Stochastic Multi-Robot Patrolling with Limited Visibility

Patrolling an environment with multiple robots is a problem with applicability to both military activities and other areas requiring security. In an adversarial environment, wireless communication between the robots may be jammed, and their sensor ranges may be limited to visibility. This increases the difficulty of the problem, but solutions will be widely applicable regardless of the environment. Robot paths that are deterministic can be observed and predicted by an adversary, permitting exploitation of known gaps in coverage. We also wish to avoid requirements for synchronization or a particular form of the environment. We, therefore, propose a method of finding patrolling policies for multiple robots that monitor any polygonal environment using limited visibility regions and non-deterministic patrolling paths. First, visibility regions are calculated for a subset of locations that cover the whole environment or a part of the environment. Then, we find distributed patrolling policies in the form of Markov chains, using convex optimization to minimize the average expected commute time for the subset of the locations permitting each robot to cover the whole environment independently. We also find centralized and Markov chain based patrolling policies that minimize the average expected commute time for the subset of locations permitting each robot to cover a part of the environment while communicating with a central base station. Finally, we evaluate the vulnerability of our patrolling policies by finding the probability of capturing an adversary and the maximum unguarded time for a location in our proposed patrolling scenarios. We present multiple simulation results and a physical implementation to show the effectiveness of our visibility-based non-deterministic patrolling method.