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Distributed Localization without Direct Communication Inspired by Statistical Mechanics

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Document pages: 17 pages

Abstract: Distributed localization is essential in many robotic collective tasks suchas shape formation and self-assembly.Inspired by the statistical mechanics ofenergy transition, this paper presents a fully distributed localizationalgorithm named as virtual particle exchange (VPE) localization algorithm,where each robot repetitively exchanges virtual particles (VPs) with neighborsand eventually obtains its relative position from the virtual particle (VP)amount it owns. Using custom-designed hardware and protocol, VPE localizationalgorithm allows robots to achieve localization using sensor readings only,avoiding direct communication with neighbors and keeping anonymity. Moreover,VPE localization algorithm determines the swarm center automatically, therebyeliminating the requirement of fixed beacons to embody the origin ofcoordinates. Theoretical analysis proves that the VPE localization algorithmcan always converge to the same result regardless of initial state and has lowasymptotic time and memory complexity. Extensive localization simulations withup to 10000 robots and experiments with 52 lowcost robots are carried out,which verify that VPE localization algorithm is scalable, accurate and robustto sensor noises. Based on the VPE localization algorithm, shape formations arefurther achieved in both simulations and experiments with 52 robots,illustrating that the algorithm can be directly applied to support swarmcollaborative tasks.

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