标题： 没有计算的自组织聚集的不可能性 显示英文标题

标题： Impossibility of Self-Organized Aggregation without Computation

摘要： 在他们开创性的工作中，Gauci 等人（2014）研究了聚合的基本任务，其中多个机器人需要聚集在一起，而无需事先约定的会合地点，使用最少的硬件。那篇论文考虑了无法记忆且无法计算的差速驱动机器人。此外，机器人之间无法相互通信，仅配备了一个简单的传感器，用于判断是否有其他机器人直接位于它们前面。尽管存在这些严重的限制，Gauci 等人引入了一个控制器，并数学上证明了该控制器可以对任何初始状态下的两个机器人系统进行聚合。不幸的是，对于更大的系统，相同的控制器在许多情况下可以经验性地进行聚合，但并非所有情况。因此，是否存在一个可以在任何数量机器人的情况下进行聚合的控制器的问题仍然开放。在本文中，我们通过研究控制器的几何结构来证明不存在这样的控制器。此外，我们否定了上述论文中针对两个机器人的聚合证明，并提出了一种替代控制器以及一个简单且严格的聚合证明。 显示英文摘要

摘要： In their seminal work, Gauci et al. (2014) studied the fundamental task of aggregation, wherein multiple robots need to gather without an a priori agreed-upon meeting location, using minimal hardware. That paper considered differential-drive robots that are memoryless and unable to compute. Moreover, the robots cannot communicate with one another and are only equipped with a simple sensor that determines whether another robot is directly in front of them. Despite those severe limitations, Gauci et al. introduced a controller and proved mathematically that it aggregates a system of two robots for any initial state. Unfortunately, for larger systems, the same controller aggregates empirically in many cases but not all. Thus, the question of whether a controller exists that aggregates for any number of robots remains open. In this paper, we show that no such controller exists by investigating the geometric structure of controllers. In addition, we disprove the aggregation proof of the paper above for two robots and present an alternative controller alongside a simple and rigorous aggregation proof.