We consider a problem of cooperative evasion between a single pursuer and multiple evaders in which the evaders are constrained to move in the positive Y direction. The evaders are slower than the vehicle and can choose their speeds from a bounded interval. The pursuer aims to intercept all evaders in a given sequence by executing a Manhattan pursuit strategy of moving parallel to the X axis, followed by moving parallel to the Y axis. The aim of the evaders is to cooperatively pick their individual speeds so that the total time to intercept all evaders is maximized. We first obtain conditions under which evaders should cooperate in order to maximize the total time to intercept as opposed to each moving greedily to optimize its own intercept time. Then, we propose and analyze an algorithm that assigns evasive strategies to the evaders in two iterations as opposed to performing an exponential search over the choice of evader speeds. We also characterize a fundamental limit on the total time taken by the pursuer to capture all evaders when the number of evaders is large. Finally, we provide numerical comparisons against random sampling heuristics.

中文翻译：

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通过变速平移目标进行合作规避

我们考虑单个追捕者和多个逃避者之间的合作逃避问题，其中逃避者被限制在正 Y 方向上移动。逃避者比车辆慢，并且可以从有界间隔中选择他们的速度。追击者的目标是通过执行平行于 X 轴移动，然后平行于 Y 轴移动的曼哈顿追击策略来拦截给定序列中的所有逃避者。逃避者的目标是合作选择他们各自的速度，以便拦截所有逃避者的总时间最大化。我们首先获得逃避者应该合作以最大化拦截总时间的条件，而不是每个人贪婪地移动以优化自己的拦截时间。然后，我们提出并分析了一种算法，该算法在两次迭代中为逃避者分配逃避策略，而不是对逃避者速度的选择执行指数搜索。当逃避者的数量很大时，我们还描述了追捕者捕获所有逃避者所花费的总时间的基本限制。最后，我们提供了与随机抽样启发式方法的数值比较。