Perimeter and road surveillance are tasks that are well suited for a team of UAVs. When little is known about the likelihood of a potential threat to appear in a region of interest, algorithms that treat the arrival rate to be uniform reduce to maximizing coverage. In applications where the expected arrival rate of threats is not uniform in the region of interest, simply maximizing coverage rate does not necessarily correspond to finding threats in minimum expected time. In a perimeter defense scenario, threats may be much more likely to arrive from certain directions than others (e.g. from the coast rather than through the mountains). This paper investigates non-uniform threat arrival rate along a network of roads and proposes a search strategy influenced by the Whittle Index in an attempt to minimize expected threat discovery time. Monte-Carlo results comparing the index heuristic to coverage maximization algorithms show that the index heuristic significantly reduces the expected time to discover threats. In addition, the proposed strategy reduces to coverage maximization when the threat arrival rate is uniform. The proposed index heuristic is augmented to generate waypoint paths and utilized in a high fidelity multiple UAV simulation.
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