Two-Dimensional Pursuit-Evasion in a Compact Domain with Piecewise Analytic Boundary

In a pursuit-evasion game, a team of pursuers attempt to capture an evader. The players alternate turns, move with equal speed, and have full information about the state of the game. We consider the most restictive capture condition: a pursuer must become colocated with the evader to win the game. We prove two general results about pursuit-evasion games in topological spaces. First, we show that one pursuer has a winning strategy in any CAT(0) space under this restrictive capture criterion. This complements a result of Alexander, Bishop and Ghrist, who provide a winning strategy for a game with positive capture radius. Second, we consider the game played in a compact domain in Euclidean two-space with piecewise analytic boundary and arbitrary Euler characteristic. We show that three pursuers always have a winning strategy by extending recent work of Bhadauria, Klein, Isler and Suri from polygonal environments to our more general setting.Comment: 21 pages, 6 figure

Search and Pursuit-Evasion in Mobile Robotics, A survey

This paper surveys recent results in pursuitevasion and autonomous search relevant to applications in mobile robotics. We provide a taxonomy of search problems that highlights the differences resulting from varying assumptions on the searchers, targets, and the environment. We then list a number of fundamental results in the areas of pursuit-evasion and probabilistic search, and we discuss field implementations on mobile robotic systems. In addition, we highlight current open problems in the area and explore avenues for future work