Multiplayer Reach-Avoid Games via Pairwise Outcomes

TL;DR

This paper introduces scalable methods for multiplayer reach-avoid games, providing real-time and performance-guaranteed strategies for defending teams against multiple attackers in complex environments.

Contribution

It develops pairwise outcome analysis and a graph-based matching approach to solve multiplayer reach-avoid games efficiently, with real-time updates and scalability.

Findings

Hamilton-Jacobi-Isaacs approach enables real-time updates

Path defense method is more scalable with maintained guarantees

Proposed methods outperform traditional intractable solutions

Abstract

A multiplayer reach-avoid game is a differential game between an attacking team with NA attackers and a defending team with ND defenders playing on a compact domain with obstacles. The attacking team aims to send M of the NA attackers to some target location, while the defending team aims to prevent that by capturing attackers or indefinitely delaying attackers from reaching the target. Although the analysis of this game plays an important role in many applications, the optimal solution to this game is computationally intractable when NA>1 or ND>1. In this paper, we present two approaches for the NA=ND=1 case to determine pairwise outcomes, and a graph theoretic maximum matching approach to merge these pairwise outcomes for an NA,ND>1 solution that provides guarantees on the performance of the defending team. We will show that the four-dimensional Hamilton-Jacobi-Isaacs approach allows for real-time updates to the maximum matching, and that the two-dimensional "path defense" approach is considerably more scalable with the number of players while maintaining defender performance guarantees.