A speed control law for pedestrian following based on visual angle

Abstract

Following another pedestrian is common in everyday locomotion, and may contribute to the collective behavior of crowds. Last year we modeled the behavioral strategy for speed control in 1D following (Rio, Rhea, & Warren 2010); this year we investigate the visual information used to regulate speed. Previously, we modeled data on the follower's acceleration in response to the leader's change in speed by (a) nulling change in distance, (b) nulling the difference in speed, and (c) combining speed and distance using a ratio (Gazis, Herman, & Rothery 1961) or a linear combination (Helly, 1959; Anderson & Sauer, 2007). The data are well-accounted for by the relative speed model. Here, we manipulate the visual angle and binocular disparity of a virtual ‘leader.’ The participant followed a virtual target pole (0.2 m diameter) viewed stereoscopically in a head-mounted display (63°H × 53°V) in the 12 × 12 m VENLab. A change in target speed over a 3s interval was specified by (1) a 50% increase, decrease, or 0% change in visual angle, achieved by shrinking or expanding the pole, and (2) a 50% decrease, increase, or 0% change in binocular disparity. The visual angle and disparity conditions were fully crossed, so that the changes could be congruent or incongruent. Participants' mean speed during the manipulation showed that they relied entirely on the change in visual angle (p < .001) and ignored the changes in disparity (ns). We combine these results to derive a speed control law for following, in which the follower matches the leader's speed by nulling change in their visual angle. Future work will expand the following model to the general 2D case, in which the leader changes direction as well as speed (Rhea, Cohen, & Warren 2009), and will investigate its role in crowd behavior (Rio, Bonneaud, & Warren 2010).