The gathering over meeting nodes problem requires the robots to gather at one of the pre-defined meeting nodes. This paper investigates the problem with respect to the objective function that minimizes the total number of moves made by all the robots. In other words, the sum of the distances traveled by all the robots is minimized while accomplishing the gathering task. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting nodes. The robots do not agree on a global coordinate system and operate under an asynchronous scheduler. A deterministic distributed algorithm has been proposed to solve the problem for all those solvable configurations, and the initial configurations for which the problem is unsolvable have been characterized. The proposed gathering algorithm is optimal with respect to the total number of moves performed by all the robots in order to finalize the gathering.
翻译：要聚集节点问题, 机器人必须在预设的会议节点之一集合。 本文调查关于尽量减少所有机器人移动总数的目标函数的问题。 换句话说, 完成集合任务时, 所有机器人所走距离的总和被最小化。 机器人部署在匿名的二维无穷网格节点上, 该网点有一组节点标记为会议节点。 机器人不同意全球协调系统, 并在一个不同步的排程器下操作。 已经提议了一种确定性分布算法, 以解决所有这些可溶性配置的问题, 并且确定了问题无法解决的初始配置 。 提议的收集算法与所有机器人完成集合的动作总数相比是最佳的。
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