Geodesic topological voronoi tessellations in triangulated environments with multi-robot systems

Positioning a group of robots at the center of their geodesic Voronoi cells minimizes the worst-case response time for any robot to arrive at an exogenous event in the workspace. We construct these cells in a distributed fashion, building on our prior work on triangulating unknown spaces with multi-robot systems. This produces a physical data structure - a set of triangles formed by the positions of the robots that can be used to perform coverage control. This paper presents: 1) A discrete approximation of the geodesic Voronoi cell using the multi-robot triangulation. We call this a topological Voronoi cell, and show that it can be computed efficiently in a distributed fashion and with theoretical guarantees compared to continuous version. 2) A local motion controller to guide navigating robots to the centroid of their topological Voronoi cell. This controller uses bounded communications with a fixed constant, but can produce local extrema that trap navigating robots away from the optimal position. 3) An enhanced local controller using navigation agents to help guide the navigating robot to the optimal position in its Voronoi cell. It also uses bounded communications, but with a constant that can be tuned to trade communications bandwidth for increased accuracy. 4) Hardware experiments that compute the topological Voronoi cell on a group of 14 robots, simulation results that demonstrate local extrema, and the effectiveness of the virtual navigation agents, and simulation results comparing the performance of the patrolling algorithm using and not using topological Voronoi cells.