Citation

Roy S, Borzì A, Habbal A. R. Soc. Open Sci. 2017; 4(9): 170648.

Affiliation

Université Côte d'Azur, Inria, CNRS, LJAD, UMR 7351, Parc Valrose, 06108 Nice, France.

Copyright

(Copyright © 2017, Royal Society Publishing)

DOI

10.1098/rsos.170648

PMID

28989767

PMCID

PMC5627107

Abstract

A new approach to modelling pedestrians' avoidance dynamics based on a Fokker-Planck (FP) Nash game framework is presented. In this framework, two interacting pedestrians are considered, whose motion variability is modelled through the corresponding probability density functions (PDFs) governed by FP equations. Based on these equations, a Nash differential game is formulated where the game strategies represent controls aiming at avoidance by minimizing appropriate collision cost functionals. The existence of Nash equilibria solutions is proved and characterized as a solution to an optimal control problem that is solved numerically.

RESULTS of numerical experiments are presented that successfully compare the computed Nash equilibria to the output of real experiments (conducted with humans) for four test cases.

Language: en

Keywords

Fokker–Planck equation; Nash equilibrium; avoidance; differential games; optimal control; pedestrian motion