Arbitrary pattern formation by opaque fat robots on infinite grid

TL;DR

This paper presents a collisionless distributed algorithm for arbitrary pattern formation by opaque fat robots on an infinite grid, addressing a novel scenario with movement restrictions and using a 9-color scheme.

Contribution

It introduces the first solution for $ ext{APF}$ with opaque fat robots on an infinite grid under movement constraints.

Findings

Successfully designed a collisionless distributed algorithm

Achieved arbitrary pattern formation with 9 colors

Addresses a new scenario with opaque fat robots on infinite grid

Abstract

Arbitrary Pattern formation ($\mathcal{APF}$) by a swarm of mobile robots is a widely studied problem in the literature. Many works regarding $\mathcal{APF}$ have been proposed on plane and infinite grid by point robots. But in practical application, it is impossible to design point robots. In \cite{BoseAKS20}, the robots are assumed opaque fat robots but the environment is plane. To the best of our knowledge, no work till now ever considered the $\mathcal{APF}$ problem assuming opaque fat robots on infinite grid where movements are restricted. In this paper, we have provided a collisionless distributed algorithm and solved $\mathcal{APF}$ using 9 colors.