Uniform k-Circle Formation by Fat Robots.

In this paper, we study the uniform k-circle formation by a swarm of mobile robots with dimensional extent. For some k > 0 , the k-circle formation problem asks the robots to form disjoint circles. Each circle must be centered at one of the pre-fixed points given in the plane. Each circle should contain exactly k distinct robot positions. The k-circle formation problem has already been studied for punctiform robots in the plane. In this paper, the robots are represented by transparent unit disks in the plane. They are autonomous, anonymous, homogeneous, and silent. The robots are oblivious and execute Look-Compute-Move (LCM) cycle under a fair asynchronous scheduler. The direction and orientation of one of the axes are agreed upon by the robots. In this setting, we have characterized all the initial configurations and values of k for which the uniform k-circle formation problem is deterministically unsolvable. For the remaining configurations and values of k , a deterministic distributed algorithm has been proposed that solves the uniform k-circle formation problem within finite time.