Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Introduction to the Theory of Computation
Introduction to the Theory of Computation
Automatically Generating Virtual Guided Tours
CA '99 Proceedings of the Computer Animation
Tunably decentralized algorithms for cooperative target observation
Proceedings of the fourth international joint conference on Autonomous agents and multiagent systems
Surveillance Strategies for a Pursuer with Finite Sensor Range
International Journal of Robotics Research
Cooperative Observation of Multiple Moving Targets: an algorithm and its formalization
International Journal of Robotics Research
Dealing with geometric constraints in game-theoretic planning
IJCAI'99 Proceedings of the 16th international joint conference on Artificial intelligence - Volume 2
Game-theoretic analysis of a visibility based pursuit-evasion game in the presence of obstacles
ACC'09 Proceedings of the 2009 conference on American Control Conference
Robotic Routers: Algorithms and Implementation
International Journal of Robotics Research
International Journal of Robotics Research
Motion planning for multitarget surveillance with mobile sensor agents
IEEE Transactions on Robotics
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In this paper, we address the problem of surveillance in an environment with obstacles. We consider the problem in which a mobile observer attempts to maintain visual contact with a target as it moves through an environment containing obstacles. This surveillance problem is a variation of traditional pursuit-evasion games, with the additional condition that the pursuer immediately loses the game if at any time it loses sight of the evader. We analyze this tracking problem as a game of kind. We use the method of explicit policy to compute guaranteed strategies for surveillance for the observer in an environment containing a single corner. These strategies depend on the initial positions of the observer and the target in the workspace. Based on these strategies a partition of the visibility polygon of the players is constructed. The partitions have been constructed for varying speeds of the observer and the target. Using these partitions we provide a sufficient condition for escape of a target in a general environment containing polygonal obstacles. Moreover, for a given initial target position, we provide a polynomial-time algorithm that constructs a convex polygonal region that provides an upper-bound for the set of initial observer positions from which it does not lose the game. We extend our results to the case of arbitrary convex obstacles with differentiable boundaries. We also present a sufficient condition for tracking and provide a lower-bound on the region around the initial position of the target from which the observer can track the target. Finally, we provide an upper bound on the area of the region in which the outcome of the game is unknown.