Robust tracking control design for spacecraft under control input saturation

A continuous globally stable tracking control algorithm is presented for spacecraft in the presence of control input saturation, parametric uncertainty, and external disturbances. The proposed control algorithm has the following properties: 1) fast and accurate response in the presence of bounded disturbances and parametric uncertainty; 2) explicit accounting for control input saturation; and 3) computational simplicity and straightforward tuning. A detailed stability analysis of the resulting closed-loop system is included. It is shown that global stability of the overall system is guaranteed with continuous control even in the presence of bounded disturbances and parametric uncertainty. In the proposed controller a single parameter is adjusted dynamically in such a fashion that it is possible to prove that both attitude and angular velocity errors will tend to zero asymptotically. The stability proof is based on a Lyapunov analysis and the properties of the quaternion representation of spacecraft dynamics. One of the main features of the proposed design is that it establishes a straightforward relationship between the magnitudes of the available control inputs and those of the desired trajectories and disturbances even with continuous control. Numerical simulations are included to illustrate the spacecraft performance obtained using the proposed controller.