Vision-based macroscopic pedestrian models

Pierre Degond; Cécile Appert-Rolland; Julien Pettré; Guy Theraulaz

doi:10.3934/krm.2013.6.809

Article Contents

2013, Volume 6, Issue 4: 809-839. Doi: 10.3934/krm.2013.6.809

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Vision-based macroscopic pedestrian models

1.
Université de Toulouse; UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, F-31062 Toulouse
2.
Laboratoire de Physique Théorique, Université Paris Sud, btiment 210, 91405 Orsay cedex
3.
INRIA Rennes - Bretagne Atlantique, Campus de Beaulieu, 35042 Rennes
4.
Centre de Recherches sur la Cognition Animale, UMR-CNRS 5169, Université Paul Sabatier, 31062 Toulouse cedex 9

Received: July 31, 2013

Revised: August 31, 2013

Published: November 2013

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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 [44] 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.

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Mathematics Subject Classification: Primary: 76Z99, 91F99; Secondary: 35L60, 35L65, 91A13.

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