Pedestrian motion modelled by Fokker-Planck Nash games
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- 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.…
Autor(en): | S. RoyORCiD, A. Borzì, A. HabbalORCiD |
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URN: | urn:nbn:de:bvb:20-opus-170395 |
Dokumentart: | Artikel / Aufsatz in einer Zeitschrift |
Institute der Universität: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Sprache der Veröffentlichung: | Englisch |
Titel des übergeordneten Werkes / der Zeitschrift (Englisch): | Royal Society Open Science |
Erscheinungsjahr: | 2017 |
Band / Jahrgang: | 4 |
Heft / Ausgabe: | 9 |
Seitenangabe: | 170648 |
Originalveröffentlichung / Quelle: | 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 |
Allgemeine fachliche Zuordnung (DDC-Klassifikation): | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Freie Schlagwort(e): | Fokker–Planck equation; Nash equilibrium; avoidance; differential games; optimal control; pedestrian motion |
Datum der Freischaltung: | 23.09.2019 |
Lizenz (Deutsch): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |