Quantitative measurement of social repulsive force in pedestrian movements based on physiological responses

The pedestrian movement in the crowds is a paradigmatic example of collective motion where social interactions play an important role. The psychological behaviors of pedestrians underlying crowd movements are usually based on intuitive assumptions, and so far a quantitative measurement of social repulsive force in pedestrian movements has been rarely reported. In this work, we perform different types of human experiments in face-to-face and face-to-back situations as well as walking, running and blind conditions to indirectly measure the social repulsive force based on the human physiological response to stress, i.e., the skin conductance response (SCR). It is demonstrated that the social repulsive force tends to increase with the moving speed of participants, and is much stronger in the face-to-face orientation compared to that in the face-to-back orientation. As interesting outcomes, a relationship between SCR amplitude and interpersonal distances is also observed, and statistical results show that the logistic functional form has a better fit to the measurement data of SCR amplitude than the classical exponential function due to the existence of a diminishing marginal utility in human psychology. Moreover, the observed repulsive force coefficients in running experiment slightly exceed those in walking experiment because faster running speed will cause more serious body conflict, thereby leading to a higher physiological arousal level. Especially, the social repulsive forces under the condition of zero visibility only occur where there is a body contact, which are significantly higher than those in walking and running experiments because of the panic psychology and unexpected danger in a blind environment. These experimental findings are further confirmed by numerical simulations performed by solving a modified social force model that incorporates logistic repulsive forces. The simulated velocity distributions in different types of psychological situations all demonstrate remarkable consistence with the experimental results. Therefore, this work establishes a direct link between behavioral responses and cognitive effort, and gives new insights into pedestrian dynamics from a social psychological perspective.