Collision-free pedestrian model
Microscopic pedestrian models are frequently used in traffic engineering and safety engineering to simulate crowd behaviors in different scenarios. The social force model is a second-order model based on a superposition of exponential repulsions with the neighbors (the social forces). Despite its simplicity, SFM can describe realistic dynamics and self-organized phenomena (lane formation, alternance at bottlenecks, etc.) for fine tunings of the parameter. However, inertia mechanisms can also provide undesired overlapping effects of the pedestrians (“tunneling” or penetration of particles), oscillating behaviors, as well as, technically, numerical complexity (i.e., small time steps in the simulations).
In contrast to acceleration-based models, the velocity in velocity-based models is instantaneously adjusted to the neighborhood and the environment with no inertia or reaction time. Such a modelling approach is largely inspired by motion planning in robotics. Constraints on the velocity in case of contact allow to model hard-core body exclusion (volume exclusion) and tdescribe collision-free pedestrian dynamics with no overlapping. Furthermore, the numerical complexity of the systems is significantly lower than those of acceleration models, making them potentially suitable for large-scale simulation. In the collision-free model, the speed depends, as for optimal velocity traffic models, on the distance spacing in front, while the direction, as the social force and gradient navigation models, results from exponential repulsion with the neighbors and the obstacles. The model is collision-free by construction, and can describe different self-organization (see, e.g., the videos #1, #2, #3, #4).
D. Helbing, P. Molnar. Social force model for pedestrian dynamics. Physical Review E, 51(5), 4282, 1995.
M. Chraibi, U. Kemloh, A. Schadschneider, A. Seyfried. Force-based models of pedestrian dynamics. Networks & Heterogeneous Media, 6(3), 425, 2011.
B. Maury, J. Venel. A discrete contact model for crowd motion. ESAIM: Mathematical Modelling and Numerical Analysis, 45(1), 145-168, 2011.
G. Köster, F. Treml, M. Gödel. Avoiding numerical pitfalls in social force models. Physical Review E, 87(6), 063305, 2013.
F. Dietrich, G. Köster. Gradient navigation model for pedestrian dynamics. Physical Review E, 89(6), 062801, 2014.
A Tordeux, M Chraibi and A Seyfried Collision-free first order model for pedestrian dynamics. Proceedings of Traffic and Granular Flow’15, Springer pp 225–232, 2015. Presentation
M Chraibi, A Tordeux, A Schadschneider, A Seyfried. Modelling of Pedestrian and Evacuation Dynamics. In: Meyers R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg, 2018.
Q Xu, M Chraibi, A Tordeux, J Zhang. Generalized collision-free velocity model for pedestrian dynamics. Physica A: Statistical Mechanics and its Applications 535:122521, 2019.