Coverage Control for Wire-Traversing Robots

In this paper we consider the coverage control problem for a team of wire-traversing robots. The two-dimensional motion of robots moving in a planar environment has to be projected to one-dimensional manifolds representing the wires. Starting from Lloyd's descent algorithm for coverage control, a solution that generates continuous motion of the robots on the wires is proposed. This is realized by means of a Continuous Onto Wires (COW) map: the robots' workspace is mapped onto the wires on which the motion of the robots is constrained to be. A final projection step is introduced to ensure that the configuration of the robots on the wires is a local minimizer of the constrained locational cost. An algorithm for the continuous constrained coverage control problem is proposed and it is tested both in simulation and on a team of mobile robots.