Distributed Voronoi Neighbor Identification From Inter-Robot Distances

Abstract

Algorithms for identifying Voronoi neighbors and constructing Voronoi regions are useful in many distributed robotics applications. Existing methods that perform these tasks using only the distances between robots assign coordinates to each potential neighbor before applying another algorithm to find the Voronoi neighbors. Our method finds the Voronoi neighbors more efficiently; identification occurs directly from inter-robot distances, without first assigning coordinates. We prove the algorithm's correctness, analyze its computational complexity, and demonstrate its effectiveness in the presence of noise via simulation with an experimentally validated sensor model.