Graph search of a moving ground target by a UAV aided by ground sensors with local information

Abstract

The optimal control of a UAV searching for a target moving, with known constant speed, on a road network and heading toward one of many goal locations is considered. To aid the UAV, some roads in the network are instrumented with unattended ground sensors (UGSs) that detect the target’s motion and record the time it passes by the UGS. When the UAV flies over an UGS location, this time stamped information, if available, is communicated to it. At time 0, the target enters the road network and selects a path leading to one of the exit nodes. The UAV also arrives at the same entry UGS after some delay and is thus informed about the presence of the target in the network. The UAV has no on-board sensing capability and so, capture entails the UAV and target being colocated at an UGS location. If this happens, the UGS is triggered and this information is instantaneously relayed to the UAV, thereby enabling capture. On the other hand, if the target reaches an exit node without being captured, he is deemed to have escaped. We transform the road network, which is restricted to a directed acyclic graph, into a time tree whose node is a tuple comprising the UGS location and evader arrival time at that location. For a given initial delay, we present a recursive forward search method that computes the minimum capture time UAV pursuit policy, under worst-case target action. The recursion scales poorly in the problem parameters, i.e., number of nodes in the time tree and number of evader paths. We present a novel branch and bound technique and a pre-processing step that is experimentally shown to reduce the computational burden by at least two orders of magnitude. We illustrate the applicability of the proposed pruning methods, which result in no loss in optimality, on a realistic example road network.