Stochastic and Dynamic Routing Problems for Multiple Uninhabited Aerial Vehicles

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. 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, i.e., 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 (UAVs), 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 dimension-less parameter is identified which completely captures this phase transition and an estimate of the critical value of the parameter is provided. A area of the bounded domain, m 2 a area per vehicle in the unbounded domain, m 2 d ρ nonholonomic vehicle density D ρ (g 1 , g 2) configuration-to-configuration Dubins distance function, m D(t) set of targets outstanding at time t g configuration (position and heading) of vehicle H m (p, Q) multi-median function, m H * m (Q) minimum value of the multi-median function, m I m the set of integers between 1 and m, included L ρ (g, q) configuration-to-position Dubins distance function, m m number of UAVs n steady-state number of outstanding targets N the set of natural numbers p position of the Voronoi generators, m q point in the domain, m Q a bounded planar domain R the set or real numbers R + the set or non-negative real numbers R t (g) the set of positions reachable from configuration g within time t SE(2) Special Euclidean group in two dimensions (i.e., the group of rigid planar motions) t time, s T the steady-state system time, s v vehicle speed, ms −1 W, …