Stochastic and Dynamic Routing Problems for Multiple Uninhabited Aerial Vehicles

Abstract

Consider a routing problem for a team of vehicles in the plane: target points appear randomly over time in a bounded environment and must be visited by one of the vehicles. It is desired to minimize the expected system time for the targets, that is, the expected time elapsed between the appearance of a target point and the instant it is visited. In this paper, such a routing problem is considered for a team of uninhabited aerial vehicles, modeled as vehicles moving with constant forward speed along paths of bounded curvature. Three algorithms are presented, each designed for a distinct set of operating conditions. Each is proven to provide a system time within a constant factor of the optimal when operating under the appropriate conditions. It is shown that the optimal routing policy depends on problem parameters such as the workload per vehicle and the vehicle density in the environment. Finally, there is discussion of a phase transition between two of the policies as the problem parameters are varied. In particular, for the case in which targets appear sporadically, a dimensionless parameter is identified which completely captures this phase transition and an estimate of the critical value of the parameter is provided.