在三角形网格上聚集七个自主移动机器人
Gathering of seven autonomous mobile robots on triangular grids
摘要：
在本文中，我们考虑了七个自主移动机器人在三角形网格上的收集问题。收集问题要求，从任何连接的初始配置开始，其中所有机器人节点（机器人存在的节点）诱导的子图构成一个连接图，机器人达到一个配置，使得两个机器人之间的最大距离最小化。对于七个机器人的情况，当一个机器人有六个相邻的机器人节点（它们形成一个类似六边形的形状）时，就可以实现聚集。在本文中，我们的目的是澄清机器人的能力和三角形网格上收集的可解性之间的关系。特别是，我们专注于机器人的可视范围。为了讨论问题的可解性的可视范围，我们考虑强的假设，除了可视范围。具体地说，我们假设机器人是完全同步的，他们同意的方向和取向的x轴，和手性的三角形网格。在这种情况下，我们首先考虑关于可见性范围的最弱假设，即，机器人的可视范围1.在这种情况下，我们表明，不存在无冲突的算法来解决收集问题。接下来，我们将可见度范围扩展到2。在这种情况下，我们表明，我们的算法可以解决任何连接的初始配置的问题。因此，所提出的算法是最佳的可视范围。
英文摘要：
In this paper, we consider the gathering problem of seven autonomous mobile robots on triangular grids. The gathering problem requires that, starting from any connected initial configuration where a subgraph induced by all robot nodes (nodes where a robot exists) constitutes one connected graph, robots reach a configuration such that the maximum distance between two robots is minimized. For the case of seven robots, gathering is achieved when one robot has six adjacent robot nodes (they form a shape like a hexagon). In this paper, we aim to clarify the relationship between the capability of robots and the solvability of gathering on a triangular grid. In particular, we focus on visibility range of robots. To discuss the solvability of the problem in terms of the visibility range, we consider strong assumptions except for visibility range. Concretely, we assume that robots are fully synchronous and they agree on the direction and orientation of the x-axis, and chirality in the triangular grid. In this setting, we first consider the weakest assumption about visibility range, i.e., robots with visibility range 1. In this case, we show that there exists no collision-free algorithm to solve the gathering problem. Next, we extend the visibility range to 2. In this case, we show that our algorithm can solve the problem from any connected initial configuration. Thus, the proposed algorithm is optimal in terms of visibility range.
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。
