多约束多规避区全程弹道快速优化方法
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摘要
研究了多约束多规避区条件下的全程弹道快速优化问题。首先,分类研究了规避区的类型和基本模型;然后,重点考虑端点约束、控制约束、典型过程约束、时间及弹道链接约束和规避区约束等,构建了弹道优化的多种约束模型;最后,提出了一种基于检测点自适应伪谱法的轨迹优化算法,即在多区间伪谱法的基础上,引入曲率和误差判据,创新设计了自适应调整区间密度和区间内配点数的改进策略,构建了自适应伪谱法,进一步在自适应伪谱法的基础上加入检测点进行检测,采用一种基于配点间的检测点法作为解的近似误差评估准则,检验配点间的检测点处对于约束方程的满足程度。仿真结果表明,在不对初值进行猜测的情况下,以全程飞行耗时最短为优化指标,整个弹道优化CPU耗时小于5 s,终端状态参数均满足所有端点约束条件,优化弹道通过侧向绕飞,成功实现对两个规避区的规避,相关参数满足突防能力设计要求。
The problem of full-course ballistic rapid planning for multi-constraint and multi-step avoidance zones was studied.Firstly,the type and basic model of the avoidance zone was described,and then the ballistic optimization constraint model were established,considering the endpoint,control,typical process,time,ballistic link and avoidance zone constraint.Then,a trajectory optimization algorithm was designed based on the detection point adaptive pseudo-spectral method. On the basis of the multi-interval pseudos-pectral method,the curvature and error criterion were used to improve the strategy of adaptive adjustment about the intervals and the points between the intervals.Furthermore,the detection points were added based on the results of the adaptive pseudo-spectral method.The detection point method based on the matching point was used as the approximate error evaluation criterion of the solution.The degree of satisfaction of the constraint equation was verified. The simulation results show that,considering the shortest flight time as the optimization indicator,the entire ballistic optimization takes less than 5 s without guessing the initial value.The terminal state parameters satisfy all the endpoint constraints,and the optimized trajectory passes the lateral flight.Two evasive zones are successfully avoided,and the relevant parameters meet the design requirements of the penetration capability.
The problem of full-course ballistic rapid planning for multi-constraint and multi-step avoidance zones was studied.Firstly,the type and basic model of the avoidance zone was described,and then the ballistic optimization constraint model were established,considering the endpoint,control,typical process,time,ballistic link and avoidance zone constraint.Then,a trajectory optimization algorithm was designed based on the detection point adaptive pseudo-spectral method. On the basis of the multi-interval pseudos-pectral method,the curvature and error criterion were used to improve the strategy of adaptive adjustment about the intervals and the points between the intervals.Furthermore,the detection points were added based on the results of the adaptive pseudo-spectral method.The detection point method based on the matching point was used as the approximate error evaluation criterion of the solution.The degree of satisfaction of the constraint equation was verified. The simulation results show that,considering the shortest flight time as the optimization indicator,the entire ballistic optimization takes less than 5 s without guessing the initial value.The terminal state parameters satisfy all the endpoint constraints,and the optimized trajectory passes the lateral flight.Two evasive zones are successfully avoided,and the relevant parameters meet the design requirements of the penetration capability.
引文
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[3]杨志红,徐宝华,姚德清.基于高斯伪谱法的吸气式高超声速飞行器爬升弹道优化研究[J].导航定位与授时,2018,5(3):35-40.YANU Zhihong,XU Baohua,YAO Deqing.Research on climbing trajectory optimization of air-breathing hypersonic vehicle based on gauss pseudospectral method[J].Navigation Positioning and Timing,2018,5(3):35-40.
[4]许强强,葛健全,杨涛,等.面向突防的多导弹协同弹道规划方法[J].中国惯性技术学报,2018,26(4):524-530.XU Qiangqiang,GE Jianquan,YANG Tao,et al.Cooperative trajectory planning for penetration of multiple missiles[J].Journal of Chinese Inertial Technology,2018,26(4):524-530.
[5]谢愈,潘亮,谷学强,等.高超声速飞行器多目标复杂约束滑翔弹道优化[J].国防科技大学学报,2017,39(2):9-17.XIE Yu,PAN Liang,GU Xueqiang,et al.Gliding trajectory optimization with multiple objective complicated constraints for hypersonic vehicles[J].Journal of National University of Defense Technology,2017,39(2):9-17.
[6]朱付涛.基于多约束优化的雷达导引头弹道规划算法研究[C]//北京力学会.北京力学会第二十四届学术年会会议论文集.2018:2.ZHU Futao.Research on radar seeker trajectory planning algorithm based on multiple constraint optimization[C]//Beijing Society of Theoretical Applied Mechanics.Proceedings of the 24th Annual Meeting of the Beijing Society of Theoretical Applied Mechanics.2018.2.
[7]洪蓓,梁欣欣,辛万青.固体运载火箭多约束弹道优化[J].导弹与航天运载技术,2012(3):1-5.HONG Bei,LIANG Xinxin,XIN Wanqing.Multi-constraint trajectory optimization for solid launch vehicle[J],Missiles and Space Vehicles,2012(3):1-5.
[8]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 Kenan,ZHOU Hao,CHEN Wanchun.Trajectory planning for hypersonic vehicle with multiple constraints and multiple maneuvering penetration strategies[J].Journal of Ballistics,2012,24(3):85-90.
[9]Wang Hong,Xie Mujun,Zhang Peng,et al.Research of asteroid landing trajectory optimization based on gauss pseudospectral method[C]//Intelligent Human-Machine Systems and Cybernetics(IHMSC),2014 Sixth International Conference on,2014.
[10]Ming C,Sun R S,Bai H Y,et al.Climb trajectory optimization with multiple constraints for air-breathing supersonic missile[J].Journal of Astronautics,2016:1443-1449.
[11]梁欣欣,陈阳,张艳,等.姿控载荷多约束下的内外弹道联合优化[J].宇航学报,2016,37(6):679-686.LIANG Xinxin,CHEN Yang,ZHANG Yang,et al.Interior and exterior ballistics coupled optimization with constraints of attitude control and flight load[J].Journal of Astronautics,2016,37(6):679-686.
[12]Zhou H,Wang X,Bai Y,et al.Ascent phase trajectory optimization for vehicle with multi-combined cycle engine based on improved particle swarm optimization[J].Acta Astronautica,2017,140:156-165.
[13]Pengling Wang,Rob M P,Goverde.Multiple-phase train trajectory optimization with signalling and operational constraints[J].Transportation Research Part C Emerging Technology,2016,69:255-275.
[14]陈琦.滑翔增程制导炮弹弹道优化及制导控制方法研究[D].南京:南京理工大学,2017.CHEN Qi.Investigation on trajectory optimization and guidance&control scheme for a type of gliding guided projectiles[D].Nanjing:Nanjing University of Science and Technology,2017.
[15]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(12):2113-2120.XU Shaobing,LI Shengbo,CHENG Bo.Theory and application of Legendre pseudo-spectral method for solving optimal control problem[J].Control and Decision,2014(12):2113-2120.