Randomized Pursuit-Evasion in a

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 lo- cate an unpredictable evader in any simply connected polygonal environment, using a randomized strategy. The evader can be ar- bitrarily 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 ran- domized 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 envi- ronment. 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 ex- pense of increased capture time).

[1]  Leonidas J. Guibas,et al.  A Visibility-Based Pursuit-Evasion Problem , 1999, Int. J. Comput. Geom. Appl..

[2]  Leonidas J. Guibas,et al.  Finding an unpredictable target in a workspace with obstacles , 1997, Proceedings of International Conference on Robotics and Automation.

[3]  Rufus Isaacs,et al.  Differential Games , 1965 .

[4]  Kyung-Yong Chwa,et al.  Visibility-Based Pursuit-Evasion in a Polygonal Region by a Searcher , 2001, ICALP.

[5]  B. Chazelle,et al.  Optimal Convex Decompositions , 1985 .

[6]  Steven M. LaValle,et al.  Optimal navigation and object finding without geometric maps or localization , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[7]  Edward M. Reingold,et al.  "Lion and Man": Upper and Lower Bounds , 1992, INFORMS J. Comput..

[8]  J. Mark Keil,et al.  Decomposing a Polygon into Simpler Components , 1985, SIAM J. Comput..

[9]  Jirí Sgall.  Solution of David Gale's lion and man problem , 2001, Theor. Comput. Sci..

[10]  Alejandro Sarmiento,et al.  An efficient strategy for rapidly finding an object in a polygonal world , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[11]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[12]  J.P. Hespanha,et al.  Multiple-agent probabilistic pursuit-evasion games , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[13]  Masafumi Yamashita,et al.  Searching for a Mobile Intruder in a Polygonal Region , 1992, SIAM J. Comput..

[14]  Kyung-Yong Chwa,et al.  Searching a Polygonal Room with One Door by a 1-Searcher , 2000, Int. J. Comput. Geom. Appl..

[15]  Rajeev Motwani,et al.  Randomized algorithms , 1996, CSUR.

[16]  S. Shankar Sastry,et al.  Probabilistic pursuit-evasion games: theory, implementation, and experimental evaluation , 2002, IEEE Trans. Robotics Autom..

[17]  Sampath Kannan,et al.  Locating and Capturing an Evader in a Polygonal Environment , 2004, WAFR.

[18]  Steven M. LaValle,et al.  Visibility-based pursuit-evasion: the case of curved environments , 2001, IEEE Trans. Robotics Autom..