2020/10/27 by Serafino Cicerone, Cicerone, Serafino, Alessia Di Fonso +5 · 1 citation
Computer Science · Engineering · #Distributed #FOS: Computer and information sciences #Modular Robots and Swarm Intelligence #Optimization and Search Problems #Parallel #Robotics and Sensor-Based Localization #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2010.14152
openalex publication_date 2020/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 square grid has been considered in the context of the classical Look-Compute-Move model. However, it is natural to consider also the other regular tessellation graphs, that are triangular and hexagonal grids. We provide a resolution algorithm for APF when the initial configuration is asymmetric and the considered topology is any regular tessellation graph.