Proceedings of the 22nd International Conference on Distributed Computing and Networking 2021 **Abstract:** Given a set R of robots, each one located at different vertices of an infinite regular tessellation graph, we aim to explore the Arbitrary Pattern Formation (APF ) problem. Given a multiset F of grid vertices such that |R| = |F |, APF asks for a distributed algorithm that moves robots so as to reach a configuration similar to F . Similarity means that robots must be disposed as F regardless of translations, rotations, reflections. So far, as possible graph discretizing the Euclidean plane only the standard squ…

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“…Recently, in [9], the authors have provided an algorithm for robots on a triangular grid to form any arbitrary pattern from any asymmetric initial configuration.…”

confidence: 99%

“…Recently, in [9], the authors have provided an algorithm for robots on a triangular grid to form any arbitrary pattern from any asymmetric initial configuration.…”

confidence: 99%

“…In their work, they have assumed that the target configuration can have multiplicities also. So the algorithm provided in [9] can be used for gathering where the target configuration contains only one location for each robot. But in their work, they have assumed the robots have full visibility which is impractical as in application it is impossible for robots to have an infinite vision.…”

confidence: 99%

“…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.…”

confidence: 99%