Convergence Properties of the Gravitational Algorithm in Asynchronous Robot Systems

This paper considers the convergence problem in autonomous mobile robot systems. A natural algorithm for the problem requires the robots to move towards their center of gravity. Previously it was known that the gravitational algorithm converges in the synchronous or semi-synchronous model, and that two robots converge in the asynchronous model. The current paper completes the picture by proving the correctness of the gravitational algorithm in the fully asynchronous model for any number of robots. It also analyses its convergence rate, and establishes its convergence in the presence of crash faults.