一种新型火星定点着陆轨迹快速优化方法

A New Method of Rapid Trajectory Optimization for Mars Pin-Point Landing

针对火星定点着陆任务大气进入段的轨迹规划问题,给出了一种基于hp-Radau伪谱法的快速优化算法。综合考虑大气进入段的动力学约束、边值约束、以及着陆器的机动能力约束和安全性约束,结合hp-Radau伪谱法的配点特性,将轨迹优化问题转换成一个大规模多约束参数优化问题,给出了大气进入段轨迹优化问题的求解框架;为了提高算法的计算效率,给出了参数优化过程中雅克比矩阵的解析表达式;并通过数学仿真对本文算法进行了数值验证,结果表明:(1)hp-Radau伪谱法可有效应用于火星着陆大气进入段的轨迹规划问题,并且比Radau伪谱法具有更强的针对性和更高的计算效率;(2)与数值差分方法求解雅克比矩阵相比,引入雅克比矩阵的解析表达式能够将算法的计算效率和耗时稳定性大大提高,分别为58.75%和85.58%。

Aiming at planning the vehicle＇s entry trajectory for Mars Pin-Point Landing,a new method based on hp-Radau pseudospectral algorithm is proposed.The vehicle＇s dynamics,state constraints during Mars Entry phase and vehicle＇s mobility and safety constraints are taken into consideration synthetically.By combining the properties of collocation points of hp-Radau pseudospectral algorithm,the problem of trajectory optimization can be converted into a large-scale parameters optimization problem with multi-constraints,thus a solving framework of trajectory optimization is obtained.Also,the analytical form of Jacbian matrix of performance index and constraint equations is derived in order to improve the method＇s efficiency.The simulation result indicates that：（1） the hp-Radau pseudospectral algorithm can be used to solve the trajectory optimization problem during Mars Entry,and has more efficient performance compared with the radau pseudospectral algorithm;（2） Compared with the numeric difference method,the analytical form of Jacbian matrix could substantially increase the method＇s efficiency and time-consuming stability by 58.75% and 85.58% respectively.