Multi-robot perimeter patrol in adversarial settings

This paper considers the problem of multi-robot patrol around a closed area with the existence of an adversary attempting to penetrate into the area. In case the adversary knows the patrol scheme of the robots and the robots use a deterministic patrol algorithm, then in many cases it is possible to penetrate with probability 1. Therefore this paper considers a non-deterministic patrol scheme for the robots, such that their movement is characterized by a probability p. This patrol scheme allows reducing the probability of penetration, even under an assumption of a strong opponent that knows the patrol scheme. We offer an optimal polynomial-time algorithm for finding the probability p such that the minimal probability of penetration detection throughout the perimeter is maximized. We describe three robotic motion models, defined by the movement characteristics of the robots. The algorithm described herein is suitable for all three models.