基于Gauss伪谱法的有限推力轨道转移优化

Optimal Orbit Transfer with Finite Thrust Based on Gauss Pseudospectral Method

研究了Gauss伪谱法在有限推力轨道转移优化问题中的应用。首先在消除奇点的拟春分点轨道要素的非奇异摄动方程基础上,选取性能指标为能量最优,控制变量为有限推力发动机加速度的3个分量;然后,利用Gauss伪谱法将最优控制问题转化为非线性规划问题,避开了求解两点边值问题的困难;最后给出了2个算例,分别计算了同面转移轨道和异面转移轨道的能量最优化转移。计算过程及结果表明本文所用方法对初值猜测敏感度较小,且平稳收敛,具有一定的鲁棒性,转移轨道平稳光滑,能够满足各种约束条件,便于对发动机进行控制,且在零倾角零偏心率轨道情况下不产生奇异。因此,Gauss伪谱法可用来求解轨道转移优化问题。

A finite-thrust orbital transfer optimization problem based on pseudo-equinoctial elements is studied by applying a new optimal control method on the basis of Gauss pseudospectral method.Using the pseudo-equinoctial elements in dynamics equations as state variables,optimality condition is derived and the optimizing problem is converted into nonlinear programming problem（NLP）.The application of Gauss pseudospectral method enables to avoid the difficulty of calculating two-point boundary value and the derivation of dynamics equations is converted into static parameter optimization problem.The state variables and control variables are selected as optimal parameters at all collocation nodes.At last,two numerical examples of orbital transfer with coplanar and different planes are analyzed respectively.The simulation results demonstrate that Gauss pseudospectral method has low sensitiveness in conditions initializing of orbital transfer and the optimal solution is fairly good in robustness and easy to control.The precision and efficiency of this trajectory optimization method are demonstrated by applying to space vehicle orbital transfer with finite thrust optimization problem.