Abstract This paper investigates an optimal fuel station (FS) arrangement problem for multiple geosynchronous (GEO) spacecrafts with many-to-many (M2M) refueling, subject to the capacity of the servicing spacecraft (SSC) and the different fuel requirements of the targets. Several FSs with their reusable SSC are arranged on GEO, while the SSC commutes between fuel-deficient targets and FSs to refuel the multiple targets. To avoid building a fuel station at the exact position of the target in traditional M2M refueling, the problem is formulated as a location–allocation problem. Based on that, a novel modified K-means clustering is proposed, in which the difficulty caused by the limitation of the SSC’s capacity is solved. With the proposed method, the FS is allowed to be arranged in the exact region without inaccessible targets, where the minimum number of the required FS and the minimized fuel cost are determined in turn. Finally, numerical simulations validate the performance of the proposed method.

中文翻译：

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多地球同步轨道航天器加油任务的最佳加油站布置

摘要 本文研究了多对多 (M2M) 加油多地球同步 (GEO) 航天器的最佳燃料站 (FS) 布置问题，受服务航天器 (SSC) 的容量和目标不同燃料需求的影响。 . GEO 上布置了几个带有可重复使用的 SSC 的 FS，而 SSC 在燃料不足的目标和 FS 之间来回为多个目标加油。为了避免在传统 M2M 加油中在目标的确切位置建立加油站，该问题被表述为位置分配问题。在此基础上，提出了一种新的改进的K-means聚类，解决了SSC容量限制带来的困难。使用所提出的方法，允许将 FS 安排在准确的区域中，而没有不可访问的目标，其中所需FS的最小数量和最小燃料成本依次确定。最后，数值模拟验证了所提出方法的性能。