This work studies formation control of multiagent systems (MASs) where its formation size is scalable via a scaling factor (scalable formation). Past works on scalable formation are limited to either fixed undirected graph or fixed directed graph with p-rooted graph condition. This work proposes a new distributed algorithm for scalable formation based on a distributed observer to estimate agents' positions. The new algorithm results in a new matrix, a Laplacian matrix with additional diagonal terms, where the desired formation pattern is embedded in this diagonal terms. With the proposed algorithm, only spanning tree condition is needed as the necessary and sufficient condition to achieve the scalable formation. Numerical examples are shown to illustrate the proposed method.

中文翻译：

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具有尺寸缩放的多智能体形成的分布式位置估计方法

这项工作研究多智能体系统 (MAS) 的编队控制，其中编队规模可通过比例因子（可扩展编队）进行扩展。过去关于可扩展形成的工作仅限于固定无向图或具有p根图条件的固定有向图。这项工作提出了一种基于分布式观察者估计代理位置的可扩展编队的新分布式算法。新算法产生一个新矩阵，一个带有附加对角项的拉普拉斯矩阵，其中所需的形成模式嵌入在这个对角项中。使用所提出的算法，只需要生成树条件作为实现可伸缩编队的充分必要条件。给出了数值例子来说明所提出的方法。