Local policies for efficiently patrolling a triangulated region by a robot swarm

We present and analyze methods for patrolling and surveillance in an environment with a distributed swarm of robots with limited capabilities. Our approach is based on a distributed triangulation of the work space, in which a set of p stationary sensors provides coverage control; in addition, there are r mobile robots that can move between the sensors. Building on our prior work on structured exploration of unknown spaces with multi-robot systems, we can make use of a triangulation that is constructed in a distributed fashion and guarantees good local navigation properties, even when sensors and robots have very limited capabilities. One of the key challenges is to develop, analyze, implement and compare local strategies for allowing such a swarm to guard an environment structured in such a manner. As it turns out, this requires not only coming up with strategies that achieve full coverage given sufficient time, but also hinges on a number of crucial aspects that can make a dramatic difference when it comes to achieving good coverage frequency. These aspects have received some theoretical attention, but gaps have remained. We present: 1) A summary of how to achieve coverage by building a triangulation of the workspace, and the ensuing properties. 2) A description of simple local policies (LRV, for Least Recently Visited and LFV, for Least Frequently Visited) for achieving coverage by the patrolling robots. 3) New analytical arguments why different versions of LRV may require worst-case exponential time between visits of triangles. 4) Analytical evidence that a local implementation of LFV on the edges of the dual graph is possible in our scenario, and immensely better in the worst case. 5) Experimental and simulation validation for the practical usefulness of these policies, showing that even a small number of weak robots with weak local information can greatly outperform a single, powerful robots with full information and computational capabilities.