Related Experiment Video
Updated: Feb 21, 2026

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior
Published on: April 13, 2016
Pedestrian motion modelled by Fokker-Planck Nash games
1Institut für Mathematik, Universität Würzburg, Emil-Fischer-Strasse 30, 97074 Würzburg, Germany.
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.
Related Concept Videos
Principle of Linear Impulse and Momentum for a System of Particles
Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the...
Principle of Linear Impulse and Momentum for a Single Particle
Delving...
Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving
Kinematic Equations - II
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...
First Law: Particles in One-dimensional Equilibrium
Energy Diagrams - II
The point in the energy diagram at which the system’s potential energy is the lowest is known as the local minima. The system tends to stay in this position indefinitely unless acted upon by a net force. The slope of the potential energy diagram at the local minima is zero, indicating that zero net force is acting on the system. The...

