Quaternion-Based Attitude Stabilization Using Synergistic Hybrid Feedback With Minimal Potential Functions

TL;DR

This work addresses robust global attitude stabilization for a rigid body using quaternion-based feedback on $\mathbb{S}^3$ to overcome the topological limitation of $\mathrm{SO(3)}$. It introduces a centrally synergistic hybrid feedback built from a minimal set of synergistic potential functions (SPFs) and an angular warping SPF construction to ensure consistency and global stability, without requiring quaternion conversion. The main contributions are (i) a minimal-SPF, centrally synergistic design that avoids unwinding and reduces chattering, and (ii) a rigorous robust UGAS proof for the closed-loop system under perturbations, together with simulations validating convergence and robustness against measurement noise. The approach promises practical benefits for aerospace and marine platforms, offering reliable attitude stabilization with reduced computational and switching complexity. \(U(Q,q)\) and the corresponding gradients enable a unified, consistent quaternion-based controller that achieves robust global performance in the presence of disturbances and noisy measurements.

Abstract

This paper investigates the robust global attitude stabilization problem for a rigid-body system using quaternion-based feedback. We propose a novel synergistic hybrid feedback with the following notable features: (1) It demonstrates central synergism by utilizing a minimal number of potential functions; (2) It ensures consistency with respect to the unit quaternion representation of rigid-body attitude; (3) Its state-feedback laws incorporate a shared action term that steers the system toward the desired attitude. We demonstrate that the proposed hybrid feedback method effectively solves the problem at hand and guarantees robust uniform global asymptotic stability.

Figures (6)

• Figure 1: Flowchart of quaternion-based attitude control.
• Figure 2: Example \ref{['exmp:non_cen_SPF']}: Chattering at a neighborhood of $\eta = 0$ when the hybrid feedback from \ref{['eq:non_SPF']} is applied to Problem \ref{['prob:GAS_sub']} by directly using quaternion measurement $Q_m = sQ$, where $s(t)$ is a square wave with a frequency of $5\mathrm{Hz}$. Initial conditions are set as $Q(0) = [0,0.6,0.8,0]^\top$ and $q(0) = 1$.
• Figure 3: Simulation 1: CSH versus CSH $q=1$. The initial conditions: $Q(0) = [0.297, -0.028, 0.013, 0.954]^\top$, $\omega(0) = [0,0,0]^\top$, $q(0) = 1$.
• Figure 4: Simulation 2: CSH versus NCSH. The initial conditions: $Q(0) = [0, 0.6, 0.8, 0]^\top$, $\omega(0) = [0,0,0]^\top$, $q(0) = -1$ for CSH, and $q(0) = 1$ for NCSH.
• Figure 5: Simulation 3: CSH versus NCSH. The initial conditions: $Q(0) = [0, 0.6, 0.8, 0]^\top$, $\omega(0) = [0,0,0]^\top$, $q(0) = -1$ for CSH, and $q(0) = 1$ for NCSH.