This paper discusses generalized weak rigidity theory, and aims to apply the theory to formation control problems with a gradient flow law. The generalized weak rigidity theory is utilized in order that desired formations are characterized by a general set of pure inter-agent distances and angles. As the first result of its applications, the paper provides analysis of locally exponential stability for formation systems with pure distance/angle constraints in the $2$- and $3$-dimensional spaces. Then, as the second result, if there are three agents in the $2$-dimensional space, almost globally exponential stability for formation systems is ensured. Through numerical simulations, the validity of analyses is illustrated.

中文翻译：

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广义弱刚性：理论以及地层的局部和全局收敛

本文讨论广义弱刚性理论，旨在将该理论应用于具有梯度流动规律的地层控制问题。使用广义弱刚性理论，以便期望的构造由一组通用的纯代理间距离和角度来表征。作为其应用的第一个结果，本文提供了在 $2$- 和 $3$-维空间中具有纯距离/角度约束的地层系统的局部指数稳定性分析。然后，作为第二个结果，如果 $2$ 维空间中有三个代理，则可以确保编队系统的几乎全局指数稳定性。通过数值模拟，说明了分析的有效性。