Arbitrary pattern formation by opaque fat robots on infinite grid

Kundu, Manash Kumar; Goswami, Pritam; Ghosh, Satakshi; Sau, Buddhadeb

doi:10.1080/17445760.2022.2088750

Cited by 8 publications

(1 citation statement)

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“…APF problem aims to design an algorithm such that robots move to a particular position and form a specific but arbitrary pattern which is already given to every robot as input. There is a vast literature of APF in both discrete and continuous domains ( [18,19,14,11,4,5,7,2,3,1,8,16,6]). Most of the works of APF in continuous domain considered on the Euclidean plane.…”

Section: Introductionmentioning

confidence: 99%

Arbitrary Pattern Formation on a Continuous Circle by Oblivious Robot Swarm

Mondal¹,

Goswami²,

Sharma³

et al. 2023

Preprint

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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 APF problem is discussed on continuous circle by a swarm of homogeneous, anonymous, oblivious, silent mobile robots with no chirality. The algorithm discussed here, can solve APF problem deterministically within O(n) epochs without collision under Semi Synchronous scheduler with n (where n is odd) mobile robots if the initial configuration is rotationally asymmetric. For any even number of robots (grater than three) the algorithm can be modified to a probabilistic one to solve APF. Also if the initial configuration is rotationally symmetric then APF problem can't be solved by any deterministic algorithm.

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