Justine Saint-Aubert
email: saint-aubert@isir.upmc.fr

Loïc P Heurley

St éphane R égnier Nicolas Morgado

Sinan Haliyo

S Régnier

Pre-calibrated Visuo-Haptic Co-location Improves Execution in Virtual Environments

Keywords: Visual and Haptic Co-location, Virtual Reality, User Experiment, Cable Device. !

A common approach to visio-haptic human-machine interfaces adopts a simpler design by shifting grounded force feedback away from the virtual scene. The alternative design favors intuitiveness by displaying visual and grounded force feedback at the same location (i.e. visuo-haptic co-location) but requires a sensibly more complex implementation and a tedious kinematic conception. The benefits of one approach over the other had not been fully investigated. Notably, (i) while users seem to better operate under co-located condition, it's not always the case. (ii) In the case of a desktop interface, the cost of a complex implementation to achieve co-location is challenged. We aim here to resolve (i) by conducting a user-centered experiment in which participants performed two generic tasks in co-located and delocated configurations, and comparing their performances. Additionally, we intend to fill the gap (ii) by testing a design without continuous head tracking, i.e with static co-location. Participants' performances are assessed in terms of execution time, accuracy and force variation, while their subjective experiences are collected via a survey. Findings indicate that co-located configurations lead to shorter execution times, more accurate motions, better management of forces and are largely preferred by users, even when the co-location is pre-calibrated staticly.

INTRODUCTION

V ISUO-HAPTIC CO-LOCATION refers to spatial congruence between visual and haptic signals and is inherent to interactions with objects in everyday life. However, it is much more difficult to achieve in virtual reality (VR), where distinct devices convey visual and haptic feedback separately. This study focuses on desktop use-case with an interface composed of a monitor coupled with a grounded force feedback device. Head mounted display [START_REF] Desai | A review paper on oculus rift-a virtual reality headset[END_REF] are not considered here because they are more dedicated to short simulations or may be too immersive. Target applications are dedicated to a single user performing long and fine operations, such as robotic teleoperation, remote surgery, or computer aided design. An intuitive human-machine interaction is then a considerable benefit. When users perform a manual task in such setup, they are shown an avatar (virtual replica) representing their actions, while feeling the force feedback in their hand though the handle of a mechanical motion input device. The common straightforward approach avoids superimposing spatially the avatar and the handle. This visuo-haptic delocation results in a simpler implementation in contrast with visuo-haptic co-location which supposedly brings a more intuitive interaction but requires a more complex design. The main difficulty is that the display has to deliver visual feedback at the same apparent location at which the haptic device delivers force feedback. In particular, it is required to continuously track user's head or eyes such that the avatar is superimposed with the end-effector of the haptic device.

Questions for human-machine interface designers then pertain to knowing first, in what extent the co-location helps users to operate and second, if a trade off can be found by implementing co-location without head tracking. Our purpose was to provide answers through a user-centered behavioral experiment.

Integration issues

How the nervous system combines signals from various sensory modalities to reach a unified percept is one of the main questions in cognitive psychology and neurosciences. Several theories explain this multimodal perceptual integration [START_REF] Clark | Data fusion for sensory information processing systems[END_REF]. A popular one suggests a weak fusion, where inputs are individual boxes estimated separately [START_REF] Marr | Vision: A computational investigation into the human representation and processing of visual information. freeman and company[END_REF] then combined linearly, each weighted according to its reliability [START_REF] Landy | Measurement and modeling of depth cue combination: In defense of weak fusion[END_REF], [START_REF] Landy | Ideal cue combination for localizing texture-defined edges[END_REF] [START_REF] Ernst | Humans integrate visual and haptic information in a statistically optimal fashion[END_REF]. The sensory binding depends on the temporal, structural, and, more importantly, spatial congruence between the various sensory signals [START_REF] Stein | The merging of the senses[END_REF]. Visual and haptic signals provided at different locations result in integration breakdown [START_REF] Gepshtein | The combination of vision and touch depends on spatial proximity[END_REF]. Evidence that signals refer to a single object can help to establish a correlation, for instance if stimuli are linked by a kinematic relation [START_REF] Debats | Kinematic crosscorrelation induces sensory integration across separate objects[END_REF]. However, the implication of haptic stimuli is lowered in delocated configurations [START_REF] Congedo | The influence of spatial delocation on perceptual integration of vision and touch[END_REF]. It could then be argued that executions may be impaired, especially that involved in actions requiring fine grained processing of force feedback. Several studies have used prismatic distortions inducing either a slight or a massive delocation of visual signals compared to haptic signals. Accumulated results support the idea that discrepancies alter perception and action, and induce more or less important sensorimotor adaptations [START_REF] Pick | Adaptation to prismatic distortion[END_REF], [START_REF] Sachse | the world is upside down-the innsbruck goggle experiments of theodor erismann (1883-1961) and ivo kohler[END_REF], [START_REF] Yarossi | The effects of mirror feedback during target directed movements on ipsilateral corticospinal excitability[END_REF], [START_REF] Ossmy | Behavioral and neural effects of congruency of visual feedback during short-term motor learning[END_REF]. Even if such adaptations allow to reach good motor performances, training sessions of varying duration are necessary depending on the magnitude of adaptations. Moreover, one has to plan and control his actions in order to act. When we want to reach an object with the hand, it has to be located relative to the location of the body. There are 3 possible reference frames: objects are located either relative to the hand, the eye, or the entire body. Recent data suggests that visual location and haptic location do not necessarily rely on the same reference frame [START_REF] Avillac | Reference frames for representing visual and tactile locations in parietal cortex[END_REF]. Thus, providing delocated visuo-haptic signals could induce a competition between various reference frames during handobject interactions. Together, these data support the idea that actions could depend on the spatial integration of visuohaptic signals and that delocating them could induce a decrease of performances during executions, an increase in sensorimotor adaptation phases and/or difficulties in locating objects in space. In order to act, an additional critical aspect is the need for users to have a feeling of effector ownership. Such a feeling occurs naturally in everyday life, and various studies using the rubber-hand-illusion have shown that integration of visuo-haptic signals is involved. Indeed, when visual and haptic feedback is temporally synchronized, participants can feel a rubber hand as if it were their own hand [START_REF] Botvinick | Rubber hands feeltouch that eyes see[END_REF], [START_REF] Slater | First person experience of body transfer in virtual reality[END_REF]. It is noteworthy that the visual signal (of the rubber hand) and the haptic one (of the actual hand) are slightly delocated (the rubber hand is placed near the actual hand, which itself is hidden). Even if such data support that some brain mechanisms can overcome a slight delocation of visuo-haptic signals, only a portion of participants report the rubberhand-illusion while some never experience it. Furthermore, when the illusion occurs, it is not immediate, with visuohaptic signals having to be temporally synchronized during several minutes (around 5 minutes). Also, the actual hand has to remain static. When participants move it, the illusion vanishes. And finally, even if the illusion occurs, it does not seem strong enough to influence actions performed with the actual hand [START_REF] Kammers | The rubber hand illusion in action[END_REF]. These data support that delocation of visuo-haptic signals could deeply diminish the feeling of ownership. Such a disturbance can decrease the sense of agency (i.e. the feeling of controlling our actions; e.g. [START_REF] Ma | The role of agency for perceived ownership in the virtual hand illusion[END_REF]). All in all, these converging lines of research support the idea that visuo-haptic delocation could affect users' execution.

Impact on Execution

Previous findings

Past studies tend to show that co-located configurations lead to better performance in terms of time, accuracy and efforts necessary to achieve a task. An immediate benefit is shorter execution times in co-located configurations when compared with delocated ones, in the case of a task in which participants had to align a virtual cube with other intangible cubes. With [START_REF] Swapp | Interaction with co-located haptic feedback in virtual reality[END_REF] or without haptic feedback [START_REF] Mine | Exploiting proprioception in virtual-environment interaction[END_REF] (i.e hand was displayed at the same location than the virtual environment but did not get any force feedback), participants were faster in the co-located configuration. A speed gain in co-located configurations was also found during a pointing task [START_REF] Rolland | Quantification of adaptation to virtual-eye location in see-thru headmounted displays[END_REF] as well as during needle insertion into surgical body phantoms [START_REF] Wu | Psychophysical evaluation of in-situ ultrasound visualization[END_REF]. However, both these tasks were performed on real objects which provide much more cues than current haptic devices [START_REF] Graham | Physical versus virtual pointing[END_REF], so care must be taken when interpreting these results. Shorter execution times in co-located configurations were also observed during a surgical task where participants had to cut a virtual gut without touching its surrounding wall [START_REF] Lev | The effects of 3d collocated presentation of visuohaptic information on performance in a complex realistic visuomotor task[END_REF]. A second improvement seems to be greater accuracy in the co-located configuration. In the gut cutting task, this was indirectly demonstrated by the higher number of walls touched in the delocated configuration. More direct proofs were obtained from a 3D Fitts tapping experiment [START_REF] Fu | Effect of visuo-haptic co-location on 3d fitts' task performance[END_REF] where a significant decrease in end point error was obtained in the co-located configuration. A similar result was found in a task in which participants had to juggle a ball with racket in a virtual environment [START_REF] Swapp | Interaction with co-located haptic feedback in virtual reality[END_REF]. A perfect positioning between the ball and the racket was required to successfully accomplish the task. A third possible enhancement concerns a better management of forces, i.e. better motor-control. In a task where participants explored the softness of an object [START_REF] Widmer | Effects of the alignment between a haptic device and visual display on the perception of object softness[END_REF], authors concluded that in co-located configurations, the same perception can be achieved with less energy consumption than in delocated configurations.

Limitations

Although several studies argue for an enhancement of participants' performances during executions in co-located configurations, the issue is not thoroughly settled. Results are disparate across studies. While sometimes a greater accuracy is observed in one task, it is not the case in another one. Some studies did not even conform to these results at all. For instance, in an user experiment where participants had to use a stylus haptic device to navigate between cubes placed in a 3D maze game [START_REF] Swapp | Interaction with co-located haptic feedback in virtual reality[END_REF], no significant difference could be found between co-located and delocated configurations. The same conclusion was obtained during a 3D Fitts pointing exercise [START_REF] Teather | Evaluating visual/motor co-location in fish-tank virtual reality[END_REF]. In some others studies performances in delocated configurations was even found to be better than in co-located configurations: In an experiment where participants were requested to point to the corner of a cube using a haptic device, accuracy was found to be better in delocated configurations [START_REF] Olsson | Physically colocated haptic interaction with 3d displays[END_REF]. However, when the exact same group of participants had to follow a spiral with the same set up, they were more accurate in co-located configurations. The nature of the task therefore seems to influence results. Unfortunately, all tasks tested in the literature are very loosely pertain to real executions in virtual environments, or lack external relevance as they are too specific.

Implementation Trade-Off

Co-location of visual and haptic feedbacks is matter of discussion because it complexifies the implementation. Indeed, the avatar in the virtual environment and the handle have to continuously occupy the same location from the user's point of view. It requires tracking his eyes or head in respect to the screen. It raises a first difficulty since the robustness of the tracking is often an issue. Once the different poses are inferred, they are used to find the correct location and orientation of a virtual camera in the VR environment. Consecutive frame changes are necessary in order to get the correct perspective, which sum the relative error in each step. Consequently, the implementation of co-located feedback is more arduous than for delocated configuration for which none of these operations are critical. In the case of a "desktop" interfaces which refer to a small working space, the head tracking may be less critical. In such devices, users' motions are quite limited and it seems that co-location can be achieved with an initial calibration and without continuous tracking. This idea is supported by results in a reaching task for targets where no differences in terms of performances were raised with and without head tracking after a pre-calibration [START_REF] Boritz | A study of interactive 3 d point location in a computer simulated virtual environment[END_REF]. All prior experiments presented required real-time tracking or HMD technologies that directly include trackers. The issue remains unanswered in case of desktop interface. We would like to explore here if a simpler implementation, with solely pre-calibrated co-location, is sufficient. In the affirmative, this could be an interesting trade-off for designers.

Aims of the Study and Methodology

This study investigates the effects of the relative location of visual and haptic feedbacks on user's manual execution on generic tasks and explores if a pre-calibrated static co-location is sufficient to improve performances. For this purpose, two tasks are devised : a manipulation task consisting of moving an object along a line and an exploration task consisting of haptically circumventing a fixed obstacle. A total of 36 participants performed these tasks with a dedicated human-machine interface in a static (i.e without head tracking) co-located configuration

METHODS

System Design

Visual Display

The visual display is a computer monitor. Head-mounted displays (HMD) are not considered here for the desktop usecase. Hand access to the displayed scene and objects can be provided by using a 3D perspective, via stereoscopic cues. This requires the virtual scene to appear solely in front of the display as the hand can not go through the monitor and results in a very limited volume. The surface of the screen, also called the null parallax is a physical boundary and only the negative parallax volume is accessible. Screen/mirror apparatus [START_REF] Graham | Physical versus virtual pointing[END_REF], [START_REF] Hilliges | Holodesk: direct 3d interactions with a situated see-through display[END_REF] are the only technologies providing hand access to both positive and negative parallax spaces. The users see the screen reflected on a one-way mirror and put their hands below. They then can see their own hands inside the virtual environment reflected on the mirror as depicted in Fig. 1. Note that if a HMD was used, a complex virtual representation of the hand would have been necessary.

Co-Located Cable Interface

Current haptic technologies are not designed and are illadapted to achieve the co-located configuration [C]. The shared location with the virtual scene implies a non invasive device, yet most existing solutions are made of grounded rigid links. An interesting alternative consists in switching from rigid links to cables [START_REF] Sato | Development of string-based force display: Spidar[END_REF]. Such devices have already been implemented for the purpose of co-location with a large screen [START_REF] Bouguila | Effect of coupling haptics and stereopsis on depth perception in virtual environment[END_REF] but not for screen/mirror display. We have designed such a co-located desktop interface shown on Fig. 2, explained in detail in [START_REF] Saint-Aubert | Cable driven haptic interface for co-localized desktop vr[END_REF]. A screen (1) is tilted by π 4 rad around the x c axis from the vertical plane and placed above a one-way mirror [START_REF] Clark | Data fusion for sensory information processing systems[END_REF]. The haptic device is composed of five direct drive actuators (3) connected to a 5cm diameter spherical handle (4) via Spectra cables (5) through a system of pulleys [START_REF] Ernst | Humans integrate visual and haptic information in a statistically optimal fashion[END_REF]. The actuators are arranged in an inverted pyramid with the base located 10 cm below the mirror in order to generate forces isotropically up to 5N applied to the handle within a cubic workspace about (37x25x20)cm 3 . Virtual items are displayed in the virtual scene using the open-source simulation software Blender 1 , in which the avatar is a faithful white copy of the real 5 cm diameter handle. The user's hand is not reproduced since it is visible across the mirror. When an interaction occurs, forces are generated by the haptic device in impedance mode. The spatial location is known via the length of wires and sent to the physics engine to control the avatar. God-object method performs the impedance/admittance conversion [START_REF] Zilles | A constraint-based god-object method for haptic display[END_REF] to satisfy physical constraints and the coupling. When forces F are detected by the physics engine in the software, each cable is loaded so as to build the equivalent mechanical action via the pseudo-inverse method specific to redundant mechanisms [START_REF] Kurtz | Dexterity measures with unilateral actuation constraints: the n+ 1 case[END_REF]. In no-contact situations, cables are simply taut and compensate each other's action.

The co-located interface

The bandwidth is limited by the frame rate of the physics engine, including the communication with the haptic device, to around 500 Hz for both tasks tested in the experiment. Since the bandwidth of human sensing is about 300 Hz [START_REF] Samur | Performance metrics for haptic interfaces[END_REF], the response time is adapted.

The monitor is capable of active 3D stereo with shutter-glass goggles. A pilot experiment tested the display with or without 3D and the choice is made to use only perspective cues. Users reported visual fatigue probably because the display did not succeed to keep up with the accommodation process of human eyes [START_REF] Padmanaban | Optimizing virtual reality for all users through gazecontingent and adaptive focus displays[END_REF]. The conflict between accommodation and convergence on users' comfort has been established previously [START_REF] Hiruma | Accommodation response to binocular stereoscopic tv images and their viewing conditions[END_REF], [START_REF] Inoue | Accommodation and convergence when looking at binocular 3d images[END_REF].

Users operate the interface holding the handle of the device which they can freely move in the workspace while visualizing the avatar in the virtual scene and feeling the force feedback when in contact with other virtual objects.

Pre-calibrated Static Co-Location

For the purposes of the study, a static calibration, without head tracking, is employed. Fixed frame changes corresponding to the screen tilt and mirror image are implemented. Visual scaling and perspective between virtual and real items is guaranteed by setting the focal length and pose of the virtual scene as equal to those of the human eye. Finally the pose is simply adjusted to the users' height at the beginning of each session.

The Delocated Configuration [V']

The same interface is used to set up delocated configurations in order to avoid bias that could be introduced by eventual mechanical differences. In the [V'] configuration, the visual feedback is delocated while keeping the haptic feedback (i.e the cable device) in the same location as in the [C] configuration (Fig. 3). The virtual scene is shown in front of the participants with the screen simply set upwards, barring the mirror. The frame change is adapted in order to limit the shift between handle and avatar to a fixed translation of

O c O v =[0,+0.2,+0.4]m from R c {x c , y c , z c }.
The haptic sensation remains the same than in the [C] configuration.

The Delocated Configuration [H']

The because they do not report any visual impairment (including color blindness), physical issues and are not regular consumers of psychoactive substances which could affect performance [START_REF] Wittenborn | Effects of benzodiazepines on psychomotor performance[END_REF]. Only right-handed subjects according to Coren's handedness test [START_REF] Coren | The left-hander syndrome: The causes and consequences of left-handedness[END_REF] are recruited in order to perform the task in the [H'] configuration without bias.

Overview of Trials

Participants perform two tasks. In the manipulation task they guide a sphere from one point to another following a line. In the exploration task they probe and avoid an obstacle 2 . The virtual environment reproduces Newtonian physics without gravity and some amount of damping is applied to avoid excessive speeds and motions. At the beginning of each task, the experimenter explains the overall procedure based on a pre-established script. She also informs participants that they can rest for as long as necessary between each trial. Next, participants perform one or two practice trials to ensure that they understand the procedure, after which pink noise is played to them and they perform the complete task.

Manipulation Task

At the beginning of a trial, a ghost grey line (0.25-m-long) with green and red extremities appears in the center of the screen (Fig. 5 (a)). Participants grasp the handle of the haptic device to control the avatar. They are requested to touch the green extremity, causing a tangible purple sphere to appear at a distant location (Fig. 5 They are asked to bring back the purple sphere in contact with the green extremity of the grey line by pushing it solely with the handle avatar. The line turns green to confirm contact (Fig. 5 (c)). They then push the purple object along the line (Fig. 5 (d)) to the red extremity (Fig. 5 (e)) where it should stay in contact for at least 2 seconds, to avoid ballistic strategies. After this, another trial starts (Fig. 5 (f)).

They perform a total of 20 trials with some variations. First of all, the orientation of the line changes from 0 to 2π in the null parallax plane. Furthermore, different initial locations of the purple sphere are displayed, and its weight changes between 0.25 kg, 0.5 kg and 1 kg. The other features of the object (color, size, texture, friction=0.5 ) remain constant. The objectives of these variations is mainly to prevent participants from losing focus and to perform on-line adaptation.

The order of variations is randomly predefined so that the same variations always appear in the same order between configurations and participants.

Other features are added in the virtual scene. Intangible but visible walls are shown around the scene to prevent participants from losing the purple sphere from view. A 0.15m-long box is thus constructed. If the purple sphere touches the boundaries the trial is considered a failure and the next trial automatically begins. Moreover, participants from a pilot study showed difficulties in moving the purple sphere efficiently, probably because of the lack of a stereoscopic-3D display. To help them, the purple sphere has the same dimensions as the handle of the haptic device and the background turns from black to dark red when the purple sphere moves off the line.

2. A third task in which they have to resist a perturbation was additionally conducted but not included in this study. They push the magenta sphere using the handle's avatar.

Virtual scene during manipulation task

Exploration Task

At the beginning of a trial, a ghost grey line (0.25m-long) with green and red extremities appears in the center of the screen (Fig. 6 (a)). Participants first touch the green extremity with the avatar which coupled to the handle of the haptic device. The line turns green in order to confirm contact (Fig. 6 (b)). They are then requested to travel along the line towards the red extremity (Fig. 6 (c)) until they experience a contact indicating the presence of an invisible curved obstacle. They are asked to circumvent it by keeping contact (Fig. 6 (d)). These instructions make participants to explore the object quite naturally while their movements are sufficiently constrained to allow subsequent analyses. Once participants finish probing the obstacle, they proceed as before until they reach the red extremity (Fig. 6 (e)). After three seconds, another trial starts.

Participants perform a total of 30 trials with some variations. Again, the orientation of the line changes from 0 to 2π in the null parallax plane. Furthermore, the location of the curved object as well as its shape vary along the line. The shape is created from one or several smooth spheres partially merged together. Thus, the distance traveled remains the same regardless of the direction of exploration chosen to circumvent the object. These variations are randomly predefined so that the same variations always appear in the same order between configurations and participants.

In the same way as in the manipulation task, participants are helped (except during contact with the object) by the background turning from black to dark red when the handle moves off the line.

Sequence of Configurations

Each participant complete the exploration task and then the manipulation task, respectively in all three configurations. A fully counterbalanced design is used to control potential effects of the session order, resulting in six groups in which participants are randomly assigned :

r Group 1 : [C] -[V'] -[H'] r Group 4 : [H'] -[C] -[V'] r Group 2 : [C] -[H'] -[V'] r Group 5 : [V'] -[H'] -[C] r Group 3 : [H'] -[V'] -[C] r Group 6 : [V'] -[C] -[H']
One session is about 45 minutes, subjects are then tested on different days in order to reduce fatigue and increase focus.

Collected Data

Information about time, position and force is recorded. The time is inferred using an Intel Core i5-6600 cpu clock at 3.30 GHz but is limited to 2 ms precision by the physics engine frequency. The position is tracked via the cable system. With the hardware used, the system could theoretically achieve a precision below 1mm. However, an experimental set up is rarely perfect, so the position detection was pretested with an Atracsys 3 camera system commonly used for surgical applications. This system uses infrared signals and passive markers to detect the actual handle position with submillimetric accuracy at over 300 Hz. The locations detected with this system are compared to those recorded via the acquisition of cable lengths and a maximum absolute error of 5 mm at a distance up to 15 cm from the center of the device (i.e. the area of interest) was found. Finally, contact forces are inferred in the physics engine with th god-object approach, with a spring-damper model. Since they relate to location of the proxy and the handle in the virtual world, the accuracy of the measurement depends on the cumulative error between the instant of contact and the penetration in the virtual world and is therefore complicated to estimate.

In the manipulation task, the time taken by participants to bring the sphere from its home position/the beginning to the end of the line is collected and defined as "Travel time". The recorded position is that of the purple sphere and defined as "Travel distance". The force corresponding to the contact force between the avatar and the purple sphere and is used to determine "Contact force variability". Finally, the percentage of wall hits is calculated and labeled "Failed trials". This last measurement influence all the other data since failed trials are left out in the estimation of the mean.

In the exploration task, the time taken by participants to bring the handle from the green to the red extremit is recorded and once again defined as "Travel Time". The position information of the handle during this lapse of time is used to define a "Distance to line" measurement. It corresponds to the error surface between the line and the handle, computed as the sum of distances between 1000

3. Atracsys System fusionTrack 500. https://www.atracsysmeasurement.com/wp-content/documents/fTk500-datasheet.pdf points regularly spaced on the line and their corresponding nearest points of the handle center position. It is only recorded in the case where no contact with the probed object exists. Otherwise, when the handle touches the object, its position is used to determine the surface explored. It is then subtracted from the existing surface to obtain the "Exploration error" 4 , and is either negative when participants miss some surfaces or positive when deviations occur. Finally, the force is recorded and corresponds to the contact between the avatar and the invisible object. It is used to compute "Contact force variability".

Surveys

Participants' impressions are collected with a questionnaire. Points of particular interest concern the evaluation of their own performances, their difficulties during both tasks, their fatigue and relative preferences about the configurations. They fill out a questionnaire at the end of each of the three sessions relating to each individual configuration as well as a questionnaire at the end of the study which aim to compare all configurations. Subjects participate on three different days. Each one is dedicated to the test of one configuration and between 3 and 5 days elapse between the first and the last configuration. We deem this duration short enough to get reliable comparison. In any case, users' subjective judgment reported during the last session will be correlated with users' subjective judgment reported at the end of each session. Participants answer questions on a visual analog scale (track bar) ranging from 0 to 100 and whose extremities are associated with verbal labels. They enter their observations by adjusting a cursor on the line using the computer mouse with a step precision of 1 (this information is not displayed to participants). The default location of the cursor is the middle of the line. Their answers are recorded only if participants click on the corresponding location so as to avoid missing answers. In the comparison questionnaire, three analog scales are presented for each question, one for each configuration. These three scales are all independent and displayed one above the other so as to simplify comparisons. The experimenter explain how to fill out these questionnaires before leaving the room. The participants are asked several questions. Since some of them are intended to investigate similar concepts, we decide to gather questions are :

• Self-assessed efficiency during manipulation/ line exploration/shape exploration : The higher this combined score, the more participants felt efficient in performing the task. • Workload. The higher this combined score, the more participants felt overloaded. • Intuitiveness : The higher this score, the more participants felt that a given configuration is intuitive. • Spatial Spotting : The higher this score, the more participants felt that they could spot their spatial location in a given configuration. • Preference : The higher this score, the more participants preferred a given configuration.

4. More details on the "Distance to line" and "Exploration error" data can be found in Annex

The respective questions are listed in Tab. 1.

RESULTS

Results

Results are shown as the means from every trial for all participants and for each configuration. Fig. 7 depicts results for the manipulation and Fig. 8 for the exploration. Results from the surveys are presented in Fig. 9.

Orthogonal Contrast Analyses

The travel time, travel distance, mean force and force variability for each task (manipulation and exploration) are the dependent variables for the analysis of performances. For the analysis of the survey, the dependent variables are the self-assessed efficiency in manipulation, self-assessed efficiency in line exploration, self-assessed efficiency in shape exploration, workload, intuitiveness, spatial spotting and preference scores. In both analyses, the relative location of the visual and haptic feedback is the within-subject independent variable with three levels ( [C], [H'] and[V']). Since the independent variable has more than two levels, conducting an omnibus repeated measure ANOVA to test its main effect would lead to a vague test of the hypotheses [START_REF] Brauer | L'utilisation des contrastes dans l'analyse des données: Comment tester les hypothèses spécifiques dans la recherche en psychologie?[END_REF]. We therefore conduct separate analyses on each dependent variable for each task by testing two orthogonal contrasts. First, the delocated haptic [H'] configuration (coded as -1) is compared with the delocated vision [V'] configuration (coded as +1) without considering the co-located configuration [C] (coded as 0). Second, these two delocated configurations are grouped (both coded as -1) and compared to the colocated configuration (coded as +2). The results of the null hypothesis significance tests conducted with a significance threshold at 0.05 are provided for each analysis (i.e. test statistics and p-value) along with an unstandardized effect size estimate (i.e. mean difference) with its 95% confidence interval (CI) and a common standardized effect size np

2 )

expressing the percent of variance in the dependent variable explained by the independent variable. For all the analyses, we checked whether our data were [m] 0.4 0.5

Travel time

Mean

[C] [V¡] [H¡] [C] [V¡] [H¡]

20.46 0.494 0.499

[C] [V¡] [H¡]

Contact force variability Force var.

[N] [m²]

[C] [V¡] [H¡] [C] [V¡] [H¡]

Force var.

[N]

Contact force variability [C] [V¡] [H¡] [C] [V¡] [H¡]

Efficency shape exploration

Efficency line exploration Efficency manipulation

Spatial spo�ing [C] [Vʹ] [Hʹ]

✁ ✁

[C] [Vʹ] [Hʹ] [C] [Vʹ] [Hʹ]

✁ ✁

[C] [Vʹ] [Hʹ] [C] [Vʹ]

[Hʹ] reasonably compatible with the normality and homoscedasticity assumptions of the generalized linear model 5 by using quantile-quantile plots and residual-against-prediction plots (e.g. [START_REF] Berry | Understanding regression assumptions[END_REF], [START_REF] Fox | Regression diagnostics: An introduction[END_REF]). Moderate violations of assumptions were observed for some analyses. However, we did not use data transformations to correct them because we judged that the analytic benefits did not compensate for interpretative costs. For all the analyses, we also checked the presence of out-5. We handle the sphericity assumption common in within-subject designs by testing contrasts with only one degree of freedom, making this assumption unnecessary [START_REF] Judd | Data analysis: a model comparison approach to regression, ANOVA, and beyond[END_REF].

Questions

Verbal Labels

Self-assessed efficiency manipulation

Cronbachs α = 0.80, CI [0.64, 0.90] Do you think that you succeeded in pushing the sphere along the line ?

[I didn't succeed at all -I perfectly succeeded] Do you think that you succeeded in pushing the sphere along the line ?

[It was very difficult -It was very easy] For each day, express the difficulty you had to follow the line.*

[It was very difficult -It was very easy] Self-assessed efficiency for line exploration Cronbachs α = 0.76, CI [0.58, 0.87] Do you think that you succeeded in following the line ?

[I didn't succeed -I perfectly succeeded] Do you think that you succeeded in following the line ?

[It was very difficult -It was very easy] For each day, express the difficulty you had to follow the line.*

[It was very difficult -It was very easy] Self-assessed efficiency for shape exploration Cronbachs α = 0.81, CI [0.66, 0.90] Do you think that you succeeded in circumventing the object while keeping in contact ? [I didn't succeed -I perfectly succeeded] Do you think that you succeeded in circumventing the object while keeping in contact ? [It was very difficult -It was very easy] For each day, express the difficulty you had to circumvent the object while keeping in contact.* lying trials for each participants and outlying participants in our sample. We defined an outlier as a data point for which the absolute studentized deleted residual (also called externalized studentized residual) is equal to or larger than 3 [START_REF] Judd | Data analysis: a model comparison approach to regression, ANOVA, and beyond[END_REF]. To limit the decrease of our sample size resulting from blindly discarding outliers, we conducted our analyses with and without outliers and discarded only those that dramatically changed our results. A non-trivial number of outliers is discarded. Some of them came from obvious bugs in the recording of the data while others came from the users struggling to operate in the virtual environment.

Complementary Analyses

As frequentist analyses have received a lot of criticism (e.g. [START_REF] Cumming | Understanding the new statistics: Effect sizes, confidence intervals, and meta-analysis[END_REF]), the analyses are complemented with Bayes Factors (BF) which indicate the relative evidence for one hypothesis against another. We computed these with JASP 6 using the default multivariate Cauchy prior recommended by [START_REF] Wagenmakers | Bayesian inference for psychology. part i: Theoretical advantages and practical ramifications[END_REF].

For more technical details, see [START_REF] Rouder | Default bayes factors for anova designs[END_REF]. In the analyses, the BF10 7 is interpreted as the strength of evidence supporting the existence of an effect (H1) relative to the strength of evidence supporting the non-existence of that effect (H0). The classification proposed by [START_REF] Wagenmakers | Bayesian inference for psychology. part i: Theoretical advantages and practical ramifications[END_REF] is used to qualify this strength of evidence as null (BF = 1), anecdotal (BF = [START_REF] Desai | A review paper on oculus rift-a virtual reality headset[END_REF][START_REF] Marr | Vision: A computational investigation into the human representation and processing of visual information. freeman and company[END_REF]), moderate (BF = [START_REF] Marr | Vision: A computational investigation into the human representation and processing of visual information. freeman and company[END_REF][START_REF] Congedo | The influence of spatial delocation on perceptual integration of vision and touch[END_REF]), strong (BF = [START_REF] Congedo | The influence of spatial delocation on perceptual integration of vision and touch[END_REF][START_REF] Boritz | A study of interactive 3 d point location in a computer simulated virtual environment[END_REF]), very strong (BF = [START_REF] Boritz | A study of interactive 3 d point location in a computer simulated virtual environment[END_REF]100]), and extremely strong (BF > 100).

The complete statistical analysis is provided in Table 3.

6. https://jasp-stats.org/ 7. BF01 expresses the strength of evidence supporting the nonexistence of an effect (H0) relative to the strength of evidence supporting the existence of that effect (H1).

Co-Located [C] versus Delocated [H',V']

Manipulation Task

For the manipulation task, speed, accuracy and contact stability are found to be higher in co-located configurations. Indeed, we observe lower execution times. If we consider the mean total time necessary to perform the complete task to be about 6 min 50 s, a gain of 1 min and 12 s is obtained in the co-located configuration. In the same vein, the "Distance to Line" data show that accuracy is higher in the co-located configuration than in delocated ones, a result which is confirmed by the "Self-assessed efficiency manipulation" data from the survey. These findings support an enhancement of performances in term of speed and accuracy in the colocated configuration. An increase of force variability "Contact force variability" is also observed in the delocated configurations. The colocated configuration somehow leads to more stable operation. This observation correlates with the higher percentage of "Failed Trials" in delocated configurations when compared to the co-located configuration.

Exploration Task

Again, speed and accuracy are found to be better in colocated configurations. An increase in execution time is observed in delocated configurations when compared to the co-located configuration. If we consider the mean total time necessary to perform the complete task to be about 4 min 14 s, a gain of 46 s is noticed in the co-located configuration. Moreover, the accuracy is higher in the colocated configuration during the no-contact phase where participants had to follow the ghost line. This result is confirmed by the "Distance to line" quantitative data and the "Spatial spotting" as well as "Self-assessed efficiency line exploration" data from the survey. Nevertheless, these results do not hold during the contact phase. The "Contact force variability" and "Exploration error" data are not significantly different.

General Comparison

In both tasks, participants exhibit a lack of confidence in delocated configurations which is reflected by the "Selfassessed efficiency manipulation", "Self-assessed efficiency line exploration" and "Self-assessed efficiency shape exploration" data. It's also the case even when the task is well executed, based on the "Exploration error" data. In general, participants prefer the co-located configuration over delocated configurations because they feel less overloaded and find the interface more intuitive, as depicted by the "Preference", "Workload" and "Intuitiveness" data.

Delocated [V'] versus Delocated [H']

Manipulation and Exploration Task

No significant differences in terms of time or accuracy error are observed in the manipulation task. The only significant finding concerned the "Contact Force Variability", which is higher in the [H'] configuration and correlated with more "Failed Trials". This is confirmed by the "Self-efficacy data" from the survey. No significant differences are observed between delocated configuration during the exploration task.

General Comparison

The data relative to the general comparison between configurations do not show any significant difference. We had doubts about the fatigue caused by the [H'] configuration when compared to the [V'] configuration. Indeed, the distance between the elbow and the trunk in the former was larger than in the latter, so maintaining posture in the former was more tiring. However, no significant differences are found in terms of "Workload", leading us to conclude that participants were not biased by fatigue during operations.

DISCUSSIONS

Better Performances

The role of visio-haptic location on users' performances during a manipulation task is investigated. Past studies on the issue showed that operations were sometimes performed faster, sometimes more accurately in co-located configurations. The present study informs that time and accuracy are both better managed during the same application. Additional result indicate a difference in contact stability, while previously only a change in the maximum forces was exhibited during a softness exploration tasks [START_REF] Widmer | Effects of the alignment between a haptic device and visual display on the perception of object softness[END_REF]. The stability issue here highlights a permanent effect that disturb operation all over the simulation. The difference between co-located and delocated configurations can seem quite low since of a total of 20 simulations, the mean increase of 4.66 % represents about 1 failed simulation, but we believe that this number is mainly low because of the dynamics implemented in the virtual environment. The inertia and dumping of the purple sphere are set in order to allow its movement while giving participants some leeway before failing. Lower values for these parameters could lead to a higher number of fails. In summary, those findings strengthen that the co-location of visual and haptic feedback helps users to manipulate.

Task Dependency

The role of visio-haptic location on users' performances during an exploration task is also investigated. The operation mainly concerns the contact phase, however no difference are found between co-located and delocated configurations. The effect of the delocation then depends on the task performed. This evidence is consistent with the deviation of results between previous studies exhibited in the introduction section. Indeed, some did not conclude on an enhancement of performances in co-located configuration. The present study profits that the same participants used the same devices to perform the manipulation and the exploration task in the experiment. Hence, a reliable comparison can be performed. A first factor that can explained the variation of performances between the tasks is the type of feedback. In the exploration task, the only visual cue that is available is the handle/avatar location, as the object is invisible. And since it doesn't concern direct information about the object but information derived from the force feedback, we can assume that haptics are somehow dominant in the process. If the visual cues are reduced, small conflicts should occur between visual and haptic cues regardless of the configuration. This is the case here. Unlike this phase, the nocontact phase of the exploration task and the manipulation task both involved visual and haptic feedback, that can lead to differences between configurations. A similar comment applies to a previous study that explored performances in a 3D Fitts task [START_REF] Teather | Evaluating visual/motor co-location in fish-tank virtual reality[END_REF]. No haptic feedback was provided and no difference were found between co-located and delocated configurations. However, in the same experiment with haptic feedback [START_REF] Fu | Effect of visuo-haptic co-location on 3d fitts' task performance[END_REF], difference were identified. Another factor that may influence results is the level of complexity. In the manipulation task, participants are required to handle the avatar and a dynamic object in the scene, while object to probe in the exploration task is static. Previous studies that involved complex operations (e.g needle insertion [START_REF] Wu | Psychophysical evaluation of in-situ ultrasound visualization[END_REF], surgery [START_REF] Wu | Psychophysical evaluation of in-situ ultrasound visualization[END_REF] or juggle [START_REF] Swapp | Interaction with co-located haptic feedback in virtual reality[END_REF]) found differences between co-located and delocated configurations. A last, but not least, possible factor concerns the dimension of the space. The manipulation task is performed in 3D space while the exploration one is mainly executed in a plan. In past studies, no enhancement of performances was raised in co-located configuration during a pointing task [START_REF] Olsson | Physically colocated haptic interaction with 3d displays[END_REF]. However, the same participants followed a 3D spiral in co-located configuration with higher accuracy. Additionally, enhancement of performances was exhibited when an entire cube has to be aligned [START_REF] Swapp | Interaction with co-located haptic feedback in virtual reality[END_REF], [START_REF] Mine | Exploiting proprioception in virtual-environment interaction[END_REF], a task that required to handle correctly the position of each face in the 3D space.

Confidence Issue and Cognitive Load

A lower confidence coming from participants in delocated configuration is detected in the exploration task. A lower score for the [V'-H'] contrast than for the [C] in terms of strengthen our conviction that the trade-off to drop the continuous head tracking is relevant. The approach would lend itself well for use in any desktop interfaces that do not directly dispose of head tracker or for which the precision of co-location is not critical.

Stereoscopic Cues

One downside of our methodology is the absence of visual stereoscopic cues. Pilot experiments showed that users preferred to avoid 3D glasses. This shortcoming is probably stems form the light polarization introduced by the reflection resulting in a disagreeable experience. However, stereoscopic cues were absent in each configuration. This absence equally affects both colocated and delocated configurations in our design, hence comparative results remain valid. With stereoscopic cues, the reliability of the visual signal would have been higher in all cases, but how this impact is cognitively integrated remains to explore.

CONCLUSION AND PERSPECTIVES

The spatial congruence between visual and haptic feedbacks has been investigated in the case of a desktop display coupled with a grounded haptic device. In tested task users' execution is faster, more accurate and they better manage their motor-control in a co-located configuration. The also have a higher opinion of their performances indicating a lesser cognitive load. These findings are observed with a static pre-calibration. These argue that a simple co-location improves users' performances, without technical complexity of head tracking. Moreover, these indicate that an acceptable discrepancy range exists in the handle/avatar superposition. This range and its influence on users' performances can be explored further.

  (noted [C]) and two delocated configurations (noted [V'] and [H']). In the [V'], the visual feedback is shifted compared to the [C], while in the [H'] the haptic feedback is shifted compared to the [C]. Testing both [V'] and [H'] allows accounting for the posture difference between configurations and to differentiate the effects of co-location and the user posture. Position, time and force variability are recorded in all three configurations in order to evaluate performances. Furthermore, user's subjective experiences are collected with a post-study questionnaire.

Fig. 1 :

 1 Fig.1: Screen/mirror apparatus allowing co-location of the virtual environment and user's hand.

27 Fig. 2 :

 272 Fig. 2: Visual and haptic feedbacks are co-located by superimposing the reflection of the screen with a cable device.

Fig. 3 :Fig. 4 :

 34 Fig. 3: In the [V'] delocated configuration, participants directly look at the screen without the mirror and operate in the same space as in the [C] configuration.

Fig. 5 :

 5 Fig.5: Manipulation scene as seen by participants. They push the magenta sphere using the handle's avatar.

Fig. 6 :

 6 Fig. 6: Exploration scene as seen by participants. They follow the line with the handle and circumvent an invisible obstacle.

Fig. 7 :

 7 Fig. 7: Data collected during the manipulation task. Each graph presents the corrected mean of participant's mean values for all 20 trials respectively for the [C], [V'] and [H'] configurations. Error bars illustrate the 95% confidence interval for between-participant spread.

Fig. 9 :

 9 Fig. 9: Data collected in the survey. Each graph presents the corrected mean of participant's mean values for all 20 trials respectively for the [C], [V'] and [H'] configurations. Error bars illustrate the 95% confidence interval for betweenparticipant spread.

  [It was very difficult -It was very easy]

	Workload	Cronbachs α = 0.69, CI [0.49, 0.83]
	Did you stay focussed during the entire task?	[Not at all -Totally]
	Did you feel tired?	[Not at all -Completely]
	For each day, express the difficulty you had to staying focussed.*	[It was very hard -It was very easy]
	For each day, express your state of mental fatigue.*	[I was not tired at all -I was very tired]
	For each day, express your state of physical fatigue.*	[I was not tired at all -I was very tired]
	Intuitiveness
	Do you think that the interface is intuitive?	[Not at all -Totally]
	Spatial Spotting
	For each day, express the difficulty you had to locate yourself in space.*	[It was very difficult -It was very easy]
	Preference
	If you had the opportunity of using this device again, would you choose to ?*	[Not at all -Totally]

TABLE 1 :

 1 Set of questions and verbal labels grouped for each item in the survey. The combination consistency is confirmed for every item by computing an average Cronbachs α across configurations. Questions stamped with * correspond to the cross-configuration evaluation performed at the tail end of the experiments.

*This work was performed within the Labex SMART supported by French state funds managed by the ANR within the Investissements d'Avenir programme under reference ANR-11 IDEX-0004-02. Manuscript received ?; revised ?.

Data

Mean values The second last column shows the frequentist analyses, N.S stands for "not significant" and S for "significant". Finally, the last column corresponds to the bayesian analyses and shows the correlated classifications.

"Self-assessed efficiency" appears in the survey. Although their performances were similar in all 3 configurations, most participants indicated that they thought to have done better in the co-located case.

Our assumption is that this self-assessed efficiency score is correlated to subjective rating of mental effort, indicating a lower cognitive load [START_REF] Paas | Assessment of Cognitive Load in Multimedia Learning Theory[END_REF], [START_REF] Haji | Measuring cognitive load: performance, mental effort and simulation task complexity[END_REF]. The task hence appears easier to the user because less demanding.

Delocated [V'] Versus Delocated [H']

The direct comparison between [V'] and [H'] brings supplemental information. No differences in terms of time or accuracy are found. However, a difference in terms of contact stability and failed trials is apparent. These findings are first relevant in order to judge the effect of the co-location of feedback. Indeed, they show that a part of the difference in term of stability and failed trials found in the [H',V']-[C] contrast could be attributed to the change of posture. The other part is due to the delocation itself. Additionally, the differences between delocated configurations are particularly interesting when co-location is not an option, for instance when visual and haptic have different working spaces. User's velocity, accuracy and management of forces are then affected by the fact that feedbacks are not co-located. But the management of forces is also impaired by the posture of the user. The type of delocation should then be considered.

"Simple" Co-Location

All these conclusions are established with a pre-calibrated simple co-location, i.e without head tracking. This introduces a small error in superimposition of the handle and its virtual avatar when the user moves his head during the simulation. The improvement in execution in the colocated configuration, supported by two statistical analyzes Sinan Haliyo is an associate professor at Institute of Intelligent Systems and Robotics (ISIR), Sorbonne University and has been active in robotics since 1999. His main topics of interest include control and design issues, physical interactions and user interfaces for micro-scale applications in assembly, characterization and user training. He also takes a particular interest in human-computer interaction issues in remote handling and teleoperation, especially with haptics and multimodal interfaces.


Rémy Grünblatt

Isabelle Guérin Lassous
email: isabelle.guerin-lassous@ens-lyon.fr

Olivier Simonin
email: olivier.simonin@insa-lyon.fr

Leveraging Antenna Orientation to Optimize Network Performance of Fleets of UAVs

In this paper, we investigate the problem of optimizing the network performance of a fleet of unmanned aerial vehicles (UAVs) in static positions. More precisely, we allow each UAV to change its orientation in order to improve the quality of communication with its neighbours. This form of controlled mobility takes advantage of the effective radiation pattern of each UAV. We build a decentralized scheme based on the hill climbing optimization approach without a priori knowledge of the antennas radiation patterns. Then, we propose a simulation framework, based on ns-3, allowing to evaluate the gain in network performance. We provide results in several deployment scenarios involving different rate adaptation algorithms and network sizes.

INTRODUCTION

Fleets of unmanned aerial vehicles (UAVs) can be used for search and rescue missions, emergency deployment of communication networks, surveillance, or even natural phenomena monitoring. While these different applications have different needs in terms of communication quality, throughput, coverage or infrastructure, the IEEE 802.11 set of standards is a good candidate to enable communication throughout the fleet and between the fleet and the ground. Indeed, WiFi supports both ad-hoc and infrastructure modes, is readily available and can be used without license worldwide, while being the de-facto standard wireless communication technology for a whole set of devices such as laptops or phones. Moreover, the latest WiFi version (WiFi5) (or the upcoming version WiFi6) offers (or will offer) very high throughputs enabling to consider the transmission of high demanding flows within UAV networks.

Experiments regarding UAV 802.11 networks and their air-toground and air-to-air links underline that antenna radiation patterns play a big role in the performance of the deployed network [START_REF] Hayat | Experimental analysis of multipoint-to-point UAV communications with[END_REF][START_REF] Yanmaz | Experimental performance analysis of two-hop aerial 802.11 networks[END_REF][START_REF] Yanmaz | Achieving air-ground communications in 802.11 networks with three-dimensional aerial mobility[END_REF]. This conclusion is also highlighted in a very recent work [START_REF] Badi | Experimental Evaluation of Antenna Polarization and Elevation Effects on Drone Communications[END_REF] that, via experiments, shows the impact of different physical parameters on the UAV communication performance. Yet, theoretical works and simulations often assume that omnidirectional antennas (also called isotropic antennas) are used in UAV networks. Whether the use of directional antennas can improve the communication performance within UAV networks and how to take into account these directional antennas are still, from our point of view, open questions. In this paper, we explore how to leverage the orientation of directional antennas in order to improve the network performance of a fleet of UAVs. The main contributions of this paper are summarized as follows:

• We propose a controlled mobility algorithm based solely on the orientation of the UAVs, without an a priori knowledge of the radiation pattern of the used antennas. The proposed algorithm is distributed and each UAV asynchronously runs its own algorithm based on local measurements on the power of the received packets. • We have developed and implemented a simulation framework to simulate a network of UAVs equipped with directional antennas of any possible radiation pattern. The simulation framework consists of two main components: one component simulates the UAVs and the orientation of their antenna while the second component is based on the ns-3 network simulator to simulate the network communications.

The interactions between the two components are realized via a message-passing approach. • Based on this simulation framework, we have evaluated the proposed antenna orientation solution. Different network topologies with different number of UAVs are considered with several rate adaptation algorithms. The solution convergence time, the obtained throughput for each transmitted flow as the network Jain's index have been studied.

The paper is organized as follows: the studied problem is formally modeled in Section 2. From this modeling, we describe the proposed antenna orientation algorithm in the same section. Then, the simulation framework developed to simulate UAV and antenna orientation is described in Section 3. In Section 4, we describe the different scenarios that have been evaluated as the obtained results. Papers that relate to the studied problem are discussed in Section 5. We conclude in Section 6.

PROBLEM MODELING AND OPTIMIZATION OF ANTENNA ORIENTATION

In this section, we first introduce the studied problem and we then describe the proposed solution for the antenna orientation.

We consider a set of UAVs (also named as agents or nodes hereafter), each equipped with a wireless network interface controller using WiFi and a directional antenna whose the radiation pattern (also named the antenna gain pattern) is unknown. All the agents use the same Wi-Fi channel to communicate. The studied problem is the following: given a UAV fleet configuration, can each agent optimize its local antenna orientation in order to enhance the communication performance, such as throughput? We focus on multi-rotor UAVs because their three-dimensional positions and orientations can be fully controlled and maintained through time by the flight controller, while, for example, fixed-wing UAVs cannot hover at a given position. We also limit this study to UAVs whose 3D positions are static, but whose orientations in their horizontal plane, around the normal axis, named yaw, can be changed. Indeed, as the 3D UAVs positions are often application dependent, we focus on parameters that can be modified without interactions with the applications, for the sake of generality. These requirements cover, in particular, the class of coverage applications, such as surveillance, continuous monitoring or network coverage. As changing the roll (orientation along the longitudinal axis) or the pitch (orientation along the transverse axis) of a multi-rotor changes its 3D position when it is not subject to external forces apart from gravity, we assume those two quantities are also fixed.

In this study, we want to optimize the overall network throughput by changing the agent antenna orientations when the agents are in fixed positions. The throughput obtained by each transmitted flow in the network depends, among others, on the transmission rate used to transmit the flow, the quality of the channel used for the communication, the transmission power and the antenna types and orientations. The transmission rate is very often adaptive and regulated by a rate adaptation algorithm (also noted RAA hereafter). There exist many different rate adaptation algorithms [START_REF] Qi | Rate Adaptation With Thompson Sampling in 802.11ac WLAN[END_REF] and a large number of Wi-Fi interfaces use proprietary solutions for which the used algorithm is unknown. These algorithms can lead to very different performance for the same scenario, as shown in [START_REF] Grünblatt | Simulation and Performance Evaluation of the Intel Rate Adaptation Algorithm[END_REF]. We thus think that it is difficult to design a generic antenna orientation solution leveraging the used rate adaptation algorithm. We have therefore decided to use, in our solution, a simpler metric like the power of the received signal. This metric is impacted by the antenna orientation and the channel quality, but it also has an indirect impact on the used rate adaptation algorithm. In Section 4, we will study the performance of our proposed solution with different rate adaptation algorithms.

Problem Modeling

Let 𝐺 = {𝑉 , 𝐸} be an undirected graph representing a set of 𝑁 networked agents, where 𝑉 = {𝐴 1 , 𝐴 2 , . . . , 𝐴 𝑁 } and 𝐸 ⊂ 𝑉 × 𝑉 denote respectively the set of vertices and the set of edges. We denote by 𝐴𝑑 = (𝑎 𝑖,𝑗 ) (𝑖,𝑗) ∈𝑁 ×𝑁 the adjacency matrix of the graph: 𝑎 𝑖,𝑗 = 1 if (𝑖, 𝑗) ∈ 𝐸 meaning that agents 𝐴 𝑖 wants to communicate with agent 𝐴 𝑗 , and 𝑎 𝑖,𝑗 = 0 if (𝑖, 𝑗) ∉ 𝐸 meaning that agent 𝐴 𝑖 does not wish to communicate with agent 𝐴 𝑗 .

Each agent is equipped with a directional antenna. The antenna radiation pattern is represented by a function 𝑔. As 𝑔 can be different from one agent to another, we use 𝑔 𝑖 representing the antenna radiation pattern of agent 𝐴 𝑖 . It is expressed in decibels and in the Figure 1: 3D view of two agents 𝐴 𝑖 and 𝐴 𝑗 spherical coordinates system described in [START_REF] Balanis | Antenna theory: analysis and design[END_REF]Chapter 2.2]. Figure 2 gives an example of two antenna gain patterns in a plane (one directional antenna and one omnidirectional antenna). Depending on the antenna orientation between two neighbor agents (there exists a link between these 2 agents in 𝐺), these two agents may be able to communicate or not. When they are able to communicate, this orientation has also an impact on the power of the received signal. The higher the received power, the more likely the communication will be of good quality and will use a high transmission rate.

The objective of the agents is then to cooperatively solve the following optimization problem: max which represent respectively the relative polar and the relative azimuth angles between agents 𝐴 𝑖 and 𝐴 𝑗 . These quantities are represented on Figure 1. 𝑆 𝑖,𝑗 is a non null value if 𝑆 𝑖,𝑗 is higher than a given threshold 𝑇ℎ representing the minimal signal-to-noise ratio required to receive data. Finding a solution to this optimization problem involves determining the different agent antenna orientations to optimize the sum of the powers of the received signals in the network. In the next section, we propose a distributed solution in which each agent determines its antenna orientation based on local measurements, without knowing its antenna gain pattern nor the ones of the other agents, or their positions.

Optimization of Antenna Orientation

As the explicit expression of 𝑔 is unknown from the agents, the proposed solution will be based on measurements that each agent can carry out. More precisely, agent 𝐴 𝑖 can measure 𝑆 𝑖,𝑗 (𝑡) at time 𝑡 if the following conditions are met: agent 𝐴 𝑗 is transmitting at time 𝑡, 𝑎 𝑖,𝑗 = 1 and 𝑆 𝑖,𝑗 (𝑡) is bigger than the given threshold 𝑇ℎ (for the SNR). When agent 𝐴 𝑖 carries out such a measurement, it knows its yaw orientation 𝜙 𝑖 (𝑡). These measurements will be stored in a measurement vector 𝑀: each agent 𝐴 𝑖 maintains 𝑀 𝑖,𝑗 = [𝑚 𝑖,𝑗,0 , 𝑚 𝑖,𝑗,1 , . . . , 𝑚 𝑖,𝑗,359 ] for each agent 𝐴 𝑗 such that (𝑖, 𝑗) ∈ 𝐸. The scalar components 𝑚 𝑖,𝑗,𝑘 corresponds to the measurement of the mean received power, at agent 𝐴 𝑖 , of the signals sent by agent 𝐴 𝑗 when 𝐴 𝑖 has a yaw orientation equals to 𝑘. Because we are not requiring the knowledge of 𝐺 and 𝐸 from the agent 𝐴 𝑖 , 𝑀 𝑖,𝑗 is created "on the fly" when the connection between 𝐴 𝑖 and 𝐴 𝑗 is first established. It is then initialized to 𝑀 𝑖,𝑗 := [None, . . . , None].

Each agent executes its own algorithm without being synchronized with its neighbors. The proposed algorithm consists of an infinite loop. In each passage in the loop, each agent realizes different steps. First, the agent fetches the frames it has received since the last loop execution, in its network interface queue, and updates its measurement vectors. Then, if the agent lacks some data in its measurement vector with at least one neighbor, it seeks which orientation to move to, to get this measurement. Finally, if its measurement vectors are complete, it tries to optimize its orientation based on their values. Each agent runs the algorithm while it changes its orientation according to online results and while it communicates with its neighbors if required by the data traffic.

The proposed algorithm is based on the hill climbing approach [START_REF] Stuart | Artificial intelligence: a modern approach[END_REF]. We have chosen hill climbing for two reasons: 1) it is an anytime algorithm (it can find better and better solutions as long as it keeps running) and 2) even if it does not guarantee convergence towards a global optimum, it provides an efficient way to find a good solution in a decentralized multi-agent problem. Algorithm 1 describes the algorithm executed by agent 𝐴 𝑖 .

Algorithm 1: Antenna Orientation Optimization (agent 𝐴 𝑖 )

;

; ;

As the orientation 𝜙 𝑖 (𝑡) and the power measurement 𝑆 𝑖,𝑗 (𝑡) of the received signal depend on the instant at which these 2 parameters are considered, they are expressed in function of the time 𝑡. The 𝑊 𝑖𝑛𝑑𝑜𝑤 variable represents the search space. Initially, the search space includes all the possible orientations ([0; 360[). In order to speed up the algorithm convergence, the size of the space search is divided by 2 as soon as a maximal solution is found in the current space search (line 18 of Algorithm 1). The 𝐶𝑜𝑢𝑛𝑡 variable represents the maximum number of loop passages during which the agent stays in the same orientation. If the agent stays in a given orientation for too long while trying to fill its measurement vector, the agent considers that it is not a good orientation and sets a very low value to the corresponding measurement element (line 13 of Algorithm 1). The 𝐺𝑜𝑎𝑙 variable represents the orientation the agent is currently trying to reach. In the first loop passages, 𝐺𝑜𝑎𝑙 corresponds to unexplored orientations for which no measurement value has been collected. Once measurements have been collected for all the orientations and neighbors, then an optimal orientation (in respect to the defined objective function) can be computed. Then, the parameter 𝑑 𝑖 , representing the direction to follow (i.e. right, left, or do not move), is updated in order to reach the orientation 𝐺𝑜𝑎𝑙.

Note that finding an optimal orientation does not mean the end of the algorithm. The search continues with new possible measurements and on a reduced search space. A new optimal solution can thus be found.

Evaluating this algorithm is a difficult task because the algorithm is distributed and executed in parallel by all the agents in an asynchronous way, but also because it depends on the data traffic, the medium access, the used transmission rates, the channel quality and the agent controller. Moreover, we are interested in the network performance. A dedicated simulation framework has therefore been developed to evaluate the proposed antenna orientation solution in a realistic context.

SIMULATION FRAMEWORK

To simulate antennas and UAVs and to evaluate our proposition, we chose to develop a framework based on the ns-3 network simulator. This development is necessary as existing simulation frameworks do not offer the possibility to both simulate UAV controllers and the UAV communications using directional antennas easily. While ns-3 has some support for antenna modelling, this support is only compatible with Long-Term Evolution networks and not with WiFi networks. Nodes, which represent the physical objects in ns-3, are point-like objects with Cartesian coordinates, but no orientation coordinates are provided. These two facts together make it difficult to simulate spinning nodes embedding non-isotropic antennas for WiFi networks, at least without rewriting much of the ns-3 models. UAV simulators based on ns-3 such as CUSCUS [START_REF] Roberto Zema | The CUSCUS simulator for distributed networked control systems: Architecture and use-cases[END_REF] or FlyNetSim [START_REF] Baidya | FlyNetSim: An open source synchronized UAV network simulator based on ns-3 and ardupilot[END_REF] are focused on hardware-in-the-loop, software-in-the-loop or real-time simulations, and do not model the antennas. The developed simulation framework is available as an open source project at GitHub 2 .

Architecture

The architecture of our framework, as depicted in Figure 3, is divided into two main components. The first component is the network simulator ns-3, including the user simulation script or program (bottom left), backed by a custom ns-3 module implementing a propagation loss model and a mobility model (bottom right), and the second component is the discrete-event antenna and UAV simulator, called Phi (top). A third optional component, the visualization frontend, can be plugged into the Phi simulator in order to follow the state of the simulations in "real" (simulated) time.

The goal of Phi is to simulate the behaviour and dynamics of multiple UAVs equipped with non-isotropic antennas. Phi provides, according to the antenna orientation, the power gains to use in the ns-3 simulator, simulator that will in turn simulate the UAV network and the networking stack. The controllers and the sensors of the UAVs are therefore modelled by Phi. The simulator has been implemented in C++, which is also the language used by ns-3, but 2 Phi codebase: https://github.com/rgrunbla/Phi. as the interface between Phi and ns-3 relies on message passing, the language could easily be changed.

Communications. The two components (ns-3 and Phi) exchange Protocol Buffers messages, used to serialize and deserialize structures, and communicate using the Zero MQ asynchronous messaging library. Interactions between ns-3 and Phi take the form of two types of messages: Meta messages that are used to set up and control the simulations life cycle, and Meso messages that concern the simulation itself. The socket connecting the two components uses the ZeroMQ request-reply pattern, ensuring their synchronization, and currently uses a local inter-process communication transport. A third type of message, called Viz, serves as a way to serialize the state of the simulation in order to send it to the visualization front-end. ○ containing the number of agents and their types are sent to Phi's simulation manager component, which will instantiate the simulation, and reply with a simulation ID 2 ○. This simulation ID is included in every subsequent Meta or Meso messages exchanged between the two components and allows a single instance of Phi to be used by concurrent ns-3 simulations. When the simulation ends in ns-3, a Meta message is sent to the Phi's simulation manager to end the simulation and release the resources.

ZeroMQ

Mobility Model and Physics Engine. In ns-3, mobility models are in charge of tracking and changing nodes' positions, speeds and accelerations. These quantities are used by the propagation loss and delay models to compute a loss depending on the distance between nodes, and to compute the delay between the transmission and reception of the frames. A custom ns-3 mobility model has been developed, allowing to set the position in Phi from the ns-3 simulation 3

○, for example at the beginning of a scenario, as well as querying node positions 4 ○, e.g. to calculate propagation delays. As the simulator was developed for scenarios where the UAVs have a static position and dynamic orientation, we chose to only consider constant rotation speeds for the UAVs. This allows to model their movements and rotations with simple multiplication operations without having to go through the use of a differential equation solver. This approach is also used by ns-3, which only supports constant speed or constant acceleration mobility models.

Propagation Loss and Delay Model. In ns-3, propagation loss models and propagation delay models are used to model the propagation of the signal between any two nodes, by respectively calculating the signal power and the signal delay. These models can be chained, for example adding a model of Nakagami fading to a free space path loss model leading to a link budget calculation performed by the channel model. The custom module implements a propagation loss model which queries Phi 5

○ about the gains brought by the antennas of the agents, gains which are sent back to ns-3 6 ○. Phi does not model any other effect such as the free space loss as one can use the ns-3 models directly. No custom propagation delay model is needed, as this calculation can be done by ns-3 directly by using the positions set by the custom mobility model. Clock Synchronization. The clock state of a ns-3 simulation is included into every Meso message sent to Phi, for example in a propagation loss query, or a position query. The only way for a simulation in Phi to advance through time is to receive a Meso message and synchronize its clock with the value it contains. Before the clock update, all the events in the event queue of Phi that are scheduled to occur before the new clock value are executed, with each event being preceded by an update of the environment and agents states.

Agent Simulation and Environment. Each agent simulated by Phi is specified by a type and the associated blueprint located in the Agent Library component. This blueprint contains the implementation of the controller, of the sensors and the actuators. These components are functions executed at their own frequency using events, e.g. 100 Hz for the controller or 10 Hz for a magnetometer. The controller is only capable of interacting with its environment through the use of a shared memory with sensors and actuators, in an asynchronous way. Messages originating from the ns-3 simulation intended for a specific agent are called Network Events 7 ○ and are placed in a queue in the shared memory. Such messages are for example sent by ns-3 when a frame is received, and contain the frame characteristics, such as the reception power, or the MAC address of the transmitter if applicable.

EVALUATION

In this section, we present different scenarios used to evaluate the performance of our approach (Algorithm 1). The different scenarios share some parameters, described in Table 1, but differ in the number of nodes and their positions. We use the ns-3 Friis propagation loss model, also known as the free-space path loss model, which accurately models the path loss of air-to-air communications between UAVs [START_REF] Yanmaz | Achieving air-ground communications in 802.11 networks with three-dimensional aerial mobility[END_REF]. All of the simulations rely either on an isotropic antenna or a directional antenna whose orientation is regulated by Algorithm 1. The directional antenna represents the Ubiquiti 1: ns-3 simulation parameters UAP-AC-Mesh Antenna, also named as mesh antenna hereafter, whose radiation pattern is shown on Figure 2. The radiation pattern is provided by the constructor on its website [START_REF]UAP Antenna Radiation Patterns[END_REF] as an ant file type, covering the horizontal plane with a granularity of 1 • . This antenna has been chosen for its small size and weight, making it compatible with airborne applications, as well as its balanced radiation pattern suitable for mesh applications. The tested antenna has a maximal gain of 4 dBi. Considering a link with two agents equipped with the directional antenna with a 4 dBi gain, 63% of all the possible orientations between the two agents yield a higher gain than a link with two isotropic antennas.

Three rate adaptation, named MinstrelHT, Intel and Ideal, have been considered. MinstrelHT is implemented in the mac80211 component of the Linux kernel and is open source [START_REF] Fietkau | Minstrel HT: New rate control module for 802[END_REF]. MinstrelHT is used in the ath9k driver. The Intel rate adaptation algorithm is used on Intel WiFi interfaces and on Intel Aero Ready-to-Fly UAV [START_REF] Grünblatt | Simulation and Performance Evaluation of the Intel Rate Adaptation Algorithm[END_REF]. Ideal is another rate adaptation algorithm implemented in ns-3 and supporting 802.11ac. These three algorithms have different behaviors and lead to different performance, as studied in [START_REF] Grünblatt | Simulation and Performance Evaluation of the Intel Rate Adaptation Algorithm[END_REF]. Our evaluation will thus also study the impact of these three algorithms on the performance of our solution.

We present the obtained results in Sections 4.1, 4.2 and 4.3. The initial orientations of the nodes are distributed uniformly over [0; 2𝜋], and each simulation is repeated 20 times with different initial orientations. Several results are reported with the box plot representation.

Scenario #1: Simple

In this scenario, two nodes are separated by a fixed distance, with one node acting as a source and one node acting as a sink, as shown on top of Figure 4. The two nodes are either both equipped with omnidirectional antennas, in which case Algorithm 1 is not used, or both equipped with directional antennas using our antenna orientation algorithm. The throughput of the source is set to 180 Mbps, which exceeds the maximum physical throughput for the WiFi physical layer parameters used in the simulation, which is 173.3 Mbps. The received throughput at the sink is plotted on Figure 5 as a function of time, rate adaptation algorithm, and the used antenna, for a single simulation and when the distance between the two nodes is 100𝑚. We can observe that the three rate adaptation algorithms are almost the same when an omnidirectional antenna is used, and the received throughput remains stable throughout the simulation (with some variations with MinstrelHT). When the directional antenna is used, we observe two main phases. The first phase, where the throughput varies a lot corresponds to the execution of the antenna orientation algorithm: as the channel between the two nodes changes, the rate adaptation algorithms react and change the transmission rates, affecting the received throughput. The second phase starts after the antenna orientation algorithm has converged to its best solution in terms of received power. The received throughput remains fairly stable during this phase as the only source of change is the RAA decisions. We can however observe that when MinstrelHt is used, it takes more time to reach the stabilized received throughput, which is consistent with the previous observations made about the algorithm in [START_REF] Grünblatt | Simulation and Performance Evaluation of the Intel Rate Adaptation Algorithm[END_REF]. The convergence time for the antenna orientation algorithm and the convergence time on the received throughput for the simulations using the directional antenna are plotted on Figure 6 (with the box plot representation). The convergence time for the antenna orientation algorithm is the elapsed time between the start of the algorithm and the time when the last agent stops to change its orientation. The convergence time on the received throughput is the elapsed time between the start of the algorithm and the time when the received throughput on the sink is different to at most 5% of the final achieved received throughput. We can note that the convergence time of our algorithm is always smaller than 20s in Scenario #1. The convergence time on the received throughput is also smaller than 20s for Ideal and Intel, and it is never larger than 40s with MinstrelHT. We can observe a strong correlation between the two quantities for the Ideal and the Intel RAAs, which underlines those algorithms are fast to react to changes in the channel, while the throughput convergence time of MinstrelHt illustrates the inertia of the algorithm, which can be linked to its sampling approach. Using physical layers metrics, such as signal strength, and not application layer metrics, such as the received throughput, appears therefore justified for such an algorithm, as higher layer metrics may introduce important delay with certain RAA. Figure 7 shows the distribution of the achieved throughput for Scenario #1 when the two nodes are 100𝑚 away. The achieved throughput is measured when the antenna orientation has converged. The obtained results show that our antenna orientation solution improves the achieved throughput whatever the used RAA. For instance, with the Ideal RAA, the mean achieved throughput is 144.2 Mbps with directional antennas compared to 116.8 Mbps with omnidirectional antennas, whereas it is 136.9 Mbps with directional antennas compared to 113.2 Mbps with isotropic antennas for the Intel RAA. For MinstrelHT the use of directional antenna with our orientation algorithm leads to 137.4 Mbps compared to 111.5 Mbps with ominidirectional antennas. We analyzed the antenna orientations obtained when our algorithm has converged for the different simulation repetitions and for the different RAAs. The values obtained on the antenna orientations vary but are mainly scattered on good positions as 95% of the achieved orientations lead to a better link budget than with isotropic antennas. These orientations lead to better link qualities which also lead to a use of higher transmission rates, which, at the end, results in higher achieved throughputs. Finally, one can note that the obtained values on the throughput are more dispersed with directional antennas than with isotropic antennas. This is explained by the fact that the obtained orientations vary, which results in different link budgets implying more various throughputs, though these latter are, most of the time, better than the ones obtained with isotropic antennas.

Rate Adaptation Algorithm

Scenario #2: Sink

In this scenario, one node serves as a sink while other nodes serve as sources. The sources are located on a circle with a fixed radius 𝑟 , while the sink is located at the center of the circle, as shown on the middle of Figure 4. The sink can be seen as a UAV receiving video feeds from the sources, and sending them to the ground using another network component not studied here. The sink is equipped with an isotropic antenna. We have observed, on the different simulations, that the antenna orientation algorithm converges in less than 30s. The distribution of the average received throughput per link, at the sink, for a radius of 100m and for different application rates at the source, is shown on Figure 8. One can observe an increase in the obtained throughput when using the directional antenna, no matter which RAA is used. The increase is more limited with MinstrelHT. As 100% of the simulations obtain a better link budget than with an omnidirectional antenna, this more limited improvement can be explained by the larger time needed for MinstrelHT to converge towards the final throughput when the antenna orientation has ended, leading to a smaller throughput than with Ideal and Intel. When the application rate is low enough, e.g. 10 Mbps, it can be fulfilled by both the isotropic and the directional antennas in any direction, leading to very similar obtained throughput.

We have measured whether the different sources are receiving a fair "share" of the received throughput at the sink or not with the Jain's fairness index [START_REF] Rajendra K Jain | A quantitative measure of fairness and discrimination[END_REF]. The results obtained for 𝑟 = 100𝑚 and 𝑛 = 3, 5, 10, and an application throughput of 50 Mbps show that the use of the mesh antenna does not decrease the fairness between the nodes with rather a slight increase of the Jain's index values (between 0.94 to 1 for directional antennas compared to 0.92 to 1 with isotropic antennas).

Scenario #3: Chain

In this scenario, one node serves as a source, one node serves as a sink, and the other nodes serve as relays between the source and the sink as depicted in the bottom of Figure 4. The source and the sink are separated by a fixed distance 𝑑, and the relays are equidistantly placed between them. We plot the distribution of the received throughput at the sink on Figure 9, for a distance between the source and the sink of 𝑑 = 1000m, and for 5 and 10 nodes in total, that is to say for respectively 3 and 8 relays, for an application throughput of 50 Mbps. While for a chain of 5 nodes, the use of the directional antenna with the antenna orientation algorithm improves the overall throughput, for any RAA, no improvement is observed for a chain of 10 nodes with the Intel and MinstrelHT RAAs.

We observe that while the percentage of failed MAC transmissions at the source is higher with the directional antenna, the frame transmission rate also increases, leading to lower air-time per frame, allowing more frames to be exchanged. This property is also verified on the different links of the chain. This results in higher throughput with directional antennas than with omnidirectional ones. On the other hand, with 10 nodes, a too high number of retransmissions has been observed whatever the used antenna, leading to low throughput in both cases. One can also note that Intel exhibits poor performance, in this scenario, compared to Ideal and MinstrelHT. It can be explained by the conservative behavior of the Intel RAA when too many retransmissions are triggered [START_REF] Grünblatt | Simulation and Performance Evaluation of the Intel Rate Adaptation Algorithm[END_REF].

RELATED WORK

The interest of using directional antennas in UAV networks has been shown in some experiments. In [START_REF] Gu | Airborne WiFi networks through directional antennae: An experimental study[END_REF], the authors show that, when using Wi-Fi directional antennas, 2 UAVs can communicate with an acceptable throughput (of the order of several Mb/s) even if the distance between the 2 UAVs is large (around 1 km). In these experiments, IEEE 802.11g is used and there is no indication on the used rate adaptation algorithm or if any such algorithm is disabled. In [START_REF] Badi | Experimental Evaluation of Antenna Polarization and Elevation Effects on Drone Communications[END_REF], the authors experimentally show the impact of the antenna orientations on the UAV communications. Different effects are studied like the UAV body, the UAV relative direction and the In [START_REF] Chen | Long-range and broadband aerial communication using directional antennas (ACDA): Design and implementation[END_REF], an antenna heading control system is proposed for UAVs equipped with directional antenna. This system is mainly based on GPS information, but also on a RSSI (Received Signal Strength Indicator) scan when GPS data are not available. The directional antennas are used for the communications between UAVs, communications realized with the proprietary protocol AirMax. The RSSI scan algorithm is a two-stage algorithm in which first step finds a first orientation via a coarse-grained scanning. From this first orientation, the second step reduces the scan step as the search space. The algorithm is designed for a link with 2 UAVs that are able to schedule the start of the algorithm: as one UAV runs the algorithm, the second UAV waits for the execution completion before starting its own run of the algorithm. This synchronization is realized with handshaking signals (via the Xbee system). MATLAB simulations and real experiments are carried out on a scenario with 2 UAVs. The same authors study the same problem in [11], but, in this paper, the authors use a reinforcement learning approach to learn the communication channel model. The proposed solution is validated with 2 UAVs and with a focus on the reached angles and the learned antenna radiation pattern. These two studies are the closest to our work but they differ from ours on different aspects: we consider the WiFi communication protocol and more general scenarios with possibly more than 2 UAVs; the antenna orientation algorithm is local to each UAV without any synchronization between UAVs; we consider the possible use, by the WiFi interface, of a rate adaptation algorithm that may significantly impact the communication performance.

In some papers, the authors consider the possible mobility of the devices to improve the communication performance. This is for instance the case in [START_REF] Gowda | The case for robotic wireless networks[END_REF][START_REF] Miranda | On the Impact of Routers' Controlled Mobility in Self-Deployable Networks[END_REF]. But in most cases, terrestrial robots are considered and the objective is to move some robots in some "good" locations in order to obtain more efficient communications. Very often, the antenna orientation and the WiFi rate adaptation are not taken into account as we do in our study.

CONCLUSION

The antenna radiation pattern is clearly an important factor when looking at the performances of a communication network. In this paper, we have underlined that, even without knowing the radiation pattern of its antennas, nor the positions of its peers, thanks to our antenna orientation algorithm, a node can improve its own network performances, as well as the ones of the whole network. However, this improvement depends on the underlying rate adaptation algorithms used by the WiFi interfaces, as well as the radiation patterns of the antennas. While this conclusion is limited to the studied simulation scenarios and the considered simulation environment, we believe that, given small modifications of the orientation algorithm, the conclusions would translate well in the real world.

Figure 2 :

 2 Figure 2: Radiation pattern of the antennas used during the simulations for 𝜃 = 90 • (horizontal plane), in dBi (decibel relative to the isotropic antenna).

Figure 4 :

 4 Figure 4: Overview of the studied scenarios

Figure 5 :

 5 Figure 5: Evolution of the application throughput in function of time for Scenario #1, with 2 nodes 100m apart and a saturating UDP application rate of 180 Mbps.

Figure 6 :

 6 Figure 6: Comparison of the convergence time for the antenna orientation algorithm and application throughput for Scenario #1 at 𝑑 = 100𝑚.

Figure 7 :

 7 Figure 7: Comparison of the achieved throughput for Scenario #1 at 𝑑 = 100𝑚.

Figure 8 :

 8 Figure 8: Comparison of the average received throughput per link for Scenario #2 with 𝑟 = 100m and 5 nodes.

Figure 9 :

 9 Figure 9: Comparison of the average received throughput at the sink for Scenario #3 with 𝑑 = 1000m, 5 and 10 nodes. elevation angle on different parameters like the Received Signal Strength and the cross-polarization discrimination. The obtained results show the importance of the antenna orientation and their impact on the expected communication performance.In[START_REF] Chen | Long-range and broadband aerial communication using directional antennas (ACDA): Design and implementation[END_REF], an antenna heading control system is proposed for UAVs equipped with directional antenna. This system is mainly based on GPS information, but also on a RSSI (Received Signal Strength Indicator) scan when GPS data are not available. The directional antennas are used for the communications between UAVs, communications realized with the proprietary protocol AirMax. The RSSI scan algorithm is a two-stage algorithm in which first step finds a first orientation via a coarse-grained scanning. From this first orientation, the second step reduces the scan step as the search space. The algorithm is designed for a link with 2 UAVs that are able to schedule the start of the algorithm: as one UAV runs the algorithm, the second UAV waits for the execution completion before starting its own run of the algorithm. This synchronization is realized with handshaking signals (via the Xbee system). MATLAB simulations and real experiments are carried out on a scenario with 2 UAVs. The same authors study the same problem in[11], but, in this paper, the authors use a reinforcement learning approach to learn the communication channel model. The proposed solution is validated with 2 UAVs and with a focus on the reached angles and the learned antenna radiation pattern. These two studies are the closest to our work but they differ from ours on different aspects: we consider the WiFi communication protocol and more general scenarios with possibly more than 2 UAVs; the antenna orientation algorithm is local to each UAV without any synchronization between UAVs; we consider the possible use, by the WiFi interface, of a rate adaptation algorithm that may significantly impact the communication performance.In some papers, the authors consider the possible mobility of the devices to improve the communication performance. This is for instance the case in[START_REF] Gowda | The case for robotic wireless networks[END_REF][START_REF] Miranda | On the Impact of Routers' Controlled Mobility in Self-Deployable Networks[END_REF]. But in most cases, terrestrial robots are considered and the objective is to move some robots in some "good" locations in order to obtain more efficient communications. Very often, the antenna orientation and the WiFi rate adaptation are not taken into account as we do in our study.

  𝑒 𝑗 + 𝑔 𝑗 (𝜋 -𝜃 𝑖,𝑗 , 𝜙 𝑖,𝑗 + 𝜋 -𝜙 𝑗 ) + 𝑔 𝑖 (𝜃 𝑖,𝑗 , 𝜙 𝑖,𝑗 -𝜙 𝑖 ) -𝐶 𝑖,𝑗 if 𝑆 𝑖,𝑗 ≥ 𝑇ℎ = 0 otherwise 𝑆 𝑖,𝑗 represents the received power, at agent 𝐴 𝑖 , of the signal sent by agent 𝐴 𝑗 and 𝝓 is the yaw orientation vector giving the yaw orientation of each agent (𝜙 𝑖 is the yaw orientation of agent 𝐴 𝑖 ). The scalar 𝑒 𝑗 represents the transmission power of agent 𝐴 𝑗 in 𝑑𝐵𝑚 and the scalar 𝐶 𝑖,𝑗 represents the loss induced by the channel between agents 𝐴 𝑗 and 𝐴 𝑖 , in 𝑑𝐵. The antenna gains used during the communication between agent 𝐴 𝑖 and agent 𝐴 𝑗 depend on their position and their relative orientation.Assuming agent 𝐴 𝑖 is located at (𝑥 𝑖 , 𝑦 𝑖 , 𝑧 𝑖 ) and agent 𝐴 𝑗 is located at (𝑥 𝑗 , 𝑦 𝑗 , 𝑧 𝑗 ), we have 𝑥 𝑖 ) 2 + (𝑦 𝑗 -𝑦 𝑖 ) 2 , 𝑧 𝑗 -𝑧 𝑖 ) and 𝜙 𝑖,𝑗 = atan2(𝑦 𝑗 -𝑦 𝑖 , 𝑥 𝑗 -𝑥 𝑖 )

	𝑓 (𝝓) :=	∑	∑	𝑎 𝑖,𝑗 * 𝑆 𝑖,𝑗
	𝝓 ∈ [0;360[ 𝑁		𝑖 ∈ {1,...,𝑁 }	𝑗 ∈ {1,...,𝑁 }
					𝑗≠𝑖
	with
	𝑆 𝑖,𝑗 = 𝜃 𝑖,𝑗 = atan2(	√	(𝑥 𝑗 -

The authors would like to thanks the Direction Générale de l'Armement (DGA) and the Fédération Informatique de Lyon (FIL) for their financial support.