Year: 2023
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Mondal, Brati, Goswami, Pritam, Sharma, Avisek, Sau, Buddhadeb
Institution: Jadavpur University
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4330337445