The coverage problem for loitering Dubins vehicles

In this paper we study a facility location problem for groups of Dubins vehicles, i.e., nonholonomic vehicles that are constrained to move along planar paths of bounded curvature, without reversing direction. Given a compact region and a group of Dubins vehicles, the coverage problem is to minimize the worst-case traveling time from any vehicle to any point in the region. Since the vehicles cannot hover, we assume that they fly along static closed curves called loitering curves. The paper presents circular loitering patterns for a Dubins vehicle and for a group of Dubins vehicles that minimize the worst-case traveling time in sufficiently large regions. We do this by establishing an analogy to the disk covering problem.