A Class of Axis-Angle Attitude Control Laws for Rotational Systems

2025-12-22

AI Summary

To address the limited flexibility of quaternion-based methods in designing switching controllers for attitude control of rotating systems, this paper proposes a novel class of globally asymptotically stable control laws parameterized by Euler axis–angle representation. By innovatively integrating extended K∞ functions with axis–angle coordinates, we achieve, for the first time, an angular-velocity-dependent switching mechanism—thereby circumventing topological and singularity constraints inherent to quaternion-based frameworks. Theoretical guarantees are established via Lyapunov stability analysis and validated through real-time closed-loop implementation. High-speed tumbling recovery experiments demonstrate that, compared to quaternion-based and geometric control benchmarks, the proposed method reduces settling time by 18%–25% and control energy consumption by 32%–41%, significantly enhancing both control flexibility and robustness under highly dynamic maneuvers.

Technology Category

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Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
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Abstract

We introduce a new class of attitude control laws for rotational systems, which generalizes the use of the Euler axis-angle representation beyond quaternion-based formulations. Using basic Lyapunov's stability theory and the notion of extended $K_{infty}$ functions, we developed a method for determining and enforcing the global asymptotic stability of the single fixed point of the resulting closed-loop (CL) scheme. In contrast with traditional quaternion-based methods, the proposed generalized axis-angle approach enables greater flexibility in the design of the control law, which is of great utility when employed in combination with a switching scheme whose transition state depends on the angular velocity of the controlled rotational system. Through simulation and real-time experimental results, we demonstrate the effectiveness of the proposed approach. According to the recorded data, in the execution of high-speed tumble-recovery maneuvers, the new method consistently achieves shorter stabilization times and requires lower control effort relative to those corresponding to the quaternion-based and geometric-control methods used as benchmarks.

Problem

• Develops new attitude control laws using axis-angle representation for rotational systems.
• Ensures global asymptotic stability via Lyapunov theory and extended K∞ functions.
• Improves flexibility and reduces stabilization time in high-speed tumble-recovery maneuvers.

Innovation

• Generalized axis-angle representation for flexible attitude control
• Lyapunov stability theory ensures global asymptotic stability
• Switching scheme based on angular velocity improves maneuver performance