A Time-Varying Control of an Underactuated Rigid Spacecraft

The problem of stabilization was studied for an underactuated rigid spacecraft. First of all, the system dynamic and kinematic equations are given, the kinematic equation is described by the (w, z) parametrization. Some continuous time-varying control laws are then designed based on the characteristic of the system model. The accessorial variables v, v₁, and v₂ are imported in the designing course of the control laws. The equations of the system model are predigested using the averaging method, then the control laws of the v, v₁, and v₂ are contrived via backstepping method. The cross coupling relation of angular velocity is utilized to regulate the uncontrollable attitude component. Simulating results validate the availability of the proposed control algorithm.