A new collision avoidance model with random batch resolution strategy

TL;DR

This paper introduces a novel 2D agent-based collision avoidance model for crowd simulation, extending it to a mean field limit, and proposes an efficient hybrid resolution strategy combining random batch methods to significantly reduce computational complexity.

Contribution

It presents a new collision avoidance model with a hybrid resolution strategy that reduces computational complexity from quadratic to linear, enabling efficient large-scale crowd simulations.

Findings

Model effectively guides particles to destinations without collisions.

Hybrid resolution strategy reduces computational complexity to O(N).

Numerical tests demonstrate robustness and efficiency.

Abstract

Research on crowd simulation has important and wide range of applications. The main difficulty is how to lead all particles with a same and simple rule, especially when particles are numerous. In this paper, we firstly propose a two dimensional agent-based collision avoidance model, which is a $N$-particles Newtonian system. The collision interaction force, imminent interaction force and following interaction force are designed, so that particles can be guided to their respective destinations without collisions. The proposed agent-based model is then extended to the corresponding mean field limit model as $N\to\infty$. Secondly, notice that direct simulation of the $N$-particles Newtonian system is very time-consuming, since the computational complexity is of order $\mathcal{O}(N^2)$. In contrast, we propose an efficient hybrid resolution strategy to reduce the computational complexity. It is a combination of the Random Batch method (Shi Jin, Lei Li, and Jian-Guo Liu. Random batch methods (RBM) for interacting particle systems. Journal of Computational Physics, 400:108877, 2020.) and the method based on local particles Newtonian system. Thanks to this hybrid resolution strategy, the computational complexity is reduced to $\mathcal{O}(N)$. Finally, various tests are presented to show robustness and efficiency of our collision avoidance model and the hybrid resolution strategy.