Distributed minimum time servicing for a team of Dubins vehicles

In this paper we study the following problem for a team of Dubins vehicles, i.e. nonholonomic vehicles moving at constant longitudinal speed along planar paths with bounded curvature. Given the initial configurations of the vehicles, find the point in the plane that minimizes the time to be reached by all vehicles. We call it minimum-time servicing problem. We show that this problem can be approximated by an abstract linear program, namely a generalized version of linear programming, that can be solved in a distributed way over a network. We provide a control and communication law for a wireless network of Dubins vehicles to compute and reach the minimum-time servicing point while maintaining the network connected.