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Leader-follower strategies for robotic patrolling in environments with arbitrary topologies

Game theoretic approaches to patrolling have become a topic of increasing interest in the very last years. They mainly refer to a patrolling mobile robot that preserves an environment from intrusions. These approaches allow for the development of patrolling strategies that consider the possible actions of the intruder in deciding where the robot should move. Usually, it is supposed that the intruder can hide and observe the actions of the patroller before intervening. This leads to the adoption of a leader-follower solution concept. In this paper, mostly theoretical in its nature, we propose an approach to determine optimal leader-follower strategies for a mobile robot patrolling an environment. Differently from previous works in literature, our approach can be applied to environments with arbitrary topologies.