Distributed anonymous mobile robots: Formation of geometric patterns

Consider a system of multiple mobile robots in which each robot, at infinitely many unpredictable time instants, observes the positions of all the robots and moves to a new position determined by the given algorithm. The robots are anonymous in the sense that they all execute the same algorithm and they cannot be distinguished by their appearances. Initially they do not have a common x-y coordinate system. Such a system can be viewed as a distributed system of anonymous mobile processes in which the processes (i.e., robots) can "communicate" with each other only by means of their moves. In this paper we investigate a number of formation problems of geometric patterns in the plane by the robots. Specifically, we present algorithms for converging the robots to a single point and moving the robots to a single point in finite steps. We also characterize the class of geometric patterns that the robots can form in terms of their initial configuration. Some impossibility results are also presented.