Distributed Motion Constraints for Algebraic Connectivity of Robotic Networks

Abstract

This paper studies connectivity maintenance of robotic networks that communicate at discrete times and move in continuous space. We propose a distributed coordination algorithm that allows the robots to decide whether a desired collective motion breaks connectivity. We build on this procedure to design a second coordination algorithm that allows the robots to modify a desired collective motion to guarantee that connectivity is preserved. These algorithms work under imperfect information caused by delays in communication and the robots’ mobility. Under very outdated information, the proposed algorithms might prevent some or all of the robots from moving. We analyze the correctness of our algorithms by formulating them as games against a hypothetical adversary who chooses system states consistent with observed information. The technical approach combines tools from algebraic graph theory, linear algebra, and nonsmooth analysis.