Stochastic Strategies for Autonomous Robotic Surveillance

Abstract

In this paper, we consider a team of autonomous mobile robotic agents engaged in a surveillance mission. It is desirable not to have the agents move in a predictable fashion so no intruder or invader can plan their movements to avoid the surveillance agents. This paper investigates the use of stochastic rules to guide the motions of the agents throughout their surveillance missions. The research emphasizes methods which minimize centralized computation and communication requirements by focusing on local rules for each agent. We define a formal mathematical approach to analyzing the surveillance problem. We take a general environment and impose some mathematical structure on it. We then define a measure of non-uniformity by which we can compare the surveillance coverage of different systems as well as employ a technique to measure the parametric randomness of each strategy. Drawing on the existing literature on stochastic techniques for searching a graph by a single agent, we study the problem of finding optimal rules for searching a graph using a team of agents. In certain cases, search strategies may be evaluated in terms of explicit closed-form expressions for steady-state distributions. In general, however, strategies must be evaluated by Monte-Carlo methods. We present a decomposition technique by means of which any of the graphs types under discussion may be uniquely decomposed into a collection of complete subgraphs. We developed a surveillance strategy for handling general graphs through a hybrid solution to our less complex decompositions.