Terminating grid exploration with myopic luminous robots

TL;DR

This paper studies how autonomous luminous robots with limited visibility can explore and terminate on a grid, providing necessary conditions and multiple algorithms under different synchronization and visibility assumptions.

Contribution

It establishes the minimum number of robots needed for exploration with limited visibility and introduces fourteen algorithms for various models and conditions.

Findings

Three robots are necessary for semi-synchronous and asynchronous models with visibility one.

Six algorithms are proven optimal regarding the number of robots.

Multiple algorithms are provided for different synchronization, visibility, and color assumptions.

Abstract

We investigate the terminating grid exploration for autonomous myopic luminous robots. Myopic robots mean that they can observe nodes only within a certain fixed distance, and luminous robots mean that they have light devices that can emit colors. First, we prove that, in the semi-synchronous and asynchronous models, three myopic robots are necessary to achieve the terminating grid exploration if the visible distance is one. Next, we give fourteen algorithms for the terminating grid exploration in various assumptions of synchrony (fully-synchronous, semi-synchronous, and asynchronous models), visible distance, the number of colors, and a chirality. Six of them are optimal in terms of the number of robots.