Angle-based Localization and Rigidity Maintenance Control for Multi-Robot Networks
🤖 AI Summary
This study addresses the problem of localization and rigidity maintenance in multi-robot systems under sensing constraints. By leveraging directed sensing graphs and bearing measurements expressed in body-fixed coordinate frames, the work establishes—for the first time—the equivalence between angular rigidity and bearing rigidity in both two- and three-dimensional spaces. Building on this theoretical insight, the authors propose a distributed control framework that employs the eigenvalues of angular rigidity as a quantitative measure. A distributed controller is then designed by integrating gradient descent with stability analysis under switching topologies, simultaneously achieving task execution and rigidity preservation. The resulting closed-loop system guarantees locally exponentially stable localization. Numerical simulations demonstrate the effectiveness and practicality of the proposed approach.
Application Category
📝 Abstract
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.
Problem
Research questions and friction points this paper is trying to address.
angle-based localization
rigidity maintenance
multi-robot networks
bearing rigidity
angle rigidity
Innovation
Methods, ideas, or system contributions that make the work stand out.
angle rigidity
bearing rigidity
distributed localization
rigidity maintenance control
switching sensing graphs
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