Potential for the dynamics of pedestrians in a socially interacting group

We introduce a simple potential to describe the dynamics of the relative motion of two pedestrians socially interacting in a walking group. We show that the proposed potential, based on basic empirical observations and theoretical considerations, can qualitatively describe the statistical properties of pedestrian behavior. In detail, we show that the two-dimensional probability distribution of the relative distance is determined by the proposed potential through a Boltzmann distribution. After calibrating the parameters of the model on the two-pedestrian group data, we apply the model to three-pedestrian groups, showing that it describes qualitatively and quantitatively well their behavior. In particular, the model predicts that three-pedestrian groups walk in a V-shaped formation and provides accurate values for the position of the three pedestrians. Furthermore, the model correctly predicts the average walking velocity of three-person groups based on the velocity of two-person ones. Possible extensions to larger groups, along with alternative explanations of the social dynamics that may be implied by our model, are discussed at the end of the paper.