PCE-Based Robust Trajectory Optimization of Launch Vehicles via Adaptive Sample and Truncation
Publication: Journal of Aerospace Engineering
Volume 35, Issue 5
Abstract
To reduce the sensitivity of trajectory to uncertainty, this paper concerns the robust trajectory optimization of the solid ascent launch vehicles with the uncertainty of aerodynamic parameters and engine mass flow. Due to the strong nonlinearity and fast time-varying characteristics, the traditional robust trajectory optimization method based on polynomial chaos expansion (PCE) has slow convergence speed and large prediction errors. To overcome these difficulties, an improved robust optimization algorithm based on sample updating and adaptive truncated PCE (UAPCE) is put forward. Compared with the conventional PCE optimization methods, our contributions mainly focus on three aspects: First, to optimize the standard deviation of the terminal trajectory under uncertainty conditions, the original state is sampled and expanded by PCE, and the statistical characteristics of the original state, constraints, and indicators are described by the expanded state. Second, in order to promote the convergence speed of PCE, the sampling points are updated automatically by the proposed sample updating method in the pseudo-spectral optimization of the expanded state. Finally, the adaptive polynomial truncation method is creatively proposed to break through the fitting accuracy limit of the conventional PCE method under the same computation complexity. Through Monte Carlo simulations, the proposed UAPCE greatly reduces the standard deviation of the terminal state compared with the nonrobust optimization, demonstrating strong robustness to the uncertainty. Simultaneously, the UAPCE method has better convergence speed and prediction accuracy compared with the traditional PCE method.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 61627810, 61790562, and 61403096).
References
Bataleblu, A. A., and J. Roshanian. 2015. “Robust trajectory optimization of space launch vehicle using computational intelligence.” In Proc., IEEE Congress on Evolutionary Computation, 3418–3425. New York: IEEE. https://doi.org/10.1109/CEC.2015.7257318.
Chai, R., A. L. Savvaris, and A. Tsourdos. 2017. “Violation learning differential evolution-based hp-Adaptive pseudospectral method for trajectory optimization of space maneuver vehicle.” IEEE Trans. Aerosp. Electron. Syst. 53 (4): 2031–2044. https://doi.org/10.1109/TAES.2017.2680698.
Chai, R., A. L. Savvaris, and A. Tsourdos. 2020a. “Solving trajectory optimization problems in the presence of probabilistic constraints.” IEEE Trans. Cybern. 50 (10): 4332–4345. https://doi.org/10.1109/TCYB.2019.2895305.
Chai, R., A. Tsourdos, and A. Savvaris. 2020b. “Real-time reentry trajectory planning of hypersonic vehicles: A two-step strategy incorporating fuzzy multiobjective transcription and deep neural network.” IEEE Trans. Ind. Electron. 67 (8): 6904–6915. https://doi.org/10.1109/TIE.2019.2939934.
Eldred, M., C. Webster, and P. Constantine. 2008. “Evaluation of non-intrusive approaches for Wiener-Askey generalized polynomial chaos.” In Proc., 10th AIAA Non-Deterministic Approaches Conf. Reston, VA: American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2008-1892.
Foust, R., S. Chung, and F. Y. Hadaegh. 2019. “Optimal guidance and control with nonlinear dynamics using sequential convex programming.” J. Guidance Control Dyn. 43 (4): 633–644. https://doi.org/10.2514/1.G004590.
Greco, C., S. Campagnola, and M. L. Vasile. 2020. “Robust space trajectory design using belief stochastic optimal control.” In Proc., AIAA Scitech Forum, 1471. Reston, VA: American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2020-1471.
Huang, G., Y. Lu, and Y. Nan. 2012. “A survey of numerical algorithms for trajectory optimization of flight vehicles.” Sci. China Technol. Sci 55 (9): 2538–2560. https://doi.org/10.1007/s11431-012-4946-y.
Huang, Y. 2018. “Optimal Mars entry trajectory planning and guidance design considering uncertainties.” Ph.D. dissertation, College of Aerospace Science and Engineering, Graduate School of National Univ. of Defense Technology. https://doi.org/10.1016/j.actaastro.2019.05.033.
Huang, Y., and H. Li. 2018. “Reliability-based trajectory optimization using nonintrusive polynomial chaos for Mars entry mission.” Adv. Space Res. 61 (11): 2854–2869. https://doi.org/10.1016/j.asr.2018.03.009.
Huang, Y., H. Li, and X. Du. 2019. “Mars entry trajectory robust optimization based on evidence under epistemic uncertainty.” Acta Astronaut. 163 (Oct): 225–237. https://doi.org/10.1016/j.actaastro.2019.01.034.
Huang, Y., H. Li, and J. Zhang. 2017. “Uncertainty analysis of reachable set for planetary entry using polynomial chaos.” Adv. Space Res. 60 (11): 2491–2504. https://doi.org/10.1016/j.asr.2017.09.028.
Jha, D., P. Kolaric, and D. Romeres. 2019. “Robust optimization for trajectory-centric model-based reinforcement learning.” Accessed December 18, 2019. http://www.merl.com.
Jiang, X., and S. Li. 2019. “Mars entry trajectory planning using robust optimization and uncertainty quantification.” Acta Astronaut. 161 (Aug): 249–261. https://doi.org/10.1016/j.actaastro.2019.05.033.
Jiang, Z., and R. Ordóñez. 2009. “On-line robust trajectory generation on approach and landing for reusable launch vehicles.” Automatica 45 (7): 1668–1678. https://doi.org/10.1016/j.automatica.2009.03.017.
Li, X., P. Nair, and Z. Zhang. 2014. “Aircraft robust trajectory optimization using nonintrusive polynomial chaos.” J. Aircr. 51 (5): 1592–1603. https://doi.org/10.2514/1.C032474.
Liu, B. 2018. “The method of uncertainty quantification of flight vehicle guidance and control system.” Master’s dissertation, Control and Simulation Center, Harbin Institute of Technology.
Liu, X., and P. Lu. 2014. “Solving nonconvex optimal control problems by convex optimization.” J. Guidance Control Dyn. 37 (3): 750–765. https://doi.org/10.2514/1.62110.
Liu, X., P. Lu, and B. Pan. 2017. “Survey of convex optimization for aerospace applications.” Astrodynamics 1 (1): 23–40. https://doi.org/10.1007/s42064-017-0003-8.
Miller, A. T., and A. V. Rao. 2017. “Rapid ascent-entry vehicle mission optimization using hp-adaptive gaussian quadrature collocation.” In Proc., AIAA Atmospheric Flight Mechanics Conf. Reston, VA: American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2017-0249.
Ni, Y. 2020. “Optimization of the reference Trajectory of the ascending phase for the launch vehicle considering parameter uncertainty.” Master’s dissertation, Control and Simulation Center, Harbin Institute of Technology. https://doi.org/10.27061/d.cnki.ghgdu.2020.004058.
Pan, Y., E. A. Theodorou, and K. Bakshi. 2015. “Robust trajectory optimization: A cooperative stochastic game theoretic approach.” Rob. Sci. Syst. 11 (Jul): 29. https://doi.org/10.15607/RSS.2015.XI.029.
Peng, K., R. Peng, Z. Huang, and B. Zhang. 2019. “Implicit shooting method to solve optimal Lunar soft landing trajectory.” Acta Aeronaut. Astronaut. Sin. 40 (7): 159–167. https://doi.org/10.7527/s1000-6893.2018.22641.
Ren, C., F. Xiong, and B. Mo. 2021. “Design sensitivity analysis with polynomial chaos for robust optimization.” Struct. Multidiscip. Optim. 63 (1): 357–373. https://doi.org/10.1007/s00158-020-02704-2.
Saunders, B. R. 2012. “Optimal trajectory design under uncertainty.” Ph.D. dissertation, Dept. of Aronautics and Astronautics, Massachusetts Institute of Technology. http://hdl.handle.net/1721.1/76902.
Sun, Z., T. Chao, S. Wang, and M. Yang. 2017. “Optimization method of multi-stages launch vehicle trajectory based on segmental Chebyshev pseudo spectral method.” In Proc., 36th Chinese Control Conf., 901–906. New York: IEEE. https://doi.org/10.23919/ChiCC.2017.8028283.
Sun, Z., T. Chao, S. Wang, and M. Yang. 2018. “Convex method for ascent trajectory optimization using iterative narrowing trust region.” In Proc., IEEE China Guidance Navigation and Control Conf. New York: IEEE. https://doi.org/10.1109/GNCC42960.2018.9019086.
Tang, J., Y. Liu, and R. Cao. 2020a. “Robust optimization of key mission points in climbing phase for air-breathing hypersonic vehicle.” J. Astronaut. 41 (5): 507–520. https://doi.org/10.3873/j.issn.1000-1328.2020.05.001.
Tang, S., X. Wang, and J. Guo. 2020b. “Trajectory optimization and guidance for hypersonic gliding vehicles based on hp pseudospectral convex programming.” Tactical Missile Technol. 5: 66–75. https://doi.org/10.16358/j.issn.1009-1300.2020.1.015.
Wang, F., F. Xiong, and H. Jiang. 2018. “An enhanced data-driven polynomial chaos method for uncertainty propagation.” Eng. Optim. 50 (2): 273–292. https://doi.org/10.1080/0305215X.2017.1323890.
Wang, F., S. Yang, and F. Xiong. 2019. “Robust trajectory optimization using polynomial chaos and convex optimization.” Aerosp. Sci. Technol. 92 (Sep): 314–325. https://doi.org/10.1016/j.ast.2019.06.011.
Xiong, F., Y. Xiong, and B. Xue. 2015. “Trajectory optimization under uncertainty based on polynomial chaos expansion.” In Proc., AIAA Guidance, Navigation, and Control Conf., 1761. Reston, VA: American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2015-1761.
Xiu, D., and G. Karniadakis. 2002. “The wiener-Askey polynomial chaos for stochastic differential equations.” SIAM J. Sci. Comput. 24 (2): 619–644. https://doi.org/10.1137/S1064827501387826.
Yang, B., J. Lei, and Y. Wang. 2020. “Fast optimization method of reentry trajectory considering aerodynamic parameter perturbation.” Chin. J. Theor. Appl. Mech. 52 (6): 1610–1620. https://doi.org/10.6052/0459-1879-20-117.
Yang, X. 2016. “Research on trajectory optimization and control approach for hypersonic vehicle under uncertainty.” Master’s dissertation, College of Aerospace Science and Engineering, Graduate School of National Univ. of Defense Technology.
Zhao, J., Y. Huang, and H. Li. 2021. “Uncertainty optimization for return trajectory of vertical takeoff and vertical landing launch vehicle.” Acta Aeronaut. Astronaut. Sin. 42 (11): 524829. https://doi.org/10.7527/S1000-6893.2020.24829.
Zhou, X., R. He, H. Zhang, J. Tang, and W. Bao. 2021. “Sequential convex programming method using adaptive mesh refinement for entry trajectory planning problem.” Aerosp. Sci. Technol. 109 (Feb): 106374. https://doi.org/10.1016/j.ast.2020.106374.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 35 • Issue 5 • September 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Dec 3, 2021
Accepted: Apr 8, 2022
Published online: Jun 24, 2022
Published in print: Sep 1, 2022
Discussion open until: Nov 24, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Wenzhe Fu, Bo Wang, Jinya Su, Zhongtao Cheng, Lei Liu, Yongji Wang, Three-Dimensional Ascent Guidance Method for Two-Stage Solid Rocket Launch Vehicles under Multiple Constraints and Uncertainties, Journal of Aerospace Engineering, 10.1061/JAEEEZ.ASENG-5055, 37, 1, (2024).