  We present and analyze methods for patrolling an environment with a
distributed swarm of robots. Our approach uses a physical data structure - a
distributed triangulation of the workspace. A large number of stationary
"mapping" robots cover and triangulate the environment and a smaller number of
mobile "patrolling" robots move amongst them. The focus of this work is to
develop, analyze, implement and compare local patrolling policies. We desire
strategies that achieve full coverage, but also produce good coverage frequency
and visitation times. Policies that provide theoretical guarantees for these
quantities have received some 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.
