Kinetic description of collision avoidance in pedestrian crowds by sidestepping

TL;DR

This paper develops a kinetic model for pedestrian collision avoidance via sidestepping, capturing emergent phenomena like lane formation and velocity alignment, and analyzes its behavior through theoretical and numerical methods.

Contribution

It introduces a new kinetic framework for pedestrian sidestepping that links microscopic rules to macroscopic flow phenomena, with rigorous analysis and simulations.

Findings

Directional alignment occurs under certain sidestepping rules.

The model reproduces lane and stripe formation.

Numerical experiments reveal complex pedestrian flow dynamics.

Abstract

In this paper we study a kinetic model for pedestrians, who are assumed to adapt their motion towards a desired direction while avoiding collisions with others by stepping aside. These minimal microscopic interaction rules lead to complex emergent macroscopic phenomena, such as velocity alignment in unidirectional flows and lane or stripe formation in bidirectional flows. We start by discussing collision avoidance mechanisms at the microscopic scale, then we study the corresponding Boltzmann-type kinetic description and its hydrodynamic mean-field approximation in the grazing collision limit. In the spatially homogeneous case we prove directional alignment under specific conditions on the sidestepping rules for both the collisional and the mean-field model. In the spatially inhomogeneous case we illustrate, by means of various numerical experiments, the rich dynamics that the proposed model is able to reproduce.