In this work, we study angle-based localization and rigidity maintenance control for multi-robot networks under sensing constraints. We establish the first equivalence 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 angle rigidity strongly depends on the robots' spatial configuration, 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：本研究针对传感约束下的多机器人网络，探讨了基于角度的定位方法与刚性保持控制问题。我们首次建立了考虑有向传感图和本体坐标系下二维与三维空间中的角度刚性与轴承刚性之间的等价关系。具体而言，我们证明了$\mathrm{SE}(d)$中的框架是无穷小轴承刚性的当且仅当其同时满足无穷小角度刚性条件且每个机器人至少获得$d-1$个轴承测量值（其中$d \in \{2, 3\}$）。基于上述发现，本文提出了一种分布式角度定位方案，并在切换传感图场景下证明了局部指数稳定性，该方法仅需所访问拓扑结构满足无穷小角度刚性。进一步地，由于角度刚性高度依赖于机器人的空间构型，我们研究了刚性保持控制问题。引入角度刚性特征值作为刚性度量指标，提出了一种能够执行任务特定指令同时维持充分角度刚性水平的分散梯度控制方法。通过仿真实验验证了该方案的有效性与实用性。