Multiple Pursuer Multiple Evader Differential Games

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. I. INTRODUCTION Differential game theory provides the right framework to analyze pursuit-evasion problems and, as a corollary, combat games. Pursuit-evasion scenarios involving multiple agents are important but challenging problems in aerospace, control, and robotics. Pursuit-evasion problems were first formulated in the seminal work [1]. Concerning many players games, reference [2] addressed the interesting dynamic game of a fast pursuer trying to capture in minimal time two slower evaders in succession. Motivated by the work in [2], the paper [3] analyzed the case where the fast pursuer tries to capture multiple evaders. Reach and avoid differential games which include time-varying dynamics, targets and constraints were addressed in [4] by means of a This work has been supported in part by AFOSR LRIR No. 18RQCOR036.

An Introduction to Pursuit-evasion Differential Games

“…Another means of task allocation was proposed in [83] where Awheda and Schwartz proposed a fuzzy logic based decentralized control scheme using the Apollonius circles construct. A formal analysis of both optimal guidance and optimal assignments of N pursuers to M evaders, for N ≥ M , was undertaken in [84]. Finally, the papers [85]- [87] address multiplayer differential games based on numerical solutions of Hamilton-Jacobi-Isaacs (HJI) equations.…”