Planning for robust visibility-based pursuit-evasion

This paper addresses the problem of planning for visibility-based pursuit evasion, in contexts where the pursuer robot may experience some positioning errors as it moves in search of the evader. Specifically, we consider the case in which a pursuer with an omnidirectional sensor searches a known environment to locate an evader that may move arbitrarily quickly. Known algorithms for this problem are based on decompositions of the environment into regions, followed by a search for a sequence of those regions through which the pursuer should pass. In this paper, we note that these regions can be arbitrarily small, and thus that the movement accuracy required of the pursuer may be arbitrarily high. To resolve this limitation, we introduce the notion of an ε-robust solution strategy, in which ε is an upper bound on the positioning error that the pursuer may experience. We establish sufficient conditions under which a solution strategy is ε-robust, and introduce an algorithm that determines, for a given environment, the largest value of ε for which a solution strategy satisfying those sufficient conditions exists. We de-scribe an implementation and show simulated results demonstrating the effectiveness of the approach.