Surveillance strategies for a pursuer with finite sensor range

This paper addresses the pursuit-evasion problem of maintaining surveillance by a pursuer of an evader in a world populated by polygonal obstacles. This requires the pursuer to plan colision-free motions that honor distance constraints imposed by sensor capabilities, while avoiding occlusion of the evader by any obstacle. The paper extends the three-dimensional cellular decomposition of Schwartz and Sharir to represent the four-dimensional configuration space of the pursuer-evader system, and derive necessary conditions for surveillance (equivalently, sufficient conditions for escape) in terms of this new representation A game theoretic formulation of the problem is then given, and this formulation is used to characterize optimal escape trajectories for the evader. A shooting algorithm is proposed that finds these trajectories using the minimun principle. Finally, noting the similarities between this surveillance problem and the problem of cooperative manipulation by two robots, several cooperation strategies are presented that maximize system performance for cooperative motions.