The problem of adversarial multi-robot patrol has gained interest in recent years, mainly due to its immediate relevance to various security applications. In this problem, robots are required to repeatedly visit a target area in a way that maximizes their chances of detecting an adversary trying to penetrate through the patrol path. When facing a strong adversary that knows the patrol strategy of the robots, if the robots use a deterministic patrol algorithm, then in many cases it is easy for the adversary to penetrate undetected (in fact, in some of those cases the adversary can guarantee penetration). Therefore this paper presents a non-deterministic patrol framework for the robots. Assuming that the strong adversary will take advantage of its knowledge and try to penetrate through the patrol's weakest spot, hence an optimal algorithm is one that maximizes the chances of detection in that point. We therefore present a polynomial-time algorithm for determining an optimal patrol under the Markovian strategy assumption for the robots, such that the probability of detecting the adversary in the patrol's weakest spot is maximized. We build upon this framework and describe an optimal patrol strategy for several robotic models based on their movement abilities (directed or undirected) and sensing abilities (perfect or imperfect), and in different environment models - either patrol around a perimeter (closed polygon) or an open fence (open polyline).

We study the problem of multi-robot perimeter patrol in adversarial environments, under uncertainty of adversarial behavior. The robots patrol around a closed area using a nondeterministic patrol algorithm. The adversary's choice of penetration point depends on the knowledge it obtained on the patrolling algorithm and its weakness points. Previous work investigated full knowledge and zero knowledge adversaries, and the impact of their knowledge on the optimal algorithm for the robots. However, realistically the knowledge obtained by the adversary is neither zero nor full, and therefore it will have uncertainty in its choice of penetration points. This paper considers these cases, and offers several approaches to bounding the level of uncertainty of the adversary, and its influence on the optimal patrol algorithm. We provide theoretical results that justify these approaches, and empirical results that show the performance of the derived algorithms used by simulated robots working against humans playing the role of the adversary is several different settings.