Multiple Pursuer Multiple Evader Differential Games

TL;DR

This paper extends differential game theory to multi-pursuer and multi-evader scenarios, devising saddle-point strategies and optimal guidance laws for team conflicts, overcoming high-dimensional challenges in pursuit-evasion problems.

Contribution

It introduces a comprehensive framework for simultaneous weapon assignment and pursuit-evasion strategies in multi-player differential games, including cases where pursuers outnumber evaders.

Findings

Value function is continuous and satisfies Hamilton-Jacobi-Isaacs equation.

Optimal strategies are derived for various pursuer-evader configurations.

Cooperative guidance strategies enhance pursuer effectiveness when outnumbering evaders.

Abstract

In this paper an N-pursuer vs. M-evader team conflict is studied. The differential game of border defense is addressed and we focus on the game of degree in the region of the state space where the pursuers are able to win. This work extends classical differential game theory to simultaneously address weapon assignments and multi-player pursuit-evasion scenarios. Saddle-point strategies that provide guaranteed performance for each team regardless of the actual strategies implemented by the opponent are devised. The players' optimal strategies require the co-design of cooperative optimal assignments and optimal guidance laws. A representative measure of performance is proposed and the Value function of the game is obtained. It is shown that the Value function is continuous, continuously differentiable, and that it satisfies the Hamilton-Jacobi-Isaacs equation - the curse of dimensionality is overcome and the optimal strategies are obtained. The cases of N=M and N>M are considered. In the latter case, cooperative guidance strategies are also developed in order for the pursuers to exploit their numerical advantage. This work provides a foundation to formally analyze complex and high-dimensional conflicts between teams of N pursuers and M evaders by means of differential game theory.