A Topological Perspective on Cycling Robots for Full Tree Coverage

摘要

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 S_n. 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.