Persistent Patrol in Stochastic Environments with Limited Sensors

In this paper, we propose and analyze policies for what we call the Persistent Patrol and Detection Problem (PPDP), in which an unmanned aerial vehicle (UAV) with limited sensing capability patrols a planar region, in order to detect stochastic spatially localized incidents. Incidents occur according to a renewal process with known time intensity and spatial distribution. The goal is 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 sensor footprint is negligible with respect to the patrol region. Second, we present three online policies: i) an asymptotically optimal policy called Biased Tile Sweep, ii) a policy whose performance is provably within a constant factor of the optimal called TSP Sampling, and iii) TSP Sampling with Receding Horizon. Third, we present a Markov Decision Process approach to the PPDP that attempts to solve for optimal policies offline. Finally, we use numerical experiments to compare performance of the four approaches and suggest suitable operational scenarios for each one.