Universal power law governing pedestrian interactions

TL;DR

This paper uncovers a universal, anticipatory power law governing pedestrian interactions based on projected collision time, providing a new quantitative understanding of crowd dynamics applicable across diverse scenarios.

Contribution

It introduces a novel statistical-mechanical method to measure pedestrian interaction energy, revealing a simple power law based on future collision time rather than physical distance.

Findings

The interaction law is based on projected collision time.

The law applies across various speeds and densities.

Simulations reproduce known crowd phenomena.

Abstract

Human crowds often bear a striking resemblance to interacting particle systems, and this has prompted many researchers to describe pedestrian dynamics in terms of interaction forces and potential energies. The correct quantitative form of this interaction, however, has remained an open question. Here, we introduce a novel statistical-mechanical approach to directly measure the interaction energy between pedestrians. This analysis, when applied to a large collection of human motion data, reveals a simple power law interaction that is based not on the physical separation between pedestrians but on their projected time to a potential future collision, and is therefore fundamentally anticipatory in nature. Remarkably, this simple law is able to describe human interactions across a wide variety of situations, speeds and densities. We further show, through simulations, that the interaction law we identify is sufficient to reproduce many known crowd phenomena.