Homicidal Chauffeur Reach-Avoid Games via Guaranteed Winning Strategies

This article studies a planar Homicidal Chauffeur reach-avoid differential game, where the pursuer is a Dubins car and the evader has simple motion. The pursuer aims to protect a goal region from the evader. The game is solved in an analytical approach instead of solving Hamilton–Jacobi–Isaacs equations numerically. First, an evasion region 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 deviated (Non-IO), a heading adjustment pursuit strategy is proposed, and the condition to achieve IO within a finite time is given. Based on it, a two-step pursuit strategy is proposed for the SC and Non-IO case. A nonconvex optimization problem is introduced to give a condition guaranteeing the winning of the pursuer. A polynomial equation gives a lower bound of the nonconvex problem, providing a sufficient and efficient pursuit winning condition. Finally, we extend to multiplayer games by collecting pairwise outcomes for pursuer–evader matchings. Simulations are provided to illustrate the theoretical results.