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

TL;DR

This paper introduces a novel axis-angle attitude control law for rotational systems that ensures a unique equilibrium and improves stability, validated through simulations and real quadrotor experiments, outperforming traditional quaternion-based methods.

Contribution

The paper proposes a new attitude control law based on axis-angle representation that guarantees a unique equilibrium and enhances control effectiveness for rotational systems.

Findings

Achieves a unique closed-loop equilibrium attitude-error quaternion.

Demonstrates improved stabilization time in simulations and real quadrotor tests.

Ensures uniform asymptotic stability of the rotational system.

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 {\pi}rad, 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.