When walking in open space, collision avoidance with other pedestrians is a process that successfully takes place many times. To pass another pedestrian (an interferer) walking direction, walking speed or both can be adjusted. Currently, the literature is not yet conclusive of how humans adjust these two parameters in the presence of an interferer. This impedes the development of models predicting general obstacle avoidance strategies in humans’ walking behavior. The aim of this study was to investigate the adjustments of path and speed when a pedestrian is crossing a non-reactive human interferer at different angles and speeds, and to compare the results to general model predictions. To do so, we designed an experiment where a pedestrian walked a 12 m distance to reach a goal position. The task was designed in such a way that collision with an interferer would always occur if the pedestrian would not apply a correction of movement path or speed. Results revealed a strong dependence of path and speed adjustments on crossing angle and walking speed, suggesting local planning of the collision avoidance strategy. Crossing at acute angles (i.e. 45° and 90°) seems to require more complex collision avoidance strategies involving both path and speed adjustments than crossing at obtuse angles, where only path adjustments were observed. Overall, the results were incompatible with predictions from existing models of locomotor collision avoidance. The observed initiations of both adjustments suggest a collision avoidance strategy that is temporally controlled. The present study provides a comprehensive picture of human collision avoidance strategies in walking, which can be used to evaluate and adjust existing pedestrian dynamics models, or serve as an empirical basis to develop new models.

Introduction

When walking in a shopping center or in a train station, pedestrians usually cross their paths with dozens of other people without colliding into them. To avoid collisions, two principal movement parameters have to be coordinated: the walking path and the speed. Here, walking path refers to the spatial parameter (i.e., changes in position) of a pedestrian’s trajectory, regardless of the temporal evolution. Walking speed refers to tangential velocity along the planned path, that is, independent of the movement direction. Although the combination of these two parameters allows for infinite possibilities to avoid collisions with obstacles, the observed movements appear to exhibit stereotypical trajectories within and across people [1] [2]. This indicates that pedestrians use specific strategies to avoid obstacles while moving towards their intended locations. In principal, while the adjustment of path can always lead to successful obstacle avoidance, the adjustment of speed alone may not be sufficient. Imagine a person standing in your way or approaching you in a head-on encounter: collision avoidance in this case cannot be achieved without changing the path.

The question of whether pedestrians adjust movement path or speed to avoid collision with another person has been of recent scientific interest, but results thus far have been inconsistent. In the presence of static objects, obstacle avoidance is mainly explained by path adjustment. This adjustment seems to be governed by the information about the person’s own movement in relation to the objects in the scene, namely, the distance to the goal, the distance to the static obstacle, as well as the obstacle’s angle with respect to the heading direction, as proposed by Fajen and Warren [3]. Recent work by Fajen and Warren [4] extents this model to moving obstacles. Further empirical evidence comes from Moussaid et al. [5], who reported that when passing a static human, people simply change their movement direction to avoid collisions when passing a non-moving human. On the other hand, adjusting the speed has the advantage of keeping the intended path so that a spatial re-planning of the movement trajectory is not necessary. Thus, braking seems to be favored when the field of view is restricted [6], in small areas, or crowded places [7], and when the environment or the obstacle’s behavior is uncertain [1]. Furthermore, Cinelli and Patla [8] report that braking is the only option in the presence of spatiotemporal restrictions, such as when passing through an oscillating door.

Besides these findings favoring either path or speed adjustment as a collision avoidance strategy, a number of studies also found adjustments in both parameters. Cinelli and Patla [9], for example, showed that when a human doll directly approached a walking person, the person changed its movement path prior to its walking speed. By contrast, Olivier et al. [10] reported a collision avoidance behavior for a moving obstacle crossing at an angle of 90°, starting with an adjustment of speed followed by an additional path adjustment. As the two studies provide inconsistent results regarding the order of initiation of path and speed adjustments, it seems that the opted obstacle avoidance strategy is highly dependent on the environmental constraints and the dynamics of the obstacle.

Inconsistency of human collision avoidance strategies exists not only in the empirical data, but also in the models that attempt to describe this behavior. These models differ not only in their basic assumptions but also in their predictions about the deployment of path or speed adjustments in collision avoidance. To exemplify this, let us assume a scenario without considerable spatial constraints, and with only one moving obstacle (another person) walking at different speeds. Furthermore, the crossing person (i.e. the obstacle) does not react to the pedestrian by any means. A navigation model based on the heuristics [7] proposes that, as a first rule, a pedestrian chooses a walking direction that allows for the most direct path towards the goal, taking into account the obstacles in between. This model [7] uses a default maximum “horizon distance” of a pedestrian, for which obstacles are taken into account. Critically, this default “horizon distance” leads to adjustments of the path at a fixed distance to the obstacle, independently of the pedestrian’s walking speed (see Fig. 1B). A second rule of this model describes that the pedestrian tries to keep a minimal safety distance to the obstacles, which becomes relevant only within small distances to the obstacle or in the presence of spatial constraints. Given enough space to navigate, together the two rules converge to an adjustment of the path rather than of the speed. Other models inspired by Newton’s laws of motion (e.g., the “social force model” [11], or a modification of it [12]) describe the pedestrian’s motion as a combination of a driving force pointing towards the goal position, and repulsive forces originating from the obstacles. Due to the repulsive and driving forces, adjustments of the walking path are expected rather than adjustments of the walking speed. These models predict that path and speed adjustments are initiated closer to the interfering person when the pedestrian moves at a higher speed (see Fig. 1A). A third approach, based on the theories of optimal control, suggests that the smoothness of the movement is optimized [13]. In an improved version of this model, a penalty for speed changes was introduced [14], favoring path adjustments rather than speed adjustments in collision avoidance. As another approach, Fajen and Warren [3] modeled an obstacle avoidance behavior, in which the angular acceleration was described as a function of the goal, the obstacle angle and distance, taking into account only path adjustments, and ignoring speed changes, thereby predicting path adjustments at the same distance to an obstacle (see Fig. 1B). A last possible collision avoidance strategy, known as the time-to-collision strategy [15], proposes that the initiation of path and speed adjustments starts at larger distance to the obstacle with higher walking speed of the pedestrian, while the time point for the adjustment remains the same (see Fig. 1C).

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larger image TIFF original image Download: Figure 1. Illustration of model predictions about the influence of the obstacle distance on the avoidance strategy. The dashed arrows symbolize a fast walking speed of the pedestrian, the solid arrow a slower speed. A: The obstacle is represented as a repulsive potential. The fast speed allows the pedestrian to climb up the potential higher before the repulsive force leads to a significant change of the path as compared to a slow walking speed. B: A fixed spatial horizon (dashed and solid circle) specifies when an obstacle (grey circle) is taken into account. The horizon is not dependent on the speed (dashed and solid arrows) of the pedestrian [3] [7]. C: The horizon is speed dependent. Therefore, the obstacle is taken into account at a greater distance for a higher walking speed. This is comparable to a time-to collision mechanism [15]. https://doi.org/10.1371/journal.pone.0089589.g001

In addition, different models predict different positions where static or moving obstacles become relevant. While models dealing with static obstacles mainly derive the collision avoidance behavior from the position of the obstacle [3], it is not yet clear which position of a moving obstacle is used as a cue. The “social force model” assumes a potential around the current position of the moving obstacle, which is shifted to the moving direction of the pedestrian, as the “pedestrian requires space for the next step” [11]. Other models pose that the pedestrians estimate possible collision points in the future and correct their trajectories according to their predictions [7] [12]. As previous empirical studies varied in the experimental conditions and environmental constraints, it is difficult to compare the existing data with different model predictions.

The goal of this study is to investigate obstacle avoidance strategies in several different pedestrian-obstacle constellations, and to compare the results with principle model predictions. Specifically, we investigated whether and how pedestrians, walking at different speeds, adjusted their movement path and speed in the presence of a human obstacle who crossed at different angles without reacting to the pedestrian’s behavior. Note that the behavioral variables, which guide these adjustments were not within the scope of this study, but rather how the pedestrians actually perform the adjustments of walking path and velocity. Different crossing angles were included, as we intended to examine its influence on the applied collision avoidance strategy. Furthermore, we aimed to reveal whether adjustments in both path and walking speed are jointly or independently controlled in space. Lastly, by analyzing different model predictions we intended to establish which position of the moving obstacle is taken into account to avoid a collision.