In the field of distributed system, Arbitrary Pattern Formation (APF) problem is an extensively studied problem. The purpose of APF is to design an algorithm to move a swarm of robots to a particular position on an environment (discrete or continuous) such that the swarm can form a specific but arbitrary pattern given previously to every robot as an input. In this paper the solvability of the APF problem on a continuous circle has been discussed for a swarm of oblivious and silent robots without chirality under a semi synchronous scheduler. Firstly a class of configurations called \textit{Formable Configuration}(FC) has been provided which is necessary to solve the APF problem on a continuous circle. Then considering the initial configuration to be an FC, an deterministic and distributed algorithm has been provided that solves the APF problem for n robots on a continuous circle of fixed radius within O(n) epochs without collision.
@article{arxiv.2303.10366,
title = {Arbitrary Pattern Formation on a Continuous Circle by Oblivious Robot Swarm},
author = {Brati Mondal and Pritam Goswami and Avisek Sharma and Buddhadeb Sau},
journal= {arXiv preprint arXiv:2303.10366},
year = {2023}
}