无定向机器人在无限网格中的探索
Infinite Grid Exploration by Disoriented Robots
摘要：
我们处理一组在无限网格上移动的自主机器人。这些机器人是不透明的，具有有限的可见性功能，并使用同步的Look-Compute-Move循环运行。他们都同意一个共同的手性，但没有全球指南针。最后，他们可能会使用不同颜色的灯光，但除此之外，机器人既没有持久的记忆，也没有沟通手段。我们考虑无限网格探索（IGE）问题。对于这个问题，我们给出了两个不可能的结果和三个算法，其中包括一个是最佳的机器人数量。更详细地说，我们首先表明，两个机器人是不够的，在我们的设置来解决这个问题，即使机器人有一个共同的坐标系。然后，我们表明，如果机器人的坐标系不是自洽的，三个或四个机器人是不足以解决这个问题。最后，我们提出了三种算法，解决IGE问题，在各种设置。第一种算法使用六个机器人，颜色不变，可见度范围为1。第二种方法使用最少数量的机器人，即，五个，以及五个可修改的颜色，仍然在可见度之下。最后一个算法需要7个不经意的匿名机器人，但假设可见性为2。注意，最后两个算法也满足实现排他性。
英文摘要：
We deal with a set of autonomous robots moving on an infinite grid. Those robots are opaque, have limited visibility capabilities, and run using synchronous Look-Compute-Move cycles. They all agree on a common chirality, but have no global compass. Finally, they may use lights of different colors, but except from that, robots have neither persistent memories, nor communication mean. We consider the infinite grid exploration (IGE) problem. For this problem we give two impossibility results and three algorithms, including one which is optimal in terms of number of robots. In more detail, we first show that two robots are not sufficient in our settings to solve the problem, even when robots have a common coordinate system. We then show that if the robots' coordinate systems are not self-consistent, three or four robots are not sufficient to solve the problem. Finally, we present three algorithms that solve the IGE problem in various settings. The first algorithm uses six robots with constant colors and a visibility range of one. The second one uses the minimum number of robots, i.e., five, as well as five modifiable colors, still under visibility one. The last algorithm requires seven oblivious anonymous robots, yet assuming visibility two. Notice that the two last algorithms also satisfy achieve exclusiveness.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
