Angle-based Localization and Rigidity Maintenance Control for Multi-Robot Networks

TL;DR

This paper introduces a novel angle-based localization and rigidity control method for multi-robot networks, establishing theoretical relationships and proposing distributed algorithms to maintain rigidity under switching sensing conditions.

Contribution

It establishes the equivalence between angle rigidity and bearing rigidity in directed graphs, and develops a decentralized control scheme for rigidity maintenance.

Findings

Distributed angle-based localization achieves exponential stability.

Rigidity maintenance controller effectively preserves network structure.

Simulations confirm the approach's practicality and robustness.

Abstract

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.