  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.
