Almost Global and Singularity-Free Fixed-Time Sliding Mode Satellite Attitude Control: A Geometric Control Framework

• Published in: IEEE transactions on aerospace and electronic systems pp. 1 - 11
• Main Authors: Barman, Saumitra, Sinha, Manoranjan
• Format: Journal Article
• Language: English
• Published: IEEE 02.09.2024
• Subjects: Aerospace electronics; Attitude control; fixed-time stability; geometric control; Kinematics; Lie groups; Manifolds; nonlinear systems; Satellites; Sliding mode control
• ISSN: 0018-9251; 1557-9603
• DOI: 10.1109/TAES.2024.3453781

In this paper, a robust singularity-free fixed-time satellite attitude control in a geometric control framework is proposed. The satellite attitude is represented by the rotation matrices defined on the special orthogonal matrix group <inline-formula><tex-math notation="LaTeX">\textrm {SO}(3)</tex-math></inline-formula> to achieve unique, global, and kinematic singularity-free attitude representation. A nonsingular fixed-time sliding manifold for the attitude control system evolving on the Lie group <inline-formula><tex-math notation="LaTeX">\textrm {SO}(3)\times \mathbb {R}^{3}</tex-math></inline-formula> is proposed. A complete mathematical analysis is carried out to prove and establish that the proposed sliding manifold is a Lie subgroup of <inline-formula><tex-math notation="LaTeX">\textrm {SO}(3)\times \mathbb {R}^{3}</tex-math></inline-formula>. Along this manifold, the reduced-order dynamics is almost globally fixed-time attractive to a residual set containing the stable equilibrium point. Based on the proposed sliding manifold, a nonsingular geometric fixed-time sliding mode control (NGFTSMC) law is proposed for the satellite attitude control in the presence of external disturbance torques. It is proved through five propositions that the NGFTSMC facilitates an attitude maneuver on the phase space <inline-formula><tex-math notation="LaTeX">\textrm {SO}(3)\times \mathbb {R}^{3}</tex-math></inline-formula> excluding a set of measure zero. This guarantees almost global, unwinding-free, and singularity-free closed-loop attitude dynamics. Simulation results are presented and compared with a quaternion-based fixed-time sliding mode control (QFTSMC) to show superiority of the NGFTSMC in terms of the time of convergence, unwinding, and control effort.