We address a discrete-time pursuit-evasion problem involving multiple pursuers and a single evader in an unbounded, planar environment in which each player has limited-range sensing. The evader appears at a random location in a bounded region and moves only when sensed. We propose a sweep-pursuit-capture strategy for a group of at least three pursuers and determine a lower bound on the probability of capture for the evader. This bound is a function of the pursuer formation and independent of the initial evader location and the evader strategy. We then propose a novel cooperative pursuit algorithm and show that the problem is reduced to one with unlimited sensing. We provide an upper bound on the time for our pursuit strategy to succeed. The final capture is achieved by using the established algorithm SPHERES. Our results show that on the basis of maximizing the probability of evader capture per pursuer, the pursuers should search the bounded region as a single group (conjoin) rather than to divide the region into smaller parts and search simultaneously in smaller groups (allocate).
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