Relative rate of expansion controls speed in one-dimensional pedestrian following.

Patterns of crowd behavior are believed to result from local interactions between pedestrians. Many studies have investigated the local rules of interaction, such as steering, avoiding, and alignment, but how pedestrians control their walking speed when following another remains unsettled. Most pedestrian models assume the physical speed and distance of others as input. The present study compares such "omniscient" models with "visual" models based on optical variables. We experimentally tested eight speed control models from the pedestrian- and car-following literature. Walking participants were asked to follow a leader (a moving pole) in a virtual environment, while the leader's speed was perturbed during the trial. In Experiment 1, the leader's initial distance was varied. Each model was fit to the data and compared. The results showed that visual models based on optical expansion (\(\dot{\theta }\)) had the smallest root mean square error in speed across conditions, whereas other models exhibited increased error at longer distances. In Experiment 2, the leader's size (pole diameter) was varied. A model based on the relative rate of expansion (\(\dot{\theta }/\theta \)) performed better than the expansion rate model (\(\dot{\theta }\)), because it is less sensitive to leader size. Together, the results imply that pedestrians directly control their walking speed in one-dimensional following using relative rate of expansion, rather than the distal speed and distance of the leader.