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.

翻译：由一群移动机器人任意形成模式 ($\ mathcal{ APF}$) 是文献中广泛研究的一个问题。 许多关于$\ mathcal{ APF}$的作品都是由点机器人在平面上和无限网格上提出的。 但在实际应用中,无法设计点机器人。 在\ cite{BoseAKS20}中, 机器人被假定为不透明的脂肪机器人, 但环境却是平面的。 据我们所知, 迄今从未有工作考虑过 $\ mathcal{ APF}$的问题, 假设在限制运动的无限网格上使用不透明的脂肪机器人。 在本文中, 我们提供了无碰撞分布算法, 用9个颜色解决了$\ mathcal{APF} 。