Abstract: Trajectory tracking control of spacecraft undergoing large-range relative motion is a key problem in on-orbit servicing and related space missions. However, the traditional Clohessy-Wiltshire (C-W) dynamics model based on local linearization suffers from insufficient accuracy in large-range relative motion scenarios and thus fails to meet engineering requirements. To address this issue, a Koopman-based integrated control approach was proposed, in which dynamic modeling, state estimation, and closed-loop control were unified within the global linearization framework of the Koopman operator, aiming to improve control accuracy and performance while maintaining computational efficiency. In this approach, tensor products of state variables were employed as basis functions, and the Koopman operator was efficiently constructed via δ-inner-product operations. On this basis, an online state estimation method was developed by incorporating conjugate unscented transform(CUT), enabling high-accuracy state estimation with only a small number of samples. By freezing the control term, the inherently non-convex optimization problem arising in Koopman-based model predictive control(MPC) was transformed into a convex program, allowing efficient online computation of closed-loop control inputs. Numerical simulations for large-range relative motion trajectory tracking scenarios demonstrate that the proposed method achieves computational efficiency comparable to that of conventional C-W model-based control, while exhibiting clear advantages in control accuracy and performance: fuel consumption is reduced to approximately 35% of that required by the traditional method, and trajectory tracking errors are reduced to about 2% of those obtained using the C-W model. Under near-distance relative motion conditions, the proposed approach naturally reduces into the conventional control strategy, verifying its consistency and generality. The proposed Koopman-based integrated control method provides an effective engineering implementation framework for large-range relative motion trajectory tracking and exhibits promising engineering applicability. 

Key words: large-range relative motion, trajectory tracking, koopman operator, conjugate unscented transform, model predictive control