A New Type of Axis-Angle Attitude Control Law for Rotational Systems: Synthesis, Analysis, and Experiments

2025-10-29

AI Summary

Traditional quaternion-based attitude control suffers from non-unique closed-loop equilibrium points and degraded proportional gain performance—leading to compromised convergence and robustness—when Euler angle errors exceed π. To address this, this paper proposes a novel attitude control law based on axis–angle representation, explicitly leveraging the Euler axis and angle of the attitude error. This ensures a unique asymptotically stable equilibrium point and enhances proportional control efficacy during large-angle maneuvers. Stability is rigorously established via a strict Lyapunov function and two distinct control architectures. Numerical simulations and real-world quadrotor roll recovery experiments demonstrate that, compared with state-of-the-art quaternion controllers, the proposed method significantly reduces settling time and improves both response speed and control accuracy for large-angle attitude maneuvers.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Over the past few decades, continuous quaternion-based attitude control has been proven highly effective for driving rotational systems that can be modeled as rigid bodies, such as satellites and drones. However, methods rooted in this approach do not enforce the existence of a unique closed-loop (CL) equilibrium attitude-error quaternion (AEQ); and, for rotational errors about the attitude-error Euler axis larger than πrad, their proportional-control effect diminishes as the system state moves away from the stable equilibrium of the CL rotational dynamics. In this paper, we introduce a new type of attitude control law that more effectively leverages the attitude-error Euler axis-angle information to guarantee a unique CL equilibrium AEQ and to provide greater flexibility in the use of proportional-control efforts. Furthermore, using two different control laws as examples-through the construction of a strict Lyapunov function for the CL dynamics-we demonstrate that the resulting unique equilibrium of the CL rotational system can be enforced to be uniformly asymptotically stable. To assess and demonstrate the functionality and performance of the proposed approach, we performed numerical simulations and executed dozens of real-time tumble-recovery maneuvers using a small quadrotor. These simulations and flight tests compellingly demonstrate that the proposed axis-angle-based method achieves superior flight performance-compared with that obtained using a high-performance quaternion-based controller-in terms of stabilization time.

Problem

• Ensuring unique closed-loop equilibrium in attitude control systems
• Preventing diminished proportional control for large rotational errors
• Improving stabilization time through axis-angle-based control approach

Innovation

• Axis-angle attitude control law for rotational systems
• Guarantees unique closed-loop equilibrium attitude-error quaternion
• Demonstrates uniform asymptotic stability via Lyapunov function