In this work, we study angle-based localization and rigidity maintenance control for multi-robot networks. First, we establish the relationship between angle rigidity and bearing rigidity considering \textit{directed} sensing graphs and \textit{body-frame} bearing measurements in both $2$ and $3$-\textit{dimensional space}. In particular, we demonstrate that a framework in $\mathrm{SE}(d)$ is infinitesimally bearing rigid if and only if it is infinitesimally angle rigid and each robot obtains at least $d-1$ bearing measurements ($d \in \{2, 3\}$). Building on these findings, this paper proposes a distributed angle-based localization scheme and establishes local exponential stability under switching sensing graphs, requiring only infinitesimal angle rigidity across the visited topologies. Then, since the set of available angles strongly depends on the robots' spatial configuration due to sensing constraints, we investigate rigidity maintenance control. The \textit{angle rigidity eigenvalue} is presented as a metric for the degree of rigidity. A decentralized gradient-based controller capable of executing mission-specific commands while maintaining a sufficient level of angle rigidity is proposed. Simulations were conducted to evaluate the scheme's effectiveness and practicality.

翻译：本文研究多机器人网络中的基于角度的定位与刚性保持控制。首先，我们建立了在d维空间（d∈{2,3}）中，考虑有向感知图与机体坐标系下方位测量的角度刚性与方位刚性之间的关系。具体而言，我们证明了一个在SE(d)中的框架是无穷小方位刚性的，当且仅当它是无穷小角度刚性的且每个机器人至少获得d-1个方位测量（d∈{2,3}）。基于这些发现，本文提出了一种分布式角度定位方案，并建立了在切换感知图下局部指数稳定的结果，该方案仅要求所遍历拓扑结构具有无穷小角度刚性。随后，由于可获取的角度集合因感知约束而强烈依赖于机器人的空间构型，我们研究了刚性保持控制。提出了角度刚性特征值作为刚性程度的度量指标，并设计了一种能够执行任务指定指令同时保持足够角度刚性水平的分布式梯度控制器。通过仿真实验评估了该方案的有效性与实用性。