可回收火箭大氣層內動(dòng)力下降的多階段魯棒優(yōu)化制導方法
doi: 10.16383/j.aas.c230552
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中國科學(xué)院大學(xué)數學(xué)科學(xué)學(xué)院 北京 100049
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中國科學(xué)院數學(xué)與系統科學(xué)研究院系統控制重點(diǎn)實(shí)驗室 北京 100190
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北京航空航天大學(xué)宇航學(xué)院 北京 100191
A Multi-stage Robust Optimization Guidance Method for Endoatmospheric Powered Descent of Reusable Rockets
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School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049
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The Key Laboratory of Systems and Control, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190
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School of Astronautics, Beihang University, Beijing 100191
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摘要: 針對大氣層內可回收火箭的動(dòng)力下降問(wèn)題, 提出一種多階段的魯棒優(yōu)化(Robust optimization, RO)方法. 由于大氣層內存在未知風(fēng)場(chǎng), 如何在火箭下降段考慮這種不確定性具有十分重要的意義. 首先, 建立一個(gè)關(guān)于高度的不確定風(fēng)場(chǎng)模型, 在該風(fēng)場(chǎng)下給出火箭動(dòng)力下降的魯棒最優(yōu)控制問(wèn)題. 為了求解該問(wèn)題, 使用一種對不等式約束采取一階近似并將一階項作為安全裕量加入約束的魯棒優(yōu)化方法, 得到一個(gè)可以求解的單階段魯棒優(yōu)化算法. 其次, 定量給出安全裕量的上界, 基于該上界提出一種多階段魯棒優(yōu)化算法, 避免單階段魯棒優(yōu)化算法中安全裕量可能過(guò)大導致無(wú)法求解的問(wèn)題. 最后, 通過(guò)仿真對比各個(gè)算法在多個(gè)實(shí)際風(fēng)場(chǎng)下的性能, 結果表明所提出的多階段魯棒優(yōu)化方法同時(shí)具有較高的落點(diǎn)精度和對于不同風(fēng)場(chǎng)的魯棒性.
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關(guān)鍵詞:
- 大氣層內動(dòng)力下降 /
- 魯棒優(yōu)化 /
- 可回收火箭 /
- 制導與控制 /
- 不確定風(fēng)場(chǎng)
Abstract: This paper proposes a multi-stage robust optimization (RO) method for the endoatmospheric powered descent problem of reusable rockets. Due to the unknown wind field in the atmosphere, it is of great significance to consider this uncertainty during the rocket descent phase. Firstly, a model of uncertain wind field with respect to altitude is established, and a robust optimal control problem for rocket powered descent is formulated under this wind field. To solve this problem, a tractable single-stage RO algorithm is developed by approximating the inequality constraints using a first-order expansion and incorporating the first-order term as a safety margin. Secondly, an upper bound on the safety margin is quantitatively derived. Based on this upper bound, a multi-stage RO algorithm is proposed, which avoids the infeasibility problem caused by the excessively large safety margin in the single-stage RO algorithm. Finally, simulation results are presented to compare the performance of each algorithm under various actual wind fields. The results demonstrate that the proposed multi-stage RO method achieves both high landing accuracy and robustness against different wind fields. -
圖 2 $ y$軸的六個(gè)實(shí)際風(fēng)場(chǎng)和一個(gè)標稱(chēng)風(fēng)場(chǎng)
Fig. 2 Six actual wind fields and one nominal wind field on the y-axis
圖 3 實(shí)際風(fēng)場(chǎng)參數與標稱(chēng)風(fēng)場(chǎng)參數的距離
Fig. 3 Distances between parameters of actual wind fields and parameters of nominal wind field
圖 5 單階段RO算法和多階段RO算法在不同風(fēng)場(chǎng)下的最終位置誤差
Fig. 5 The terminal position errors of single-stage RO algorithm and multi-stage RO algorithm under different wind fields
圖 6 單階段RO算法和多階段RO算法在不同風(fēng)場(chǎng)下的最終速度誤差
Fig. 6 The terminal velocity errors of single-stage RO algorithm and multi-stage RO algorithm under different wind fields
圖 7 單階段RO算法和多階段RO算法在各個(gè)實(shí)際風(fēng)場(chǎng)下的軌跡
Fig. 7 The trajectories of single-stage RO algorithm and multi-stage RO algorithm under each actual wind field
圖 10 單階段RO算法在不同風(fēng)場(chǎng)下的最終位置與約束范圍
Fig. 10 The terminal position and its constraint range of single-stage RO algorithm under different wind fields
圖 11 單階段RO算法在不同風(fēng)場(chǎng)下的最終速度與約束范圍
Fig. 11 The terminal velocity and its constraint range of single-stage RO algorithm under different wind fields
圖 12 多階段RO算法在不同風(fēng)場(chǎng)下的最終位置與約束范圍
Fig. 12 The terminal position and its constraint range of multi-stage RO algorithm under different wind fields
圖 13 多階段RO算法在不同風(fēng)場(chǎng)下的最終速度與約束范圍
Fig. 13 The terminal velocity and its constraint range of multi-stage RO algorithm under different wind fields
圖 14 單階段RO算法與NO算法在不同風(fēng)場(chǎng)下的最終位置誤差
Fig. 14 The terminal position errors of single-stage RO algorithm and NO algorithm under different wind fields
表 1 仿真參數值
Table 1 Simulation parameter values
參數 取值 初始狀態(tài) ${\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 期望落點(diǎn)狀態(tài) ${\boldsymbol{r}}_f =\left[0~{\rm{m}},0~{\rm{m}},0~{\rm{m}}\right]^{\rm{T}}$, $ {\boldsymbol{v}}_f =\left[0~{\rm{m/s}},0~{\rm{m/s}},0~{\rm{m/s}}\right]^{\rm{T}}$ 火箭燃料消耗常數 $\kappa=2~975$ 火箭參考面積 $S_{{{\rm{ref}}}}=8.814\ {\rm{m}}^2 $ 空氣動(dòng)力學(xué)阻力系數 $C_D=4.5$ 標稱(chēng)風(fēng)場(chǎng)參數 $\hat{{\boldsymbol{s}}}=\left[-0.073,4.460,5.230\right]^{\rm{T}},\ \mu=2~234,\ \sigma=1~635$, $ k=2.16\times{10}^{-3}, b=0.35$ ${\boldsymbol{S}}_\tau $中的參數 $\tau=1,\ {\boldsymbol{D}}=\text{ diag}\left\{0.83,\ 1.20,\ 2.66\right\}$ 終端約束范圍 單階段RO算法${\boldsymbol{L}}=\left[L_{rx},L_{ry},L_{rz},L_{vx},L_{vy},L_{vz}\right]=\left[7,35,7,35,35,35\right]$
多階段RO算法${\boldsymbol{L}}=\left[4,20,4,4,4,4 \right]$多階段RO算法的階段數 2 
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表 2 單階段RO算法和多階段RO算法的運行時(shí)間
Table 2 Running time of single-stage RO algorithm and multi-stage RO algorithm
算法 運行時(shí)間(s) 單階段RO算法 6.61 多階段RO算法 13.14
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