Geometric approach to attitude dynamics and control of spacecraft with variable speed control moment gyroscopes

The attitude dynamics of a spacecraft with a variable speed control moment gyroscope (VSCMG), in the presence of conservative external inputs, are derived in the framework of geometric mechanics. A complete dynamics model, that relaxes some of the assumptions made in prior literature on control moment gyroscopes, is obtained. These dynamics equations show the complex nonlinear coupling between the internal degrees of freedom associated with the CMG and the spacecraft base body's attitude degrees of freedom. General ideas on how this coupling can be used to control the angular momentum of the base body of the spacecraft using changes in the momentum variables of a finite number of VSCMGs, are provided. Placement of VSCMGs in the spacecraft base body is carried out in a manner that avoids singularities in the transformation between VSCMG angular rates and required instantaneous base body angular momentum. A control scheme using n VSCMGs for slew to rest attitude maneuvers in the absence of external torques and when the total angular momentum of the spacecraft is zero, is presented. Numerical simulation results obtained for a spacecraft with three VSCMGs confirm the stability properties of the feedback system.