Second-order sliding-mode on SO(3) and fault-tolerant spacecraft attitude control

As one of attitude representation methods for a rigid body, the rotation matrices defined on the special orthogonal matrix group SO(3) can give the unique, global and nonsingular solution. For the attitude control systems evolving on Lie group SO(3)×R3, a second-order sliding surface is constructed and proved to be a Lie subgroup, along which the reduced-order dynamics is almost globally asymptotically stable at the equilibrium state. Based on the new sliding-mode surface, a fault-tolerant controller is designed to deal with the actuator faults and external disturbances in attitude control systems. The new method is numerically simulated and further implemented in a semi-physical simulation system of an air-bearing platform to verify its effectiveness in spacecraft practical engineering.