Optimal Perimeter Patrol Alert Servicing with Poisson Arrival Rate ∗ P. Chandler, 1Lt. J. Hansen, R. Holsapple † S. Darbha ‡ M. Pachter § This paper addresses a base perimeter patrol scenario where alerts are generated from a set of stations at random intervals. A Unmanned Aerial Vehicle patrols the perimeter and responds to alerts. After arriving at an alert site, the vehicle loiters for a time to enable the operator to determine if the alert is a nuisance trip or an actual threat. The false alarms are modeled as a Poisson process. A stochastic control optimization problem is developed to determine the optimal loiter time. The optimal length of time that a vehicle can dwell at an alert site while minimizing the expected service time is a function of the size of the alert queue and the alert rate. Results from where the algorithm was flight tested as part of a base defense scenario is presented. I. Introduction A. COUNTER Scenario The previous effort in stochastic control optimization was for the COUNTER 1 scenario. COUNTER is an acronym for Cooperative Operations in UrbaN TERrain, which uses a team of UAVs to investigate task assignment and path planning algorithms for use in ISR missions in urban areas. COUNTER uses a team of UAVs—one SAV and four MAVs. The SAV loiters over the urban area while an operator views the streaming video from the SAV for objects of interest. After an operator selects a collection of objects to view more closely, a task assignment algorithm assigns a tour to each MAV that is to be launched. The MAVs, flying at a lower altitude, inspects the objects of interest, which may enable the operator to discern discriminating features. The operator is not asked to give a response whether or not a particular object of interest is a target or a non-target based on inspection of the video. Instead, the operator is asked whether or not he has seen a distinguishing feature. The assumption about this feature is that it uniquely separates targets from non-targets. B. Stochastic Controller A human operator would be overwhelmed if expected to manage multiple MAVs while simultaneously de- tecting object features in multiple video streams. Therefore, a stochastic controller was developed to decide when a revisit for additional information is needed. 2, 3 The key feature of this approach is the inclusion of an operator error model, sometimes called a confusion matrix. Stochastic dynamic programming is used to solve this decision making under uncertainty problem. The MAV views the objects in sequence 4 with a small level of fuel reserve for revisits. Given the operator’s observation of the objects, the controller performs an information gain analysis where it computes an expected reward for performing a revisit using a priori probabilities of target density and operator’s confusion matrix. Essentially, the controller maximizes the expected information gain over the tour with the available reserve. * This is declared work of the U.S. Government and is not subject to copyright protection in the United States † AFRL/RBCA, 2210 8th Street, WPAFB, OH 45433-7531 ‡ Texas A&M University, College Station, TX 77843-3123 § AFIT/ENG, 2950 Hobson Way, Bldg. 640, Wright-Patterson AFB, OH 45433-7765 1 of 7 American Institute of Aeronautics and Astronautics