高超声速飞行器多约束再入轨迹快速优化
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摘要
针对高超声速飞行器再入过程中面临测控区和绕飞区的再入轨迹设计问题,提出了一种基于Gauss伪谱法(GPM)的分段轨迹优化策略。将轨迹优化的一般最优控制问题转换为多段最优控制问题,进而将各段轨迹按Gauss伪谱方法进行离散化,将连续多段最优控制问题转换为非线性规划问题(NLP)进行求解。所得再入轨迹能够使得飞行器在满足各种约束条件的情况下成功进入测控区并且有效规避绕飞区,最终到达指定点。此外,本文综合考虑飞行器再入飞行的快速性和工程实用性,并提出了再入时间、弹道倾角以及航向角相关指标的加权性能指标,同时保证了轨迹规划快速、再入轨迹平滑以及控制量变化平缓等实际需求,提高了计算效率。仿真结果表明,本文所提出的分段优化方案能够快速规划出适应不同飞行任务的再入轨迹。
A segmented trajectory optimization strategy based on the Gauss pseudospectral method( GPM) is proposed for hypersonic vehicles during reentry where some monitoring and no-fly zones are inevitably encountered. The segmentation of the trajectory converts the original optimal control problem of the trajectory optimization into the multi-segment optimal control problem. With the help of GPM,each segment trajectory is planned according to the standard computing procedure of GPM. The whole trajectory thus obtained can make the vehicle smoothly enter into the monitoring zones,successfully circumvent the no-fly areas,and finally reach the predetermined point. Besides,considering the requirements of the high computing efficiency and the engineering practicability,we put forward a weighted performance index of reentry time and path-and-heading-angle related variables. The proposed performance index and corresponding optimization strategies definitely provide us the rapidity of the path planning,the smoothness of the flight trajectory,the flatness of the controlled variables,and the improvement of the computational efficiency. The simulation results show that the piecewise optimization scheme proposed in this paper can quickly plan a reentry trajectory for a hypersonic vehicle with complex constraints.
A segmented trajectory optimization strategy based on the Gauss pseudospectral method( GPM) is proposed for hypersonic vehicles during reentry where some monitoring and no-fly zones are inevitably encountered. The segmentation of the trajectory converts the original optimal control problem of the trajectory optimization into the multi-segment optimal control problem. With the help of GPM,each segment trajectory is planned according to the standard computing procedure of GPM. The whole trajectory thus obtained can make the vehicle smoothly enter into the monitoring zones,successfully circumvent the no-fly areas,and finally reach the predetermined point. Besides,considering the requirements of the high computing efficiency and the engineering practicability,we put forward a weighted performance index of reentry time and path-and-heading-angle related variables. The proposed performance index and corresponding optimization strategies definitely provide us the rapidity of the path planning,the smoothness of the flight trajectory,the flatness of the controlled variables,and the improvement of the computational efficiency. The simulation results show that the piecewise optimization scheme proposed in this paper can quickly plan a reentry trajectory for a hypersonic vehicle with complex constraints.
引文
[1]张卫东.滑翔式高超声速飞行器再入轨迹规划与姿态控制[D].哈尔滨:哈尔滨工业大学,2017.[Zhang Wei-dong.Reentry trajectory planning and attitude control for gliding hypersonic vehicle[D].Harbin:Harbin Institute of Technology,2017.]
[2]黄长强,国海峰,丁达理.高超声速滑翔飞行器轨迹优化与制导综述[J].宇航学报,2014,35(4):369-379.[Huang Chang-qiang,Guo Hai-feng,Ding Da-li.Overview of trajectory optimization and guidance for hypersonic gliding vehicle[J].Journal of Astronautics,2014,35(4):369-379.]
[3]谢愈,刘鲁华,汤国建.多约束条件下高超声速滑翔飞行器轨迹优化[J].宇航学报,2011,32(12):2499-2504.[Xie Yu,Liu Lu-hua,Tang Guo-jian.Trajectory optimization of hypersonic gliding vehicle under multiple constraints[J].Journal of Astronautics,2011,32(12):2499-2504.]
[4]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):397-405.[Yong En-mi,Chen Lei,Tang Guo-jin.Overview of numerical methods for aircraft trajectory optimization[J].Journal of Astronautics,2008,29(2):397-405.]
[5]Huntington G T.Advancement and analysis of a Gauss pseudospectral transcription[D].Cambridge,MA:Massachusetts Institute of Technology,2007.
[6]Benson A,Thorvaldsen T,Rao V.Direct trajectory optimization and costae estimation via an orthogonal collocation method[J].Journal of Guidance,Control and Dynamics,2006,29(6):1435-1440.
[7]罗建军,王明光,袁建平.基于伪光谱方法的月球软着陆轨道快速优化[J].宇航学报,2007,28(5):1119-1122.[Luo Jian-jun,Wang Ming-guang,Yuan Jian-ping.Rapid optimization of lunar soft landing trajectory based on pseudospectral method[J].Journal of Astronautics,2007,28(5):1119-1122.]
[8]Reddien G W.Collocation at Gauss points as a discretization in optimal control[J].Control Optimization,1979,17(2):298-306.
[9]李铁鹏,王中原,陈琦.基于Gauss伪谱法的滑翔弹道优化算法研究[J].弹道与制导学报,2014,34(2):113-116.[Li Tie-peng,Wang Zhong-yuan,Chen Qi.Research on gliding trajectory optimization algorithm based on Gauss pseudospectral method[J].Journal of Ballistics and Guidance,2014,34(2):113-116.]
[10]和争春,何开锋,朱国林.过载限制条件下升力体再入大气层弹道优化设计[J].弹道学报,2007,19(2):8-12.[He Zheng-chun,He Kai-feng,Zhu Guo-lin.Optimal design of reentry trajectory for lifting body under overload constraints[J].Journal of Ballistics,2007,19(2):8-12.]
[11]张科南,周浩,陈万春.高超声速飞行器多约束多种机动突防模式弹道规划[J].弹道学报,2012,24(3):85-90.[Zhang Ke-nan,Zhou Hao,Chen Wan-chun.Trajectory planning for hypersonic vehicle with multiple constraints and multiple maneuvering penetration modes[J].Journal of Ballistics,2012,24(3):85-90.]
[12]Shen Z J,Lu P.On-board generation of three-dimensional constrained entry trajectories[C].AIAA Guidance,Navigation,and Control Conference and Exhibit,Monterey,USA,August 5-8,2002.
[13]Darby C L,Garg D,Rao A V.Costate estimation using multipleintervalpseudospectral methods[J].Journal of Spacecraft and Rockets,2011,48(5):856-866.
[14]Wang L,Xing Q H,Mao Y F.Reentry trajectory rapid optimization for hypersonic vehicle satisfying waypoint and no-fly zone constraints[J].Journal of Guidance,Control and Dynamics,2009,32(2):551-572.
[15]Jorris T R,Cobb R G.Three-dimensional trajectory optimization satisfying waypoint and no-fly zone constraints[J].Journal of Guidance,Control and Dynamics,2009,32(2):551-572.
[16]Elnagar J,Kazemi M A.Pseudospectral Chebyshev optimal control of constrained nonlinear dynamical systems[J].Computational Optimization and Applica-tions,1998,11(2):195-217.
[17]Vinh N X.Optimal trajectories in atmospheric flight[C].The32nd International Astronautical Congress Rome,Italy,September 6-12,1981.
[18]Hui T L,Ping Y J,Qun F,et al.Reentry skipping trajectory optimization using direct parameter optimization method[C].The14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference,Canberra,Australia,November 6-9,2006.
[19]Betts J T.Survey of numerical methods for trajectory optimization[J].Journal of Guidance,Control and Dynamics,1998,21(2):193-206.
[20]张熠,张万鹏,陈璟,等.基于Gauss伪谱法的UAV对地攻击武器投放轨迹规划[J].航空学报,2011,32(7):1239-1251.[Zhang Yi,Zhang Wan-peng,Chen Jing,et al.Trajectory planning of UAV ground attack weapon delivery based on Gauss pseudospectral method[J].Journal of Aeronautics,2011,32(7):1239-1251.]
[21]高长生,陈尔康,荆武兴.高超声速飞行器机动规避轨迹优化[J].哈尔滨工业大学学报,2017,49(4):16-21.[Gao Chang-sheng,Chen Er-kang,Jing Wu-xing.Optimization of maneuvering avoidance trajectory for hypersonic vehicle[J].Journal of Harbin Institute of Technology,2017,49(4):16-21.]
[22]刘晓慧,聂万胜,杨新垒.高超声速飞行器多约束再入滑翔机动弹道优化设计[J].导弹与航天运载技术,2017,352(2):6-11.[Liu Xiao-hui,Nie Wan-sheng,Yang Xin-lei.Optimization design of maneuvering trajectory for hypersonic vehicle with multiple constraints reentry gliding maneuver[J].Missile and Spaceflight Transport Technology,2017,352(2):6-11.]
[23]王彩霞.LQR最优控制系统中加权阵的研究[J].西北民族大学学报,2003,24(48):29-31.[Wang Cai-xia.Study of weight matrix in LQR optimal control system[J].Journal of Northwestern University of Nationalities,2003,24(48):29-31.]
[24]Lincoln B,Bernhardsson B.LQR optimization of linear system switching[J].IEEE Transactions on Automatic control,2002,47(10):1701-1705.
[25]Cao Y,Ren W.Optimal linear-consensus algorithms:an LQRperspective[J].IEEE Transactions on Systems Man&Cybernetics,2010,40(3):819-830.
[26]Huntington G T,Rao A V.Optimal reconfiguration of spacecraft formations using the Gauss pseudospectral method[J].Journal of Guidance,Control and Dynamics.2012,31(3):689-698.
[27]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(6):1766-1772.[Yong En-mi,Tang Guo-jin,Chen Lei.Fast reentry trajectory optimization of hypersonic vehicle based on Gauss pseudospectral method[J].Journal of Astronautics,2008(6):1766-1772.]
[28]徐少兵,李升波,成波.最优控制问题的Legendre伪谱法求解及其应用[J].控制与决策,2014,29(12):2113-2120.[Xu Shao-bing,Li Sheng-bo,Cheng Bo.Legendre pseudospectral method for optimal control problem and its application[J].Control and Decision,2014,29(12):2113-2120.]
[29]雍恩米,唐国金,陈磊.助推-滑翔式导弹中段弹道方案的初步分析[J].国防科技大学学报,2006,28(6):6-10.[Yong En-mi,Tang Guo-jin,Chen Lei.Preliminary analysis of midcourse trajectory for boost gliding missile[J].Journal of National University of Defense Technology,2006,28(6):6-10.]
[30]Phillips T H.A common aero vehicle(CAV)model,description,and employment guide[R].Schafer Corporation for AFRL and AFSPC,Arlington,VA,2003.
[2]黄长强,国海峰,丁达理.高超声速滑翔飞行器轨迹优化与制导综述[J].宇航学报,2014,35(4):369-379.[Huang Chang-qiang,Guo Hai-feng,Ding Da-li.Overview of trajectory optimization and guidance for hypersonic gliding vehicle[J].Journal of Astronautics,2014,35(4):369-379.]
[3]谢愈,刘鲁华,汤国建.多约束条件下高超声速滑翔飞行器轨迹优化[J].宇航学报,2011,32(12):2499-2504.[Xie Yu,Liu Lu-hua,Tang Guo-jian.Trajectory optimization of hypersonic gliding vehicle under multiple constraints[J].Journal of Astronautics,2011,32(12):2499-2504.]
[4]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):397-405.[Yong En-mi,Chen Lei,Tang Guo-jin.Overview of numerical methods for aircraft trajectory optimization[J].Journal of Astronautics,2008,29(2):397-405.]
[5]Huntington G T.Advancement and analysis of a Gauss pseudospectral transcription[D].Cambridge,MA:Massachusetts Institute of Technology,2007.
[6]Benson A,Thorvaldsen T,Rao V.Direct trajectory optimization and costae estimation via an orthogonal collocation method[J].Journal of Guidance,Control and Dynamics,2006,29(6):1435-1440.
[7]罗建军,王明光,袁建平.基于伪光谱方法的月球软着陆轨道快速优化[J].宇航学报,2007,28(5):1119-1122.[Luo Jian-jun,Wang Ming-guang,Yuan Jian-ping.Rapid optimization of lunar soft landing trajectory based on pseudospectral method[J].Journal of Astronautics,2007,28(5):1119-1122.]
[8]Reddien G W.Collocation at Gauss points as a discretization in optimal control[J].Control Optimization,1979,17(2):298-306.
[9]李铁鹏,王中原,陈琦.基于Gauss伪谱法的滑翔弹道优化算法研究[J].弹道与制导学报,2014,34(2):113-116.[Li Tie-peng,Wang Zhong-yuan,Chen Qi.Research on gliding trajectory optimization algorithm based on Gauss pseudospectral method[J].Journal of Ballistics and Guidance,2014,34(2):113-116.]
[10]和争春,何开锋,朱国林.过载限制条件下升力体再入大气层弹道优化设计[J].弹道学报,2007,19(2):8-12.[He Zheng-chun,He Kai-feng,Zhu Guo-lin.Optimal design of reentry trajectory for lifting body under overload constraints[J].Journal of Ballistics,2007,19(2):8-12.]
[11]张科南,周浩,陈万春.高超声速飞行器多约束多种机动突防模式弹道规划[J].弹道学报,2012,24(3):85-90.[Zhang Ke-nan,Zhou Hao,Chen Wan-chun.Trajectory planning for hypersonic vehicle with multiple constraints and multiple maneuvering penetration modes[J].Journal of Ballistics,2012,24(3):85-90.]
[12]Shen Z J,Lu P.On-board generation of three-dimensional constrained entry trajectories[C].AIAA Guidance,Navigation,and Control Conference and Exhibit,Monterey,USA,August 5-8,2002.
[13]Darby C L,Garg D,Rao A V.Costate estimation using multipleintervalpseudospectral methods[J].Journal of Spacecraft and Rockets,2011,48(5):856-866.
[14]Wang L,Xing Q H,Mao Y F.Reentry trajectory rapid optimization for hypersonic vehicle satisfying waypoint and no-fly zone constraints[J].Journal of Guidance,Control and Dynamics,2009,32(2):551-572.
[15]Jorris T R,Cobb R G.Three-dimensional trajectory optimization satisfying waypoint and no-fly zone constraints[J].Journal of Guidance,Control and Dynamics,2009,32(2):551-572.
[16]Elnagar J,Kazemi M A.Pseudospectral Chebyshev optimal control of constrained nonlinear dynamical systems[J].Computational Optimization and Applica-tions,1998,11(2):195-217.
[17]Vinh N X.Optimal trajectories in atmospheric flight[C].The32nd International Astronautical Congress Rome,Italy,September 6-12,1981.
[18]Hui T L,Ping Y J,Qun F,et al.Reentry skipping trajectory optimization using direct parameter optimization method[C].The14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference,Canberra,Australia,November 6-9,2006.
[19]Betts J T.Survey of numerical methods for trajectory optimization[J].Journal of Guidance,Control and Dynamics,1998,21(2):193-206.
[20]张熠,张万鹏,陈璟,等.基于Gauss伪谱法的UAV对地攻击武器投放轨迹规划[J].航空学报,2011,32(7):1239-1251.[Zhang Yi,Zhang Wan-peng,Chen Jing,et al.Trajectory planning of UAV ground attack weapon delivery based on Gauss pseudospectral method[J].Journal of Aeronautics,2011,32(7):1239-1251.]
[21]高长生,陈尔康,荆武兴.高超声速飞行器机动规避轨迹优化[J].哈尔滨工业大学学报,2017,49(4):16-21.[Gao Chang-sheng,Chen Er-kang,Jing Wu-xing.Optimization of maneuvering avoidance trajectory for hypersonic vehicle[J].Journal of Harbin Institute of Technology,2017,49(4):16-21.]
[22]刘晓慧,聂万胜,杨新垒.高超声速飞行器多约束再入滑翔机动弹道优化设计[J].导弹与航天运载技术,2017,352(2):6-11.[Liu Xiao-hui,Nie Wan-sheng,Yang Xin-lei.Optimization design of maneuvering trajectory for hypersonic vehicle with multiple constraints reentry gliding maneuver[J].Missile and Spaceflight Transport Technology,2017,352(2):6-11.]
[23]王彩霞.LQR最优控制系统中加权阵的研究[J].西北民族大学学报,2003,24(48):29-31.[Wang Cai-xia.Study of weight matrix in LQR optimal control system[J].Journal of Northwestern University of Nationalities,2003,24(48):29-31.]
[24]Lincoln B,Bernhardsson B.LQR optimization of linear system switching[J].IEEE Transactions on Automatic control,2002,47(10):1701-1705.
[25]Cao Y,Ren W.Optimal linear-consensus algorithms:an LQRperspective[J].IEEE Transactions on Systems Man&Cybernetics,2010,40(3):819-830.
[26]Huntington G T,Rao A V.Optimal reconfiguration of spacecraft formations using the Gauss pseudospectral method[J].Journal of Guidance,Control and Dynamics.2012,31(3):689-698.
[27]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(6):1766-1772.[Yong En-mi,Tang Guo-jin,Chen Lei.Fast reentry trajectory optimization of hypersonic vehicle based on Gauss pseudospectral method[J].Journal of Astronautics,2008(6):1766-1772.]
[28]徐少兵,李升波,成波.最优控制问题的Legendre伪谱法求解及其应用[J].控制与决策,2014,29(12):2113-2120.[Xu Shao-bing,Li Sheng-bo,Cheng Bo.Legendre pseudospectral method for optimal control problem and its application[J].Control and Decision,2014,29(12):2113-2120.]
[29]雍恩米,唐国金,陈磊.助推-滑翔式导弹中段弹道方案的初步分析[J].国防科技大学学报,2006,28(6):6-10.[Yong En-mi,Tang Guo-jin,Chen Lei.Preliminary analysis of midcourse trajectory for boost gliding missile[J].Journal of National University of Defense Technology,2006,28(6):6-10.]
[30]Phillips T H.A common aero vehicle(CAV)model,description,and employment guide[R].Schafer Corporation for AFRL and AFSPC,Arlington,VA,2003.