ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Optimal Trajectory Design Under Uncertainty for a Gliding Guided Projectile
Received date: 2013-12-03
Revised date: 2014-05-07
Online published: 2014-05-16
Supported by
National Natural Science Foundation of China (11272356); China Postdoctoral Science Foundation (2013M541676)
Due to the limited control authority of a gliding guided projectile with tradeoffs between hardware and cost, a novel trajectory optimization method under uncertainty used to reduce the sensitivity of reference trajectories to various uncertainties is presented. The models of uncertainties that may be encountered in a real operating environment are established, and the analytic expression of the Jacobian for the glide guided projectile dynamics is derived, which can provide faster computational speeds in evaluations. The covariance propagation equation of the system is obtained by using covariance techniques, and the trajectory optimization model under uncertainties is also established. The Chebyshev pseudospectral method is implemented to transform the trajectory optimization problem into a nonlinear programming problem which is solved by an interior point filter line search algorithm package (Ipopt). The simulation results show that the proposed method has a good performance and could reduce the terminal downrange and crossrange covariance, compared with the baseline trajectory which is generated without any robustness considerations.
CHEN Qi , WANG Zhongyuan , CHANG Sijiang , SHU Jingrong . Optimal Trajectory Design Under Uncertainty for a Gliding Guided Projectile[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014 , 35(9) : 2593 -2604 . DOI: 10.7527/S1000-6893.2014.0094
[1] Costello M. Extended range of a gun launched smart projectile using controllable canards[J]. Shock and Vibration, 2001, 8(3-4): 203-213.
[2] Sarsar R B, Mukhedkar R J, Naik S D. Study on extending range of artillery rocket using control surfaces[J]. Journal of Aerospace Science and Technologies, 2011, 63(2): 153-157.
[3] Shi J G, Wang Z Y, Yi W J, et al. Analysis on the ballistic characteristics of gliding extended range projectile[J]. Acta Armamentarii, 2006, 27(2): 210-214.(in Chinese) 史金光, 王中原, 易文俊, 等. 滑翔増程弹弹道特性分析[J]. 兵工学报, 2006, 27(2): 210-214.
[4] Trent A, Venkataraman R, Doman D. Trajectory generation using a modified simple shooting method[C]//Proceedings of IEEE Aerospace Conference, 2004: 2723-2729.
[5] Sun R S, Xue X Z, Shen J P. Trajectory optimization for a hypersonic waverider missile in extended range period by means of optimal control[J]. Journal of Ballistics, 2008, 20(4): 57-60. (in Chinese) 孙瑞胜, 薛晓忠, 沈坚平. 一种乘波外形导弹増程段弹道的最优控制解法[J]. 弹道学报, 2008, 20(4): 57-60.
[6] Li J F, Chen W C. Numerical solution of optimal trajectory for hypersonic vehicle with constraints[J]. Acta Aeronautica et Astronautica Sinica, 2009, 30(9): 1605-1611. (in Chinese) 李佳峰, 陈万春. 带约束的高超声速飞行器最优弹道的数值算法[J]. 航空学报, 2009, 30(9): 1605-1611.
[7] Kang B N, Tang S. Trajectory design and optimization of powered common aero vehicles[J]. Acta Aeronautica et Astronautica Sinica, 2009, 30(4): 738-743. (in Chinese) 康炳南, 唐硕. 有动力通用再入飞行器的轨迹设计与优化[J]. 航空学报, 2009, 30(4): 738-743.
[8] Li Y, Yang Z H, Cui N G. Optimization of overall penetration trajectory for intercontinental boost-glide missile[J]. Journal of Solid Rocket Technology, 2010, 33(2): 125-130. (in Chinese) 李瑜, 杨志红, 崔乃刚. 洲际助推-滑翔导弹全程突防弹道优化[J]. 固体火箭技术, 2010, 33(2): 125-130.
[9] Chen X Q, Hou Z X, Liu J X. Reentry trajectory optimization for hypersonic glide vehicle[J]. Aeronautical Computing Technique, 2010, 40(1): 37-41. (in Chinese) 陈小庆, 侯中喜, 刘建霞. 基于直接配点法的滑翔轨迹快速优化设计[J]. 航空计算技术, 2010, 40(1): 37-41.
[10] Rao A V. A survey of numerical methods for optimal control[C]//AAS/AIAA Astrodynamics Specialist Conference, 2009: 497-528.
[11] Senses B, Rao A V. A preliminary analysis of small spacecraft finite-thrust aeroassisted orbital transfer, AIAA-2012-4812[R]. Reston: AIAA, 2012.
[12] Yong E M, Tang G J, Chen L. Rapid trajectory optimization for hypersonic reentry vehicle via Gauss pseudospectral method[J]. Journal of Astronautics, 2008, 29(6): 1766-1772. (in Chinese) 雍恩米, 唐国金, 陈磊. 基于Gauss伪谱方法的高超声速飞行器再入轨迹快速优化[J]. 宇航学报, 2008, 29(6): 1766-1772.
[13] Peng Q B, Li H Y, Shen H X. Rapid lunar exact-landing trajectory optimization via Gauss pseudospectral method[J]. Journal of Astronautics, 2010, 31(4): 1012-1016. (in Chinese) 彭祺擘, 李海洋, 沈红新. 基于高斯-伪谱法的月球定点着陆轨道快速优化设计[J]. 宇航学报, 2010, 31(4): 1012-1016.
[14] Zhang Y, Zhang W P, Chen J, et al. Air-to-ground weapon delivery trajectory planning for UCAVs using Gauss pseudospectral method[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(7): 1240-1251. (in Chinese) 张煜, 张万鹏, 陈璟, 等. 基于Gauss伪谱法的UCAV对地攻击武器投放轨迹规划[J]. 航空学报, 2011, 32(7): 1240-1251.
[15] Wang H L, Pei Y F, Ni S B, et al. Design of emergency landing region and landing trajectory for unpowered aircraft[J]. Acta Aeronautica et Astronautic Sinica, 2014, 35(5): 1404-1415. (in Chinese) 王宏伦, 裴云峰, 倪少波, 等.飞行器无动力应急着陆域和着陆轨迹设计[J]. 航空学报, 2014, 35(5): 1404-1415.
[16] Francolin C C. Direct trajectory optimization and costate estimation of state inequality path-constrained optimal control problems using a Radau pseudospectral method[C]//AIAA Guidance, Navigation, and Control Conference, 2012.
[17] Yi W J, Wang Z Y, Shi J G, et al. Trajectory of glide extended-range projectile with canards configuration[J]. Journal of Nanjing University of Science and Technology: Natural Science, 2008, 32(3): 322-326.(in Chinese) 易文俊, 王中原, 史金光, 等. 带鸭舵滑翔增程炮弹方案弹道研究[J]. 南京理工大学学报: 自然科学版, 2008, 32(3): 322-326.
[18] Xiu G, Wang L M. Trajectory optimization for boost glide range-extended projectile[J]. Journal of Computer Simulation, 2011, 28(12): 14-16.(in Chinese) 修观, 王良明. 助推-滑翔增程弹弹道优化[J]. 计算机仿真, 2011, 28(12): 14-16.
[19] Geller D K. Linear covariance techniques for orbital rendezvous analysis and autonomous onboard mission planning[J]. Journal of Guidance, Control, and Dynamics, 2006, 29(6): 1404-1414.
[20] Zanetti R, Woffinden D C, Sievers A. Multiple event triggers in linear covariance analysis for spacecraft rendezvous[J]. Journal of Guidance, Control, and Dynamics, 2012, 35(2): 353-366.
[21] Qian X F, Lin R X, Zhao Y N. Missile flight dynamics[M]. Beijing: Beijing Institute of Technology Press, 2008: 49-57. (in Chinese) 钱杏芳, 林瑞雄, 赵亚男. 导弹飞行力学[M]. 北京:北京理工大学出版社, 2008: 49-57.
[22] Justus C G, Leslie F W. The NASA marshall space flight center earth global reference atmospheric model 2010 version, NASA/TM 2011216467. Washington, D. C.: NASA, 2011.
[23] Gong Q, Ross I M, Fahroo F. A Chebyshev pseudospectral method for nonlinear constrained optimal control problems[C]//Proceedings of the 48th IEEE Conference on Decision and Control, 2009: 5057-5062.
[24] Vlassenbroeck J, Van Dooren R. A Chebyshev technique for solving nonlinear optimal control problems[J]. IEEE Transactions on Automatic Control, 1988, 33(4): 333-340.
[25] Gong Q, Ross I M, Fahroo F. Costate computation by a Chebyshev pseudospectral method[J]. Journal of Guidance, Control, and Dynamics, 2010, 33(2): 623-628.
[26] Wchter A, Biegler L T. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming[J]. Mathematical Programming, 2006, 106(1): 25-57.
[27] McLachlan G J, Peel D, Basford K E, et al. The EMMIX software for the fitting of mixtures of normal t-components[J]. Journal of Statistical Software, 1999, 4(2): 1-14.
[28] DeMars K J, Bishop R H, Jah M K. Entropy-based approach for uncertainty propagation of nonlinear dynamical systems[J]. Journal of Guidance, Control, and Dynamics, 2013, 36(4): 1047-1057.
[29] Jones B A, Doostan A, Born G H. Nonlinear propagation of orbit uncertainty using non-intrusive polynomial chaos[J]. Journal of Guidance, Control, and Dynamics, 2013, 36(2): 430-444.
[30] Mendel J M. Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications[J]. Proceedings of the IEEE, 1991, 79(3): 278-305.
/
| 〈 |
|
〉 |
CJA