中国空间科学技术

中国空间科学技术 ›› 2026, Vol. 46 ›› Issue (3): 130-142.doi: 10.16708/j.cnki.1000-758X.2026.0042

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

月面飞跃轨迹优化的最优协方差控制方法

苏文杰1，桂海潮1,2,3,*    

  1. 1.北京航空航天大学宇航学院，北京102206
    2.北京航空航天大学具身智能机器人研究院，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，北京102206
  • 收稿日期:2025-12-15 修回日期:2026-02-09 录用日期:2026-03-02 发布日期:2026-05-21 出版日期:2026-05-31

Optimal covariance control for lunar surface hop trajectory optimization

SU Wenjie1, GUI Haichao1,2,3,*    

  1. 1.School of Astronautics, Beihang University, Beijing 102206, China
    2.Embodied Intelligence Robotics Institute, Beihang University, Beijing 100191, China
    3.Key Laboratory of Spacecraft Design Optimization & Dynamic Simulation Technologies of Ministry of Education, Beijing 102206, China
  • Received:2025-12-15 Revision received:2026-02-09 Accepted:2026-03-02 Online:2026-05-21 Published:2026-05-31

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摘要： 月面环境的不确定性以及测量信息误差可能会造成飞跃制导精度的下降。为此，提出了一种基于最优协方差控制的轨迹优化方法，将随机不确定性引入轨迹优化过程，提高了轨迹对不确定性的鲁棒性。首先，采用机会约束最优协方差控制对飞跃轨迹优化问题进行建模，以燃料最优为性能指标，将随机不确定性下的飞行器动力学建模为随机微分方程，并引入了机会约束描述状态和推力约束。而后，设计了序列凸优化算法求解优化问题。第一步，采用零阶保持器对动力学进行离散化，引入卡尔曼滤波对状态进行实时估计，结合闭环系统的不确定性传播分析，建立离散时间随机最优控制问题。进一步，根据高斯分布的统计特征，将机会约束松弛为确定性约束，结合序列线性化方法转化为凸约束。迭代求解上述步骤得到的凸问题可以得到原问题的近似解。为验证算法的有效性，以月面平地飞跃和陨石坑探测为例进行仿真测试，在相同的约束条件下与确定性优化得到的最优轨迹对比。结果表明，提出的方法得到的闭环最优轨迹的位置和速度的标准差约为2m和1m/s，名义轨迹燃料消耗相比于开环方法只增加了不到0.1kg，闭环轨迹燃料消耗小于线性二次型调节器方法（LQR）。因此，基于协方差控制的轨迹优化方法能够应对测量和动力学的随机不确定性，提高飞跃任务的着陆精度。

关键词: 月面飞跃转移, 轨迹优化, 随机优化, 机会约束, 凸优化

Abstract: Lunar environmental uncertainties and measurement errors can degrade guidance accuracy. To address this issue, an optimal covariance control based method was proposed to incorporate stochastic uncertainties into the trajectory optimization process, thereby enhancing robustness against such disturbances. First, the trajectory optimization problem was formulated as a chance-constrained optimal covariance control problem, with fuel optimality as the performance metric. Stochastic differential equations were used to model dynamic uncertainties, and chance constraints were introduced to represent state and thrust constraints. Subsequently, a successive convex optimization algorithm was developed to solve the problem. The dynamics were discretized using a zero-order hold, and a Kalman filter was employed for real-time state estimation. Based on uncertainty propagation in the filtered closed-loop system, a discrete-time stochastic optimization problem was established. Furthermore, the chance constraints were relaxed into deterministic constraints using Gaussian distribution functions. These constraints were then convexified via successive linearization. An approximate solution to the original problem could thus be obtained by iteratively solving the convex subproblem. In numerical simulations, two scenarios are examined to demonstrate the effectiveness of the proposed algorithm, including hopping on a flat lunar surface and hopping into a pit. Under the same constraints, a comparison with deterministic optimization results shows that the closed-loop optimal trajectory obtained by the proposed method has standard deviations of approximately 2m in position and 1m/s in velocity, which are significantly smaller than those of the open-loop method. The fuel consumption for nominal trajectories increases by less than 0.1kg compared with open-loop method, and is less than the linear quadratic regulator (LQR). Therefore, the proposed method can effectively handle the stochastic uncertainties in measurements and dynamics, and significantly improve landing accuracy.

Key words: lunar hop；trajectory optimization, stochastic trajectory optimization, chance constraints, convex optimization