基于角度的多机器人定位与刚性控制，实现稳定分布式定位。
Angle-based Localization and Rigidity Maintenance Control for Multi-Robot Networks
- 通过角度测量实现分布式定位，仅需微小角度刚性即可工作。
- 在动态通信拓扑下仍保持局部指数稳定，适应实际场景变化。
- 提出角度刚性度量与去中心化控制器，适合任务导向的机器人编队。
本文研究多机器人网络中的角度基定位与刚性保持控制。首先，在二维和三维空间中，针对有向感知图和机体坐标系下的方位测量，建立了角度刚性与方位刚性的关系。特别地，证明了在SE(d)框架下，系统在无穷小意义上具备方位刚性当且仅当其具备无穷小角度刚性，并且每个机器人至少获得d−1个方位测量（d ∈ {2, 3}）。基于此，本文提出一种分布式角度基定位方案，并在切换感知图条件下建立了局部指数稳定性，仅需在所访问拓扑中满足无穷小角度刚性。由于可用角度受机器人空间构型及感知约束影响显著，进一步研究了刚性保持控制。引入角度刚性特征值作为刚性程度的度量，设计了一种去中心化的梯度控制器，可在执行特定任务指令的同时维持足够的角度刚性水平。仿真验证了该方案的有效性与实用性。
原文摘要 · Abstract (English)
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.
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