Control Strategies in Multi-Player Pursuit and Evasion Game

Abstract

This paper presents a new methodology for solving multi-player pursuit and evasion games. The proposed control strategies are derived from direct differentiation of chosen value (or level set) functions, instead of solving the associated Hamilton Jacobi Isaacs (HJI) equations. The corresponding strategies offer a simple form of the control laws that can be implemented on real-time control systems for autonomous vehicles. In order to guarantee a minimum separation distance between players, a new method to compute a reachable set, which only requires a set of ordinary differential equations, is developed. We also explore different value functions which lead to different performance measures for some players. We illustrate our approach on a three player pursuit and evasion game and present simulation results. I.