Uncertainties in adversarial patrol

In this work, we study the problem of multi-robot perimeter patrol in adversarial environments, under uncertainty. In this problem, the robots patrol around a closed area, where their goal is to patrol in a way that maximizes their chances of detecting an adversary trying to penetrate into the area. Uncertainties may rise in different aspects in this domain, and herein our focus is twofold. First, uncertainty in the robots' sensing capabilities, and second uncertainty of the adversary's knowledge of the patrol's weak points. In this work we provide an initial discussion and initial results concerning these two aspects of uncertainty in the multi-robot perimeter patrol problem. Specifically, we first consider the case in which the robots have realistic sensors, and thus they are imperfect. These sensors cannot always detect the adversary even if it close to the robot, and their detection capability changes with their range. We then deal with different possible choices of penetration spots by the adversary, and discuss possible optimal solutions for the patrolling robots in each such case.