Kinematically Coupled Relative Spacecraft Motion Control Using the State-Dependent Riccati Equation Method

Abstract

This paper presents kinematically coupled relative spacecraft motion control in the close proximity of a tumbling target using the state-dependent Riccati equation method for proximity operation mission. In general, a rigid-body dynamics can be expressed as both translation and rotation about the center of mass. However, a kinematic coupling between the rotational and translational dynamics occurs when it is not expressed about the center of mass. Thus, kinematically coupled relative spacecraft motion model is derived to describe the relative motion about the selected arbitrary points on both the target and spacecraft. Then, spacecraft relative motion is represented by combining the relative translational and rotational dynamics of arbitrary points on the spacecraft. The spacecraft is required to achieve the desired position and attitude to track a tumbling spacecraft quickly in the effect of kinematic translation and rotation coupling. The state-dependent Riccati equation method is implemented to design a nonlinear controller in six degrees of freedom. Numerical simulation results validate kinematically coupled relative spacecraft motion control with respect to a tumbling target.