Gathering Problems for Autonomous Mobile Robots with Lights

TL;DR

This paper investigates the Gathering problem for autonomous robots with lights, demonstrating algorithms that are optimal in color usage and exploring how light capabilities influence gathering in semi-synchronous settings.

Contribution

It extends the robot light model to facilitate Gathering algorithms and establishes the relationship between light types and assumptions, providing optimal color algorithms.

Findings

Gathering algorithms with three light types are developed.

The algorithms are optimal in the number of colors used.

The relationship between light capabilities and system assumptions is clarified.

Abstract

We study the Gathering problem for n autonomous mobile robots in semi-synchronous settings with persistent memory called light. It is well known that Gathering is impossible in a basic model when robots have no lights, if the system is semi-synchronous or even centralized (only one robot is active in each time). On the other hand, Rendezvous (Gathering when n = 2) is possible if robots have lights of various types with a constant number of colors. In this paper, we extend the model of robots with lights so that Gathering algorithms can be discussed properly. Then we show Gathering algorithms with three types of lights in the semi-synchronous settings and reveal relationship between the power of lights and other additional assumptions. The most algorithms shown here are optimal in the number of colors they use.