Trajectory Optimization of Aerocraft Based on Shaping and Dimension Reduction

doi:10.3969/j.issn.1000-1093.2016.06.022

Abstract

Abstract: A dimension reduction optimization strategy based on trajectory shaping is presented to improve the accuracy of trajectory optimization. The proposed method is able to improve the performance of the direct trajectory optimization method in solving non-smooth trajectory optimization problem. According to the boundary conditions, the unknown trajectory is shaped using the Bezier curves with a few shape variables. The concepts of inverse dynamic and parametric transform are introduced to reduce the original problem to a lower dimensional optimal control problem. The result shows that lower dimensional problem tends to have a better conditioning number when it is solved by direct optimization method, and the accuracy of solutions is improved dramatically. The validation of the proposed method over conventional direct optimization method is demonstrated by the simulation results.

Key words: control and navigation technology of aerocraft, trajectory optimization, trajectory shaping, Bezier trajectory, pseudo-spectral method

CLC Number:

ZHANG Song, HOU Ming-shan. Trajectory Optimization of Aerocraft Based on Shaping and Dimension Reduction[J]. Acta Armamentarii, 2016, 37(6): 1125-1130.

References

［1］ Betts J T. Survey of numerical methods for trajectory optimization［J］. Journal of Guidance, Control and Dynamic, 1998, 21(2):193-206.
［2］雍恩米，陈磊，唐国金. 飞行器轨迹优化数值方法综述［J］.宇航学报，2008，29(2):7-16.
YONG En-mi, CHEN Lei, TANG Guo-jin. A survey of numerical methods for trajectory optimization of spacecraft［J］. Journal of Astronautics, 2008, 29(2):7-16.(in Chinese)
［3］ Vinh N X, Chern J S, Lin C F．Phugiod osillations in optimal reentry trajectories［J］. Acta Astronautica, 1981, 8(4):311-324．
［4］ Istratie V. Optimal skip entry with terminal maximum velocity and heat constraint［C］∥7th AIAA/ASME Joint Thermophysics and Heat Transfer Conference. Albuquerque, US: AIAA, 1998.
［5］ Gath P F. CAMTOS-a software suite combining direct and indirect trajectory optimization methods［D］. Stutgart:University of Stuttgart, 2002.
［6］ Clarke K A. Performance optimization study of a common aero vehicle using a Legendre pseudo-spectral method［D］.Massachusetts:Massachusetts Institute of Technology, 2003.
［7］ Benson A, Thorvaldsen T, Rao V. Direct trajectory optimization and costate estimation via an orthogonal collocation method［J］. Journal of Guidance, Control and Dynamics, 2006, 29(6):1435-1440.
［8］袁宴波, 张科, 薛晓东. 基于Radau伪谱法的制导炸弹最优滑翔弹道研究［J］. 兵工学报, 2014, 35(8):1179-1186.
YUAN Yan-bo, ZHANG Ke, XUE Xiao-dong. Optimization of glide trajectory of guided bombs using a Radau pseudo-spectral method［J］. Acta Armamentarii, 2014, 35(8):1179-1186.(in Chinese)
［9］陈琦, 王中原, 常思江. 带落角约束的间接Gauss伪谱最优制导律［J］. 兵工学报, 2015, 36(7):1203-1212.
CHEN Qi, WANG Zhong-yuan, CHANG Si-jiang. Optimal guidance law with impact angle constraints based on indirect Gauss pseudospectral method［J］. Acta Armamentarii, 2015, 36(7):1203-1212.(in Chinese)
［10］ Berrut J P, Baltensperger R, Mittelman H D. Recent developments in barycentric rational interpolation［J］. International Series of Numerical Mathematics, 2005, 151:27-51.
［11］ Darby C L, Rao A V. A state approximation-based mesh refinement algorithm for solving optimal control problems［C］∥AIAA Guidance, Navigation , and Control Conference. Chicago, US:AIAA, 2009:10-13.
［12］ Darby C L, Hager W W, Rao A V. An hp-adaptive pseudospectral method for solving optimal control problems［J］. Optimal Control Application and Methods, 2011, 32(4): 476-502.
［13］ Milan M B, Mushumbi K, Murray R M. A new computational approach to real-time trajectory generation for constrained mechanical systems［C］∥IEEE Conference on Decision and Control. Sydney, NSW: IEEE, 2000:845-851.
［14］ Lu P. Inverse dynamics approach to trajectory optimization for an aerospace plane［J］. Journal of Guidance, Control and Dynamics, 1993, 16(4):726-732.
［15］施法中.计算机辅助几何设计与非均匀有理B样条［M］. 北京:高等教育出版社, 2001:55-62.
SHI Fa-zhong. CAGD & NURBS［M］. Beijing: Higher Education Press, 2001:55-62.(in Chinese)
［16］ Fumiaki I, Takeshi K, Susumu M. Optimal thrust control of a missile with a pulse motor［J］. Journal of Guidance, Control, and Dynamics, 1991, 14(2):377-382.
［17］ Huntigton G T. Advancement and analysis of a Gauss pseudospectral transcription for optimal control［D］. Cambridage:Massachusetts Institute of Technology, 2007.
［18］ Rao A V, Benson D A. Algorithm 902: GPOPS, a MATLAB software for solving multiple-phase optimal control problems using Gauss pseudo-spectral method［J］. ACM Transactions on Mathematical Software, 2010, 37(2):22:1-22:39.

[1]	WANG Qinghai, CHEN Qi, WANG Zhongyuan, YIN Qiulin. Trajectory Programming of Laser-guided Projectile Considering the Attenuation Effect of Clouds [J]. Acta Armamentarii, 2024, 45(2): 474-487.
[2]	WANG Weijia, WANG Yubing, TIAN Jin, MAO Zhaojun, DU linlin. Optimal Configuration of Aircraft Swarm’s Active Localization with One Transmitter and Multiple Receivers [J]. Acta Armamentarii, 2023, 44(6): 1655-1664.
[3]	LI Qiang， LU Bao-gang， WANG Xiao-hui， WANG Yong-hai， ZHUANG Ling. A Terminal Multi-constraint Optimal Guidance Law for Missile [J]. Acta Armamentarii, 2016, 37(6): 1131-1137.
[4]	ZHANG Yi-fei， DONG Shou-quan， BI Kai-bo. Warship Formation Recognition Algorithm Based on Hough Transform and Clustering [J]. Acta Armamentarii, 2016, 37(4): 648-655.
[5]	LI Cheng， LI Jian-xun， TONG Zhong-xiang， JIA Lin-tong， ZHANG Zhi-bo. Research on Partial Image Recognition and Tracking in Infrared Imaging Terminal Guidance [J]. Acta Armamentarii, 2015, 36(7): 1213-1221.
[6]	ZHANG Meng-ying， TANG Qian-gang， HAN Xiao-jun， ZHANG Qing-bin， GE Jian-quan. Iterative Method to Solving Re-entry Trajectory Optimization with Complex Constraints [J]. Acta Armamentarii, 2015, 36(6): 1015-1023.
[7]	ZHAO Jiang， ZHOU Rui. Predictor-corrector Reentry Guidance Based on Feedback Bank Angle Control [J]. Acta Armamentarii, 2015, 36(5): 823-830.
[8]	FAN Shi-peng， LIN De-fu， YAO Huai-jin, LU Yu-long， QI Zai-kang. Research on Three-loop Autopilot for Rolling Missile Based on Linear Quadratic Optimal Control Theory [J]. Acta Armamentarii, 2015, 36(5): 831-838.
[9]	LU Tian-yu， YIN Jian， DU Xiao， XIA Qun-li. Effect of Phantom-bit Technology on Guidance Performance of Phased Array Radar Seeker [J]. Acta Armamentarii, 2015, 36(12): 2262-2268.
[10]	LI Hao, SHE Hao-ping. Trajectory Shaping Guidance Law Based on Ideal Line-of-sight [J]. Acta Armamentarii, 2014, 35(8): 1200-1204.
[11]	YUAN Yan-bo， ZHANG Ke， XUE Xiao-dong. Optimization of Glide Trajectory of Guided Bombs Using a Radau Pseudo-spectral Method [J]. Acta Armamentarii, 2014, 35(8): 1179-1186.
[12]	TANG Chuan-lin，HUANG Chang-qiang，DU Hai-wen，HUANG Han-qiao，DING Da-li，LUO Chang. Study of Trajectory Planning for UCAV Formation Cooperative Attack [J]. Acta Armamentarii, 2014, 35(4): 523-530.
[13]	GUO Hai-feng, DING Da-li, WU Wen-chao, LIU Yao-lin. Long-range Penetration and Cooperative Search Decision-making of Multiple UAVs [J]. Acta Armamentarii, 2014, 35(2): 248-255.
[14]	SUN Ming-wei, ZHANG Li-min, CHEN Zeng-qiang. Sensitivity Analysis of Design Bandwidth of Missile Three-loop Acceleration Control [J]. Acta Armamentarii, 2014, 35(12): 2023-2029.
[15]	LIU Zhong, GAO Xiao-guang, FU Xiao-wei, XI Wen-qing. Three-dimensional Path tracking Guidance and Control for Unmanned Aerial Vehicle Based on Back-stepping andNonlinear Dynamic Inversion [J]. Acta Armamentarii, 2014, 35(12): 2030-2040.