高超声速飞行器平稳滑翔弹道解析解及其应用

Analytical solutions of steady glide trajectory for hypersonic vehicle and planning application

针对高超声速飞行器平稳滑翔弹道在线规划问题,提出了一种高精度的平稳滑翔弹道解析求解方法。首先,将升力系数分解为横向分量、平衡滑翔纵向分量和平稳滑翔纵向分量3个部分,并在此基础上将纵向运动方程、横向运动方程和速度方程解耦;然后,分别采用解析积分、正则摄动法、高斯积分法和单步龙格-库塔积分获得了滑翔段高度及射程、弹道偏角、经度、纬度和速度的解析解,并通过分段求解来提高解的精度;最后,利用上述解析解,提出了一种规划升力系数平稳滑翔纵向分量和横向分量的平稳滑翔弹道快速生成算法。仿真校验表明,本文解析解的精度比经典的Bell解析解高1个数量级,所对应的弹道规划方法具有计算量小、规划速度快的特点,有利于实现在线弹道规划。

A kind of analytical solving method for the three-dimensional steady glide trajectory of the hypersonic vehicle is presented in this paper for the online planning problem. Firstly,the lift coefficient is separated into three components of lateral component,steady glide normal component and equilibrium glide normal component. Then,the longitudinal trajectory,lateral trajectory and velocity are decoupled in the dynamics.After that,the solutions of height,downrange and velocity azimuth angle are obtained by the analytical integration and the regular perturbation method,while the solutions of longitude,latitude and velocity are obtained by the Gaussian quadrature and single-step Runge-Kutta integration separately,and the accuracy of those solutions are improved by increasing the computational steps. Finally,a rapid steady glide trajectory programming algorithm is proposed based on the above analytical solutions,and the planning parameters are the lateral lift coefficient and steady glide normal lift coefficient. The simulation results show that those analytical solutions are more accurate than the Bell＇s solutions,and the planning algorithm only needs a small amount of calculation and obtains the result quickly,which can be used for online trajectory planning.