Partial barrier coverage: Using game theory to optimize probability of undetected intrusion in polygonal environments

In this paper, we formalize the problem of partial barrier coverage, that is, the problem of using robot sensors (guards) to minimize the probability of undetected intrusion in a particular region by an intruder. We use ideas from noncooperative game theory together with previous results from complete barrier coverage - the problem of completely preventing undetected intrusion - to develop new methods that solve this problem for the specific case of bounded-range line-of-sight sensors in a two-dimensional polygonally-bounded region. Our solution constructs equilibrium strategies for the intruder and guards, and calculates the level of partial coverage.