Dynamics and control of underactuated multibody spacecraft

In this dissertation, we develop equations of motion for a class of multibody spacecraft consisting of a rigid base body and multiple rigid appendages connected to the base body. There has been much prior research on this topic; however, much of this research is not appropriate for nonlinear control design purposes. The motion of a multibody spacecraft is described by the position and attitude of a base body in an inertial frame and by the relative position and attitude of the attached bodies with respect to the base body; these latter quantities define the shape of the multibody spacecraft. Our aim is to develop equations of motion that reveal important nonlinear coupling effects between the translation, rotation and shape dynamics, but are simple enough for control design purposes. A rotation matrix is used to represent the attitude of the spacecraft. This allows us to avoid complexity related to the use of parameter representations such as Euler angles. Hamilton's variational principle gives three sets of nonlinear equations of motion.; The latter part of this dissertation presents results of control problems for several underactuated multibody spacecraft examples. These include spacecraft with an unactuated internal sliding mass, spacecraft with unactuated fuel slosh dynamics, tethered spacecraft with attachment point actuation and the triaxial attitude control testbed with two proof mass actuation devices. These examples illustrate important features related to the dynamics and control of various underactuated multibody spacecraft. Differences in geometries of the spacecraft and gravitational assumptions require adoption of different types of control schemes. We use the multibody equations in this dissertation to formulate control equations for the models and to construct feedback controllers that achieves asymptotic stability (or convergence) to the desired (relative) equilibrium manifolds. Computer simulations demonstrate the effectiveness of the controllers.