Optimal Role Assignment for Multiplayer Reach-Avoid Differential Games in 3D Space

TL;DR

This paper analyzes a 3D multiplayer reach-avoid differential game, providing optimal strategies and role assignment algorithms for pursuers and evaders to reach targets or avoid capture.

Contribution

It introduces an optimal role assignment algorithm for multiplayer scenarios and analytically characterizes winning regions and strategies.

Findings

Optimal solution for 1v1 case extended to multiplayer scenarios.

Analytical characterization of winning regions and game value.

Development of a linear program-based role assignment algorithm.

Abstract

In this article an $n$-pursuer versus $m$-evader reach-avoid differential game in 3D space is studied. A team of evaders aim to reach a stationary target while avoiding capture by a team of pursuers. The multiplayer scenario is formulated in a differential game framework. This article provides an optimal solution for the particular case of $n=m=1$ and extends it to a more general scenario of $n\geq m$ via an optimal role assignment algorithm based on a linear program. Consequently, the pursuer and the evader winning regions, and the Value of the game are analytically characterized providing optimal strategies of the players in state feedback form.