Uniform k-circle formation by asynchronous fat robots

Article Type

Research Article

Publication Title

Computer Journal

Abstract

The k-circle formation problem requires a swarm of robots to divide themselves into groups of equal sizes and to form disjoint circles by each group. Each circle must be centered at one of the pre-fixed points given in the plane and should contain exactly k distinct robot positions. The k-circle formation problem has already been studied for dimensionless robots represented by points in the plane. In all the reported results, the circles need not be uniform. In this paper, we investigate the uniform k-circle formation problem for a swarm of robots with dimensional extent in the plane. The robots are represented by transparent unit disks. The robots are autonomous, anonymous, homogeneous, and silent. They are oblivious and they execute Look-Compute-Move cycle under a fair asynchronous scheduler. The robots are assumed to have an agreement on the direction and orientation of one of the axes. First, all the initial configurations and values of k for which the uniform k-circle formation problem is deterministically unsolvable have been characterized. Next, a deterministic distributed algorithm has been proposed that solves the uniform k-circle formation problem for the remaining configurations and values of k. Also, we have characterized all the deterministically solvable initial configurations when n ≠ km.

First Page

1641

Last Page

1656

DOI

10.1093/comjnl/bxaf064

Publication Date

11-1-2025

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