Circle Formation of Weak Robots and Lyndon Words

TL;DR

This paper introduces a novel method using Lyndon words to coordinate anonymous, memoryless robots in forming regular polygons, specifically an n-gon for prime n, with a simple deterministic protocol.

Contribution

It presents the first application of Lyndon words in distributed control of weak robots for geometric formation tasks.

Findings

Protocol successfully forms regular n-gons for prime n

The method is deterministic and efficient

Applicable to anonymous, memoryless robots without communication

Abstract

A Lyndon word is a non-empty word strictly smaller in the lexicographic order than any of its suffixes, except itself and the empty word. In this paper, we show how Lyndon words can be used in the distributed control of a set of n weak mobile robots. By weak, we mean that the robots are anonymous, memoryless, without any common sense of direction, and unable to communicate in an other way than observation. An efficient and simple deterministic protocol to form a regular n-gon is presented and proven for n prime.