火星大气进入段纵向可达区生成的解析同伦法

An Analytical Homotopic Method to Generate the Reachable Longitudinal Area for Mars Entry

针对火星大气进入段飞行器的飞行能力分析问题,提出一种基于解析同伦法的纵向可达区(开伞点高度-航程剖面)计算方法。该方法首先分别为最大航程问题/最小航程问题和最大/小开伞高度问题构造最优解已知的初始辅助优化问题,并以此为出发点最终求取原最优问题的解。在求解4个子优化问题的基础上,通过构造合适的同伦参数延拓出纵向可达区。仿真结果表明,该方法有效避免了最优问题协态初值猜测困难的问题,通过设计合适的同伦参数,可以快速求取任意初始路径角下的开伞点最大/最小航程、最大开伞高度以及纵向可达区。

To analyze the flight capability of a Mars atmospheric entry vehicle,a method based on the analytical homotopic approach is proposed to generate the reachable longitudinal area(the profile of deployment altitude versus downrange).Three initial auxiliary optimization problems with definitely known solutions are established for the maximum/minimum downrange and maximum/minimum deployment altitude problems respectively.Starting from the auxiliary problems,the original problems of interest can be finally solved by the homotopic method.Based on the solutions of the four optimization problems,the reachable longitudinal area can be determined iteratively by setting a proper continuation parameter.The proposed method is finally tested in the MATLAB environment.The simulation results demonstrate the effectiveness of the method in obtaining the values of the initial costate variables.By selecting the reasonable continuation parameters,the reachable longitudinal area can be determined quickly under different initial flight path angles.