Visibility-based persistent monitoring with robot teams

We study the problem of planning paths for a team of robots motivated by coverage, persistent monitoring and surveillance applications. The input is a set of target points in a polygonal environment that must be monitored using robots with omni-directional cameras. The goal is to compute paths for all robots such that every target is visible from at least one path. The cost of a path is given by the weighted combination of the length of the path (travel time) and the number of viewpoints along the path (measurement time). The overall cost is given by the maximum cost over all robot paths and the objective is to minimize the maximum cost. In its general form, this problem is NP-hard. In this paper, we present an optimal algorithm and a constant factor approximation for two special versions of the problem. In both cases, the paths are restricted to lie on a pre-defined curve in the polygon. We show that if the curve satisfies a special property, termed chain-visibility, then there exists an optimal algorithm for monitoring a given set of target locations. Furthermore, if we restrict the input polygon to the class of street polygons, then we present a constant-factor approximation which is applicable even if the set of target locations is the entire polygon. In addition to theoretical proofs, we also present results from simulation studies.