Distributed Non-Uniform Scaling Control of Multi-Agent Formation via Matrix-Valued Constraints
For multi-agent systems, this work addresses the limitation of existing formation control methods to uniform scaling, enabling non-uniform scaling with minimal leaders and sparse sensing.
This paper proposes a distributed control scheme for non-uniform scaling of multi-agent formations using matrix-valued constraints, requiring only two leaders and a 2-rooted bidirectional sensing graph. The method achieves global convergence and extends to joint position-attitude formations, outperforming affine formation control in sparsity and leader count.
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.