Asynchronous Gathering Algorithms for Autonomous Mobile Robots with Lights

TL;DR

This paper improves asynchronous gathering algorithms for autonomous robots with lights by reducing the required number of colors from 10 to 3, enabling more efficient coordination in asynchronous environments.

Contribution

It introduces a new algorithm that achieves gathering with only 3 colors of lights in asynchronous settings, and provides a simulation method for SSYNC algorithms with 3k colors.

Findings

Gathering achievable with 3 colors in ASYNC.

Simulation of SSYNC algorithms with 3k colors in ASYNC.

Reduction of color complexity from previous 10 to 3.

Abstract

We consider a Gathering problem for n autonomous mobile robots with persistent memory called light in an asynchronous scheduler (ASYNC). It is well known that Gathering is impossible when robots have no lights in basic common models, if the system is semi-synchronous (SSYNC) or even centralized (only one robot is active in each time). It is known that Gathering can be solved by robots with 10 colors of lights in ASYNC. This result is obtained by combining the following results. (1) The simulation of SSYNC robots with k colors by ASYNC robots with 5k colors, and (2) Gathering is solved by SSYNC robots with 2 colors. In this paper, we improve the result by reducing the number of colors and show that Gathering can be solved by ASYNC robots with 3 colors of lights. We also show that we can construct a simulation algorithm of any unfair SSYNC algorithm using k colors by ASYNC robots with 3k colors, where unfairness does not guarantee that every robot is activated infinitely often. Combining this simulation and the Gathering algorithm by SSYNC robots with 2 colors, we obtain a Gathering algorithm by ASYNC robots with 6 colors. Our main result can be obtained by reducing the number of colors from 6 to 3.