Julien Bruneau

Anne-H Él Ène Olivier

Julien Pettr

Going through, going around: A study on individual avoidance of groups

Keywords: Crowd simulation, Interaction, Perception, Action, Groups, Virtual Reality

Left: Our paper focuses on interactions between individual walkers and groups. We study and simulate decisions made by a walker to go through or around groups of people. Middle: Our approach is an experimental one. We observe decisions made by users during collision avoidance tasks with virtual groups performed in Virtual Reality. Right: Experimental results showing going through or around decisions of one user.

INTRODUCTION

Virtual reality technologies are constantly evolving to render more and more realistic immersive environments. Realistic environments, such as cities or public buildings, need virtual populations to resemble real ones. Crowd simulators are available to animate populations in virtual environments. Among existing techniques, microscopic approaches provide the highest level of realism for virtual environment applications. They simulate each agent as well as the interactions they have together or with the user. However, solutions generally consider interactions between individual agents only, whereas it has been shown that pedestrian are more often walking in small groups than alone [START_REF] Aveni | The not-so-lonely crowd: Friendship groups in collective behavior[END_REF]. One reason for the absence of groups in simulators is that local interactions involving groups are not fully understood, and thus, not captured by numerical models of local interactions.

While there are many studies on how people navigate together as a group, we are missing information on how individuals interact with these groups. In this context, the main objective of this paper is to study interactions between individual and groups in order to create For information on obtaining reprints of this article, please send e-mail to: tvcg@computer.org.

new simulation algorithms that correctly handle such situations. Not only Virtual Reality benefits from the improvements of crowd simulators to populate immersive virtual environments, but it plays a great role in our study. Indeed, we use a Virtual Reality platform to study individual locomotion behaviors during interactions with groups.

More specifically, we focus on the situation of collision avoidance: how do individuals avoid collision with groups of people? Our objective is to understand under which conditions individuals may traverse groups or decide to circumvent them as a whole. We first approach this question under the perspective of the Principle of Minimum Energy. The Principle of Minimum Energy (PME) already used to simulate other navigation mechanism [START_REF] Guy | Pledestrians: A least-effort approach to crowd simulation[END_REF], states that humans tend to optimize their trajectory to use as little energy as possible to reach their goals. It is obvious that the circumventing of groups of a large size will represent a considerable loss of energy along the travel path. By contrast, it is also obvious that going through small groups will require several collision avoidance maneuvers whereas it is a small detour to go around. However, several questions remain: according to PME, what are the energetic thresholds which give preference to one decision? Is the energetic difference always significant? Do real humans actually follow the rules dictated by the PME?

This paper addresses these issues and proposes three contributions:

1. We study interactions between individual walkers and groups from a theoretical point of view by applying the PME. We study groups of changing size and density, we compare go around and go through solution paths. Three kinds of situations are drawn.

In the group size-density space, we delimit two regions for which go around paths are significantly different on the energetic level from go through paths. In between, go around and go through paths represent the same amount of energy consumption. We call them inconclusive situations.

2. We use VR to study how real humans behave when avoiding virtual groups of changing size and density. We corroborate our theoretical study: humans behave as predicted by the PME. In addition, we take interest in results obtained for inconclusive situations. We demonstrate that decision changing, between going around and going through, is made according to some individual threshold, and that this threshold can be influenced by secondary factors such as the appearance of the group, or relative direction of motion.

3. We build on the results of both our theoretical and experimental studies. We propose an algorithm to imitate humans in their decision to go around or through a group of people, with few intuitive parameters.

Altogether, these contributions enable us to design the first model of local interactions in crowds (between individual and groups) fully validated through a VR-based study. The paper is organized as follows. Section 2 presents related work. Section 3 presents our study on effort as a main factor to decide on a strategy to avoid a group of people. Section 4 presents a behavioral study conducted in Virtual Reality to confirm our results, and to complete our results with the considering of secondary factors. Finally, Section 5 draws guidelines to integrate our results into crowd simulators, and demonstrates some results based on RVO2, before ending with the conclusion.

RELATED WORK

Virtual Reality has a wide range of applications ranging from games [START_REF] Zyda | From visual simulation to virtual reality to games[END_REF][START_REF] Lecuyer | Brain-computer interfaces, virtual reality, and videogames[END_REF] to the study of human behaviors [START_REF] Bideau | Using virtual reality to analyze sports performance[END_REF][START_REF] Fink | Obstacle avoidance during walking in real and virtual environments[END_REF][START_REF] Warren | Optic Flow and Beyond, chapter From optic flow to laws of control[END_REF][START_REF] Mallot | Behavioral experiments in spatial cognition using virtual reality[END_REF][START_REF] Mohler | The influence of feedback on egocentric distance judgments in real and virtual environments[END_REF] or even as a tool to provide health care services [START_REF] Herbelin | Virtual reality exposure therapy for social phobia[END_REF][START_REF] Kwon | A study of visual perception: Social anxiety and virtual realism[END_REF]. The purpose of such applications may require immersing users in large environments. The quality of immersion, such as presence [START_REF] Witmer | Measuring presence in virtual environments: A presence questionnaire[END_REF][START_REF] Schuemie | Research on presence in virtual reality: A survey[END_REF], is improved when virtual characters are found wherever expected. Large environments require crowds of them. It is thus important to have virtual crowds of characters that act as close as possible as real people to keep a high sense of presence [START_REF] Mcdonnell | Eye-catching crowds: Saliency based selective variation[END_REF][START_REF] Ennis | Perceptually plausible formations for virtual conversers[END_REF].

Crowd simulators offer solutions to populate virtual environments. Microscopic models are the most adequate for this purpose, various approaches are to be found in the literature: rule-based [START_REF] Reynolds | Flocks, herds and schools: A distributed behavioral model[END_REF], cellular automatons [START_REF] Schadschneider | Cellular automaton approach to pedestrian dynamicstheory[END_REF], social forces [START_REF] Helbing | Simulating dynamical features of escape panic[END_REF] and velocity based [START_REF] Berg | Reciprocal n-body collision avoidance[END_REF]. All these approaches simulate individual agents. In the real world, groups (families, couples, friends,...) are often more frequent than isolated individuals [START_REF] Aveni | The not-so-lonely crowd: Friendship groups in collective behavior[END_REF].

Many studies have been performed to integrate groups in simulations to enhance realism of the simulated crowd [START_REF] Musse | A model of human crowd behavior: Group inter-relationship and collision detection analysis[END_REF][START_REF] Karamouzas | Simulating and evaluating the local behavior of small pedestrian groups[END_REF][START_REF] Crociani | Pedestrian dynamics in presence of groups: an agent-based model applied to a real world case study[END_REF]. Focus is typically given to group formations, leaving the question of the interaction (e.g., collision avoidance) between individuals and groups unanswered. One reason is that there is a little knowledge about such interactions. Analysis is required to extend these approaches, but capturing and observing corresponding behaviors is difficult. Our paper considers Virtual Reality as a powerful mean to lead study on individual behaviors in crowds, to extend knowledge on interactions with groups and to extend simulation algorithms accordingly.

We focus on the individual decision to go around or to go through a group. Our approach is a 2-stage one. In a first stage, we apply the Principle of Minimum Energy as a main criterion in such decision taking. It has been shown that humans often follow the least effort principle for a multitudes of different behaviors [START_REF] Zipf | Human Behaviour and the Principle of Least-Effort[END_REF]. PME has already been applied on avoidance behaviors in [START_REF] Guy | Pledestrians: A least-effort approach to crowd simulation[END_REF]. There are major differences in the way our paper considers PME in avoidance situations. Guy et al. use PME to find the best local adaptation amongst a set of valid ones. Only collision avoidance between individual agents is considered. In contrast, our paper considers interactions between individual and groups, we use PME to compare avoidance strategies. The energetic consumption is evaluated for global solution paths.

Real observations are required to perform crowd simulator calibration and assessment [START_REF] Wolinski | Parameter estimation and comparative evaluation of crowd simulations[END_REF][START_REF] Kapadia | Scenario space: Characterizing coverage, quality, and failure of steering algorithms[END_REF]. Data can be recorded in a real environment (ecological dataset). For example, metrics defining group formations have been extracted from such observations [START_REF] Costa | Interpersonal distances in group walking[END_REF][START_REF] Moussaid | The walking behaviour of pedestrian social groups and its impact on crowd dynamic[END_REF]. However, the exact conditions of interactions between people are often unknown in such datasets (e.g., motivations, constraints or relations between people). In complement, laboratory datasets are useful to complete such studies with more control over the studied situation and more accurate kinematics data. They are useful to understand human motion control mechanisms [START_REF] Lemercier | Realistic following behaviors for crowd simulation[END_REF][START_REF] Olivier | Collision avoidance between two walkers: Role-dependent strategies[END_REF] or to evaluate existing models [START_REF] Seyfried | The fundamental diagram of pedestrian movement revisited empirical results and modelling[END_REF]. However, such data are expensive to acquire and complex situations remain hardly controllable and repeatable. This is especially true for crowd motion studies which require many participants. To this end, VR-based experimental platforms offer a convenient control over experimental factors and parameters. Part of real subjects can be replaced by virtual ones. We can expose a population to precise stimuli allowing us to analyze very specific behaviors. Logically, VR was previously used to perform studies on motion control or interactions with virtual humans [START_REF] Garau | The responses of people to virtual humans in an immersive virtual environment[END_REF][START_REF] Fink | Obstacle avoidance during walking in real and virtual environments[END_REF]. Our paper use VR to corroborate the theoretical PME-based analysis with real human behaviors facing situations of avoiding a virtual group. In comparison with those previous studies, to our knowledge, our study is the first to consider individual motion behaviors in crowds for the purpose of extending crowd simulation algorithms.

PRINCIPLE OF MINIMUM ENERGY: A SIMULATION STUDY

An individual walker has two solutions to avoid a group he crosses during his travel: either he goes through it or around it. Going around a group results into a longer travel path whereas going through asks the walker to perform local adaptations maneuvers, i.e., successive changes of speed and orientation. Both strategies raise additional energetic cost along the travel path. How significant are those differences? Do these differences explain human behavior? This section answers the first question.

Group size and density change the length of the path going around the group, as well as the number of local interactions when going through the group. They are both fundamental factors of our study. To evaluate and compare the energy cost of avoidance strategies, we need to have examples of the two kinds of avoidance paths, going around or going through ones, performed under various conditions of group size and density. To face the obvious difficulty to obtain empirical data, we use simulation tools to synthesize data.

Our approach is the following. In simulations, we set situations of interactions between individuals and groups. For each situation, we first simulate the agent going through the group, and then we force him to go around. We record the two kinds of resulting trajectories, evaluate their energetic cost and compare them. Method and Results are detailed below.

Method

Simulations are based on the RVO2 algorithm [START_REF] Berg | Reciprocal n-body collision avoidance[END_REF]. RVO2 considers interaction between individual agents only. Interactions between individuals and groups will naturally result into a going-through strategy. To compare with the going around strategy, we extended RVO2 to force going-around behaviors as suggested in [START_REF] Yeh | Composite agents[END_REF]: the group is simulated as a single 'big' agent with a large radius. The initial setup situation is illustrated in figure 2. All agents comfort speed was set to 1.33m.s -1 . The shape of the group was defined as a circle. The positions of agents inside the group are computed randomly according to a Poisson distribution. We considered the following factors values to simulate interactions between the individual agent and the group:

• Group size: the group circle radius varied from 1m to 11m with a 0.5m step (21 different values).

• Group density: Density is expressed as the mean distance between agents. Interpersonal distance between agents varied from 0.75m to 3.75m with a 0.05m step (61 different values). Graphs on the middle show the results of the Wilcoson signed-rank tests which compare the energetic costs for both decisions. Significant differences between both decisions are illustrated in red when going around the group is less costly than going through it, in blue when going around the group is more costly than going through it. When there is no significant difference, the result of the comparison is shown in yellow.

• Group relative movement: the individual agent and the group had orthogonal or collinear trajectories (initial distance to the crossing point was 40m in both cases).

We studied all the possible combinations of factors values, i.e., 2562 situations. When interpersonal distance is superior to the group size, groups consist of 1 member only. These irrelevant situations were removed from our study (212 removals). For each situation, there can be variations in the energetic cost of avoidance paths depending on the placement of the agents in the group, especially when going through given the exact interactions occurring there. We averaged this cost by calculating the 50 different distributions for agents' positions in group and by simulating one go-around path and one go-through path for each of the 50 distributions.

In the end, our simulations resulted into two sets of 117500 paths each (going around vs. going through sets, made of 50 paths for 2350 situations each). The energetic cost evaluation was performed for each path based on the equation proposed by [START_REF] Whittle | Gait analysis: an introduction[END_REF]:

E = m (e s + e w |v| 2 )dt ( 1
)
where m is the mass of a person, v the instantaneous speed and e s and e w are constants. The energy is computed only to be compared with each other to find the trajectory that minimize the energy consumption, the mass has no influence on such computation and has been set to m = 1kg. The two constants have been set to e s = 2.23J.Kg -1 .s -1 and e w = 1.26J.s.Kg -1 .m -2 which are values given by [START_REF] Whittle | Gait analysis: an introduction[END_REF] to represent the average human. We used the Wilcoxon signed-rank tests to compare sets of going around and going through paths computed under identical conditions.

Results

Figure 3 shows the average energetic cost of simulated paths depending on group size and interpersonal distance. Left and right plots are respectively for go around and go through paths. Collinear (top) and orthogonal (bottom) relative movements are displayed separately. The figure also summarizes the statistical results (middle) from the comparison between the energy spent with go around or go through strategies.

The energy graphs highlight how energetic cost varies with respect to group size and interpersonal distance. The cost of going around increases with the group size. This was expected because larger groups result in longer avoidance paths. The cost of going through decreases with an increase of the group interpersonal distance. This was also expected as the decrease of distance result in denser groups and more numerous people to be locally avoided one after the other. Note that an increase of the group size also results into more local avoidances and in an increase of the path cost, but in smaller amounts.

The comparison test results between go through and go around paths is reported in figure 3. Three cases can be distinguished. The red area corresponds to when going around is significantly less costly than going through. Conversely, the blue area corresponds to when going through is significantly less costly than going around. Finally, the yellow zone corresponds to a transition zone from the red to the blue: there, no significant difference in energy between going through and around is found.

Discussion

Our results show that, considering the energetic cost of collision avoidance paths, the PME can suggest clear strategies: walkers have strong interest in going through large and sparse groups, and conversely, go- Fig. 2. Simulation setting with one agent avoiding a group on an orthogonal or collinear trajectory. On the left, the starting position with movement direction. On the right, example of computed trajectories relative to the group (For the top: group radius=3, interpersonal distance=0.8, for the bottom: group radius=8, interpersonal distance=2) ing around small and dense groups of people. However, the PME is unable to determine a better strategy for some combinations of group size and interpersonal distance. These are called inconclusive situations.

In the next section, we propose a study with a twofold objective. Using VR, we observe interaction between real individuals and groups of people. We first check that users behave as predicted by the PME. We expect that users will choose their strategy to go through or around a group in accordance to PME results for situations picked in the red or the blue areas of figure 3. Second, we examine the role of secondary factors in inconclusive situations.

GROUPS AVOIDANCE: A VR-BASED USER STUDY

Objectives

In the previous section we showed that PME is a relevant decision criterion for individual to set avoidance strategies during avoidance with groups. However, several questions remain: do humans behave as dictated by the PME? How do they make a transition in the inconclusive situations (where PME cannot distinguish one best strategy)? Do some non-physical factors influence avoidance strategies?

An obvious way to answer these questions is to replicate some of the previously studied situations. It is not trivial to get a group of people to walk in a perfectly controlled way, or to accurately replicate similar situations for several subjects. For these reasons, we decided to conduct our study using an immersive virtual reality platform: individual subjects interact with groups of virtual agents. We picked several situations considered in the PME study, some where going around is the best strategy, some where going through is the best one, and finally some where PME cannot determine a best option. For the two first kinds of situations, we expect subjects to behave as predicted by our previous study. We inspect how there is a sudden or a smooth change in their strategy for the latter kind of situations. Beyond physical factors, we also consider the effect of a social factor. We consider the role of the visual appearance of the group on the avoidance decision. Two hypotheses are tested: humans try not to go between people that have a visually perceptible social link and they try to stay out of groups that have a repulsing aspect. Our baseline condition is groups with ordinary aspect: ordinary groups are made of virtual men and women with individual appearance each (cloth, hair, skin). To give groups a repulsing appearance, we composed them with virtual zombies (see fig. 4). Finally, to visually exhibit social links in groups, we composed them with soldiers. Participants 13 people (1 woman, 12 men) volunteered for this experiment. They were 28.4 (±7.5) years old (range: 23 to 52). They were naive with respect to the purpose of the experiment. All had normal or corrected-to-normal vision. They gave written and informed consent and the study conformed to the declaration of Helsinki.

Materials and Methods

Apparatus Experiments took place in the 4-screen Computer Assisted Virtual Environment (CAVE) as illustrated on figure 5, equipped with 13 projectors, 15MPixels resolution in total, 9m large, 3m high and 3m deep. 3D environment display and character animation were designed in the Unity game engine. Multi-surface rendering was performed by the MiddleVR plugin. Active stereoscopy was achieved with Volfony ActiveEyes Pro Radiofrequency wearable glasses. Glasses were tracked by an ART tracking system made up of 16 cameras. Participants were standing in the CAVE and were immersed in a first person perspective in a street-like virtual environment. They were given a joystick to control their virtual motion. The longitudinal axis of the joystick controls speed linearly from 0.8m.s -1 to 2.0m.s -1 . The lateral axis control the angular rotation speed linearly from -25deg.s -1 to 25deg.s -1 . When the joystick is in rest position (nobody is touching it), the speed is 1.4m.s -1 and the angular rotation speed is 0deg.s -1 .

Task Participants were asked to go to a visible target (a gate in the wall in front of them, see figure 4). They were asked to move like they would have done in real conditions, especially they should try to avoid any collision with the virtual characters walking in the environment. The task was described to participants using slides with images and text. First, they trained with the joystick in a dedicated environment. Then, they performed the experimental task 6 times before we began recording data. At the end of the experiment, participants filled a questionnaire to report their feedback.

Conditions We fixed the virtual group radius to 3m. We reuse two factors (interpersonal distance and group relative movement) from the PME experiment. We introduced a new factor in this experiment on visual appearance. Factors are illustrated in figure 4. We considered the following conditions:

• Interpersonal Distance: the distances between characters in groups were: {1.1, 1.4, 1.7, 2, 2.3}m. With a group of 3m radius, 1.1 and 2.3 corresponds to situations where PME has a well defined optimized strategy while 1.4, 1.7 and 2 are distances from the inconclusive zone.

• Group relative movement: participants interacted with groups coming from the front (Collinear motion), or from the left or the right (Orthogonal motion). We did not distinguish the left and right conditions in our analysis. There were as many repetitions from the front as from the left plus the right.

• Appearance of the group: we used various 3D shapes and textures for virtual characters. We studied groups made of ordinary people, zombies, and soldiers. They were all animated by a single walking cycle and soldiers had a synchronized walk.

In this study, we selected only one condition of group radius to avoid a huge number of repetitions for participants. The relative position of characters in the group was computed according to a homogeneous Poisson distribution.

Plan There were 4 repetitions for each condition, i.e., 120 trials in total. They were presented in a randomized order. We recorded the trajectories performed by participants in the virtual environment.

Analysis Dependent variables were the percentages of trials for which real humans went around or through the group of virtual walkers. Each dependent variable was analyzed into separate 3-way analysis of variance (ANOVA) with repeated measures on the following factors: interpersonal distance, character appearance and group relative movement. Greenhouse-Geisser adjustments to the degrees of freedom were applied when appropriate, to avoid any violation of the sphericity assumption. The effect size was computed using partial eta squared (η 2 p ). When appropriate, Bonferroni post-hoc tests were used to further analyze significant effects between conditions. We also compared going around and going through strategies using Wilcoxon signed-rank test to evaluate the preferred strategy across participants.

Results

Figure 6 illustrates all the trajectories performed in the virtual environment by the participants, going towards the gate while avoiding collisions with a group of walkers. Virtual trajectories are grouped by conditions of interpersonal distances, relative motion, and appearance. Trajectories are plotted relatively to the moving group position to easily distinguish going through from going around paths. From these trajectories, we can already notice a switch in strategy from 1.1m interpersonal distance to 2.3m which corroborates the PME results. There are visually no real differences between collinear or orthogonal relative movement or among the different appearances.

The quantitative results concerning the decisions made to go around or through the group during the interactions are summarized in figure 7. Results showed that users performed more going around trajectories when the direction of the group motion was orthogonal to their own motion (54.1% of going around) than when it was collinear (44.2% of going around) (F(1, 12) = 7.33, p < 0.02, η 2 p = 0.38). Participants also avoided groups of soldiers (54.4%) using more going around decisions than for zombies, and ordinary people (respectively 49% and 44%, F(1.3, 15.5) = 8.22, p < 0.01, η 2 p = 0.41). Note that the difference between zombies and ordinary people is not significant. Finally, interpersonal distance had an effect on the user decisions (F(1.8, 21.5) = 26.46, p < 0.0001, η 2 p = 0.69). The percentage of going around trajectories w.r.t. distance was: 85,2% for 1.1m, 66.9% for 1.4m, 48.7% for 1.7m, 25% for 2m, and 19.9% for 2.3m. The behavior was not significantly different between 1.1m and 1.4m nor between 1.4m and 1.7m.

Discussion

As a main result to this experiment, we corroborate the strategies predicted by the PME is representative of the observed users' behavior. On average, whatever the other factors values, sparse groups are traversed by users in large proportions, and conversely, dense groups are avoided as a whole.

Subjects operate a smooth transition between those extreme groups density. Figure 8 gives a parallel view on the results of our 2 studies, we can see similar trends with the best strategy switching from going around to going through when the interpersonal distance grow bigger. On average, strategies are equally set when the group interpersonal distance is 1.7m. This situations as well as the surrounding ones (1.4m and 2m) belong to the inconclusive set of situations according to the PME. For intermediary density values, we revealed the importance of rel-ative motion: effect is more important than what is predicted by the PME study. We believe that, even if situations are similar on the energetic point of view, the situation is visually very different for users. The difference in the group motion perception may explain this difference in the avoidance decisions set by users. Out of inconclusive conditions, when the difference of energy consumption is significant (according to the PME study), the difference concerning the relative proportion in users' decisions is very clear (order of magnitude 80 vs. 20 % for extreme conditions of interpersonal distances).

Individual preferences were not a studied factor. Nevertheless, figure 9 shows a variability in decision amongst participants. Such variation amongst people is common [START_REF] Costa | Interpersonal distances in group walking[END_REF][START_REF] Hayduk | Personal space: Where we now stand[END_REF] and is even stronger between culture [START_REF] Seyfried | Enhanced empirical data for the fundamental diagram and the flow through bottlenecks[END_REF][START_REF] Beaulieu | Intercultural study of personal space: A case study[END_REF]. As expected, we could influence the strategy set by users by playing on the visual appearance of groups. The result is clear for groups of soldiers, where a tendency to go around more often is observed. However, we did not obtain expected reactions to groups of zombies: they did not have any effect on participants in comparison with ordinary people. Zombies are not real, which might have hindered the participants' capacity to experience it as a real situation.

Finally, trajectories can also be a bias as the input device (a joystick in our experiment) is far from the actual walking action. This bias has been studied by [START_REF] Cirio | Kinematic evaluation of virtual walking trajectories[END_REF]. But in our experiment we analyze the decision made and not the trajectory shape. Such a decision is mainly based on perception and is done pretty soon during the avoidance which should minimize the bias.

APPLICATIONS

Sections 3 and 4 provide us theoretical and experimental results on individual strategies and decisions to avoid a group of walkers. Based on these results, we propose an algorithm for group avoidance decision that selects the strategy that best fits the human one. This section presents the algorithm as well as an example of integration to the RVO2 model ([3]).

Decision algorithm: Around or through the group?

The PME study has delimited three zones where the best strategy is well defined. The first zone concerns very small groups, below 2m radius, that are so small that going around is always a good strategy. For the groups that are bigger, there is a zone with interpersonal distance below 1.35m where going around is better and a zone with interpersonal distance above 2.05m where going through is better. Between these two zones, the user case study has shown that the decision rate goes from a majority of people going around the group to a majority of people going through the group between 1.1m and 2.3m interpersonal distance. Figure 7 show that this evolution is linear and the user case study has highlighted personal preferences as a reason for this linear evolution. Moreover, the group's appearance and the relative movement have both demonstrated some influence over this decision.

From these results, we developed the algorithm 1. This algorithm takes as input both an agent and a group and returns a Boolean answering the question whether the agent should cross the group or go input : agentID, groupID output: true if the agent should cross the group, false otherwise // test if groupSize(groupID) < 2 then return false; // Get the personal preference of the agent ρ a ← getAgentThreshold(agentID); // Get the visual factor of the group G vu ← getGroupVisualFactor(groupID) ; // G vu ∈ [0 : 1] // Compute the relative movement factor # » dir a ← getAgentDirection(agentID); # » dir g ← getGroupDirection(groupID);

G θ ← 1 - # » dir a . # » dir g ; // G θ ∈ [0 : 1]
// Compute threshold and choose strategy threshold

← ρ a + G vu .C vu + G θ .C θ ;
if groupInterDistance(groupID) < threshold then return false; return true; Algorithm 1: Function that select a strategy to avoid a specific group for a specific agent around. If the group size is less than 2m than the strategy is to go around as hinted by the PME study. Otherwise, a specific threshold is computed according to the agent own preference ρ a , the group appearance score G vu and the relative motion score G θ . Both appearance and relative score measure the effect of these factors on the threshold. For example, a group of soldier will have the highest effect on the threshold with an appearance score of 1. The relative motion score goes from 0 to 1 with 0 being collinear and 1 being orthogonal. For the three parameters: the personal preference ρ a , the appearance maximum effect C vu and the relative movement maximum effect C θ , we propose default values based on our best guest from our previous results. To represent the variability in decisions between people and the linear progression seen in figure 7, the ρ de f ault was set by a uniform distribution from 1.3m to 2.1m. We set C vu = 0.15m, by considering that soldiers have the highest effect from group appearance, and C θ = 0.06m.

Integration in RVO2

The algorithm we proposed determines individual decisions to avoid a group of walkers depending on several factors. It appeared to be easy to combine it with existing crowd simulation models to adapt their avoidance behavior to groups. To prove the feasibility of such an adaptation, we proposed to combine our decision algorithm with RVO2 model. This model deals with local interactions and was not designed to consider groups as a whole. The objective here was then to define in the simulation which agents should be merged into a group to be avoided by going around it. The first adaptation was to include a group criterion. It was based on [START_REF] Yeh | Composite agents[END_REF]. When agents are identified as part of a group, all of them are replaced by a single 'big' proxy agent, as presented in figure 10. The proxy agent current speed was set as the average speed of all agents of the group. In that way, the group is avoided as a whole and agents of the group are not considered individually with succession of local avoidances: the resulting avoidance trajectories will go around the whole group instead of going through the group around each individual agent.

To improve the trajectories performed to avoid a group (by going around the group), we also proposed another adaptation. Indeed, when avoiding large obstacles, the resulting trajectory can be jerky if the adaptation is performed too late. In such a case, walkers need to adapt their motion earlier to go around the group while keeping a smooth trajectory. To consider this point, we adjusted the timeHorizon parameters of RVO2 which defined how soon an agent should avoid other Fig. 10. On the left: the situation as it really is, on the right: the situation as it is perceived by the red agent (All the blue agents are seen as one big agent because they are considered as a group while the green ones are too far from each other to be considered as a group)

agents. We defined it as a factor of the size of the agent or proxy agent to avoid, allowing sooner avoidance when interacting with larger groups.

Results of the combination of RVO2 with the decision algorithm are presented in the companion video. An example of RVO2 behavior after its combination with our decision algorithm is illustrated on figure 11. On the left, the purple agent goes through the group, only considering local interactions. After combining RVO2 with the decision algorithm (on the right), the purple agent avoids all the red agents as part of a whole group instead of trying to go through it.

User-study evaluation

We integrated our decision algorithm in RVO2 simulation model. The objective of this study is to check if our decision algorithm is able to improve the visual quality of crowd simulation results. To this end, we proposed a subjective evaluation based on a perceptual user study: we asked some participants to compare simulation results from ROV2 only with ones from RVO2 extended with our algorithm. 10 male participants volunteered for this experiment. They were 28.3 (±4.7) years old (range: 24 to 40). They were naive with respect to the purpose of the experiment. All had normal or corrected-to-normal vision. They gave written and informed consent and the study conformed to the declaration of Helsinki.

We prepared 4 situations (20s each) where one single agent walks counter flow in front of a crowd of walking people. This crowd was made up of individuals and groups of various densities. For each situation, agent motion was simulated both with RVO2 and with RVO2 combined with the decision algorithm, creating 2 video stimuli. Participants were seated in front of a desk (cf. figure 12). Stimuli were dis-played on a 24inches screen. Participants were asked to observe successively the 2 video stimuli and to evaluate which one complies the most with the decision they would have made as a single walker avoiding other people in the same conditions. The 2 video were made from a third person view point to give participants a good view of the situation as the computer screen limits greatly the field of view of a first person view point. In total, they repeated this task 20 times (4 situations*5 repetitions). Stimuli were presented in a randomized order. We compared the percentage of answers supporting RVO2 with respect to the percentage of answers supporting RVO2 combined with the decision algorithm using a Wilcoxon signed-rank test. Results showed that RVO2 combined with the decision algorithm was perceived as more compliant with decisions a human would have used to avoid people than RVO2 alone (RVO2+Decision algorithm= 77.5% ± 17.36, RVO2= 22.5% ± 17.36, Z = 2.66, p < 0.01). The participants were asked which criteria they used to choose between the two video stimuli. Some answers are transcribed below; globally people chose what seems to be the most natural motion for them. Trying to go through a dense group is the main reason that breaks the naturalness of the motion, according to the commentary 3 below, splitting small group is worse than having weird trajectories.

1. I chose according to what the path I would have selected for my own motion.

2. Avoiding most of dense crowds seems more natural.

3. Splitting small groups is a deal-breaker (happened in some cases where trajectories were actually better than other solution)

4. My criteria would change according to the density (homogeneous or heterogeneous). In homogeneous density, the behavior "I go directly toward the goal" seems more realistic as there were no visible group to break. In heterogeneous density, I preferred the other behavior that seems to preserve the groups from the other agents.

This result is promising and shows that including our decision algorithm to existing crowd simulator will improve their level of realism. The commentary 4 highlighted a difference for homogeneous and heterogeneous density. In higher density situation, people get closer to each other leading to smaller personal space and less visible groups. It is fair to say that this could greatly influence the group avoidance strategy. The experiment done in this paper was done with no other agent then the group members to be able to consider only the interaction with the group. But experiments in high density are also needed to check how the environment around the groups influences this group avoiding behaviors. Beyond that, our perception study shows that spectators perceive improvements on simulation results, and find them more natural. Some people find that the reaction facing a group can be even more important than the avoidance trajectory itself for realism. This demonstrates the need for improving the ability of crowd simulators to deal with more complex situations of interactions.

CONCLUSION

In this paper, we study interaction between individuals and groups; we focus on strategies set by individuals to go through or around a group of people. We extend the use of the Principle of Minimum Energy from choosing local speed variation to selecting global avoidance strategy. We confirm the influence of the energy factor, in this specific situation, and complete its results with an experiment where real individuals were interacting with different groups. We also highlight, with the experiment, two secondary factors that influence the chosen strategy: the relative motion and the visual aspect of the group. We propose an algorithm to simulate realistic avoidance strategies between individuals or groups. We also integrate our results in an existing crowd simulator and demonstrate that spectators can perceive some improvement in the crowd animation.

This work opens various perspectives. We propose to use VR as a new method to gather observation on crowd behaviors and local interactions in crowds. We show its strength and how it can help to better understand complex interactions that are hard to study using regular observation gathering method: only one subject is required to observe behaviors in crowds, we have no technical difficulty with tracking, we can perfectly control complex experimental conditions. Especially, crowd simulation has only considered interactions between individuals for too long, real situations of interactions in crowds are often much more complex. We focused on interactions between individuals and groups. Our results also reveal how humans process and simplify interactions, e.g., by considering a group of many as a whole. We need to continue performing experiments on individual behaviors in crowds: simulators would widely benefit from conclusions about the way people in crowds filter, select and combine the numerous interactions they have. We expect large improvement of microscopic crowd simulation algorithm in the near future thanks to next iteration of experiments to come based on our VR-based experimental facility.

Fig. 3 .

 3 Fig.3. Energetic cost of paths performed to avoid a group for collinear (Top) and orthogonal (Bottom) relative movements. Graphs on the left and right show respectively the average energy consumed by going around trajectories (Left) or going through trajectories (Right) according to group sizes and group interpersonal distances. Graphs on the middle show the results of the Wilcoson signed-rank tests which compare the energetic costs for both decisions. Significant differences between both decisions are illustrated in red when going around the group is less costly than going through it, in blue when going around the group is more costly than going through it. When there is no significant difference, the result of the comparison is shown in yellow.

Fig. 4 .

 4 Fig. 4. Conditions for the experiment on group avoidance. Top: spacing between the characters of the group was: {1.1, 1.4, 1.7, 2, 2.3}m. Bottom left: participants avoided a group coming from: left, front or right. Bottom right: the visual appearance of the characters of the group was: ordinary people, soldiers or zombies.

Fig. 5 .

 5 Fig. 5. Pictures of the experiment showing participants navigating with a joystick in a VR environment and avoiding virtual agents.

Fig. 6 .

 6 Fig. 6. Participants' trajectories relative to the group position (gray circle) with respect to experimental conditions: interpersonal distance (left), direction (top right) and appearance (bottom right). Going around trajectories are displayed in red. Going through trajectories are displayed in blue.

Fig. 7 .

 7 Fig. 7. Proportion between going around and going through decisions per distance, over all trials.

Fig. 8 .

 8 Fig. 8. Decisions to go through or around amongst the participants and the energy spent in the same condition. For comparison purposes, we only consider decisions for ordinary group.

Fig. 9 .

 9 Fig. 9. Proportion between going around and going through decisions per participant, over all trials.

Fig. 11 .

 11 Fig. 11. Example of avoidance decision made by the purple agent. The agent goes through the very dense group in RVO2 while going around it in the modified RVO2.

Fig. 12 .

 12 Fig. 12. Experimental setup to evaluate the decision algorithm.

ACKNOWLEDGMENTS

This work is funded by the French National Research Agency ANR, project PERCOLATION number ANR-13-JS02-0008.


ABSTRACT

In this paper, we investigate obstacle avoidance behavior during real walking in a large immersive projection setup. We analyze the walking behavior of users when avoiding real and virtual static obstacles. In order to generalize our study, we consider both anthropomorphic and inanimate objects, each having his virtual and real counterpart. The results showed that users exhibit different locomotion behaviors in the presence of real and virtual obstacles, and in the presence of anthropomorphic and inanimate objects. Precisely, the results showed a decrease of walking speed as well as an increase of the clearance distance (i. e., the minimal distance between the walker and the obstacle) when facing virtual obstacles compared to real ones. Moreover, our results suggest that users act differently due to their perception of the obstacle: users keep more distance when the obstacle is anthropomorphic compared to an inanimate object and when the orientation of anthropomorphic obstacle is from the profile compared to a front position. We discuss implications on future large shared immersive projection spaces.

Index Terms: H.5.1 [Information Interfaces and Presentation]: Multimedia Information Systems-Artificial, Augmented, and Virtual Realities; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism-Virtual Reality

INTRODUCTION

CAVE-like immersive projection environments enable users to see both virtual and real objects, including the user's own body. With recent advances in VR technologies it becomes possible to build large-scale tracked immersive projection environments, which enable users to control their position in a large region of interest by real walking. Moreover, advances in stereoscopic display technologies [START_REF] Kulik | C1x6: A stereoscopic six-user display for co-located collaboration in shared virtual environments[END_REF] or light-field projection displays [START_REF] Balogh | Holovizio 3D display system[END_REF] may enable natural perspectives for multiple users in the near future. In such environments virtual and real objects as well as multiple users or avatars may coexist in the same interaction space. Hence, it becomes important to gain an understanding of how the user's behavior is affected by the differences in perception and affordances of such real and virtual obstacles. Particularly, in this paper we analyze potential changes in the user's locomotion behavior when avoiding virtual and real obstacles. Understanding and faithfully simulating natural locomotion dynamics between the user and the environment is of great interest to many virtual reality (VR) applications, including architectural review, training, and 3D entertainment.

In the real world we navigate with ease by walking in the presence of obstacles, we develop avoidance strategies and behaviors which govern the way we locomote in the proximity of physical objects and other persons during everyday tasks. Humans accurately perceive and control their self-motion -i. e., acceleration, speed and direction of travel, relative to their surroundings -based on consistent multi-sensory feedback including vestibular, proprioceptive, and efferent copy signals as well as visual information. However, realistic behavioral dynamics in immersive virtual environments (IVEs) are difficult to achieve especially due to the diminished perception of the virtual content [START_REF] Mohler | Visual flow influences gait transition speed and preferred walking speed[END_REF]. Although modern real-time rendering systems can create compelling immersive experiences, offering most of the spatial visual cues we can find in the real world [START_REF] Thompson | Visual Perception from a Computer Graphics Perspective[END_REF], not all visual cues can be faithfully reproduced when displaying virtual objects or humans. In this scope, it is wellknown that users tend to over-or underestimate spatial relations in immersive virtual environments [START_REF] Loomis | Visual perception of egocentric distance in real and virtual environments[END_REF]. Moreover, natural behavior while immersed is often limited by the user's illusions of place and plausibility [START_REF] Slater | Place illusion and plausibility can lead to realistic behaviour in immersive virtual environments[END_REF]. This paper presents an experiment which analyzes the locomotion behavior of users' in a large immersive projection environment (10m) when avoiding static obstacles. To our knowledge, this is the first experiment on interaction with real and virtual obstacles during locomotion tasks in a large CAVE-like immersive environment. Furthermore, in order to enable the cross comparison of the different situations that might arise in a mixed environment the experiment considers both real and virtual, anthropomorphic and inanimate obstacles (see Figure 1).

The paper is structured as follows. First, Section 2 summarizes the related work on collision avoidance in real and virtual environments. Section 3 describes the experiment in which we compared collision avoidance behavior during real walking in a ten meter shared IVE both with real and virtual objects, followed by Section 4 which describes the results. In Section 5 we discuss the results of the experiment. Finally, Section 6 concludes the paper.

RELATED WORK

Collision Avoidance in the Real World

Proxemics is a fundamental concept when focusing on collision avoidance: it describes how humans manage space during interactions with their environment. Especially, a lot of work focused on the personal space that surrounds an individual. The personal space can be considered portable territory around an individual that others should not invade. It regulates the psychophysical distance that the individual needs to maintain in order to feel comfortable. According to Goffman [START_REF] Goffman | Relations in public: microstudies of the public order[END_REF], the personal space can be represented as an oval, narrow to the sides of the individual and long in front of him/her. In locomotion, personal space can be defined as a protective zone maintained around the walker that lets a sufficient delay to perceive unexpected events or obstacles and then allows to plan and perform required locomotor adjustments [START_REF] Templer | Human territoriality and space needs on stairs[END_REF]. Gérin-Lajoie et al. [START_REF] Gérin-Lajoie | The negociation of stationary and moving obstructions during walking: anticipatorylocomotor adaptations and preservation of personal space[END_REF] have experimentally confirmed Goffman's observations and found that this area can be defined by an elliptic curve.

A large amount of work has considered the way humans maintain this security distance by adapting their motion to avoid collisions with obstacles on their travel path. From a global point of view, the interactions between a walker and the environment can be modeled as a pair of coupled dynamical systems [START_REF] Fajen | Behavioral dynamics of steering, obstable avoidance, and route selection[END_REF]. Heading is adapted according to the distance and the angle between the walker and stationary goals and obstacles: goals act as attractors and obstacles as repellors. Other authors suggested that path planning precedes dynamic control to navigate in a cluttered environment [START_REF] Patla | What visual information is used for navigation around obstacles in a cluttered environment[END_REF]. From a local point of view, some studies focused on the circumvention of non-human static obstacles [START_REF] Vallis | Locomotor adjustments for circumvention of an obstacle in the travel path[END_REF]. Vallis and MacFadyen [START_REF] Vallis | Locomotor adjustments for circumvention of an obstacle in the travel path[END_REF] showed that a walker avoids a cylinder (2m high, 0.23m diameter) using anticipatory locomotor adjustments three steps before the obstacle.

Step width is adapted before obstacle crossing compared to a control situation in straight walking inducing a mediolateral center of mass displacement around 50cm and the approaching velocity is constant. Other studies focused on the circumvention of human-shaped obstacles. Gérin-Lajoie et al. [START_REF] Gérin-Lajoie | The negociation of stationary and moving obstructions during walking: anticipatorylocomotor adaptations and preservation of personal space[END_REF] demonstrated also anticipatory locomotor adjustments to avoid a mannequin on the travel path. Two phases in the avoidance where identified: an anticipatory phase with an initial deviation of the center of mass six steps before the obstacle and an adjustment of the trajectory during the last stride before the obstacle; and a clearance phase when the walker circumvents the obstacle. They showed that the avoidance strategy is initiated at a constant distance from the obstacle and that the clearance distance keeps constant values around one-third of the walkers' step-length.

Collision Avoidance in Virtual Environments

Since most CAVE-like systems do not provide sufficient interaction space to consider walking over more than a few meters, collision avoidance while walking in virtual environments has been studied only in head-mounted display (HMD) environments. Fink et al. [START_REF] Fink | Obstacle avoidance during walking in real and virtual environments[END_REF] focused on collision avoidance of non-human stationary obstacles during goal reaching tasks. They compared tasks performed in physical and virtual environments. They showed some differences in the generated trajectories such as a larger lateral deviation, a larger obstacle clearance as well as a slower walking speed in virtual conditions compared to real ones. Gérin-Lajoie et al. [START_REF] Gérin-Lajoie | Characteristics of personal space during obstacle circumvention in physical and virtual environments[END_REF] considered collision avoidance with a static cylinder. Performed in an HMD environment, they showed that the global shape of the personal space is preserved, but is slightly increased in virtual conditions compared to real ones. Moreover, Bailenson et al. [START_REF] Bailenson | Interpersonal distance in immersive virtual environments[END_REF] took interest in the interpersonal distance between a human and a virtual human in an HMD environment. They showed that participants maintained greater distance from virtual humans when walking towards them from their fronts compared to their backs. They also maintain a larger personal space to virtual agents who engaged them in mutual gaze.

In summary, all studies agree that humans keep a comparable behavior when avoiding virtual obstacles as they do with real ones. However, there are still not clear the causes of why humans consistently keep greater distances from virtual obstacles than from they real counterparts. While Fink et al. [START_REF] Fink | Obstacle avoidance during walking in real and virtual environments[END_REF] hypothesize that the differences could be explained by the increased uncertainty about the obstacle egocentric location in IVEs, Gérin-Lajoie et al. [START_REF] Gérin-Lajoie | Characteristics of personal space during obstacle circumvention in physical and virtual environments[END_REF] hypothesize that the differences could be due to limited field of view. HMDs have a limited field of view which restrict the user's view to the virtual environment (VE). For example, Fink. et al [START_REF] Fink | Obstacle avoidance during walking in real and virtual environments[END_REF] used a HMD with a FoV of 60°H and Gérin-Lajoie et al. [START_REF] Gérin-Lajoie | Characteristics of personal space during obstacle circumvention in physical and virtual environments[END_REF] an HDM with a FoV of 40°H. In addition to the limited field of view, collision avoidance behavior is dominated by visual information from the VE, although extraretinal cues and fear to collide with obstacles in the real world often reduce natural locomotion behavior and gait [START_REF] Mohler | Visual flow influences gait transition speed and preferred walking speed[END_REF].

BEHAVIORAL DYNAMICS EXPERIMENT

In this section we describe the experiment which we conducted to analyze differences in collision avoidance behavior of humans during real walking in the presence of real or virtual obstacles in a large shared IVE. The experimental task consisted in walking a distance of 8m through the interaction space while avoiding a visible obstacle of either anthropomorphic or geometrical shape that was placed straight in front of the participants.

Procedure

Participants were instructed to walk from one side of the IVE to the opposite end at comfortable speed while avoiding any visible obsta- cle. Additional visual feedback was provided to indicate the initial and final point of the trajectory via virtual markers projected on the floor (see Figure 2). During the collision avoidance task, only the obstacle was visible and the background was lighted with a medium gray color (see Figure 1). Participants had to walk a total trajectory of 8m with the obstacle to avoid being placed in the middle. The center point of the obstacle was at 1m of the front wall of the CAVE-like environment and at 2m from the missing wall. The position of the virtual object was chosen to ensure that no additional physical constraints altered the locomotion behavior. In addition, this ensured that for all conditions participants always avoided the obstacle from the same side. Finally, it made sure that the virtual obstacles would be visible over the entire trajectory without being clipped by the boundary of the projection screens.

We tested a human and a simple geometrical object using each a real-world object and a virtual replica model of the physical counterpart (see Figure 3). Regarding the virtual human, we used a visually faithful textured 3D model of a lab member (male, 1.78m height, 78kg weight, 1.62m eye height, 0.5m shoulder width, 0.3m depth). The virtual avatar was animated with an idle animation. The geometrical object was a cardboard box which matched the height, depth, and shoulder width of the human obstacle. The virtual cardboard was textured using pictures of the real one.

In order to focus participants on the tasks no communication between experimenter and participant was performed during the experiment after the initial training phase, in which we ensured that participants correctly understood the task. Written instructions were displayed on a computer prior to the experiment. Participants were allowed to take short breaks at any time between trials. For practical reasons, participants took short breaks each time there was the need to change the physical obstacles. The breaks were informed through a virtual panel appearing at the center of the IVE. The person playing the role of the real human obstacle had unnoticeable virtual guides for the participant in order to ensure that he was able to change his orientation correctly. Furthermore, he was wearing sun glasses to avoid eye-contact.

Apparatus

The experiment was conducted in a 9.6m×3m×3.1m (width, depth, and height) 4-sided immersive projection setup equipped with 16 Barco Galaxy projectors at 15MPixels resolution in total. The missing wall was closed during the experiment using an opaque black lightshield. The participants wore shutter glasses (Volfoni ActivEyes Pro Radiofrequency for stereoscopic visual stimulus presentation) during all the experiment. The shutter glasses were tracked with 6 degrees of freedom (DOF) passive markers in the laboratory using an ART optical tracking system with 16 cameras at an update rate of 60Hz.

Design

We used a repeated-measures within-subjects design. The independent variables were the obstacle (cardboard box, human), the nature of the obstacle (real, virtual), the orientation of the obstacle (ω∈{0, 90, 180, 270} degrees) and the direction of the trajectory (left-to-right, right-to-left). Due to the symmetrical layout of the cardboard box we only considered 2 orientations of the obstacle, either facing the long or short side of the projection setup.

For the human obstacle participants completed 4 (orientation) × 2 (nature) × 2 (direction) trials, as well as 2 (orientation) × 2 (nature) × 2 (direction) trials with the box-shaped obstacle. The order of the obstacle (real/virtual, cardboard box/human) was counterbalanced using a Latin-squared design, while the order of the orientation was randomized for each obstacle. For each combination, we performed four repetitions, resulting in 96 trials per participant. Additionally, at the beginning of the experiment, participants performed eight trials without any obstacle in order to gather baseline recordings.

Regarding the dependent variables, we recorded participants' trajectory as the horizontal position along time of their glasses tracked by the ART system. Of the entire 8m walking trajectory we only considered the part from x=-2.5m until x=2.5m (the obstacle was at x=0) avoiding the accelerations and decelerations of the start and the end of the locomotion. The path information allowed us to compute the participants' average walking speed and speed profile. We also computed the maximal lateral deviation from a straight line between the starting and ending point of the trajectory as well as clearance defined as the minimal distance between the participant and the obstacle.

Furthermore, we collected demographic information with a questionnaire before the experiment and measured the participants' sense of presence with the Slater-Usoh-Steed (SUS) questionnaire [START_REF] Usoh | Using presence questionnaires in reality[END_REF], as well as simulator sickness with the Kennedy-Lane SSQ [START_REF] Kennedy | Simulator sickness questionnaire: An enhanced method for quantifying simulator sickness[END_REF] before and after the experiment. The total time per participant including pre-questionnaires, instructions, training, experiments, breaks, and debriefing was 1 hour. Participants were immersed in the VE for about 45 minutes.

Considering our design, we hypothesize: H1 Subjects will exhibit different locomotion trajectories with virtual obstacles vs. real obstacles. As found in previous experiments using HMDs, we expect slower walking speed and larger avoidance distance and clearance with virtual obstacles.

H2 Subjects will exhibit different locomotion trajectories during interaction with human vs. box obstacles. We expect that greater clearance is set with human obstacles, because social distances add to pure collision avoidance clearance.

H3 The orientation of the human obstacle will result in changes in the clearance distance, but at the opposite, the orientation of the box obstacle won't.

Participants

We recruited 17 participants for our experiment. 14 of them were male, 3 were female (ages 21-38, M=26.8). The participants were either students or professionals in computer science or engineering. 14 participants were right-handed, 3 participants were lefthanded. The Lateral Preference Inventory questionnaire [START_REF] Coren | The lateral preference inventory for measurement of handedness, footedness, eyedness, and earedness: norms for young adults[END_REF] confirmed that 14 participants were right-handed and 3 left-handed (rating scale -4=left, 4=right, M=2.53, SD=2.60). Moreover, it showed that 15 participants were right-footed and 2 left-footed (M=2.29, SD=2.17). 15 participants were right-eyed and 1 lefteyed whereas the test was inconclusive for 1 participant (M=2.71, SD=2.11). 8 participants wore glasses and 3 wore contact lenses during the experiment. One participant reported red-green color weakness; no other known vision disorders or displacements of balance were reported by the participants. Using the technique proposed by Willemsen et al. [START_REF] Willemsen | Effects of stereo viewing conditions on distance perception in virtual environments[END_REF] we measured the interpupillary distance (IPD) of each participant before the experiment started (M=6.32cm, SD=0.28cm). Prior to the experiment we measured the eye height (M=1.65cm, SD=0.08cm) and the shoulder width (M=38.44cm, SD=3.84cm) of each participant. 16 participants reported previous experience with 3D stereoscopy (rating scale 0=yes, 4=no, M=1.47, SD=1.23). 15 participants had participated in a study in the immersive projection setup before.

RESULTS

Statistics were performed using the Statistica Software. Normality was assessed using a Kolmogorov-Smirnov test. To evaluate the influence of the experimental factors on average walking speed, maximal lateral deviation, and clearance, we performed separate threeway analysis of variance (ANOVA) with repeated measures on the conditions (2: real,virtual), the obstacle (2: human and box) and the orientation of the obstacle (2: 0°and 90°). When appropriate, Bonferroni post-hoc tests were used to further analyze significant effects. To consider all the orientations, we also performed for the human obstacle condition a two-way analysis of variance (ANOVA) with repeated measures on the conditions (2: real,virtual) and the orientation of the obstacle (4: 0°, 90°, 180°and 270°) associated with Bonferroni post-hoc tests.

Average values of the kinematic variables depending on the experimental conditions are reported in Figure 4. Figure 5 shows the average trajectories performed by participants to avoid the obstacle depending on the orientation of the obstacle (a,b). We excluded the few data sets from the analysis in which the participant walked between the front screen and the obstacle (5% trials). Furthermore, no ordering effects were observed.

Walking Speed Results showed that only the real/virtual condition influences the average walking speed (F(1, 16)=4.78, p<0.05, η 2 p =0.23): walking speed is significantly higher in real conditions (1.17m/s) than in virtual conditions (1.13m/s).

Maximal Lateral Deviation

Results showed an influence of real/virtual conditions (F(1, 16)=16.03, p<0.005, η 2 p =0.50), the obstacle (F(1, 16)=17.58, p<0.001, η 2 p =0.52) and the orientation (F(1, 16)=103.05, p<0.001, η 2 p =0.86). Bonferroni post-hoc tests showed that deviation is significantly higher in virtual conditions (0.71m) compared to real ones (0.66m); it is higher when the obstacle is a human (0.72m) compared to a box (0.65m); and it is higher when orientation is 90°(0.72m) compared to 0°(0.65m).

When considering the human obstacle condition only, results showed that real/virtual condition (F(1, 15)=8.08, p<0.01, η 2 p =0.37), orientation (F(3, 45)=6.04, p<0.005, η 2 p =0.29) as well as the interaction between real/virtual and orientation (F(3, 45)=11.35, p<0.001, η 2 p =0.43) influence the maximal deviation. Bonferroni post-hoc test showed that maximal deviation is higher in virtual conditions(0.76m) compared to real conditions (0.69m). Maximal lateral deviation is also higher for 90°and 270°(0.74m) than for 0°(0.70m). Considering the interaction effect between real/virtual conditions and orientation of the human obstacle, post-hoc tests showed that maximal lateral deviation is higher in virtual conditions for orientations 90°, 180°and 270°.

Clearance Distance Results showed an influence of the real/virtual conditions (F(1, 16)=7.51, p<0.05, η 2 p =0.32), the obstacle (F(1, 16)=19.16, p<0.001, η 2 p =0.54) and the orientation (F(1, 16)=61.91, p<0.001, η 2 p =0.79). Bonferroni post-hoc tests showed that clearance distance is higher in virtual conditions (0.61m) compared to real conditions (0.56m); it is higher when the obstacle is a human (0.62m) compared to a box (0.55m); and it is higher when orientation is 0°(0.61m) compared to 90°(0.55m).

For the human obstacle condition only, ANOVA showed that real/virtual condition (F(1, 15)=7.06, p<0.05, η 2 p =0.32), orientation (F(3, 45)=38.08, p<0.001, η 2 p =0.71) as well as the interaction between real virtual conditions and orientation (F(3, 45)=16.23, p<0.001, η 2 p =0.52) significantly influenced the clearance distance. Bonferroni post-hoc test show that clearance distance is higher in virtual conditions(0.66m) compared to real conditions (0.60m) and that it is higher when orientation is 0°(0.66m) or 180°(0.70m) compared to 90°(0.58m) and 270°(0.57m). Furthermore, the virtual human condition at 180°leads to significantly higher clearance.

Questionnaires

We measured a mean SSQ-score of M=18.118 (SD=2.261) before the experiment, and a mean score of M=18.647 (SD=2.370) after the experiment. There was no significant difference of the SSQscore before and after the experiment (t(16)=1.21, p=0.245). The mean SUS-score for the reported sense of feeling present in the VE was M=4.30 (SD=0.60), which indicates a reasonably high level of presence. Participants judged whether they were more careful avoiding the real than the virtual box (rating scale 0=yes, 4=no, M=3.35, SD=1.22) as well as the real than the virtual human (rating scale 0=yes, 4=no, M=2.77, SD=1.48). Additionally, participants judged whether they had the impression of being able to walk "through" a virtual obstacle (rating scale 0=yes, 4=no, M=2.29, SD=1.26).

DISCUSSION

When comparing the virtual and real conditions, we observe that our results show the same tendency as previous studies done in HMDs [START_REF] Fink | Obstacle avoidance during walking in real and virtual environments[END_REF][START_REF] Gérin-Lajoie | Characteristics of personal space during obstacle circumvention in physical and virtual environments[END_REF]. Walking speed is slower, and the maximal lateral deviation as well as the clearance are higher when avoiding virtual obstacles than real ones, thus supporting H1. This results are also observed in the subjective questionnaires were users judged in general to be more careful when avoiding virtual objects. Although, it is not possible to perform a quantitative comparison between our study and previous ones due to differences in the experimental protocols, we obtained lower differences among virtual and real conditions. For example, in Fink et al. [START_REF] Fink | Obstacle avoidance during walking in real and virtual environments[END_REF] mean speed differences where ∆=0.13m/s while in our experiment where ∆=0.04m/s. But, do large IVEs or mixed reality environment induce less bias in kinematic data than HMDs? Additional work and dedicated experiments are required to answer this question. Nevertheless, large IVEs enable more ecological VR situations (no helmet, no limitation on field of view). Considering the absence of direct body feedback during locomotion with HMDs as well as the potential impact of hard-and software factors in HMD setups, future work may focus on identifying the contributing factors for this difference.

Regarding the nature of the obstacle (human vs. box), the maximal lateral deviation of the path and the clearance distance are higher for anthropomorphic obstacles whereas the walking speed is not affected. Participants keep greater distances when the obstacle is anthropomorphic in comparison with an inanimate obstacle. This effect suggests that participants take greater security distance to avoid the collision. This result also supports H2.

Considering the orientation, results showed an influence on the maximal lateral deviation of the locomotor path with higher values for 90°and 270°conditions. This effect can easily be explained by the experimental conditions since obstacles at 90°and 270°obstruct more the path in front of the walker and require more lateral adaptations to avoid the collision. More interesting is the influence of the orientation on the clearance distance when the obstacle is anthropomorphic. Orientations of the obstacles at 0°and 180°resulted in significantly larger clearance distances, thus supporting H3. This effect of orientation on the clearance distance may be explained by the shape of the personal space, that was shown to be elliptic [START_REF] Gérin-Lajoie | The negociation of stationary and moving obstructions during walking: anticipatorylocomotor adaptations and preservation of personal space[END_REF] with larger distance in the anteroposterior axis than the mediolateral one. In that sense, other authors attribute some role dependent strategies for collision avoidance between two walkers to the asymmetry of personal space [START_REF] Olivier | Collision avoidance between two walkers: Role-dependent strategies[END_REF]. This suggests that even in virtual conditions, users consider the personal space of the human obstacle in the collision avoidance task. When the human obstacle is viewed from profile, the larger part of the personal space is in the direction of the mediolateral adaptation, which should induce larger clearance distances as illustrated in Figure 6. However, we did not observe a difference between front and back orientation of the virtual human such as observed by Bailenson et al. [START_REF] Bailenson | Interpersonal distance in immersive virtual environments[END_REF] who showed that a user lets more distance with a virtual human when approaching it from the front than from the back. This difference may be explained by the difference in the experimental protocol. In their study, the goal was to approach the virtual human and not avoid it to go toward a target. Also, when users were instructed to approach the virtual human from the back, they first go towards the front and walk around it.

CONCLUSION AND FUTURE WORK

In this paper, we investigated obstacle avoidance behavior during real walking in IVEs. Contrary to previous studies, we considered a large immersive projection setup instead of an HMD. We compared in a kinematic analysis study how users avoid static obstacles of different types. We focused on real and virtual obsta- cles, which can take two forms, anthropomorphic or inanimate, and with different orientations (front, back and profile). First of all, the results showed changes on the collision avoidance behavior between virtual and real obstacles, which validates the findings of previous experiment for CAVE-like setups. However, although we observed differences in collision avoidance behavior between real and virtual obstacles, which indicate biases of natural locomotion introduced by the setup, their magnitude seem lower compared to typical results found in HMD environments. In addition, the differences between the real and virtual conditions, even being significant, showed small effects. This suggests that although the user's behavior in mixed environments varies depending on the nature of the stimulus, in our particular setup (and potentially in most projection-based systems), the user's locomotion behavior and the management of his/her interaction space is comparable with the ones in real life.

Considering these findings, our results open promising vistas for using large CAVE-like setups for socio-physical experiments, in particular in the fields of locomotion and behavioral dynamics. In reality it is difficult to obtain standard conditions to study proxemics because they depend on relative kinematics states (relative position and motion). In contrast to real conditions, VR opens the ability to accurately steer the virtual character with respect to the real subject motion. Future VR-based proxemics studies could consider the presence of moving obstacles and characters, different types of interactions between obstacles or characters and real subjects (e.g. reaching, meeting, fleeing), as well as multiple interactions. Some kind of interactions could require more detailed kinematics analysis, with full body motion capture data (e.g. feet placement, postures, swaying amplitudes).

Figure 1 :

 1 Figure 1: Experimental conditions considered on the collision avoidance experiment. We analyzed the participants' avoidance behavior for real (left) and virtual objects (right), considering anthropomorphic and inanimated objects.

Figure 2 :

 2 Figure 2: Layout of the experiment considering the physical boundaries of the IVE. The green dot represents the starting point and the red cross the end point of the path. The obstacle was placed in the middle of the working space, at 1m from the front screen and at 2m of the missing wall.

3 :

 3 Orientation configuration for the obstacles when users walked from the left to the right. The orientation of the human obstacle for the 180°and 270°follow a clockwise rotation. For right to left conditions, 90°and 270°configurations are shifted.

Figure 4 :

 4 Figure 4: Bar plots reporting the mean values ±SD of speed, maximum lateral deviation and clearance distance computed for all experimental conditions (B0=Box obstacle with an orientation of 0°, B90=Box obstacle with an orientation of 90°, H0=Human obstacle with an orientation of 0°, H90=Human obstacle with an orientation of 90°, H180=Human obstacle with an orientation of 180°, H270=Human obstacle with an orientation of 270°).

( a )

 a Orientations 0°and 180°(b) Orientations 90°and 270°F igure 5: Average trajectories performed by participants to reach a target while avoiding a static obstacle in their travel path. Walking direction goes from negative y-values to positive y-values.

Figure 6 :

 6 Figure 6: Hypothesis with regard of the influence of the personal space of the virtual character on the clearance distance let by the user in the collision avoidance task. The elliptical shape of the personal space results in changes on the clearance distance according to the orientation of the obstacle.

ACKNOWLEDGEMENTS

This work was supported by the Vision Advanced Infrastructure for Research (VISIONAIR) project. Authors of this work are supported by the French National Research Agency ANR, project PERCO-LATION number ANR-13-JS02-0008 and by the German Research Foundation.