Arbitrary Pattern Formation on a Continuous Circle by Oblivious Robot Swarm
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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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