A Visibility-Based Pursuit-Evasion Problem

This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually "see" an evader that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. This problem was first introduced by Suzuki and Yamashita. Our study of this problem is motivated in part by robotics applications, such as surveillance with a mobile robot equipped with a camera that must find a moving target in a cluttered workspace. A few bounds are introduced, and a complete algorithm is presented for computing a successful motion strategy for a single pursuer. For simply-connected free spaces, it is shown that the minimum number of pursuers required is Θ(lg n). For multiply-connected free spaces, the bound is pursuers for a polygon that has n edges and h holes. A set of problems that are solvable by a single pursuer and require a linear number of recontaminations is shown. The complete algorithm searches a finite graph that is constructed on the basis of critical information changes. It has been implemented and computed examples are shown.

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

[2]  J. Schwartz,et al.  On the Piano Movers' Problem: III. Coordinating the Motion of Several Independent Bodies: The Special Case of Circular Bodies Moving Amidst Polygonal Barriers , 1983 .

[3]  T. D. Parsons,et al.  Pursuit-evasion in a graph , 1978 .

[4]  J. Schwartz,et al.  On the “piano movers'” problem I. The case of a two‐dimensional rigid polygonal body moving amidst polygonal barriers , 1983 .

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

[6]  Masafumi Yamashita,et al.  Searching for Mobile Intruders in a Polygonal Region by a Group of Mobile Searchers , 2001, SCG '97.

[7]  R. Bertram,et al.  Stochastic Systems , 2008, Control Theory for Physicists.

[8]  Bernard Chazelle,et al.  A theorem on polygon cutting with applications , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[9]  Dennis S. Arnon,et al.  Geometric Reasoning with Logic and Algebra , 1988, Artif. Intell..

[10]  J. T. Shwartz,et al.  On the Piano Movers' Problem : III , 1983 .

[11]  Simeon C. Ntafos,et al.  Optimum watchman routes , 1986, SCG '86.

[12]  J. O'Rourke.  Art gallery theorems and algorithms , 1987 .

[13]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[14]  Paul D. Seymour,et al.  Monotonicity in Graph Searching , 1991, J. Algorithms.

[15]  John Canny,et al.  The complexity of robot motion planning , 1988 .

[16]  Jean-Paul Laumond,et al.  Singularities and Topological Aspects in Nonholonomic Motion Planning , 1993 .

[17]  Jake K. Aggarwal,et al.  Mobile robot self-location using model-image feature correspondence , 1996, IEEE Trans. Robotics Autom..

[18]  Fillia Makedon,et al.  On minimizing width in linear layouts , 1989, Discret. Appl. Math..

[19]  Leonidas J. Guibas,et al.  The Robot Localization Problem , 1995, SIAM J. Comput..

[20]  Masafumi Yamashita,et al.  Searching for a mobile intruder in a corridor: the open edge variant of the polygon search problem , 1995, Int. J. Comput. Geom. Appl..

[21]  J. Schwartz,et al.  On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds , 1983 .

[22]  Christos H. Papadimitriou,et al.  The complexity of searching a graph , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[23]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[24]  Andrea S. LaPaugh,et al.  Recontamination does not help to search a graph , 1993, JACM.

[25]  J. Davenport.  A "Piano Movers" Problem. , 1986 .

[26]  R. Tarjan,et al.  A Separator Theorem for Planar Graphs , 1977 .

[27]  Steven M. LaValle,et al.  A game-theoretic framework for robot motion planning , 1996 .

[28]  Jérôme Barraquand,et al.  Motion planning with uncertainty: the information space approach , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[29]  T. Shermer.  Recent Results in Art Galleries , 1992 .

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