特征趋势分区Gauss伪谱法解再入轨迹规划问题

doi:10.7527/S1000-6893.2015.0115

电子与控制

本期目录 | 过刊浏览 | 高级检索

前一篇 | 后一篇

特征趋势分区Gauss伪谱法解再入轨迹规划问题

呼卫军, 卢青, 常晶, 周军

西北工业大学航天学院, 西安 710072

收稿日期:2014-09-15 修回日期:2015-05-04 出版日期:2015-10-15 发布日期:2015-05-25
通讯作者: 呼卫军, Tel.: 029-88492787 E-mail: huyanwj@126.com E-mail:huyanwj@126.com
作者简介:呼卫军男, 博士, 副教授。主要研究方向: 高超声速飞行器制导与控制技术。 Tel: 029-88492787 E-mail: huyanwj@126.com
基金资助:
国家自然科学基金 (61473226)

Reentry trajectory planning method based on Gauss pseudospectral with characteristics of trend partition

HU Weijun, LU Qing, CHANG Jing, ZHOU Jun

College of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

Received:2014-09-15 Revised:2015-05-04 Online:2015-10-15 Published:2015-05-25
Supported by:
National Natural Science Foundation of China (61473226)

摘要/Abstract

摘要：

针对强约束下的滑翔再入轨迹规划问题,采用基于特征趋势分区的Gauss伪谱法将连续最优问题转换为多个并行非线性规划问题并对其进行求解。针对传统拟谱方法在处理状态受限时,非平滑最优控制解难以收敛的问题,引入Sobolev空间证明了分区并行的收敛性和一致性。基于Letts准则提出了非连续特征趋势提取方法,通过分析离散点配置导数进行了可变分区的迭代设定,并结合导数变化趋势给出了各分区的动态配点数。利用不同阶次的多项式进行精度逼近,保证了在考虑多项强约束条件下弹道规划的可行解获取。结合状态分区的策略进行离线状态的分解,提高了计算效率。最终针对典型的再入应用进行了轨迹规划应用。仿真结果表明,所提出的方法可有效应对多种约束条件,能够根据飞行器的气动能力规划出可行的轨迹,过程条件满足约束,且可适应气动力20%的拉偏范围。

关键词: 再入轨迹, 强约束, 滑翔再入飞行器, Gauss伪谱法, 特征趋势分区

Abstract:

A new Gauss pseudospectral method based on the characteristics of trend partition which transformed continuous optimal problem into parallel nonlinear programming problem was presented in this work solving the problem of reentry trajectory planning with strong state constraints. Tradition pseudospectral method was hard to get convergent non smooth optimal control solutions with state constraint. So sobolev space was introduced to prove the convergence and consistency of partition parallel spectral method. Extraction method of non-continuous feature trend was then developed to solve the problem that non-continuous optimal control solution is difficult to convergence in the case of state constraint. This new method iteratively set the variable partition through analysis of discrete point collocation derivative. Then different partition dynamic allocation point number was computed using the derivative tendency. High-precision polynomial approximation with different orders was used to ensure the acquisition of feasible solution considering the multi constraint conditions. The computational efficiency is effectively improved by off-line partition state confirming. The final application in reentry trajectory planning shows the effectiveness of the proposed approach when facing uncertain accidence and terminal restricts condition and indicate that this method can accommodate 20% pneumatic bias and ensure the terminal precision.

Key words: reentry trajectory, strong constraint, glide reentry vehicle, Gauss pseudospectral, characteristics of trend partition

中图分类号:

V19
TP273

呼卫军, 卢青, 常晶, 周军. 特征趋势分区Gauss伪谱法解再入轨迹规划问题[J]. 航空学报, 2015, 36(10): 3338-3348.

HU Weijun, LU Qing, CHANG Jing, ZHOU Jun. Reentry trajectory planning method based on Gauss pseudospectral with characteristics of trend partition[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(10): 3338-3348.

参考文献

[1] Hunington G T. Advancement and analysis of a guass pseuospectral transcription for optimal control[D]. Cambridge: Massachusetts Institute of Technology, 2007.
[2] Benson D A. A Gauss pseudospectral transcription for optimal control[D]. Cambridge: Massachusetts institute Technoligy, 2004.
[3] Sun Y, Zhang M R, Li H. Now costato estimation of Gauss pseudospectral method for nonlinear optimal control problem[C]//Proceeding of the 2011 International Workshop on Engineering Application Research. Hangzhou, China: IEIT, 2011: 31-36.
[4] Gong Q, Fahroo F, Ross I M. Spectral algorithm for pseudospectral methods in optimal control[J]. Journal of Guidance, Control, and Dynamics, 2008, 31(3): 460-471.
[5] Yong E M, Tang G J, Chen L. Rapid trajectory optimization for hypersonic reentry vehicle via Guass pseudospectral method[J]. Journal of Astronautics, 2008, 29(6): 1766-1772 (in Chinese). 雍恩米, 唐国金, 陈磊. 基于Guass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.
[6] Tong K W, Zhou J P, He L S. Legendre-Gauss pseudospectral method for solving optimal control problem[J]. Acta Aeronautics et Astronautics Sinica, 2008, 29(6): 1531-1536 (in Chinese). 童科伟, 周建平, 何麟书. Legendre-Guass拟谱法求解最优控制问题[J]. 航空学报, 2008, 29(6): 1531-1536.
[7] Darby G L, Hager W W, Rao A V. Direct trajectory optimization using a variable low-order adaptive pseudospectral method[J]. Journal of Spacecraft and Rockets, 2011, 48(3): 433-445.
[8] Qi G, Ross I M. Autonomous pseudospectral knotting methods for space mission optimizaition[C]//Proceeding of the AAS/AIAA Space Flight Mechanics Meeting. Reston: AIAA, 2006: 779-794.
[9] Jain S, Tsiotras P. Trajectory optimization using multiresolution techniques[J]. Journal of Guidance, Control, and Dynamics, 2008, 31(5): 1424-1436.
[10] Darby G L, Hager W W, Rao A V. An hp-adaptive pseudospectral method for solving optimal problems[J]. Optimal Control Applications and Methods, 2011, 32(4): 476-502.
[11] Qin T H, Ma H P. An adaptive pseudospectral method for solving a class of optimal control problems[J]. Information and Control, 2012, 41(5): 583-589 (in Chinese). 秦廷华, 马和平. 解一类最优控制问题的一种自适应拟谱方法[J]. 信息与控制, 2012, 41(5): 583-589.
[12] Ross I M, Fahroo F. A perspective on methods for trajectory optimization[C]//Proceedings of AIAA/AAS Astrodynamics Specialist Conference and Exhibit. Reston: AIAA, 2007: 831-839.
[13] Lu P, Pan B F. Highly constrained optimal launch ascent guidance[J]. Journal of Guidance, Control, and Dynamics, 2010, 33(2): 404-414.
[14] Kameswaran S, Biegler L T. Convergence rates for direct transcription of optimal control problems using collocation at radau points[J]. Computational Optimization and Applications, 2008, 41(1): 81-126.
[15] Fahroo F, Ross I M. Direct trajectory optimization by Chebshev pseudospectral method[J]. Journal of Guidance, Control, and Dynamics, 2002, 25(1): 160-166.
[16] Zong Q, Tian B L, Dou L Q. Ascent phase trajectory optimization for near space vehicle based on Gauss pseudospectral method[J]. Journal of Astronautics, 2010, 31(7): 1775-1781 (in Chinese). 宗群, 田栢苓, 窦立谦. 基于Gauss伪谱法的临近空间飞行器上升段轨迹优化[J]. 宇航学报, 2010, 31(7): 1775-1781.
[17] Zhang Y, Zhang W P, Chen J, et al. Air-to-ground weapon delivery trajectory planning for UCACs using Gauss pseudospectrl method[J]. Acta Aeronautics et Astronautics Sinica, 2011, 32(7): 1240-1251 (in Chinese). 张煜, 张万鹏, 陈璟, 等. 基于Gauss伪谱法的UCACs对地攻击武器投放轨迹规划[J]. 航空学报, 2011, 32(7): 1240-1251.
[18] Shui Z S, Zhou J, Ge Z L. Online predictor-corrector reentry guidance law based on Gauss pseudospectral method[J]. Journal of Astronautics, 2011, 32(6): 1249-1255 (in Chinese). 水尊师, 周军, 葛致磊. 基于高斯伪谱方法的再入飞行器预测校正制导方法研究[J]. 宇航学报, 2011, 32(6): 1249-1255.
[19] Cao X Q. Optimal control for a chaotic system by means of Gauss pseudospectral method[J]. Acta Physica Sinica 2013, 62(23): 67-74 (in Chinese). 曹小群. 基于高斯伪谱方法的混沌系统最优控制[J]. 物理学报, 2013, 62(23): 67-74.
[20] Wang P, Tian X M. Partitioning and simultaneous strategy for dynamic optimization by Gauss pseudo-spectral method[J]. Control and Decision, 2011, 26(11): 1749-1752 (in Chinese). 王平, 田学民. 基于高斯伪谱法的分区联立动态优化策略[J]. 控制与决策, 2001, 26(11): 1749-1752.

E-mail：hkxb@buaa.edu.cn

关于我们

期刊社服务

专业学科

封面文章

友情链接

主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

特征趋势分区Gauss伪谱法解再入轨迹规划问题

Reentry trajectory planning method based on Gauss pseudospectral with characteristics of trend partition

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 6

编辑推荐

Metrics

本文评价

[1]	刘哲, 张羲格, 韦常柱, 崔乃刚. 亚轨道飞行器再入轨迹高精度自适应凸规划[J]. 航空学报, 2023, 44(S2): 729430-729430.
[2]	刘哲, 陆浩然, 郑伟, 闻国光, 王奕迪, 周祥. 多滑翔飞行器时间协同轨迹快速规划[J]. 航空学报, 2021, 42(11): 524497-524497.
[3]	田栢苓, 李智禹, 吴思元, 宗群. 可重复使用运载器再入轨迹与制导控制方法综述[J]. 航空学报, 2020, 41(11): 624072-624072.
[4]	赵琳, 王硕, 郝勇, 刘源. 基于能量最优的敏捷遥感卫星在轨任务规划[J]. 航空学报, 2017, 38(6): 320654-320654.
[5]	崔乃刚, 黄盘兴, 路菲, 黄荣, 韦常柱. 基于混合优化的运载器大气层内上升段轨迹快速规划方法[J]. 航空学报, 2015, 36(6): 1915-1923.
[6]	路辉, 陈晓, 刘欣, 邓小乐. 基于图禁忌的并行测试任务调度算法[J]. 航空学报, 2011, 32(9): 1669-1677.