Complete Visibility Algorithm for Autonomous Mobile Luminous Robots under an Asynchronous Scheduler on Grid Plane

TL;DR

This paper presents an algorithm enabling autonomous luminous robots on a grid to achieve complete visibility asynchronously using only two colors, advancing understanding of robot coordination under limited capabilities.

Contribution

It introduces a novel algorithm for luminous robots to attain complete visibility on a grid despite asynchrony and limited light colors, with no prior knowledge of robot count.

Findings

Achieves complete visibility with only two colors.

Operates effectively under asynchronous conditions.

Does not require knowledge of total robot number.

Abstract

An autonomous mobile robot system is a distributed system consisting of mobile computational entities (called robots) that autonomously and repeatedly perform three operations: Look, Compute, and Move. Various problems related to autonomous mobile robots, such as gathering, pattern formation, or flocking, have been extensively studied to understand the relationship between each robot's capabilities and the solvability of these problems. In this study, we focus on the complete visibility problem, which involves relocating all the robots on an infinite grid plane such that each robot is visible to every other robot. We assume that each robot is a luminous robot (i.e., has a light with a constant number of colors) and opaque (not transparent). In this paper, we propose an algorithm to achieve complete visibility when a set of robots is given. The algorithm ensures that complete visibility is achieved even when robots operate asynchronously and have no knowledge of the total number of robots on the grid plane using only two colors.