Attitude stabilization of a spacecraft by two skew single-gimbal control moment gyros

The challenging issue of stabilizing the attitude of a spacecraft by only two single-gimbal control moment gyros (CMGs) with gimbal axes skew to each other is approached under zero total angular momentum condition, which guarantees that any orientation can be reached at rest. Apart from control insufficiency and CMG singularities, the fact that the output torque vector of two skew CMGs varies in a 3-D space and hence has three components in the spacecraft body frame but only two of them are independent, severely hinders feedback stabilization law design. To overcome these obstructions, small attitude error is first assumed to derive reduced system equations only with two independent torque components as inputs. Based on this model, a novel saturated singular quaternion controller is presented to locally stabilize the spacecraft attitude; moreover, small attitude error condition also protects the CMGs from singularities. In case of large attitude error, command gimbal rates are directly derived via the generalized dynamic inverse (GDI) method. The resultant GDI controller can drive the spacecraft attitude trajectories into an arbitrary small neighborhood of the desired equilibrium, which in turn ensures small attitude error condition for implementing previous controller. Finally, a two-stage control logic is proposed to achieve the global attitude stabilization objective.