Given a set of $n\geq 1$ autonomous, anonymous, indistinguishable, silent, and possibly disoriented mobile unit disk (i.e., fat) robots operating following Look-Compute-Move cycles in the Euclidean plane, we consider the Pattern Formation problem: from arbitrary starting positions, the robots must reposition themselves to form a given target pattern. This problem arises under obstructed visibility, where a robot cannot see another robot if there is a third robot on the straight line segment between the two robots. We assume that a robot's movement cannot be interrupted by an adversary and that robots have a small $O(1)$-sized memory that they can use to store information, but that cannot be communicated to the other robots. To solve this problem, we present an algorithm that works in three steps. First it establishes mutual visibility, then it elects one robot to be the leader, and finally it forms the required pattern. The whole algorithm runs in $O(n) + O(q \log n)$ rounds, where $q>0$ is related to leader election, which takes $O(q \log n)$ rounds with probability at least $1-n^{-q}$. The algorithms are collision-free and do not require the knowledge of the number of robots.

翻译：给定一组$n\geq 1$个在欧几里得平面上遵循“观察-计算-移动”循环运行的自主、匿名、不可区分、沉默且可能迷失方向的移动单位圆盘（即胖）机器人，我们考虑模式形成问题：从任意起始位置出发，机器人必须重新定位自身以形成给定的目标模式。该问题出现在能见度受阻的条件下，即如果两个机器人之间的直线上存在第三个机器人，则该机器人无法看到另一个机器人。我们假设机器人的移动不会被对手中断，并且机器人拥有大小为$O(1)$的小型内存，可用于存储信息，但无法与其他机器人通信。为解决该问题，我们提出了一种分三步运行的算法。首先建立相互可见性，然后选举一个机器人作为领导者，最后形成所需模式。整个算法运行$O(n) + O(q \log n)$轮，其中$q>0$与领导者选举相关，该选举过程以至少$1-n^{-q}$的概率耗时$O(q \log n)$轮。算法无碰撞，且无需知晓机器人数量。