A topological perspective on cycling robots for full tree coverage

Abstract

We study the topology of the space of coverings for a metric tree with disks embedded in the tree. Focusing on the coverings with excess one disk, we prove that its topological structure is that of a Cayley graph of the permutation group Sn.What follows is a centralized algorithm for stabilizing periodic swarm coverings based upon feedback control with the designed vector field on a maximal subset of the space, removing discontinuity loci.