The relative rate of optical expansion controls speed in 1D pedestrian followin

Abstract

Last year, we compared six models of speed control for a pedestrian following behind a leader (Bai & Warren, VSS 2018). The results showed that Rio, Rhea & Warren’s (JoV, 2014) optical expansion model best fit the data, and explained the decreasing response with distance. The model uses the rate of expansion (or contraction) of the target’s visual angle to control the follower’s deceleration (acceleration), thereby canceling the optical expansion. However, the model predicts that a larger target should produce a greater acceleration, because the rate of expansion is a monotonically increasing function of target size (over a moderate range of target sizes). Here we propose an alternative model in which the relative rate of expansion (expansion rate/visual angle) controls acceleration, which mitigates the sensitivity to target size. To compare the two models, we asked participants to follow a moving target, the size of which varied randomly on each trial (width = 0.2, 0.6, 1 m, height = 3 m).12 participants walked in a virtual environment wearing a head-mounted display, while head position was recorded at 90 Hz. They were instructed to follow a virtual target (a green cylinder) on a textured ground plane. In each trial, the target appeared in front of the participant (distance = 1, 3, 6 m) and started to move on a straight path at a constant speed (1.2 m/s). After 3–4 seconds, the target changed its speed (+0.3, 0, −0.3 m/s). Bayesian model comparison revealed that the relative expansion model had a lower RMS error (.085 m/s2) and BIC value (−284.88) than the expansion model (0.094 m/s2, −272.15), which exhibited larger error for the extreme target sizes (0.2 and 1 m). The results provide ‘very strong’ support that the relative rate of expansion is used to control speed in pedestrian following.