya | Buru-Navi3: behavioral navigations using illusory pulled sensation created by thumb-sized vibrator[END_REF] and the Animotus from Spiers et al. [START_REF] Spiers | Outdoor pedestrian navigation assistance with a shape-changing haptic interface and comparison with a vibrotactile device[END_REF] for navigation guidance or the HaptiComm device from Duvernoy et al. [START_REF] Duvernoy | HaptiComm", a Haptic Communicator Device for Deafblind Communication[END_REF] for communication. This study provides a new insight about perception for the optimization or development of such technologies in the context of navigation assistance but also haptic interfaces for people with sensory impairments.

V. CONCLUSION

The apparent haptic motion (AHM) has been studied for a long time and its robustness has been widely showed on many surfaces and flat objects. Indeed, when using specific values of the signal's temporal parameters, i.e. the time delay between the activation of actuators, the duration of the signals, and the vibratory frequency, the illusion provides a movement sensation along the line drawn by the actuator positions, even though only discrete points are actually stimulated. In this study, we wanted to explore the perceptual limits of the AHM illusion. To that end, we investigated the effect of the hand-rest curvature on the perception of the apparent haptic motion on the hand. Besides this, we also investigated whether the vibration is a mandatory component to convey this illusion. Thus, a continuous mechanical stimulation induced by sustained pressure of the actuator on the finger was implemented in the study. Participants' answers suggest that the illusion has a high robustness over varying curvatures since all participants were able to perfectly discriminate the direction of the movement on their hand in all conditions of the experiment and the additional questions did not show strong differences. Moreover, participants found the two stimulation modes equally smooth, pleasant and with a similar ease for discriminating the motion direction. To summarize, the AHM illusion holds over a large range of curvatures and the "tap" stimulation is found to be possible alternative to vibrations. Future research will focus on developing improved actuators to deliver the "tap" stimulation and on investigating whether AHM speed differences are similarly discriminated in the two modes.

Fig. 3 :

 3 Fig. 3: Characterized force feedback for "tap" stimulations. The curves represent five consecutive trials.

Fig. 4 :

 4 Fig. 4: Flexible 3D printed hand-rest on the 5 tested curvatures, from flat to curved.

  (a) Vibratory mode made of sinusoïdal oscillations at 120Hz within ramp envelops. (b) "Tap" mode made of ramp signals.

Fig. 5 :

 5 Fig. 5: Signals sent to the three actuators for both actuation modes.

  (a) Perceived smoothness. (b) Perceived pleasantness.

Fig. 6 :

 6 Fig.6: Rates on a 7-point Likert scale for the AHM. The smoothness was rated after each trial of the experiment and each data point is averaged over an experimental block. The middle points correspond to the median value while the errorbars give the 1st and 3rd quartile. Same plot was made for the pleasantness.

  (a) Perceived ease to find the direction of the AHM.(b) Perceived fatigue on the hand.

Fig. 7 :

 7 Fig. 7: Rates on a 7-point Likert. The middle points correspond to the median value while the error-bars give the 1st and 3rd quartile.

ACKNOWLEDGMENT

This work was funded by the Inria Défis program, under the challenge "DORNELL". The authors thank Georges Daher, PhD student at Institut des Systèmes Intelligents et de Robotique of Sorbonne Université, for his help in creating the experimental setup. They also thank Frédéric Marie, mechatronics engineer at the Laboratoire de Génie Civil et Génie Mécanique (LGCGM) of Rennes, for the design of the 3D printed hand-rest.

This work was funded by Inria, under the challenge "DORNELL".