Elsevier

Gait & Posture

Volume 36, Issue 3, July 2012, Pages 399-404
Gait & Posture

Minimal predicted distance: A common metric for collision avoidance during pairwise interactions between walkers

https://doi.org/10.1016/j.gaitpost.2012.03.021Get rights and content

Abstract

This study investigated collision avoidance between two walkers by focusing on the conditions that lead to avoidance manoeuvres in locomotor trajectories. Following the hypothesis of a reciprocal interaction, we suggested a mutual variable as a continuous function of the two walkers’ states, denoted minimum predicted distance (MPD). This function predicts the risk of collision, and its evolution over time captures the motion adaptations performed by the walkers. By groups of two, 30 walkers were assigned locomotion tasks which lead to potential collisions. Results showed that walkers adapted their motions only when required, i.e., when MPD is too low (<1 m). We concluded that walkers are able (i) to accurately estimate their reciprocal distance at the time the crossing will occur, and (ii) to mutually adapt this distance. Furthermore, the study of MPD evolution showed three successive phases in the avoidance interaction: observation where MPD(t) is constant, reaction where MPD(t) increases to acceptable values by adapting locomotion and regulation where MPD(t) reaches a plateau and slightly decreases. This final phase demonstrates that collision avoidance is actually performed with anticipation. Future work would consist in inspecting individual motion adaptations and relating them with the variations of MPD.

Highlights

► We experimentally studied collision avoidance between two walkers. ► Walkers were able to accurately predict the risk of a future collision. ► They performed collision avoidance manoeuvres only when required. ► Collision avoidance was solved with anticipation. ► We detail the three phases that compose an avoidance: observation, reaction and regulation.

Introduction

When two humans walk in the same proximity, each can be considered as a moving obstacle for the other one. Such a situation occurs during everyday life activities such as walking in the streets. There is a fundamental difference between the avoidance of a non-human moving obstacle and the avoidance of human moving obstacles. The situation, in essence, is reciprocal: each walker is avoiding the other one while being avoided at the same time.

Previous studies have focused on the locomotion trajectory of a walker confronted with static or passive moving obstacles. Studies have mainly described the adaptation made to step over [1], [2], [3] or to circumvent [4] static obstacles. The extension to passive moving obstacles in a few studies has shown that walkers adapt their trajectories along both the anteroposterior and mediolateral axes to avoid a mannequin with a predefined trajectory [5], [6], [7]. The observed clearance area, also known as personal space, was modelled as an ellipse which dimensions depend on the level of attention required by the task [5]. In another study, Fajen and Warren [8] proposed to model interactions between a walker and the environment as a pair of coupled dynamic systems. Authors proposed to adapt heading according to the distance and the angle between the walker and stationary goals and obstacles. This model was extended to the avoidance of moving obstacles [9], [10], [11]. Following a vector–field interaction model in which goals represent attractors and obstacles represent repellors, the path of the walker was computed at each instant as the resultant of all forces applied to him/her. To the best of our knowledge, no study has considered the avoidance behavior between two human walkers. Two-human interactions have however been investigated by considering interpersonal coordination [12], [13], [14]. Ducourant et al. [12] focused on two participants (a leader and a follower) placed face to face and moving forwards and backwards. Results showed the presence of coordination mechanisms that depend on leadership and distance between people. This study provides an understanding of the interaction mechanisms during walking. However, trajectories were highly constrained and the nature of interactions between walkers was very specific. Compared to previous studies, our objective was to investigate collision avoidance between two human walkers. The main question was to identify the conditions that lead to avoidance manoeuvres in locomotor trajectories: what are the relations between the respective positions and velocities which yield motion adaptations? Based on the assumption of a reciprocal interaction, we suggested a mutual variable, common to both walkers, the minimum predicted distance (MPD), which (i) predicts potential collisions and (ii) describes the mechanism of collision avoidance over time in three successive phases.

Section snippets

Participants

Thirty participants (11 women and 19 men) volunteered for this experiment. They had no known vestibular or neurological pathology which would affect their locomotion. Participants gave written and informed consent before their inclusion and the study conformed to the Declaration of Helsinki. They were 26.1 years old (±6.9) (mean ± S.D.) and 1.74 m tall (±0.09).

Experimental protocol and apparatus

A 15 m edge square was used for the experiments. In pairs of two, starting from corners not sharing the same diagonal, participants were

Results

No collision occurred during the experiment and dmin was never below 0.41 m. Occluding walls fulfilled their role since participants reached a stable speed at tsee, i.e., before interaction. Fig. 3 illustrates a representative 90° crossing (A), the associated instantaneous velocity before tsee (B), and MPD(t) evolution during interaction (C). In this situation, the initial MPD (MPD(tsee)) is approximately 0.2 m (i.e., a future collision will occur if no adaptation is performed) and increases

Discussion

We experimentally examined interactions between two participants avoiding each other. We then considered MPD as well as its variations as kinematic clues to represent interaction. Finally, we described collision avoidance as a three-phases process.

MPD(t) is a predictive variable which is defined as the distance walkers would meet if no adaptation to their trajectories was performed. MPD(t) varies in time if and only if locomotion is adapted by one or both walkers. An experimental setup allowed

Conflict of interest statement

None.

Acknowledgements

This research was funded by the ANR-PsiRob 2007 Locanthrope Project (ANR-07-ROBO-0007) and the European FP7-ICT-2009C Tango Project (no 249858). We would like to thank Alain Berthoz and Marc Christie for helpful discussions.

References (17)

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