In this paper we investigate the computational power of a set of mobile robots with limited visibility. At each iteration, a robot takes a snapshot of its surroundings, uses the snapshot to compute a destination point, and it moves toward its destination. Robots are punctiform and memoryless, they operate in \(\mathbb {R}^m\), they have local reference systems independent of each other, and are activated asynchronously by an adversarial scheduler. Moreover, robots are non-rigid, in that they may be stopped by the scheduler at each move before reaching their destination (but are guaranteed to travel at least a fixed unknown distance before being stopped). We show that despite these strong limitations, it is possible to arrange \(3m+3k\) of these weak entities in \(\mathbb {R}^m\) to simulate the behavior of a stronger robot that is rigid (i.e., it always reaches its destination) and is endowed with k registers of persistent memory, each of which can store a real number. We call this arrangement a TuringMobile. In its simplest form, a TuringMobile consisting of only three robots can travel in the plane and store and update a single real number. We also prove that this task is impossible with fewer than three robots. Among the applications of the TuringMobile, we focused on Near-Gathering (all robots have to gather in a small-enough disk) and Pattern Formation (of which Gathering is a special case) with limited visibility. Interestingly, our investigation implies that both problems are solvable in Euclidean spaces of any dimension, even if the visibility graph of the robots is initially disconnected, provided that a small amount of these robots are arranged to form a TuringMobile. In the special case of the plane, a basic TuringMobile of only three robots is sufficient.

在本文中，我们研究了一组能见度有限的移动机器人的计算能力。在每次迭代中，机器人对其周围环境进行快照，使用快照来计算目的地点，然后向目的地移动。机器人是点状和无记忆的，它们在\(\mathbb {R}^m\) 中运行，它们具有彼此独立的本地参考系统，并由对抗性调度程序异步激活。此外，机器人是非刚性的，因为它们在到达目的地之前可能会在每次移动时被调度程序停止（但保证在停止之前至少行进一段固定的未知距离）。我们表明，尽管有这些强大的限制，但可以将这些弱实​​体的\(3m+3k\)排列在\(\mathbb {R}^m\)来模拟一个更强大的机器人的行为，该机器人是刚性的（即它总是到达目的地）并被赋予k个持久内存寄存器，每个寄存器可以存储一个实数。我们称这种安排为图灵移动. 以最简单的形式，仅由三个机器人组成的 TuringMobile 可以在飞机上行驶并存储和更新单个实数。我们还证明了用少于三个机器人完成这项任务是不可能的。在图灵移动的应用中，我们专注于能见度有限的Near-Gathering（所有机器人必须聚集在一个足够小的磁盘中）和Pattern Formation（其中Gathering是一个特例）。有趣的是，我们的研究表明这两个问题在任何维度的欧几里得空间中都是可以解决的，即使机器人的可见性图最初是断开的，只要将这些机器人中的少量排列成一个图灵移动。在飞机的特殊情况下，只有三个机器人的基本 TuringMobile 就足够了。