Stabilization of an under-actuated spacecraft

The stabilization problem for under-actuated spacecraft with two control input is revisited. A method that stabilizes the under-actuated spacecraft angular velocity use back-stepping control theory and attitude use generalized dynamic inversion method is proposed. Firstly, the dynamic equation and kinematic equation of under-actuated spacecraft are built. An angular velocity stabilization control law that use angular velocity as the pseudo-control input based on back-stepping control is designed through analysis the under-actuated dynamic equation. The controller can global asymptotic stabilize the under-actuated spacecraft angular velocity with the coupling between the actuated axis and under-actuated axis. Then, an attitude stabilization control law based on generalized dynamic inversion and the rewritten dynamic and kinematic equation is introduced. A null-control vector as a part of the control input, is designed to globally asymptotic stabilize the angular velocity and attitude under any arbitrary initial condition. The availability of the proposed control algorithm is validated by simulation results.