Gathering on Rings for Myopic Asynchronous Robots with Lights

TL;DR

This paper presents algorithms for autonomous robots on ring networks with limited visibility and lights, proving that gathering is possible under certain initial conditions using a small number of colors.

Contribution

It introduces new gathering algorithms for asynchronous robots with limited visibility and lights, showing feasibility with minimal assumptions and specific initial configurations.

Findings

Gathering feasible when initial parameters are odd with 3 or 4 colors.

Algorithms do not require knowledge of robot count or towerless initial states.

Lights enable gathering despite limited visibility constraints.

Abstract

We investigate gathering algorithms for asynchronous autonomous mobile robots moving in uniform ring-shaped networks. Different from most work using the Look-Compute-Move (LCM) model, we assume that robots have limited visibility and lights. That is, robots can observe nodes only within a certain fixed distance, and emit a color from a set of constant number of colors. We consider gathering algorithms depending on two parameters related to the initial configuration: $M_{init}$, which denotes the number of nodes between two border nodes, and $O_{init}$, which denotes the number of nodes hosting robots between two border nodes. In both cases, a border node is a node hosting one or more robots that cannot see other robots on at least one side. Our main contribution is to prove that, if $M_{init}$ or $O_{init}$ is odd, gathering is always feasible with three or four colors. The proposed algorithms do not require additional assumptions, such as knowledge of the number of robots, multiplicity detection capabilities, or the assumption of towerless initial configurations. These results demonstrate the power of lights to achieve gathering of robots with limited visibility.