Distributed motion constraints for algebraic connectivity of robotic networks

This paper studies connectivity maintenance of robotic networks that communicate at discrete times and move in continuous space. We propose a distributed algorithm that allows the robots to decide whether a desired collective motion breaks connectivity. Our algorithm works under imperfect information caused by delays in communication and the robots¿ mobility. We analyze the correctness of our algorithm by formulating it as a game against a hypothetical adversary who chooses system states consistent with observed information. The technical approach combines tools from algebraic graph theory, linear algebra, nonsmooth analysis, and systems and control.