Distributed Localization without Direct Communication Inspired by Statistical Mechanics

TL;DR

This paper introduces a novel distributed localization algorithm inspired by statistical mechanics, enabling robots to determine their positions without direct communication, using only sensor data, and supporting large-scale swarm tasks.

Contribution

The paper presents the VPE localization algorithm, a fully distributed, communication-free method that automatically finds the swarm center and scales to large robot groups.

Findings

Algorithm converges regardless of initial state

Achieves high accuracy and robustness in noisy environments

Successfully supports large-scale shape formation tasks

Abstract

Distributed localization is essential in many robotic collective tasks such as shape formation and self-assembly.Inspired by the statistical mechanics of energy transition, this paper presents a fully distributed localization algorithm named as virtual particle exchange (VPE) localization algorithm, where each robot repetitively exchanges virtual particles (VPs) with neighbors and eventually obtains its relative position from the virtual particle (VP) amount it owns. Using custom-designed hardware and protocol, VPE localization algorithm 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, thereby eliminating the requirement of fixed beacons to embody the origin of coordinates. Theoretical analysis proves that the VPE localization algorithm can always converge to the same result regardless of initial state and has low asymptotic time and memory complexity. Extensive localization simulations with up to 10000 robots and experiments with 52 lowcost robots are carried out, which verify that VPE localization algorithm is scalable, accurate and robust to sensor noises. Based on the VPE localization algorithm, shape formations are further achieved in both simulations and experiments with 52 robots, illustrating that the algorithm can be directly applied to support swarm collaborative tasks.