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).
Bibliographical noteFunding Information:
Manuscript received July 27, 2004; revised December 22, 2004. This paper was recommended for publication by Associate Editor D. Fox and Editor I. Walker upon evaluation of the reviewers’ comments. The work of V. Isler was supported in part by MURI under DAAH-19-02-1-03-83. The work of S. Kannan was supported in part by the National Science Foundation under Grant CCR0105337 and in part by the Army Research Office under Grant DAAD19-01-1-0473. The work of S. Khanna was supported in part by an Alfred P. Sloan Research Fellowship and in part by the NSF under Career Award CCR-0093117. This paper was presented in part at the Workshop on Algorithmic Foundations of Robotics, Utrecht/Zeist, The Netherlands, July 2004.
- Dynamic noncooperative game theory
- Path planning
- Pursuit-evasion games
- Randomized algorithms