Convergence of a Self-Stabilizing Circle Formation Algorithm for Cooperative Mobile Robots

We address the problem of controlling a team of robots to form a uniform circle. More specifically, we study the convergence of a distributed circle formation algorithm using computer simulation. The algorithm operates under the hypothesis that robots (1) are oblivious in the sense that they are unable to recall past actions and observations, (2) share no common sense of direction, and (3) have no direct communication. The algorithm solves the problem of circle formation in two steps, each of which is solved by a different algorithm. The first algorithm takes a configuration wherein the robots are spread arbitrarily on the plane, deterministically arranges them to form a non degenerate circle. The second algorithm, takes a configuration where the robots are already located on the boundary, eventually converges toward a situation wherein all robots are uniformly distributed on the circumference of the circle. The algorithm is self-stabilizing since starting from any arbitrary state always converges towards the formation of a circle.