Please wait a minute...
浙江大学学报(工学版)
浙江大学学报(工学版)  2020, Vol. 54 Issue (9): 1827-1838    DOI: 10.3785/j.issn.1008-973X.2020.09.020
航空航天技术     
采用牛顿迭代保辛伪谱算法的舰载机甲板路径规划
刘洁1(),董献洲1,韩维2,王昕炜4,*(),刘纯3,贾珺1
1. 军事科学院 战争研究院，北京 100850
2. 海军航空大学，山东 烟台 264001
3. 洪都航空工业集团 650所，江西 南昌 330024
4. 大连理工大学 工程力学系，辽宁 大连 116024
Trajectory planning for carrier aircraft on deck using Newton Symplectic pseudo-spectral method
Jie LIU1(),Xian-zhou DONG1,Wei HAN2,Xin-wei WANG4,*(),Chun LIU3,Jun JIA1
1. War Research Institute, Academy of Military Sciences, Beijing 100850, China
2. Naval Aviation University, Yantai 264001, China
3. 650 Aircraft Design Institute of AVIC Hongdu, Nanchang 330024, China
4. Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China
 全文: PDF(1732 KB)   HTML
摘要：

建立单机滑行、离轴无杆牵引、离轴有杆牵引3类舰载机调运模式下的运动学模型. 考虑到有杆牵引系统运动学模型的强非线性，将其转化为一个更加简单的虚拟在轴无杆牵引系统，以便于轨迹的求解. 综合考虑调运效率和安全性，将3类调运模式的轨迹规划问题转化为时间-能量混合最优问题. 为了实现对非线性最优控制问题的高效求解，基于第三类生成函数、辛理论和伪谱离散提出保辛伪谱方法（SPM），并根据终端横截条件采用牛顿迭代和SPM确定终端时间. 将提出的方法应用于3类调运模式的轨迹规划问题，并将所得结果与直接伪谱法进行对比. 仿真结果表明：所提算法能够以更高的精度和效率规划出平滑的舰载机路径，且不会出现非可行解，具有更强的可操作性和适用性.
关键词： 舰载机;  路径规划;  保辛伪谱算法（SPM）;  牛顿迭代法;  最优控制    
Abstract:

The kinematic models for three dispatch modes of carrier aircraft were established, including individually taxiing, off-axle hitching towing without drawbar, and off-axle hitching towing with drawbar. As the high nonlinearity in the kinematics, a towing system with drawbar was transformed into a simpler virtual on-axle hitching towing system so as to facilitate the trajectory planning. Considering the dispatch efficiency and security, the trajectory planning problems of three dispatch modes were formulated as time-energy hybrid optimal control problems. To solve the nonlinear optimal control problem efficiently, a Symplectic pseudo-spectral method (SPM) was firstly developed based on the third kind of generating function, Symplectic theory and pseudo-spectral discretization. Then the Newton iteration and the SPM were used to determine the optimal terminal time according to the terminal transversality condition. The developed method was applied to solve trajectory planning problems of three dispatch modes, and the direct pseudo-spectral method was implemented for comparison. The simulation results suggest that the developed method can generate smooth dispatch trajectories with higher accuracy and efficiency, where no infeasible solution occurs, leading to better operability and applicability.
Key words: carrier aircraft    trajectory planning    Symplectic pseudo-spectral method (SPM)    Newton iteration method    optimal control
收稿日期: 2019-10-17 出版日期: 2020-09-22
CLC:  TP 13  
基金资助: 国家重点研发计划资助项目（2016YFB0200702）；中国博士后科学基金资助项目（2020M670744）；国家自然科学基金资助项目（11772074，11761131005，91748203）
通讯作者: 王昕炜     E-mail: liuyexiaobao@163.com;wangxinwei@dlut.edu.cn
作者简介: 刘洁（1990—），男，助理研究员，博士，从事自动化控制与仿真研究. orcid.org/0000-0002-9418-2073. E-mail： liuyexiaobao@163.com
服务　　
把本文推荐给朋友
加入引用管理器
E-mail Alert
作者相关文章　　
刘洁
董献洲
韩维
王昕炜
刘纯
贾珺

引用本文:

刘洁,董献洲,韩维,王昕炜,刘纯,贾珺. 采用牛顿迭代保辛伪谱算法的舰载机甲板路径规划[J]. 浙江大学学报(工学版), 2020, 54(9): 1827-1838.

Jie LIU,Xian-zhou DONG,Wei HAN,Xin-wei WANG,Chun LIU,Jun JIA. Trajectory planning for carrier aircraft on deck using Newton Symplectic pseudo-spectral method. Journal of ZheJiang University (Engineering Science), 2020, 54(9): 1827-1838.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2020.09.020    或    http://www.zjujournals.com/eng/CN/Y2020/V54/I9/1827

图 1  虚拟在轴无杆牵引系统
图 2  舰载机的滑行轨迹图
图 3  滑行系统控制变量随时间的变化
图 4  滑行飞机的速度和转向角随时间的变化
滑行系统 方法 Mayer Lagrange $J$ ${t_{\rm f}}$/s tc/s
舰载机3 NSP 4.76 16.33 21.10 95.27 16.27
伪谱 5.23 15.68 20.91 104.59 91.87
舰载机5 NSP 7.27 1.92 20.91 145.49 7.73
伪谱 7.64 3.81 11.45 152.76 54.40
舰载机11 NSP 10.03 0.63 10.66 200.66 12.72
伪谱 10.11 0.51 10.63 202.28 76.29
表 1  NSP算法与伪谱法对滑行系统进行轨迹规划的对比指标及结果
图 5  无杆牵引系统中飞机和牵引车的路径曲线
图 6  无杆牵引系统的控制变量
图 7  无杆牵引系统中舰载机速度和转向角随时间变化关系图
无杆牵引系统 方法 Mayer Lagrange $J$ ${t_{\rm f}}$/s tc/s
位置7到10 NSP 8.33 5.30 13.63 83.29 5.33
伪谱 9.53 3.81 13.34 95.27 45.27
位置7到12 NSP 8.47 4.24 12.71 84.69 4.78
伪谱 10.83 65.54 76.37 108.26 68.63
位置4到11 NSP 6.55 5.51 12.06 65.55 2.32
伪谱 6.32 7.80 14.12 63.25 21.03
表 2  采用NSP与伪谱法对无杆牵引系统进行轨迹规划的对比结果
图 8  采用NPS算法得出的有杆牵引系统中飞机和牵引车的路径曲线
图 9  有杆牵引系统中飞机的速度和转向角
1 TONG H, CHAO W W, DONG X Z, et al Path planning of UAV based on Voronoi diagram and DPSO[J]. Procedia Engineering, 2012, 29: 4198- 4203
doi: 10.1016/j.proeng.2012.01.643
2 CANDELORO M, LEKKAS A M, HEGDE J, et al. A 3D dynamic Voronoi diagram-based path-planning system for UUVs [C] // OCEANS 2016 MTS/IEEE Monterey. Monterey: IEEE. 2016: 1-8.
3 张智, 林圣琳, 朱齐丹, 等 考虑运动学约束的不规则目标遗传避碰规划算法[J]. 航空学报, 2015, 36 (4): 1348- 1358
ZHANG Zhi, LIN Sheng-lin, ZHU Qi-dan, et al Genetic collision avoidance planning algorithm for irregular shaped object with kinematics constraint[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36 (4): 1348- 1358
4 司维超, 齐玉东, 韩维 基于融合Dijkstra的凸壳算法的舰载机机库调运规划[J]. 系统工程与电子技术, 2015, 37 (3): 583- 588
SI Wei-chao, QI Yu-dong, HAN Wei Carrier plane transportation in hangar based on convex hull algorithm combined with Dijkstra[J]. Systems Engineering and Electronics, 2015, 37 (3): 583- 588
5 韩维, 司维超, 丁大春, 等 基于聚类PSO算法的舰载机舰面多路径动态规划[J]. 北京航空航天大学学报, 2013, 39 (5): 610- 614
HAN Wei, SI Wei-chao, DING Da-chun Multi-routes dynamic planning on deck of carrier plane based on clustering PSO[J]. Journal of Beijing University of Aeronautics and Astronautics, 2013, 39 (5): 610- 614
6 WU Y, QU X J Path planning for taxi of carrier aircraft launching[J]. Science Chine: Technology Sciences, 2013, 56 (6): 1561- 1570
doi: 10.1007/s11431-013-5222-5
7 WU Y, QU X J Obstacle avoidance and path planning for carrier aircraft launching[J]. Chinese Journal of Aeronautics, 2015, 28 (3): 695- 703
doi: 10.1016/j.cja.2015.03.001
8 WU Y, HU N, QU X J A general trajectory optimization method for aircraft taxiing on flight deck of carrier[J]. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2019, 233 (4): 1340- 1353
doi: 10.1177/0954410017752224
9 FILIPPIS L D, GUGLIERI G, QUAGLIOTTI F A minimum risk approach for path planning of UAVs[J]. Journal of Intelligent and Robotic Systems, 2011, 61 (1-4): 203- 219
10 ZHANG K, LIU P P, KONG W R, et al An improved heuristic algorithm for UCAV path planning[J]. Journal of Optimization, 2017, (4): 1- 7
doi: 10.1155/2017/8936164
11 NIU H L, LU Y, SAVVARIS A, et al. Efficient path following algorithm for unmanned surface vehicle [C] // OCEANS 2016 - Shanghai. Shanghai: OCEANS, 2016:OCEANS 1-7.
12 ZHANG Y D, WU L N, WANG S H UCAV path planning by fitness-scaling adaptive chaotic particle swarm optimization[J]. Mathematical Problems in Engineering, 2013, 2013 (8): 147- 170
13 DAS P K, BEHERA H S, JENA P K, et al Multi-robot path planning in a dynamic environment using improved gravitational search algorithm[J]. Journal of Electrical Systems and Information Technology, 2016, 3 (2): 295- 313
doi: 10.1016/j.jesit.2015.12.003
14 GROH K, R?CK S A contribution to collision-free trajectory planning for handling systems in varying environments[J]. Production Engineering, 2010, 4 (1): 101- 106
doi: 10.1007/s11740-009-0202-0
15 HUPTYCH M, GROH K, R?CK S. Online path planning for industrial robots in varying environments using the curve shortening flow method [M] // Intelligent Robotics and Applications. Berlin Heidelberg: Springer, 2011: 73-82.
16 HUPTYCH M, R?CK S Online path planning in dynamic environments using the curve shortening flow method[J]. Production Engineering, 2015, 9 (5/6): 613- 621
17 MANCINI M, COSTANTE G, VALIGI P, et al Towards domain independence for learning-based monocular depth estimation[J]. IEEE Robotics and Automation Letters, 2017, 2 (3): 1778- 1785
doi: 10.1109/LRA.2017.2657002
18 MORALES N, TOLEDO J, ACOSTA L Path planning using a multiclass support vector machine[J]. Applied Soft Computing, 2016, 43: 498- 509
doi: 10.1016/j.asoc.2016.02.037
19 BLACKMORE L, A?IKME?E B, III J M C. Lossless convexification of control constraints for a class of nonlinear optimal control problems [C] // American Control Conference. Montreal: [s. n. ], 2012: 5519-5525.
20 MAO Y Q, SZMUK M, A?IKME?E B. Successive convexification of non-convex optimal control problems and its convergence properties [C] // IEEE 55th Conference on Decision and Control (CDC). Las Vegas: IEEE, 2016: 3636-3641.
21 A?IKME?E B, CARSON J M, BLACKMORE L Lossless convexification of nonconvex control bound and pointing constraints of the soft landing optimal control problem[J]. IEEE Transactions on Control Systems Technology, 2013, 21 (6): 2104- 2113
doi: 10.1109/TCST.2012.2237346
22 LIU X F, LU P, PAN B F Survey of convex optimization for aerospace applications[J]. Astrodynamics, 2017, 1 (1): 23- 40
doi: 10.1007/s42064-017-0003-8
23 LIU X F, LU P Solving nonconvex optimal control problems by convex optimization[J]. Journal of Guidance Control and Dynamics, 2014, 37 (3): 750- 765
doi: 10.2514/1.62110
24 GONG Q, KANG W, ROSS I M A pseudospectral method for the optimal control of constrained feedback linearizable systems[J]. IEEE Transactions on Automatic Control, 2006, 51 (7): 1115- 1129
doi: 10.1109/TAC.2006.878570
25 LEWIS L R, ROSS I M, GONG Q. Pseudospectral motion planning techniques for autonomous obstacle avoidance [C] // IEEE Conference on Decision and Control. New Orleans: IEEE, 2007: 5997-6002.
26 LI Y Y, ZHU Y F, LI Q Analysis of aircraft path planning optimal on carrier flight deck[J]. Advanced Materials Research, 2013, 664: 1122- 1127
doi: 10.4028/www.scientific.net/AMR.664.1122
27 PENG H J, GAO Q, WU Z G, et al Symplectic adaptive algorithm for solving nonlinear two-point boundary value problems in astrodynamics[J]. Celestial Mechanics and Dynamical Astronomy, 2011, 110 (4): 319- 342
doi: 10.1007/s10569-011-9360-4
28 PENG H J, GAO Q, WU Z G, et al Symplectic approaches for solving two-point boundary-value problems[J]. Journal of Guidance, Control, and Dynamics, 2012, 35 (2): 653- 659
doi: 10.2514/1.55795
29 PENG H J, GAO Q, WU Z G, et al Efficient sparse approach for solving receding-horizon control problems[J]. Journal of Guidance, Control, and Dynamics, 2013, 36 (6): 1864- 1872
doi: 10.2514/1.60090
30 JOHNSTON J S, SWENSON E D Feasibility study of global-positioning-system-based aircraft-carrier flight-deck persistent monitoring system[J]. Journal of Aircraft, 2010, 47 (5): 1624- 1635
doi: 10.2514/1.C000220
31 KARKEE M, STEWARD B L Study of the open and closed loop characteristics of a tractor and a single axle towed implement system[J]. Journal of Terramechanics, 2010, 47 (6): 379- 393
doi: 10.1016/j.jterra.2010.05.005
32 WANG X W, PENG H J, ZHANG S, et al A symplectic pseudospectral method for nonlinear optimal control problems with inequality constraints[J]. ISA Transactions, 2017, 335- 352
33 PENG H J, WANG X W, LI M W, et al An hp symplectic pseudospectral method for nonlinear optimal control[J]. Communications in Nonlinear Science and Numerical Simulation, 2017, 42: 623- 644
doi: 10.1016/j.cnsns.2016.06.023
[1] 胡凯明,李华. 轴向受压梁非线性随机最优电压有界控制[J]. 浙江大学学报(工学版), 2020, 54(5): 940-946.
[2] 刘军,冯硕,任建华. 移动机器人路径动态规划有向D*算法[J]. 浙江大学学报(工学版), 2020, 54(2): 291-300.
[3] 高德东, 李强, 雷勇, 徐飞, 白辉全. 基于几何逼近法的斜尖柔性穿刺针运动学研究[J]. 浙江大学学报(工学版), 2017, 51(4): 706-713.
[4] 肖扬,管成,王飞. 扭矩耦合式油液混合动力挖掘机能量管理[J]. 浙江大学学报(工学版), 2016, 50(1): 70-77.
[5] 马丽莎, 周文晖, 龚小谨, 刘济林. 基于运动约束的泛化Field D*路径规划[J]. J4, 2012, 46(8): 1546-1552.
[6] 陈家乾,柳玉甜,何衍,蒋静坪. 基于栅格模型和样本集合的动态环境地图创建[J]. J4, 2011, 45(5): 794-798.
[7] 刘兴高, 陈珑. 约束优先边值固定最优控制嵌套优化方法[J]. J4, 2010, 44(7): 1247-1250.
[8] 许贤, 罗尧治, 沈雁彬. 张拉整体结构的非线性主动控制[J]. J4, 2010, 44(10): 1979-1984.
[9] 茅僰 应祖光 朱位秋. 不确定结构非线性随机最优控制的鲁棒性[J]. J4, 2008, 42(7): 1101-1105.
[10] 冯毅雄 程锦 谭建荣. 基于牛顿迭代混沌特性的机构综合新方法[J]. J4, 2008, 42(3): 369-372.
[11] 祝长生 陈拥军. 部分状态可测转子系统振动控制的随机最优策略[J]. J4, 2007, 41(6): 980-984.
[12] 江万里 熊蓉 褚健. 复杂动态环境下基于侧滑力的局部路径规划[J]. J4, 2007, 41(10): 1609-1614.
[13] 陈拥军 祝长生. 随机最优策略在转子系统振动控制中的应用[J]. J4, 2006, 40(6): 1015-1018.
[14] 吴思源 周晓军 江健 杨辰龙. 超声检测中曲面重构和路径规划方法研究[J]. J4, 2006, 40(5): 763-767.
[15] 陈哲明 潘再平. 基于迭代学习的开关磁阻电动机最优控制研究[J]. J4, 2006, 40(1): 25-28.