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’ ($\mathrm{CF}\mathrm{\_FAT}\mathrm{\_GRID}$). 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 $\mathrm{CIRCLE}\mathrm{\_FG}$, resolves the $\mathrm{CF}\mathrm{\_FAT}\mathrm{\_GRID}$ 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.

GRAPHICAL ABSTRACT

Keywords:

• Swarm robot algorithm
• circle formation
• asynchronous
• infinite grid
• luminous robots
• LCM cycle

Disclosure statement

The authors report there are no competing interests to declare.

Additional information

Funding

The First author is supported by UGC [1132/(CSIR-UGC NET JUNE 2017)], the Government of India and the third author is supported by the West Bengal State government Fellowship Scheme e [P-1/RS/23/2020]. Fourth author is supported by SERB.