Nonlinear suboptimal tracking control of spacecraft approaching a tumbling target

We investigate the close-range relative motion and control of a spacecraft approaching a tumbling target. Unlike the traditional rigid-body dynamics with translation and rotation about the center of mass (CM), the kinematic coupling between translation and rotation is taken into consideration to directly describe the motion of the spacecraft's sensors or devices which are not coincident with the CM. Thus, a kinematically coupled 6 degrees-of-freedom (DOF) relative motion model for the instrument (feature point) is set up. To make the chaser spacecraft's feature point track the target's, an optimal tracking problem is defined and a control law with a feedback-feedforward structure is designed. With quasi-linearization of the nonlinear dynamical system, the feedforward term is computed from a specified constraint about the dynamical system and the reference model, and the feedback action is derived starting from the state-dependent Ricca equation (SDRE). The proposed controller is compared with an existing suboptimal tracking controller, and numerical simulations are presented to illustrate the effectiveness and superiority of the proposed method.