In this paper, we have considered two fully synchronous $\mathcal{OBLOT}$ robots having no agreement on coordinates entering a finite unoriented grid through a door vertex at a corner, one by one. There is a resource that can move around the grid synchronously with the robots until it gets co-located along with at least one robot. Assuming the robots can see and identify the resource, we consider the problem where the robots must meet at the location of this dynamic resource within finite rounds. We name this problem "Rendezvous on a Known Dynamic Point". Here, we have provided an algorithm for the two robots to gather at the location of the dynamic resource. We have also provided a lower bound on time for this problem and showed that with certain assumption on the waiting time of the resource on a single vertex, the algorithm provided is time optimal. We have also shown that it is impossible to solve this problem if the scheduler considered is semi-synchronous.
翻译:在本文中,我们考虑了两个完全同步的 $mathcal{ObLOT} 机器人。 两个机器人在坐标上没有达成协议, 在一个角落通过一个角落的门顶端进入一个限定的无方向网格, 一个接一个。 有一个资源可以在网格上与机器人同步移动, 直到它与至少一个机器人合用同一地点。 假设机器人能看到并识别资源, 我们考虑机器人必须在这个动态资源的位置在有限回合内相会的问题。 我们把这个问题命名为“ 在一个已知的动态点上相会 ” 。 在这里, 我们提供了两个机器人在动态资源的位置上聚集的算法 。 我们还为这个问题提供了更低的时间圈, 并且显示, 在对单一的顶点上的资源等待时间的某些假设下, 所提供的算法是最佳的。 我们还表明, 如果计时器认为是半同步的, 这个问题是不可能解决的 。