K-Circle formation by disoriented asynchronous robots

Abstract

For some k>0, the k-circle formation problem asks a swarm of autonomous mobile robots to form disjoint circles. Each such circle is restricted to be centered at one of the pre-fixed points given in the plane. Each circle must contain exactly k robots at distinct positions. The k-circle formation problem has already been studied under one axis agreement. In this work, the robots are assumed to be completely disoriented, i.e., they neither have any agreement on a global coordinate system nor have any agreement on a common chirality. The robots are identical, anonymous, oblivious, and homogeneous. They operate in Look-Compute-Move cycles under a fair asynchronous scheduler. In this setting, all the initial configurations and values of k for which the k-circle formation problem is deterministically unsolvable have been characterized. A deterministic distributed algorithm has been proposed that deterministically solves the k-circle formation problem for the remaining configurations and values of k.