Vision-based macroscopic pedestrian models

Abstract

We propose a hierarchy of kinetic and macroscopic models for a system consisting of a large number of interacting pedestrians. The basic interaction rules are derived from earlier work where the dangerousness level of an interaction with another pedestrian is measured in terms of the derivative of the bearing angle (angle between the walking direction and the line connecting the two subjects) and of the time-to-interaction (time before reaching the closest distance between the two subjects). A mean-field kinetic model is derived. Then, three different macroscopic continuum models are proposed. The first two ones rely on two different closure assumptions of the kinetic model, respectively based on a monokinetic and a von Mises-Fisher distribution. The third one is derived through a hydrodynamic limit. In each case, we discuss the relevance of the model for practical simulations of pedestrian crowds.

References in corpus (4)

• Novel type of phase transition in a system of self-driven particles
• Extended floor field CA model for evacuation dynamics
• Pedestrian flows in bounded domains with obstacles
• A Nash equilibrium macroscopic closure for kinetic models coupled with Mean-Field Games

Cited by in corpus (15)

• Pedestrian Models based on Rational Behaviour
• Polar active liquids: a universal classification rooted in nonconservation of momentum
• Hybrid stochastic kinetic description of two-dimensional traffic dynamics
• Time-delayed Follow-the-Leader model for pedestrians walking in line
• Universal scaling in bidirectional flows of self-avoiding agents
• Pedestrian models with congestion effects
• A local version of the Hughes model for pedestrian flow
• A Nash equilibrium macroscopic closure for kinetic models coupled with Mean-Field Games
• On a three dimensional vision based collision avoidance model
• Moving in a crowd: human perception as a multiscale process
• Comparing first order microscopic and macroscopic crowd models for an increasing number of massive agents
• Derivation and analysis of continuum models for crossing pedestrian traffic
• Stochastic and Coarse-Grained Two-Dimensional Modeling of Directional Particle Movement
• Modeling of pedestrians
• A Semi-Lagrangian scheme for a modified version of the Hughes model for pedestrian flow