Angular Velocity Observer on the Special Orthogonal Group for Velocity-Free Rigid-Body Attitude Tracking Control

TL;DR

This paper introduces an angular velocity observer on the special orthogonal group for rigid-body attitude tracking control using only attitude measurements, ensuring asymptotic convergence without singularities or discontinuities.

Contribution

It develops a novel observer directly on the special orthogonal group that guarantees convergence and integrates it with a stable attitude control system, avoiding common issues with minimal representations.

Findings

Observer guarantees asymptotic convergence of angular velocity estimates.

Combined system achieves exponential stability.

Avoids singularities and discontinuities inherent in other representations.

Abstract

This paper studies a rigid body attitude tracking control problem with attitude measurements only, when angular velocity measurements are not available. An angular velocity observer is constructed such that the estimated angular velocity is guaranteed to converge to the true angular velocity asymptotically from almost all initial estimates. As it is developed directly on the special orthogonal group, it completely avoids singularities, complexities, or discontinuities caused by minimal attitude representations or quaternions. Then, the presented observer is integrated with a proportional-derivative attitude tracking controller to show a separation type property, where exponential stability is guaranteed for the combined observer and attitude control system.