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Rapid multi-layer method on solving optimal endo-atmospheric trajectory of launch vehicles

Published online by Cambridge University Press:  06 June 2019

Changzhu Wei ,
Yepeng Han ,
Jialun Pu Open the ORCID record for Jialun Pu [Opens in a new window] ,
Yuan Li  and
Panxing Huang
Changzhu Wei*
Affiliation:
Department of Aerospace Engineering, Harbin Institute of Technology, Harbin 150001, China
Yepeng Han*
Affiliation:
Department of Aerospace Engineering, Harbin Institute of Technology, Harbin 150001, China
Jialun Pu*
Affiliation:
Department of Aerospace Engineering, Harbin Institute of Technology, Harbin 150001, China
Yuan Li*
Affiliation:
Department of Aerospace Engineering, Harbin Institute of Technology, Harbin 150001, China
Panxing Huang*
Affiliation:
Beijing Institute of Control Engineering, Beijing 100094, China
*
weichangzhu@hit.edu.cn
han_ye_peng@126.com
nosay@hit.edu.cn
liyuan@stu.hit.edu.cn
huangpanxing2006@126.com
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Abstract

In order to increase the speed, precision and robustness against the engine failure in solving optimal endo-atmospheric ascent trajectory of a launch vehicle, a rapid multi-layer solving method with improved numerical algorithms was proposed. The proposed method is capable of decomposing a large number of intervals into multiple layers with advantageous convergence property. Firstly, the problem of solving optimal endo-atmospheric ascent trajectory, which was subjected to path constraints and terminal constraints, was transformed into a Hamilton Two Point Boundary Value Problem (TPBVP). Then, through the finite difference method and numerical solving algorithm, the Hamilton TPBVP was iteratively solved with fewer initial discrete intervals. The initial values of higher-layer iterations were obtained by interpolating convergent solutions at sparse nodes into the doubly discrete nodes of high layers. The process was repeatedly performed until the solving precision met the requirements. To decrease the calculation load in solving TPBVPs, two improved solving algorithms without and with fewer Jacobian calculations were studied, respectively the Derivative-free Spectral Algorithm for Nonlinear Equations(DF-SANE) combined with the improved derivative-free nonmonotone line search strategy, and the Modified Newton method with a relaxation factor in combination with the Inverse Broyden Quasi-Newton method, denoted as ‘MN-IBQ’. Simulation verifications showed that the multi-layer method had significantly higher solving speed than the single-layer method. For the improved numerical algorithms, the DF-SANE was trapped in the local convergence problem. While using the proposed MN-IBQ can further increase the solving rate. Typical engine failure simulations showed that the multi-layer method with the MN-IBQ algorithm had not only significantly higher solving speed but also stronger robustness, where the traditional single-layer method could not adapt. In addition, the thrust loss tolerance limits for the multi-layer solving method were given for different engine failure times. The results show promising potential of the proposed approach in trajectory online generation and closed-loop guidance of launch vehicles at the endo-atmospheric ascent stage.

Keywords

Hamilton two-point boundary value problemlaunch vehicleoptimal endo-atmospheric trajectorymulti-layer iterationinverse Broyden quasi-Newton method
Type
Research Article
Information
The Aeronautical Journal , Volume 123 , Issue 1267 , September 2019 , pp. 1396 - 1414
Copyright
© Royal Aeronautical Society 2019 

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Footnotes

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References

REFERENCES

Dukeman, G.A. Atmospheric ascent guidance for rocket-powered launch vehicles, AIAA Guidance, Navigation, and Control Conference and Exhibit, AIAA, Reston, VA, 2002.CrossRefGoogle Scholar
Dukeman, G.A. and Calise, A.J., Enhancements to an atmospheric ascent guidance algorithm, AIAA Guidance, Navigation, and Control Conf. and Exhibit, AIAA Reston, VA, 2003.CrossRefGoogle Scholar
Hanson, J.M., Shrader, M.W. and Cruzen, C.A. Ascent guidance comparisons, J Astronaut Sci, 1995, 43, (3), pp 307–326.Google Scholar
Grablin, M.H., Telaar, J. and Schottle, U.M. Ascent and reentry guidance concept based on NLP-methods, Acta Astronautica, 2004, 55, (3), pp 461–471.CrossRefGoogle Scholar
Zhang, D., Liu, L. and Wang, Y. On-line ascent phase trajectory optimal guidance algorithm based on pseudo-spectral method and sensitivity updates, J Navigation, 2015, 68, (6), pp 1056–1074.CrossRefGoogle Scholar
Mahmoud, A.M., Wanchun, C., Hao, Z. and Yang, L. Trajectory optimization for ascent and glide phases using gauss pseudospectral method, Int J Model Optim, 2016, 6, (5), pp 289–295.CrossRefGoogle Scholar
Calise, A.J., Tandon, S., Young, D.H. and Kim, S. Further improvements to a hybrid method for launch vehicle ascent trajectory optimization, AIAA Guidance, Navigation, and Control Conf. and Exhibit, AIAA, Reston, VA, 2000.CrossRefGoogle Scholar
Gath, P.F. and Calise, A. Optimization of launch vehicle ascent trajectories with path constraints and coast arcs, J Guid Control Dynam, 2001, 24, (2), pp 296–304.CrossRefGoogle Scholar
Lu, P., Sun, H. and Tsai, B. Closed-loop endoatmospheric ascent guidance, J Guid Control Dynam, 2003, 26, (2), pp 283–294.CrossRefGoogle Scholar
Lu, P., Griffin, B.J., Dukeman, G.A. and Chavez, F.R. Rapid optimal multiburn ascent planning and guidance, J Guid Control Dynam, 2008, 31, (6), pp 1656–1664.CrossRefGoogle Scholar
Oscar, J., Murillo, J. and Lu, P. Fast ascent trajectory optimization for hypersonic air-breathing vehicles, AIAA Guidance, Navigation, and Control Conf. and Exhibit, AIAA, Reston, VA, August 2010 CrossRefGoogle Scholar
Chi, Z., Yang, H., Chen, S. and Li, J. Homotopy method for optimization of variable-specific-impulse low-thrust trajectories, Astrophys Space Sci, 2017, 362, (11), 216.CrossRefGoogle Scholar
Huang, P., Wei, C., Gu, Y. and Cui, N. Hybrid optimization approach for rapid endo-atmospheric ascent trajectory planning, Aircr Eng Aerosp Technol, 2016, 88, (4), pp 473–479.CrossRefGoogle Scholar
Song, E.J., Cho, S. and Roh, W.R. Analysis of targeting method for closed-loop guidance of a multi-stage space launch vehicle, Adv Space Res, 2016, 57, (7), pp 1494–1507.CrossRefGoogle Scholar
Cruz, W.L., Martinez, J.M. and Raydan, M. Spectral residual method without gradient information for solving large-scale nonlinear systems of equations Math Comput, 2006, 75, (255), pp 1429–1448.CrossRefGoogle Scholar
Grippo, L., Lampariello, F. and Lucidi, S. A nonmonotone line search technique for Newton’s method, SIAM J Numer Anal, 1986, 23, pp 707–716.CrossRefGoogle Scholar
Li, D.H. and Fukushima, M. A derivative-free line search and global convergence of Broyden-like method for nonlinear equations, Optim Methods Softw, 2000, 13, pp 181–201.CrossRefGoogle Scholar
Kvaalen, E. A faster broyden method, Bit Numer Math, 1991, 31, (2), pp 369–372.CrossRefGoogle Scholar