This paper presents a novel strategy for a multi-agent pursuit-evasion game involving multiple faster pursuers with heterogenous speeds and a single slower evader. We define a geometric region, the evader's safe-reachable set, as the intersection of Apollonius circles derived from each pursuer-evader pair. The capture strategy is formulated as a zero-sum game where the pursuers cooperatively minimize the area of this set, while the evader seeks to maximize it, effectively playing a game of spatial containment. By deriving the analytical gradients of the safe-reachable set's area with respect to agent positions, we obtain closed-form, instantaneous optimal control laws for the heading of each agent. These strategies are computationally efficient, allowing for real-time implementation. Simulations demonstrate that the gradient-based controls effectively steer the pursuers to systematically shrink the evader's safe region, leading to guaranteed capture. This area-minimization approach provides a clear geometric objective for cooperative capture.

翻译：本文提出了一种新颖的多智能体追逃博弈策略，涉及多个具有异构速度的较快追捕者与单个较慢的逃避者。我们定义了一个几何区域——逃避者的安全可达集，该集合由每个追捕者-逃避者对生成的阿波罗尼奥斯圆的交集构成。追捕策略被构建为一个零和博弈，其中追捕者协同最小化该集合的面积，而逃避者则试图最大化该面积，实质上进行一场空间围困博弈。通过推导安全可达集面积相对于智能体位置的解析梯度，我们得到了每个智能体航向的闭式瞬时最优控制律。这些策略计算效率高，可实现实时部署。仿真结果表明，基于梯度的控制能有效引导追捕者系统性地压缩逃避者的安全区域，从而确保捕获。这种面积最小化方法为协同追捕提供了清晰的几何目标。