Pedestrian motion modelled by Fokker-Planck Nash games
Please always quote using this URN: urn:nbn:de:bvb:20-opus-170395
- 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 provedA 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.…
Author: | S. RoyORCiD, A. Borzì, A. HabbalORCiD |
---|---|
URN: | urn:nbn:de:bvb:20-opus-170395 |
Document Type: | Journal article |
Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Language: | English |
Parent Title (English): | Royal Society Open Science |
Year of Completion: | 2017 |
Volume: | 4 |
Issue: | 9 |
Pagenumber: | 170648 |
Source: | Royal Society Open Science 2017, 4(9):170648. DOI: 10.1098/rsos.170648 |
DOI: | https://doi.org/10.1098/rsos.170648 |
Pubmed Id: | https://pubmed.ncbi.nlm.nih.gov/28989767 |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Tag: | Fokker–Planck equation; Nash equilibrium; avoidance; differential games; optimal control; pedestrian motion |
Release Date: | 2019/09/23 |
Licence (German): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |