Attitude control of an underactuated spacecraft using quaternion feedback regulator and tube-based MPC

Feasibility of achieving 3-axis stabilization of an asymmetric spacecraft for cases where there is no control available in one axis (underactuated spacecraft) is explored in this paper. A novel control design methodology is presented which can stabilize the underactuated spacecraft and steer it to the origin. A passive fault tolerant control (FTC) is defined which controls and maintains the attitude of the spacecraft near the desired point in presence of uncertainties, disturbances, control constraints and actuator faults. Considering the general conditions of the underactuated spacecraft, a hybrid controller combining a quaternion feedback regulator (QFR) with a tube-based model predictive controller (MPC) is developed based on the nonlinear kinematic and dynamic equations of the spacecraft motion. The hybrid controller is composed of two control stages. At the first stage, QFR decreases the angular velocities and brings the state vector to an acceptable region for the next stage. Then, tube-based MPC solves two optimal control problems, a standard problem for the nominal system to define a central guide path, and an ancillary problem to steer the state vector towards the central path with semi-optimal control effort. Numerical simulation results obtained for the underactuated spacecraft merely indicate effectiveness of the proposed attitude control method.