Persistent patrol with limited-range on-board sensors

We propose and analyze the Persistent Patrol Problem (PPP). An unmanned aerial vehicle (UAV) moving with constant speed and unbounded acceleration patrols a bounded region of the plane where localized incidents occur according to a renewal process with known time intensity and spatial distribution. The UAV can detect incidents using on-board sensors with a limited visibility radius. We want to minimize the expected waiting time between the occurrence of an incident, and the time that it is detected. First, we provide a lower bound on the achievable expected detection time of any patrol policy in the limit as the visibility radius goes to zero. Second, we present the Biased Tile Sweep policy whose upper bound shows i) the lower bound's tightness, ii) the policy's asymptotic optimality, and iii) that the desired spatial distribution of the searching vehicle's position is proportional to the square root of the underlying spatial distribution of incidents it must find. Third, we present two online policies: i) a policy whose performance is provably within a constant factor of the optimal called TSP Sampling, ii) and the TSP Sampling with Receding Horizon heuristically yielding better performance than the former in practice. Fourth, we present a decision-theoretic approach to the PPP that attempts to solve for optimal policies offline. In addition, we use numerical experiments to compare performance of the four approaches and suggest suitable operational scenarios for each one.