中国空间科学技术

中国空间科学技术 ›› 2026, Vol. 46 ›› Issue (3): 169-180.doi: 10.16708/j.cnki.1000-758X.2026.0045

• 《中国空间科学技术（中英文）》创刊45周年专刊 • 上一篇    下一篇

航天器大尺度相对运动的Koopman一体化控制研究

伦恒鹏1，王海了1，白雪1,2,3,*，徐明1,2,3   

  1. 1.北京航空航天大学宇航学院，北京100191
    2.北京航空航天大学沈元学院，北京100191
    3.航天器设计优化与动态模拟技术教育部重点实验室, 北京100191
  • 收稿日期:2026-01-04 修回日期:2026-02-06 录用日期:2026-02-10 发布日期:2026-05-21 出版日期:2026-05-31

Koopman-based integrated control for spacecraft large-range relative motion

LUN Hengpeng1，WANG Hailiao1, BAI Xue1,2,3,*，XU Ming1,2,3   

  1. 1.School of Astronautics, Beihang University, Beijing 100191, China
    2.Shen Yuan Honors College, Beihang University, Beijing 100191, China
    3.Key Laboratory of Spacecraft Design Optimization and Dynamic Simulation Technology, Ministry of Education, 
    Beijing 100191, China
  • Received:2026-01-04 Revision received:2026-02-06 Accepted:2026-02-10 Online:2026-05-21 Published:2026-05-31

PDF (PC)

21

摘要： 航天器大尺度相对运动的轨迹跟踪控制是当前在轨服务等空间任务中的关键问题，传统基于局部线性近似的C-W动力学模型精度不足，难以满足工程需求。针对上述问题，提出了一种Koopman一体化控制方法，将动力学建模、状态估计与闭环控制统一于Koopman算子的全局线性化框架中，在保证计算效率的同时有效提升了控制精度和性能。该方法以状态变量张量积作为基函数，利用δ内积运算对Koopman算子进行高效建模，并在此基础上结合共轭无迹变换提出一种在线状态估计方法，仅需少量样本即可实现高精度状态估计，进一步地引入Koopman模型预测控制，通过冻结控制项系数将预测控制中的非凸优化问题转化为凸规划问题，实现闭环控制输入的高效求解。数值仿真结果表明，对于大尺度相对运动轨迹跟踪控制任务，所提出的方法在保持与传统基于C-W模型控制相当计算效率的同时，将燃料消耗降低至35%，并将轨迹跟踪误差降低至传统方法的2%。此外，在近距离相对运动条件下，该方法可退化为传统C-W控制策略，体现了其一致性与通用性。上述研究为航天器大尺度相对运动轨迹跟踪问题提供了一种高效且具有工程可行性的解决方案。

关键词: 大尺度相对运动, 轨迹跟踪, Koopman算子, 共轭无迹变换, 模型预测控制

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