Geometric active disturbance rejection controller for spacecraft attitude control on SO(3)

A geometric active disturbance rejection controller (GADRC) is proposed in this paper to address the challenges posed by unmeasurable states and unknown external disturbances in spacecraft attitude control. The spacecraft attitude system is modeled using the differential manifold SO(3), which effectively handles the singularities of Euler angles and Rodrigues parameters, as well as the ambiguity inherent in quaternions. The spacecraft utilizes only star sensors as the sensor output, with no accelerometers involved. The output space is confined to a two-dimensional spherical surface S2[jls-end-space/]. Leveraging the variational principle and the left-invariant property of the Lie group, a geometric extended state observer (GESO) is developed to estimate both the attitude and total disturbances of the spacecraft system. Based on the Morse error function and geodesic theory on differentiable manifolds, a geometric tracking differentiator (GTD) is designed to address the spacecraft attitude transition problem. Subsequently, the GADRC is designed, offering a robust solution to the attitude disturbance rejection problem under the constraint of limited sensor measurements. Finally, numerical simulations demonstrate the effectiveness of the proposed GADRC.