Chase Your Farthest Neighbour: A simple gathering algorithm for anonymous, oblivious and non-communicating agents

We consider a group of mobile robotic agents, identical and indistinguishable, having no memory (oblivious) and no common frame of reference (neither absolute location nor a common orientation). Furthermore, these agents are assumed to posses only rudimentary sensing and computational capabilities (limited visibility and basic geometric sorting). We prove that, such robots, implementing a ”Chase the farthest neighbour” policy, preform the task of gathering to a point within a finite time or a finite expected number of time steps. In continuous time, preforming such a gathering task is rather straightforward, while in the discrete time, we prove that a randomized semisynchronised timing model leads to gathering within a finite expected number of time-steps.