宇航学报

宇航学报 ›› 2017, Vol. 38 ›› Issue (10): 1057-1067.doi: 10.3873/j.issn.1000-1328.2017.10.006

• 制导、导航、控制与电子 • 上一篇    下一篇

采用SDRE方法的无径向推力最优轨道控制

张相宇，张刚，曹喜滨   

  1. 哈尔滨工业大学卫星技术研究所，哈尔滨150001
  • 收稿日期:2016-09-12 修回日期:2017-04-21 出版日期:2017-10-15 发布日期:2017-10-25
  • 基金资助:

    国家自然科学基金（11402062,91438202）；重点实验室开放基金(HIT.KLOF.MST.201504)

Optimal Orbital Control without Radial Thrust Based on SDRE Method

ZHANG Xiang yu, ZHANG Gang, CAO Xi bin   

  1. Research Center of Spacecraft Technology, Harbin Institute of Technology, Harbin 150001, China
  • Received:2016-09-12 Revised:2017-04-21 Online:2017-10-15 Published:2017-10-25

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摘要：

针对无径向推力作用的两航天器轨道交会和编队卫星队形重构任务，采用状态依赖Riccati方程(SDRE)方法求解了其最优轨道控制问题。首先考虑J 2摄动和推力仅存在于追踪航天器的周向和法向，推导了状态依赖配点(SDC)形式的非线性相对运动方程。然后针对终端状态为零的轨道交会问题，采用SDRE方法得到了最优反馈控制律，并给出了状态依赖Riccati微分方程的近似求解策略和数值求解策略。接着扩展了SDRE方法并将其用于终端状态不为零的编队卫星队形重构问题，并给出了相应的数值求解策略。相比于伪谱法等优化方法，本文提出的方法不需要初始猜测值。此外，数值仿真表明，解析求解Riccati微分方程方法对于近圆轨道具有较高的精度，数值计算方法对即使偏心率为0.3的椭圆轨道，其最优性偏差仍小于6%。

关键词: 轨道交会, 编队重构, 状态依赖Riccati方程(SDRE), 周向推力, 轨迹优化

Abstract:

The optimal control problem of spacecraft rendezvous and formation reconfiguration without radial thrust is investigated by using the state dependent Riccati equation (SDRE) method. Considering the thrusters installed in the circumferential and normal directions, the nonlinear relative motion equations influenced by J 2 perturbation are derived and presented via the state-dependent coefficient (SDC). Then the optimal feedback control law is derived by using the SDRE method, and an approximate analytical solution of the state dependent Riccati differential equation is obtained. Moreover, a numerical version of the obtained analytical solution is extended to solve the formation reconfiguration problem. Compared with the Gauss pseudospectral spectral method, the proposed method does not need an initial guess. Numerical results show that the analytical solution of the Riccati differential equation method has high precision for the near circular orbits, and the error of the optimal index of the numerical method is less than 6% even for the elliptical orbits with an eccentricity approaching to 0.3.

Key words: Orbital rendezvous, Formation reconfiguration, State dependent Riccati equation (SDRE), Circumferential thrust, Trajectory optimization

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