微弱刚性，三体形成控制及向三维空间的扩展
Infinitesimal Weak Rigidity, Formation Control of Three Agents, and Extension to 3-dimensional Space
AI总结：
本文引入了平面框架的弱刚性矩阵和微弱刚性概念，用于直接判断框架的微弱刚性。通过邻接距离和角度确定框架的唯一性，并应用于三体形成控制问题，证明了控制系统的不稳定性及收敛性，同时提出改进的亨尼伯格构造方法并扩展至三维空间。
摘要：
本文介绍了平面框架的新概念：弱刚性矩阵和微弱刚性。弱刚性矩阵用于直接检查框架是否微弱刚性，而以前的方法只能间接检查。微弱刚性框架可通过其邻接距离和角度唯一确定（在无边的情况下还包括缩放）。我们应用这些新概念解决三体形成控制问题，证明在任何错误平衡点上控制系统的不稳定性及收敛到目标形成。此外，我们提出改进的亨尼伯格构造技术，用于生成最小刚性（或弱刚性）图。最后，我们将二维空间中的弱刚性概念扩展到三维空间。
英文摘要：
In this paper, we introduce new concepts of weak rigidity matrix and infinitesimal weak rigidity for planar frameworks. The weak rigidity matrix is used to directly check if a framework is infinitesimally weakly rigid while previous work can check a weak rigidity of a framework indirectly. An infinitesimal weak rigidity framework can be uniquely determined up to a translation and a rotation (and a scaling also when the framework does not include any edge) by its inter-neighbor distances and angles. We apply the new concepts to a three-agent formation control problem with a gradient control law, and prove instability of the control system at any incorrect equilibrium point and convergence to a desired target formation. Also, we propose a modified Henneberg construction, which is a technique to generate minimally rigid (or weakly rigid) graphs. Finally, we extend the concept of the weak rigidity in R^2 to the concept in R^3.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
