Multiplayer Homicidal Chauffeur Reach-Avoid Games via Guaranteed Winning Strategies

TL;DR

This paper develops analytical pursuit strategies for multiplayer reach-avoid games involving Dubins car pursuers and simple-motion evaders, providing conditions for guaranteed winning and strategies for different configurations.

Contribution

It introduces a decomposition approach to solve high-dimensional pursuit games analytically, deriving pursuit winning conditions and strategies without Hamilton-Jacobi-Isaacs equations.

Findings

Derived necessary and sufficient conditions for pursuit winning.

Proposed pursuit strategies for different pursuit-evader configurations.

Validated strategies through simulations demonstrating theoretical results.

Abstract

This paper studies a planar multiplayer Homicidal Chauffeur reach-avoid differential game, where each pursuer is a Dubins car and each evader has simple motion. The pursuers aim to protect a goal region cooperatively from the evaders. Due to the high-dimensional strategy space among pursuers, we decompose the whole game into multiple one-pursuer-one-evader subgames, each of which is solved in an analytical approach instead of solving Hamilton-Jacobi-Isaacs equations. For each subgame, an evasion region (ER) is introduced, based on which a pursuit strategy guaranteeing the winning of a simple-motion pursuer under specific conditions is proposed. Motivated by the simple-motion pursuer, a strategy for a Dubins-car pursuer is proposed when the pursuer-evader configuration satisfies separation condition (SC) and interception orientation (IO). The necessary and sufficient condition on capture radius, minimum turning radius and speed ratio to guarantee the pursuit winning is derived. When the IO is not satisfied (Non-IO), a heading adjustment pursuit strategy is proposed, and the condition to achieve IO within a finite time, is given. Then, a two-step pursuit strategy is proposed for the SC and Non-IO case. A non-convex optimization problem is introduced to give a condition guaranteeing the winning of the pursuer. A polynomial equation gives a lower bound of the non-convex problem, providing a sufficient and efficient pursuit winning condition. Finally, these pairwise outcomes are collected for the pursuer-evader matching. Simulations are provided to illustrate the theoretical results.