Circle Formation by Asynchronous Opaque Fat Robots on an Infinite Grid

TL;DR

This paper presents an algorithm for a swarm of fat robots to form a circle on an infinite grid, addressing practical considerations of robot size and asynchronous operation, using limited colors and one-axis agreement.

Contribution

It introduces the first solution for circle formation by fat robots on an infinite grid under asynchronous conditions with minimal color and orientation assumptions.

Findings

Successfully achieves circle formation with five colors.

Operates under asynchronous scheduler with one-axis agreement.

Extends prior point robot models to fat robots on grids.

Abstract

This study addresses the problem of "Circle Formation on an Infinite Grid by Fat Robots" ($CF\_FAT\_GRID$). Unlike prior work focused solely on point robots in discrete domain, it introduces fat robots to circle formation on an infinite grid, aligning with practicality as even small robots inherently possess dimensions. The algorithm, named $CIRCLE\_FG$, resolves the $CF\_FAT\_GRID$ problem using a swarm of fat luminous robots. Operating under an asynchronous scheduler, it achieves this with five distinct colors and by leveraging one-axis agreement among the robots.