基于hp自适应伪谱法的飞行器多阶段轨迹优化
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摘要
为解决助推-滑翔飞行器的多阶段多约束轨迹优化问题,在考虑速度约束、轨迹阶段切换点约束与轨迹末端参数约束的条件下,建立了助推-滑翔飞行器纵向运动模型与多阶段轨迹优化模型.采用基于hp自适应伪谱法的Legendre-Gauss-Radau离散点,将该最优控制问题转换为多阶段非线性规划问题,求解得到最大飞行距离轨迹.为解决多阶段轨迹优化算法难以确定位置自由的阶段切换点的问题,基于动态规划的思想,设计了新的多阶段轨迹优化策略.改进后的优化策略在得到了多阶段全局近似最优解结果的同时,减少了原优化算法的计算量.仿真结果表明,改进的hp自适应伪谱法能有效解决多阶段助推-滑翔飞行器轨迹优化问题,优化结果优于最大升阻比滑翔飞行轨迹.
In order to solve the trajectory optimization problem of a boost-glide vehicle with multiphase and multi-constraint,a longitudinal motion model and a multi-phase trajectory optimization model were built based on the constraint consideration of velocity,switch point of trajectory phase and the parameter of trajectory end.Hp-adaptive-based Legendre-Gauss-Radau points were used to transcribe the optimization problem to a finite-dimensional nonlinear programming problem,and maximal downrange optimization trajectory was obtained. An improved optimization strategy was proposed based on dynamic programming theory to decide the switch points of free phases,due to the difficulty with the multi-phase trajectory optimization arithmetic.Compared with the hp-adaptive pseudospectral method,the improved strategy can get almost the same optimization trajectory and a smaller finite-dimensional approximation. Numerical simulation results show that the boost-glide vehicle trajectory optimization problem can be solved,and the results are better than the gliding trajectory with the maximum lift-to-drag ratio.
In order to solve the trajectory optimization problem of a boost-glide vehicle with multiphase and multi-constraint,a longitudinal motion model and a multi-phase trajectory optimization model were built based on the constraint consideration of velocity,switch point of trajectory phase and the parameter of trajectory end.Hp-adaptive-based Legendre-Gauss-Radau points were used to transcribe the optimization problem to a finite-dimensional nonlinear programming problem,and maximal downrange optimization trajectory was obtained. An improved optimization strategy was proposed based on dynamic programming theory to decide the switch points of free phases,due to the difficulty with the multi-phase trajectory optimization arithmetic.Compared with the hp-adaptive pseudospectral method,the improved strategy can get almost the same optimization trajectory and a smaller finite-dimensional approximation. Numerical simulation results show that the boost-glide vehicle trajectory optimization problem can be solved,and the results are better than the gliding trajectory with the maximum lift-to-drag ratio.
引文
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[3]沈冠军,冯顺山,曹红松.简易控制超音速火箭靶弹方案最优制导律设计[J].北京理工大学学报,2015,35(3):256-261.Shen Guanjun,Feng Shunshan,Cao Hongsong.Optimal programmed guidance law design of simple control supersonic rocket target[J].Transactions of Beijing Institute of Technology,2015,35(3):256-261.(in Chinese)
[4]Garg D,Patterson M A,Francolin C,et al.Direct trajectory optimization and costate estimation of finitehorizon and infinite-horizon optimal control problems using a Radau pseudospectral method[J].Computa-tional Optimization and Applications,2011,49(2):335-358.
[5]王春利.航空航天推进系统[M].1版.北京:北京理工大学出版社,2004.Wang Chunli.Aerospace propulsion system[M].1st ed.Beijing:Beijing Institute of Technology Press,2004.(in Chinese)
[6]王丽英,张友安,赵国荣.改进的hp自适应网格细化算法及应用[J].弹道学报,2013(1):16-21.Wang Liying,Zhang Youan,Zhao Guorong.Improved hp-adaptive mesh refinement algorithm and its application[J].Journal of Ballistics,2013(1):16-21.(in Chinese)
[7]Wang Y,Zhu Y,Jiang X,et al.Comparison of LPM,GPM and RPM for optimization of low-thrust EarthMars rendezvous trajectories[C]∥Proceedings of Guidance,Navigation and Control Conference.[S.l.]:IEEE,2014:2461-2467.
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