A Class of Axis-Angle Attitude Control Laws for Rotational Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910083432054784 |
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| author | Gonçalves, Francisco M. F. R. Bena, Ryan M. Pérez-Arancibia, Néstor O. |
| author_facet | Gonçalves, Francisco M. F. R. Bena, Ryan M. Pérez-Arancibia, Néstor O. |
| contents | We introduce a new class of attitude control laws for rotational systems; the proposed framework generalizes the use of the Euler \mbox{axis--angle} representation beyond quaternion-based formulations. Using basic Lyapunov stability theory and the notion of extended class $\mathcal{K}$ function, we developed a method for determining and enforcing the global asymptotic stability of the single fixed point of the resulting \mbox{\textit{closed-loop}} (CL) scheme. In contrast with traditional \mbox{quaternion-based} methods, the introduced generalized \mbox{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 \mbox{real-time} experimental results, we demonstrate the effectiveness of the developed formulation. According to the recorded data, in the execution of \mbox{high-speed} \mbox{tumble-recovery} maneuvers, the new method consistently achieves shorter stabilization times and requires lower control effort relative to those corresponding to the \mbox{quaternion-based} and \mbox{geometric-control} methods used as benchmarks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_19846 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Class of Axis-Angle Attitude Control Laws for Rotational Systems Gonçalves, Francisco M. F. R. Bena, Ryan M. Pérez-Arancibia, Néstor O. Systems and Control Robotics We introduce a new class of attitude control laws for rotational systems; the proposed framework generalizes the use of the Euler \mbox{axis--angle} representation beyond quaternion-based formulations. Using basic Lyapunov stability theory and the notion of extended class $\mathcal{K}$ function, we developed a method for determining and enforcing the global asymptotic stability of the single fixed point of the resulting \mbox{\textit{closed-loop}} (CL) scheme. In contrast with traditional \mbox{quaternion-based} methods, the introduced generalized \mbox{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 \mbox{real-time} experimental results, we demonstrate the effectiveness of the developed formulation. According to the recorded data, in the execution of \mbox{high-speed} \mbox{tumble-recovery} maneuvers, the new method consistently achieves shorter stabilization times and requires lower control effort relative to those corresponding to the \mbox{quaternion-based} and \mbox{geometric-control} methods used as benchmarks. |
| title | A Class of Axis-Angle Attitude Control Laws for Rotational Systems |
| topic | Systems and Control Robotics |
| url | https://arxiv.org/abs/2512.19846 |