基于混沌多项式的RBCC飞行器上升段鲁棒轨迹快速优化

doi:10.7527/S1000-6893.2023.28349

Abstract

Abstract:

The ascent trajectory design for Rocket-Based Combined Cycle （RBCC） hypersonic vehicle has many typical characteristics， including complex power system working modes， strong coupling between thrust and flight state， highly nonlinear models， numerous complex constraints， parameter uncertainties， etc. In this paper， a robust trajectory optimization method for RBCC power ascent based on non-intrusive polynomial chaos， the Gaussian quadrature strategy， and sequential convex optimization is proposed to enhance the trajectory’s anti-interference ability and process reliability. Firstly， a robust trajectory optimization model for the RBCC hypersonic ascent， accounting for parameter uncertainties， is established. An uncertainty quantification propagation algorithm based on the Gaussian quadrature strategy and non-intrusive polynomial chaos is designed to transform the robust optimization model into a deterministic trajectory optimization problem with extended dimensions. Then， the extend model is convexified and discretized using convex optimization theory， and a trajectory optimization solution strategy based on sequential convex optimization algorithm is established to achieve a solution of this high-dimensional deterministic optimization problem. The optimaization results of a certain air-based vehicle’s ascent trajectory indicate that based on the constructed model and trajectory method， the robust trajectory optimization of the ascent phase of the RBCC hypersonic aircraft can be effectively completed， and the optimization results are in line with the working characteristics of the RBCC power system. Compared with the traditional deterministic trajectory optimization algorithm， the proposed method can effectively reduce the influence of random disturbances on the ascent trajectory， thereby improving the reliability and robustness of the trajectory.

Key words: Rocket-Based Combined Cycle (RBCC), hypersonic vehicle, ascent trajectory, robust optimization, uncertainty, non-intrusive polynomial chaos, Gaussian quadrature strategy, convex optimization

CLC Number:

V412

Xunliang YAN, Peichen WANG, Shumei WANG, Yuxuan YANG, Kuan WANG. Rapid robust trajectory optimization for RBCC vehicle ascent based on polynomial chaos[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(21): 528349.

Figures/Tables 16

Table 1

Correspondence between distribution type of random variables and orthogonal basis functions［31］

分布类型	基多项式	概率密度函数
高斯分布	Hermite	$1 2 π e x p - x 2 2$
均匀分布	Legendre	$12$
指数分布	Laguerre	$e x p (- x)$
$β$ 分布	Jacobi	$(1 - x) γ (1 + x) β / 2 γ + β + 1 B (γ + 1, β + 1)$

Table 1

Fig.1

Table 2

Parameter uncertainties setting

不确定参数	符号	分布类型	$3 σ$
大气密度	$δ ρ$	高斯	15%
升力系数	$δ C L$	高斯	15%
阻力系数	$δ C D$	高斯	15%
推力大小	$δ P$	高斯	1%

Table 2

Fig.2

Fig.3

Fig.4

Fig.5

Table 3

Table 4

Weight coefficients setting

工况	$k g$	$k J$	$k x$
工况1	3	0	0
工况2	3	3	0
工况3	3	3	3

Table 4

Fig.6

Fig.7

Table 5

MC shooting results of optimization control quantity under different conditions

情况	$μ (t f)$ /s	$μ (m f)$ /kg	$μ (h f)$ /km	$μ / M a f$	$σ (h f)$ /km	$σ (V f)$ /（m·s^-1）	P_e/%
标准	120.9	1 218.4	49.72	10.97	1.46	66.92	54.60
工况1	122.1	1 210.7	50.01	11.00	1.36	66.03	0.10
工况2	128.8	1 177.9	50.00	11.00	0.48	61.61	0.03
工况3	130.2	1 152.8	50.02	11.20	0.48	61.19	0.01

Table 5

Fig.8

Fig.9

Table 6

MC shooting data comparison of optimization results between GP-PC and CO-PC

算法	$μ (t f)$ /s	$μ (m f)$ /kg	$μ (h f)$ /km	$μ (M a f)$	$σ (h f)$ /km	$σ (V f)$ /（m·s^-1）	Pe/%
标准	120.9	1 218.4	49.72	10.97	1.46	66.92	54.60
CO-PC	130.2	1 152.8	50.02	11.20	0.48	61.19	0.01
GP-PC	132.1	1 131.2	50.03	11.23	0.52	61.97	0.02

Table 6

Table 7

References 31

1	王亚军，何国强，秦飞等. 火箭冲压组合动力研究进展［J］. 宇航学报， 2019， 40（10）： 1126-1133.
	WANG Y J， HE G Q， QIN F， et al. Research progress of rocket based combined cycle engines［J］. Journal of Astronautics， 2019， 40（10）： 1125-1133 （in Chinese）.
2	阮建刚，何国强，吕翔. RBCC-RKT两级入轨飞行器飞行轨迹优化方法［J］. 航空学报， 2014， 35（5）： 1284-1291.
	RUAN J G， HE G Q， LV X. Trajectory optimization method in two-stage-to-orbit RBCC-RKT launch Vehicle［J］. Acta Aeronautica et Astronautica Sinica， 2014， 35（5）： 1284-1291 （in Chinese）.
3	OLDS J， BUDIANTO I. Constant dynamic pressure trajectory simulation with post［C］∥AIAA Aerospace Sciences Meeting and Exhibit. Reston： AIAA， 1998： 1-12.
4	孙佩华，刘燕斌，陈柏屹. 基于预置动压的高超声速飞行器上升段轨迹设计［J］. 飞行力学， 2017， 35（5）：57-61.
	SUN P H， LIU Y B， CHEN B Y. Ascent trajectory design of hypersonic vehicle based on preset dynamic pressure［J］. Flight Dynamics， 2017， 35（5）：57-61 （in Chinese）.
5	李惠峰，李昭莹. 高超声速飞行器上升段最优制导间接法研究［J］. 宇航学报， 2011， 32（2）： 297-302.
	LI H F， LI Z Y. Indirect method of optimal ascent guidance for hypersonic vehicle［J］. Journal of Astronautics， 2011， 32（2）： 297-302 （in Chinese）.
6	DEREK J， DRISCOLL F. Minimum-fuel ascent of a hypersonic vehicle using surrogate optimization［J］. Journal of Aircraft， 2014， 51（6）： 1973-1986．
7	龚春林，韩璐，谷良贤. 适应于RBCC运载器的轨迹优化建模研究［J］. 宇航学报， 2013， 34（12）： 1592-1598.
	GONG C L， HAN L， GU L X. Research on modeling of trajectory optimization for RBCC-powered RLV［J］. Journal of Astronautics， 2013， 34（12）： 1592-1598.
8	周宏宇，王小刚，崔乃刚等. 基于hp自适应伪谱法的组合动力可重复使用运载器轨迹优化［J］. 中国惯性技术学报， 2016， 24（6）： 832-837.
	ZHOU H Y， WANG X G， CUI N G， et al. Trajectory optimization of reusable vehicle with combined power based on hp adaptive pseudospectral algorithm ［J］. Journal of Chinese Inertial Technology， 2016， 24（6）： 832-837.
9	WEI J L， TANG X J， YAN J. Costate estimation for a multiple-interval pseudospectral method using collocation at the flipped Legendre-Gauss-Radau points ［J］. IEEE/CAA Journal of Automatica Sinica， 2018， 12： 1-15.
10	Yang S B， Cui T， Hao X Y， et al. Trajectory optimization for a ramjet-powered vehicle in ascent phase via the Gauss pseudospectral method ［J］. Aerospace Science and Technology， 2017， 67： 88-95.
11	SONG J， SUA H Q. The ascent trajectory optimization of two-stage-to-orbit aerospace plane based on pseudospectral method ［J］. Procedia Engineering， 2015， 99： 1044-1048.
12	ZHOU H Y， WANG X G， BAI Y L， et al. Ascent phase trajectory optimization for vehicle with multi-combined cycle engine based on improved particle swarm optimization［J］. Acta Astronautica， 2017， 140： 156-165.
13	LIU X F， LU P， PAN B F. Survey of convex optimization for aerospace applications［J］. Astrodynamics， 2017， 1（1）： 23-40.
14	LU P， LIU X F. Solving nonconvex optimal control problems by convex optimization［J］. Journal of Guidance， Control， and Dynamics， 2014， 37（3）：750-765.
15	罗哲，王舒眉，闫循良，等. RBCC动力高超声速飞行器上升段轨迹优化设计［J］. 红外与激光工程， 2022， 51（8）： 478-485.
	LUO Z， WANG S M， YAN X L， et al. Trajectory optimization design of ascending stage of RBCC powered hypersonic vehicle ［J］. Infrared and Laser Engineering， 2022， 51（8）： 478-485.
16	LIU X F， SHEN Z J， LU P， Entry trajectory optimization by second-order cone programming［J］. Journal of Guidance， Control， and Dynamics， 2015， 39（2）： 227-241.
17	LU P， LIU X F， Autonomous trajectory planning for rendezvous and proximity operations by conic optimization［J］. Journal of Guidance， Control， and Dynamics. 2013， 36（2）： 375-389.
18	SONG Z Y， WANG C. Powered soft landing guidance method for launchers with non-cluster configured engines［J］. Acta Astronautica， 2021， 189： 379-390.
19	LIU X F. Fuel-optimal rocket landing with aerodynamic controls［J］. Journal of Guidance， Control， and Dynamics， 2019， 42（1）： 65-76.
20	陈琦，王中原，常思江，等. 不确定飞行环境下的滑翔制导炮弹方案弹道优化［J］. 航空学报， 2014， 35（9）： 2593-2604.
	CHEN Q， WANG Z Y， CHANG S J， et al. Optimal trajectory design under uncertainty for a gliding guided projectile［J］. Acta Aeronautica et Astronautica Sinica， 2014， 35（9）： 2593-2604 （in Chinese）.
21	YANG Z， LUO Y Z， ZHANG J. Robust planning of nonlinear rendezvous with uncertainty［J］. Journal of Guidance Control and Dynamics， 2017， 40（8）： 1954-1967.
22	FISHER J， BHATTACHARYA R. Optimal trajectory generation with probabilistic system uncertainty using polynomial chaos［J］. Journal of Dynamic Systems Measurement and Control， 2011， 133（1）： 014501.
23	WANG F， YANG S， XIONG F F， et al. Robust trajectory optimization using polynomial chaos and convex optimization［J］. Aerospace Science and Technology， 2019， 92（2）： 314-325.
24	LI X， NAIR P B， ZHANG Z G. Aircraft robust trajectory optimization using nonintrusive polynomial chaos［J］. Journal of Aircraft， 2014， 51（5）： 1592-1603.
25	JIANG X Q， LI S. Uncertainty quantification for mars atmospheric entry using polynomial chaos and spectral decomposition［C］∥AIAA Guidance， Navigation， and Control Conference. Reston： AIAA， 2018：1-18.
26	XIONG F F， Chen S S， XIONG Y. Dynamic system uncertainty propagation using polynomial chaos［J］. Chinese Journal of Aeronautics， 2014， 27（5）： 1156-1170.
27	HOSDER S， WALTERS R W， BALCH M. Point-collocation nonintrusive polynomial chaos method for stochastic computational fluid dynamics［J］. AIAA Journal， 2010， 48（12）：2721-2730.
28	JIANG X Q， LI S. Mars entry trajectory planning using robust optimization and uncertainty quantification［J］. Acta Astronautica， 2019， 161： 249-261.
29	杨奔，雷建长，王宇航. 考虑气动参数扰动的再入轨迹快速优化方法［J］. 力学学报， 2020， 52（6）： 67-77.
	YANG B， LEI J C， WANG Y H. Fast optimization method of reentry trajectory considering aerodynamic parameter perturbation［J］. Chinese Journal of Theoretical and Applied Mechanics， 2020， 52（6）：67-77 （in Chinese）.
30	杨奔，李天任，马晓媛. 基于序列凸优化的多约束轨迹快速优化［J］. 航天控制， 2020， 38（3）： 25-30.
	YANG B， LI T R， MA X Y. Fast multi-constraints trajectory optimization based on sequence convex optimization［J］. Aerospace Control， 2020， 38（3）： 25-30 （in Chinese）.
31	ELDRED M S， WEBSTER C G， CONSTANTINE P G. Evaluation of non-intrusive approaches for wiener-askey generalized polynomial chaos［C］∥49th AIAA Structural Dynamics and Materials Conference. Reston： AIAA， 2008.

方法	均值		标准差
方法	结果/km	误差/%	结果/km	误差/%
MC	49.734 5		1.459 3
n=2，p=1	49.726 7	0.015 6	1.448 6	0.739 0
n=2，p=2	49.726 7	0.015 6	1.458 9	0.032 7
n=2，p=3	49.726 7	0.015 6	1.878 1	28.694 4
n=3，p=2	49.725 1	0.018 8	1.462 2	0.193 0
n=3，p=3	49.725 1	0.018 8	1.462 3	0.201 9

优化算法	待优化变量数	迭代步数	优化耗时/s
GP-PC	3 024	6	6 250.2
CO-PC	2 562	9	862.8

[1]	Zhengyu SONG. Promoting continuous innovation in space transportation systems: Control technologies and challenges [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(6): 531446-531446.
[2]	Zhichun YANG, Te YANG. Physical embedded neural network model and method for dynamic load identification [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(5): 531450-531450.
[3]	Shenfang YUAN, Qiuhui XU, Jian CHEN. Reliability evaluation: From non-destructive testing to structural health monitoring [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(5): 531442-531442.
[4]	Feng QU, Qing WANG, Shaowen CHENG, Kaiqiang WANG. Aerodynamic shape optimization design of airframe/propulsion integrated hypersonic aircraft with aerodynamics/trajectory/ control coupling [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(4): 130874-130874.
[5]	Yousheng WANG, Liguo SUN, Jinpeng WEI, Wenqian TAN, Yonghao PAN. Optimization of climb trajectory of combined-cycle engine powered aircraft based on improved CSO-Gauss pseudospectral method [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(2): 230737-230737.
[6]	Yifei WANG, Geyong CAO, Yang CAO, Xiaojun WANG. Uncertainty technologies in aircraft digital strength twins [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(19): 532408-532408.
[7]	Yiyu WANG, Zexu ZHANG, Weimin BAO, Shuai YUAN, Hutao CUI. Approaching trajectory planning with field-of-view constraints for non-cooperative spacecraft rendezvous [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(16): 331702-331702.
[8]	Chunhui ZHAO, Anmeng LIU, Yang LYU, Quan PAN. A survey of resilient self-localization for UAV [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(8): 28839-028839.
[9]	Hua YANG, Shusheng CHEN, Zhenghong GAO, Quanfeng JIANG, Wei ZHANG. Rotor aerodynamic data fusion based on Bayesian framework [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(8): 128960-128960.
[10]	Bo YANG, He YU, Zichen FAN. Micro-energy analysis method for time-varying error of aero-optical effects [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(4): 128703-128703.
[11]	Tiancai WU, Honglun WANG, Bin REN, Guocheng YAN, Xingyu WU. Learning-based hierarchical coordination fault-tolerant method for hypersonic vehicles [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(22): 330191-330191.
[12]	Haiyue AO, Chihang YANG, Yu SHI, Hao ZHANG. Stationkeeping strategies for close formation flight on distant retrograde orbits [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(22): 330306-330306.
[13]	Chunhua LI, Jianzhong SUN, Jilong LU. Maintenance-oriented approach for HPT blade life digital twin modeling [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(21): 629385-629385.
[14]	Jiangfeng FU, Shijie ZHONG, Xianwei LIU, Pengfei WEI, Hanting HUANG. Improved PCE model with coupled double-layer parameter updating for uncertainty analysis in fuel centrifugal pump [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(21): 130126-130126.
[15]	Yingzhi ZHANG, Huibin SUN, Cheng YAN, Meng LIU. A digital twin model for rotor tip clearance prediction considering interval uncertainty [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(21): 629775-629775.

Rapid robust trajectory optimization for RBCC vehicle ascent based on polynomial chaos

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 16

References 31

Related Articles 15

Recommended Articles

Metrics

Comments