Distributed formation maneuver control refers to the problem of maneuvering a group of agents to change their formation shape by adjusting the motions of partial agents, where the controller of each agent only requires local information measured from its neighbors. Although this problem has been extensively investigated, existing approaches are mostly limited to uniform scaling transformations. This article proposes a new type of local matrix-valued constraints, via which non-uniform scaling control of position formation can be achieved by tuning the positions of only two agents (i.e., leaders). Here, the non-uniform scaling transformation refers to global scaling the position formation with different ratios along different orthogonal coordinate directions. Moreover, by defining scaling and translation of attitudes, we propose a distributed control scheme for scaling and translation maneuver control of joint position-attitude formations. It is proven that the proposed controller achieves global convergence, provided that the sensing graph among agents is a 2-rooted bidirectional graph. Compared with the affine formation maneuver control approach, the proposed approach leverages a sparser sensing graph, requires fewer leaders, and additionally enables scaling transformations of the attitude formation. A simulation example demonstrates our theoretical results.

翻译：分布式编队机动控制是指通过调整部分智能体的运动来改变编队形状的问题，其中每个智能体的控制器仅需从邻居获取局部信息。尽管该问题已被广泛研究，但现有方法大多局限于均匀尺度变换。本文提出一种新型局部矩阵值约束，通过仅调整两个智能体（即领航者）的位置，即可实现位置编队的非均匀尺度控制。这里的非均匀尺度变换是指沿不同正交坐标方向以不同比例对位置编队进行全局缩放。此外，通过定义姿态的缩放与平移，我们提出一种针对位置-姿态联合编队的缩放与平移机动控制分布式方案。理论证明，当智能体间感知图是2-根双向图时，所提控制器可实现全局收敛。与仿射编队机动控制方法相比，本文方法利用更稀疏的感知图，所需领航者数量更少，并额外实现了姿态编队的缩放变换。仿真示例验证了我们的理论结果。