Spatio-temporal collision envelope in virtual reality walking with colliding pedestrians

Safe locomotion depends on maintaining a collision envelope (i.e., safety margin) that flexibly adapts to dynamic situations. We previously characterized dynamic collision envelopes spatially as the minimum egocentric radial distance maintained while walking with other colliding pedestrians. Spatial collision envelope sizes depended on relative walking speeds between the subject and the colliding pedestrian. From this finding, we hypothesized that collision envelopes may be driven by temporal distances (time-to-collision, TTC) rather than spatial distances. To this end, we used virtual reality (VR) walking scenarios for the Meta Quest 2 head-mounted display (HMD). Normal vision (NV, n=10) and homonymous hemianopia (HH, n=7) subjects physically walked with free gaze in a VR shopping mall presented in the HMD. Subjects naturally avoided (speed/path changes) a colliding pedestrian among 10 non-colliders. Head-on (farther distance, faster relative speed) or rear-end (closer distance, slower relative speed) colliders approached from initial bearing angles of 20°, 40°, and 60°. Collisions had an initial 6-second TTC, which linearly decreased to 0 if the subject failed to avoid. We computed instantaneous TTC (which fluctuates with gait, body volumes, and path changes) in the egocentric domain as the spatial distance between subject and collider divided by the projection of the instantaneous velocity toward the walking direction of the subject. We considered the minimum TTC across relative bearing angles to be the subject’s spatio-temporal collision envelope as reaction to the collision. The radius (head-on=0.77 seconds ±0.27, read-end=0.79s ±0.54, p=0.84) and area (head-on=3.26s^2 ±1.20, rear-end=3.87s^2 ±1.79, p=0.26) of spatio-temporal collision envelopes were consistent regardless of distance and relative walking speeds. HH had more conservative spatio-temporal collision envelopes (0.86s ±0.48) than NV (0.63s ±0.23, p<0.01) during avoidance. This finding suggests that collision avoidance may be driven by the spatio-temporal collision envelope based on the minimum TTC that allows enough time (rather than distance) to react.