The Arbitrary Pattern Formation problem asks for a distributed algorithm that moves a set of autonomous mobile robots to form any arbitrary pattern given as input. The robots are assumed to be autonomous, anonymous and identical. They operate in Look-Compute-Move cycles under an asynchronous scheduler. The robots do not have access to any global coordinate system. The movement of the robots is assumed to be rigid, which means that each robot is able to reach its desired destination without interruption. The existing literature that investigates this problem, considers robots with unobstructed visibility. This work considers the problem in the more realistic obstructed visibility model, where the view of a robot can be obstructed by the presence of other robots. The robots are assumed to be punctiform and equipped with visible lights that can assume a constant number of predefined colors. We have studied the problem in two settings based on the level of consistency among the local coordinate systems of the robots: two axis agreement (they agree on the direction and orientation of both coordinate axes) and one axis agreement (they agree on the direction and orientation of only one coordinate axis). In both settings, we have provided a full characterization of initial configurations from where any arbitrary pattern can be formed.

在任意图案形成问题要求一个分布式算法，移动一组自主移动机器人，以形成给定为输入的任何任意的图案。假定这些机器人是自治的，匿名的和相同的。它们在异步调度程序下以Look-Compute-Move周期运行。机器人无法访问任何全局坐标系。假定机器人的运动是刚性的，这意味着每个机器人都可以不中断地到达其期望的目的地。研究此问题的现有文献都认为能见度不受阻碍的机器人。这项工作考虑了更现实的可见性问题模型，其中其他机器人的存在可能会阻碍机器人的视线。假定机器人是点状的，并配备了可见光，它们可以呈现恒定数量的预定义颜色。我们已根据机器人局部坐标系之间的一致性级别在两种设置下研究了该问题：两轴一致（他们同意两个坐标轴的方向和方向）和一个轴一致（他们同意方向和取向）仅一个坐标轴的方向）。在这两种设置中，我们都提供了初始配置的完整特征，可以从中形成任意图案。