Geometric Attitude Control of Spacecraft with Time Delays on the Left-error Function of SO(3)

To address spacecraft attitude control problems caused by external disturbances and remaining lumped system dynamics on SO(3), which can significantly deteriorate attitude tracking accuracy, system stability, and robustness of control system, a finite-time geometric sliding-mode control (FTGSMC) method using time delay estimation (TDE) on SO(3) is proposed. First, this modeling scheme provides a global, compact, and unique representation of attitude, avoiding the singularity problem of Euler angles and the "unwinding"phenomenon of quaternions. By introducing the left attitude error function defined on SO(3), the designed TDE scheme is capable of estimating and compensating for the lumped uncertainties and external disturbances within the SO(3) manifold. Then, a FTGSMC controller based on TDE is designed, guaranteeing the system error converges to 0. Finally, simulation experiment is carried out by comparing with FTGSMC method without TDE, which verifies effectiveness and superiority of the control method of this paper.