In this paper, we propose a novel approach to the problem of augmenting distance-based formation controllers with a secondary constraint for the purpose of preventing 3D formation ambiguities. Specifically, we introduce three controlled variables that form an orthogonal space and uniquely characterize a tetrahedron formation in 3D. This orthogonal space incorporates constraints on the inter-agent distances and the signed volume of tetrahedron substructures. The formation is modeled using a directed graph with a leader–follower type configuration and single-integrator dynamics. We show that the proposed decentralized formation controller ensures the global asymptotic stability and the local exponential stability of the desired formation for an n-agent system with no ambiguities. Unlike previous work, this result is achieved without conditions on the tetrahedrons that form the desired formation or on the control gains.

在本文中，我们提出了一种新颖的方法来解决具有辅助约束的基于距离的编队控制器问题，以防止3D编队歧义。具体来说，我们介绍了三个可控制的变量，这些变量形成一个正交空间并唯一地表征3D中的四面体结构。该正交空间结合了对主体间距离和四面体子结构的有符号体积的约束。使用带有领导者-跟随者类型的配置和单积分器动力学的有向图对地层进行建模。我们表明，所提出的分散地层控制器可确保n所期望地层的全局渐近稳定性和局部指数稳定性。-Agent系统无歧义。与先前的工作不同，在没有条件的四面体形成所需结构或控制增益的情况下即可获得此结果。