Performance Guarantee of a Sub-Optimal Policy for a Robotic Surveillance Application

Abstract

This paper focuses on the development and analysis of sub-optimal decision algorithms for a collection of robots that assist a remotely located operator in perimeter surveillance. The operator is tasked with the classification of an incursion across the perimeter. Whenever there is an incursion into the perimeter, an Unattended Ground Sensor (UGS) in the vicinity, raises an alert. A robot services the alert by visiting the alert location, collecting evidence in the form of video and other imagery, and transmitting them to the operator. The accuracy of operator's classification depends on the volume and freshness of information gathered by the robots. There are two competing needs for a robot: it needs to spend adequate time at an alert location to collect evidence for aiding the operator but it also needs to service the alert as soon as possible, so that the evidence collected is relevant. The control problem is to determine the optimal amount of time a robot must spend servicing an alert. The incursions are stochastic and their statistics are assumed to be known. This problem is posed as a Markov Decision Problem. However, even for two robots and five UGS locations, the number of states is of the order of millions. Approximate Dynamic Programming (ADP) via Linear Programming (LP) provides a way to approximate the value function and provide bounds on its sub-optimality. The novel feature of this paper is to present a lower bound via LP based techniques and state partitioning and construct a sub-optimal policy whose performance betters the lower bound. An illustrative perimeter surveillance example corroborates the results presented in this paper.