Departmental Papers (CIS)

Date of this Version

October 2005

Document Type

Journal Article


Copyright 2005 IEEE. Reprinted from IEEE Transactions on Robotics, Volume 21, Issue 5, October 2005, pages 875-884.

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This paper contains two main results. First, we revisit the well-known visibility-based pursuit–evasion problem, and show that in contrast to deterministic strategies, a single pursuer can locate an unpredictable evader in any simply connected polygonal environment, using a randomized strategy. The evader can be arbitrarily faster than the pursuer, and it may know the position of the pursuer at all times, but it does not have prior knowledge of the random decisions made by the pursuer. Second, using the randomized algorithm, together with the solution to a problem called the “lion and man problem” as subroutines, we present a strategy for two pursuers (one of which is at least as fast as the evader) to quickly capture an evader in a simply connected polygonal environment. We show how this strategy can be extended to obtain a strategy for a polygonal room with a door, two pursuers who have only line-of-sight communication, and a single pursuer (at the expense of increased capture time).


Dynamic noncooperative game theory, path planning, pursuit-evasion games, randomized algorithms



Date Posted: 03 March 2006

This document has been peer reviewed.