k-Circle Formation by Oblivious Mobile Robots

A solution to the k-circle formation problem requires the formation of disjoint circles by a swarm of mobile robots. The circles are restricted to be centered at one of the pre-fixed points. Each circle must contain exactly k robots at distinct positions. The robots are oblivious, autonomous, anonymous, homogeneous, and silent. They operate in Look-Compute-Move cycles under a fair asynchronous scheduler. This study addresses the solvability of the k-circle formation in the Euclidean plane. The k-circle formation is studied for point robots under one axis agreement. The relationship between the k-circle formation and the k-EPF (A generalized embedded pattern formation) problem is also studied. The solvability of the k-circle formation is investigated for disoriented point robots. Finally, the problem is considered for fat robots under one axis agreement.