Circle Formation by Asynchronous Opaque Fat Robots on an Infinite Grid

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.