基于高斯伪谱法的二级助推战术火箭多阶段轨迹优化
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摘要
针对二级助推战术火箭在多种约束下的高精度轨迹优化问题,提出了一种基于高斯伪谱法(GPM)的多阶段轨迹优化方法。针对二级发动机的工作特点,将全弹道划分为发射段、爬升段、续航段和制导攻击段4个阶段。为了提高禁飞区或敌方火力覆盖区附近的优化轨迹精确度,引入准接触点概念,将全弹道进一步进行阶段细分,并以连接点确保相邻阶段的顺利连接。利用GPM将轨迹规划问题转化为非线性规划问题进行求解。为了进一步提高计算效率、降低初值设置的难度,设计了基于初值生成器的迭代策略,实现了二级助推战术火箭多阶段轨迹优化。充分考虑飞行器各阶段飞行特点和约束,通过数值算例表明了该方法的优点。仿真结果表明,所提优化方法求解效率高,能够得到可行的最佳轨迹。
A multi-stage trajectory optimization method based on Gauss pseudospectral method( GPM) is proposed for optimizing the high-precision trajectory of tactical two-stage booster rockets under multiple constraints. According to the operating characteristic of the two-stage engine,the entire trajectory is divided into four flight phases,such as launching,climb,endurance and attack. In order to improve the accuracy of optimization trajectory near the no-fly zone and enemy fire coverage,the conception of quasicontact point is introduced,and the trajectory is further subdivided. The connection points are used to ensure the smooth connection between adjacent phases. GPM is used to transform the trajectory optimization problem into a nonlinear programming problem. In order to further improve the computational efficiency and reduce the difficulty of setting the initial value,an iterative strategy based on the initial value generator is designed to achieve the optimization of multi-stage trajectory. Full consideration is given to the various flight characteristics and constraints of rocket in each phase,and the numerical examples are used to demonstrate the merits of the proposed algorithm. The simulated results show that the proposed algorithm has high effectiveness and can get the feasible optimal trajectory.
A multi-stage trajectory optimization method based on Gauss pseudospectral method( GPM) is proposed for optimizing the high-precision trajectory of tactical two-stage booster rockets under multiple constraints. According to the operating characteristic of the two-stage engine,the entire trajectory is divided into four flight phases,such as launching,climb,endurance and attack. In order to improve the accuracy of optimization trajectory near the no-fly zone and enemy fire coverage,the conception of quasicontact point is introduced,and the trajectory is further subdivided. The connection points are used to ensure the smooth connection between adjacent phases. GPM is used to transform the trajectory optimization problem into a nonlinear programming problem. In order to further improve the computational efficiency and reduce the difficulty of setting the initial value,an iterative strategy based on the initial value generator is designed to achieve the optimization of multi-stage trajectory. Full consideration is given to the various flight characteristics and constraints of rocket in each phase,and the numerical examples are used to demonstrate the merits of the proposed algorithm. The simulated results show that the proposed algorithm has high effectiveness and can get the feasible optimal trajectory.
引文
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[19] HAGER W W,RAO A V,TSIOTRAS P,et al. Direct trajectoryoptimization using a variable low-order adaptive pseudospectralmethod[J]. Journal of Spacecraft&Rockets,2013,48(3):433-445.
[20]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.YONG E M,TANG G J,CHEN L. Rapid trajectory optimizationfor hypersonic reentry vehicle via Gauss pseudospectral method[J]. Journal of Astronautics,2008,29(6):1766-1772.(inChinese)
[21] ZHAO J,ZHOU R. Reentry trajectory optimization for hypersonicvehicle satisfying complex constraints[J]. Chinese Journal ofAeronautics,2013,26(6):1544-1553.
[22] PHOGAT K S,CHATTERJEE D,BANAVAR R. Discrete-timeoptimal attitude control of a spacecraft with momentum and con-trol constraints[J]. Mathematics,2017,41(1):199-211.
[23] HUNTINGTON G T,RAO A V. Comparison of global and localcollocation methods for optimal control[J]. Journal of Guidance,Control,and Dynamics,2015,31(2):432-436.
[2] BONAMI P,OLIVARES A,SOLER M,et al. Multiphase mixed-integer optimal control approach to aircraft trajectory optimization[J]. Journal of Guidance, Control, and Dynamics,2013,36(5):1267-1277.
[3] SOLER M,OLIVARES A,STAFFETTI E. Multiphase optimalcontrol framework for commercial aircraft four-dimensional flight-planning problems[J]. Journal of Aircraft,2015,52(1):274-286.
[4] RAO A V,TANG S,HALLMAN W P. Numerical optimizationstudy of multiple-pass aeroassisted orbital transfer[J]. OptimalControl Applications&Methods,2002,23(4):215-238.
[5] CHEN Q,WANG Z,CHANG S,et al. Multiphase trajectory opti-mization for gun-launched glide guided projectiles[J]. Proceed-ings of the Institution of Mechanical Engineers Part G:Journal ofAerospace Engineering,2015,230(6):995-1010.
[6] CHEN Q,WANG Z Y. Optimal trajectory for time-on-target of aguided projectile using direct collocation method[C]∥Proceedingsof International Conference on Mechatronic Sciences,Electric En-gineering and Computer. Shenyang:IEEE,2014:2803-2806.
[7] FRESCONI F,CELMINS I,FAIRFAX L. Optimal parameters formaneuverability of affordable precision munitions[C]∥Proceed-ings of Aerospace Sciences Meeting. Orlando,FL,US:AIAA,2012:3706-3727.
[8] FRESCONI F. Range extension of gun-launched smart munitions[C]∥Proceedings of the 24th International Symposium on Ballis-tics. New Orleans,LA,US:National Defense Industrial Associa-tion,2008:157-164.
[9] BETTS J T. Survey numerical methods for trajectory optimization[J]. Journal of Guidance, Control, and Dynamics, 1998,21(2):193-207.
[10]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):397-406.YONG E M,CHEN L,TANG G J. A survey of numericalmethods for trajectory optimization of spacecraft[J]. Journal ofAstronautics,2008,29(2):397-406.(in Chinese)
[11] BENSON D A,HUNTINGTON G T,THORVALDSEN T P,et al. Direct trajectory optimization and costate estimation via anorthogonal collocation method[J]. Journal of Guidance,Control,and Dynamics,2006,29(6):1435-1439.
[12] SEYWALD H,KUMAR R R. Method for automatic costate cal-culation[J]. Journal of Guidance, Control, and Dynamics,2015,19(6):1252-1261.
[13]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 Y B,ZHANG K,XUE X D. Optimization of glide trajec-tory of guided bombs using a Radau pseudo-spectral method[J].Acta Armamentarii,2014,35(8):1179-1186.(in Chinese)
[14] GARG D,PATTERSON M,HAGER W W,et al. A unifiedframework for the numerical solution of optimal control problemsusing pseudospectral methods[J]. Automatica,2010,46(11):1843-1851.
[15] BENSON D A,HUNTINGTON G T,THORVALDSEN T P. Di-rect trajectory optimization and costate estimation via an orthogo-nal collocation method[J]. Journal of Guidance,Control,andDynamics,2006,29(6):1435-1439.
[16] GUAN C P,CHEN C. Multiphase path-constrained trajectory op-timization for the boost-glide vehicle via the Gauss pseudospectralmethod[J]. Journal of Astronautics,2010,31(11):2512-2518.
[17]明超,孙瑞胜,白宏阳.基于hp自适应伪谱法的多脉冲导弹弹道优化设计[J].固体火箭技术,2015,38(2):151-155.MING C,SUN R S,BAI H Y. Optimizing design of trajectory formultiple-pulse missiles based on hp-adaptive pseudo-spectralmethod[J]. Journal of Solid Rocket Technology,2015,38(2):151-155.(in Chinese)
[18]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.ZHANG Y,ZHANG W P,CHEN J. Air-to-ground weapon deliv-ery trajectory planning for UCAVs using Gauss pseudospectralmethod[J]. Acta Aeronautica et Astronautica Sinica,2011,32(7):1240-1251.(in Chinese)
[19] HAGER W W,RAO A V,TSIOTRAS P,et al. Direct trajectoryoptimization using a variable low-order adaptive pseudospectralmethod[J]. Journal of Spacecraft&Rockets,2013,48(3):433-445.
[20]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.YONG E M,TANG G J,CHEN L. Rapid trajectory optimizationfor hypersonic reentry vehicle via Gauss pseudospectral method[J]. Journal of Astronautics,2008,29(6):1766-1772.(inChinese)
[21] ZHAO J,ZHOU R. Reentry trajectory optimization for hypersonicvehicle satisfying complex constraints[J]. Chinese Journal ofAeronautics,2013,26(6):1544-1553.
[22] PHOGAT K S,CHATTERJEE D,BANAVAR R. Discrete-timeoptimal attitude control of a spacecraft with momentum and con-trol constraints[J]. Mathematics,2017,41(1):199-211.
[23] HUNTINGTON G T,RAO A V. Comparison of global and localcollocation methods for optimal control[J]. Journal of Guidance,Control,and Dynamics,2015,31(2):432-436.