AI summaryⓘ
The authors explore how groups of robots can figure out their positions and keep their formation using only angle information, even when their sensors and communication are limited. They prove that measuring angles is just as good as measuring directions (bearings) when robots have enough sensor data, in both 2D and 3D spaces. Based on this, they create a system where robots can localize themselves and maintain the shape of their group using only angle data, with stability guaranteed during changes in the sensing network. They also introduce a way to measure how well the robots maintain their formation and design a controller that helps them stay rigid while completing tasks. Their simulations show that this approach works well in practice.
angle rigiditybearing rigiditymulti-robot localizationdistributed controlrigidity maintenancesensing graphsSE(d) frameworkexponential stabilitygradient-based controller
Authors
J. Francisco Presenza, Leonardo J. Colombo, Juan I. Giribet, Ignacio Mas
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.