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可回收火箭大气层内动力下降的多阶段鲁棒优化制导方法

冯子鑫 薛文超 张冉 齐洪胜

冯子鑫, 薛文超, 张冉, 齐洪胜. 可回收火箭大气层内动力下降的多阶段鲁棒优化制导方法. 自动化学报, 2024, 50(3): 505−517 doi: 10.16383/j.aas.c230552
引用本文: 冯子鑫, 薛文超, 张冉, 齐洪胜. 可回收火箭大气层内动力下降的多阶段鲁棒优化制导方法. 自动化学报, 2024, 50(3): 505−517 doi: 10.16383/j.aas.c230552
Feng Zi-Xin, Xue Wen-Chao, Zhang Ran, Qi Hong-Sheng. A multi-stage robust optimization guidance method for endoatmospheric powered descent of reusable rockets. Acta Automatica Sinica, 2024, 50(3): 505−517 doi: 10.16383/j.aas.c230552
Citation: Feng Zi-Xin, Xue Wen-Chao, Zhang Ran, Qi Hong-Sheng. A multi-stage robust optimization guidance method for endoatmospheric powered descent of reusable rockets. Acta Automatica Sinica, 2024, 50(3): 505−517 doi: 10.16383/j.aas.c230552

可回收火箭大气层内动力下降的多阶段鲁棒优化制导方法

doi: 10.16383/j.aas.c230552
基金项目: 国家重点研发计划(2018YFA0703800), 国家自然科学基金(62122083, 62103014), 中国科学院青年创新促进会(E129030401)资助
详细信息
    作者简介:

    冯子鑫:中国科学院大学数学科学学院博士研究生. 2018年获得郑州大学学士学位, 2022年获得中国科学院大学硕士学位. 主要研究方向为轨迹规划, 最优控制和微分博弈. E-mail: fengzixin19@amss.ac.cn

    薛文超:中国科学院数学与系统科学研究院系统控制重点实验室副研究员. 2007年获得南开大学学士学位, 2012年获得中国科学院大学博士学位. 主要研究方向为非线性不确定系统控制, 非线性不确定系统滤波和分布式滤波. 本文通信作者. E-mail: wenchaoxue@amss.ac.cn

    张冉:北京航空航天大学宇航学院副教授. 2013年获得北京航空航天大学博士学位. 主要研究方向为高速飞行器的决策、轨迹规划与制导理论. E-mail: zhangran@buaa.edu.cn

    齐洪胜:中国科学院数学与系统科学研究院研究员. 2008年获得中国科学院大学博士学位. 主要研究方向为逻辑动态系统, 博弈与控制, 量子网络和分布式优化. E-mail: qihongsh@amss.ac.cn

A Multi-stage Robust Optimization Guidance Method for Endoatmospheric Powered Descent of Reusable Rockets

Funds: Supported by National Key Research and Development Program of China (2018YFA0703800), National Natural Science Foundation of China (62122083, 62103014), and Youth Innovation Promotion Association of Chinese Academy of Sciences (E129030401)
More Information
    Author Bio:

    FENG Zi-Xin Ph.D. candidate at the School of Mathematical Sciences, University of Chinese Academy of Sciences. He received his bachelor degree from Zhengzhou University in 2018 and received his master degree from University of Chinese Academy of Sciences in 2022. His research interest covers trajectory planning, optimal control, and differential games

    XUE Wen-Chao Associate researcher at the Key Laboratory of Systems and Control, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences. He received his bachelor degree from Nankai University in 2007 and received his Ph.D. degree from University of Chinese Academy of Sciences in 2012. His research interest covers nonlinear uncertain systems control, nonlinear uncertain systems filter, and distributed filter. Corresponding author of this paper

    ZHANG Ran Associate professor at the School of Astronautics, Beihang University. He received his Ph.D. degree from Beihang University in 2013. His research interest covers decision-making, trajectory design and guidance theory for high-speed flight vehicles

    QI Hong-Sheng Researcher at the Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences. He received his Ph.D. degree from University of Chinese Academy of Sciences in 2008. His research interest covers logical dynamic systems, games and control, quantum networks, and distributed optimization

  • 摘要: 针对大气层内可回收火箭的动力下降问题, 提出一种多阶段的鲁棒优化(Robust optimization, RO)方法. 由于大气层内存在未知风场, 如何在火箭下降段考虑这种不确定性具有十分重要的意义. 首先, 建立一个关于高度的不确定风场模型, 在该风场下给出火箭动力下降的鲁棒最优控制问题. 为了求解该问题, 使用一种对不等式约束采取一阶近似并将一阶项作为安全裕量加入约束的鲁棒优化方法, 得到一个可以求解的单阶段鲁棒优化算法. 其次, 定量给出安全裕量的上界, 基于该上界提出一种多阶段鲁棒优化算法, 避免单阶段鲁棒优化算法中安全裕量可能过大导致无法求解的问题. 最后, 通过仿真对比各个算法在多个实际风场下的性能, 结果表明所提出的多阶段鲁棒优化方法同时具有较高的落点精度和对于不同风场的鲁棒性.
  • 图  1  多阶段RO算法流程图

    Fig.  1  Flow chart of multi-stage RO algorithm

    图  2  $ y$轴的六个实际风场和一个标称风场

    Fig.  2  Six actual wind fields and one nominal wind field on the y-axis

    图  3  实际风场参数与标称风场参数的距离

    Fig.  3  Distances between parameters of actual wind fields and parameters of nominal wind field

    图  4  表1的仿真参数条件下随机生成的一组风场

    Fig.  4  A set of wind fields randomly generated under the simulation parameter conditions of Table 1

    图  5  单阶段RO算法和多阶段RO算法在不同风场下的最终位置误差

    Fig.  5  The terminal position errors of single-stage RO algorithm and multi-stage RO algorithm under different wind fields

    图  6  单阶段RO算法和多阶段RO算法在不同风场下的最终速度误差

    Fig.  6  The terminal velocity errors of single-stage RO algorithm and multi-stage RO algorithm under different wind fields

    图  7  单阶段RO算法和多阶段RO算法在各个实际风场下的轨迹

    Fig.  7  The trajectories of single-stage RO algorithm and multi-stage RO algorithm under each actual wind field

    图  8  单阶段RO算法的控制–时间图

    Fig.  8  Control-time diagram of single-stage RO algorithm

    图  9  多阶段RO算法的控制–时间图

    Fig.  9  Control-time diagram of multi-stage RO algorithm

    图  10  单阶段RO算法在不同风场下的最终位置与约束范围

    Fig.  10  The terminal position and its constraint range of single-stage RO algorithm under different wind fields

    图  11  单阶段RO算法在不同风场下的最终速度与约束范围

    Fig.  11  The terminal velocity and its constraint range of single-stage RO algorithm under different wind fields

    图  12  多阶段RO算法在不同风场下的最终位置与约束范围

    Fig.  12  The terminal position and its constraint range of multi-stage RO algorithm under different wind fields

    图  13  多阶段RO算法在不同风场下的最终速度与约束范围

    Fig.  13  The terminal velocity and its constraint range of multi-stage RO algorithm under different wind fields

    图  14  单阶段RO算法与NO算法在不同风场下的最终位置误差

    Fig.  14  The terminal position errors of single-stage RO algorithm and NO algorithm under different wind fields

    表  1  仿真参数值

    Table  1  Simulation parameter values

    参数取值
    初始状态${\boldsymbol{r}}_0=\left[2~968~{\rm{m}},263~{\rm{m}},4~326~{\rm{m}}\right]^{\rm{T}} $, ${\boldsymbol{v}}_0 = \left[-295~{\rm{m/s}},27~{\rm{m/s}},-296~{\rm{m/s}}\right]^{\rm{T}}$, $m_0=48~185$ kg
    期望落点状态${\boldsymbol{r}}_f =\left[0~{\rm{m}},0~{\rm{m}},0~{\rm{m}}\right]^{\rm{T}}$, $ {\boldsymbol{v}}_f =\left[0~{\rm{m/s}},0~{\rm{m/s}},0~{\rm{m/s}}\right]^{\rm{T}}$
    火箭燃料消耗常数$\kappa=2~975$
    火箭参考面积$S_{{{\rm{ref}}}}=8.814\ {\rm{m}}^2 $
    空气动力学阻力系数$C_D=4.5$
    标称风场参数$\hat{{\boldsymbol{s}}}=\left[-0.073,4.460,5.230\right]^{\rm{T}},\ \mu=2~234,\ \sigma=1~635$, $ k=2.16\times{10}^{-3}, b=0.35$
    ${\boldsymbol{S}}_\tau $中的参数$\tau=1,\ {\boldsymbol{D}}=\text{ diag}\left\{0.83,\ 1.20,\ 2.66\right\}$
    终端约束范围单阶段RO算法${\boldsymbol{L}}=\left[L_{rx},L_{ry},L_{rz},L_{vx},L_{vy},L_{vz}\right]=\left[7,35,7,35,35,35\right]$
    多阶段RO算法${\boldsymbol{L}}=\left[4,20,4,4,4,4 \right]$
    多阶段RO算法的阶段数2
    下载: 导出CSV

    表  2  单阶段RO算法和多阶段RO算法的运行时间

    Table  2  Running time of single-stage RO algorithm and multi-stage RO algorithm

    算法运行时间(s)
    单阶段RO算法6.61
    多阶段RO算法13.14
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-09-05
  • 录用日期:  2023-11-09
  • 网络出版日期:  2024-02-23
  • 刊出日期:  2024-03-29

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