采用Gauss伪谱法的小推力日-火Halo轨道转移优化设计

针对日-地Halo轨道到日-火Halo轨道的小推力轨道转移问题，给出一种基于不变流形理论和Gauss伪谱法的优化设计方法。首先，在日心惯性坐标系中建立小推力轨道优化模型，并基于不变流形理论给出轨道转移中流形出口和入口的选择原则，应用该原则在日-地系统中选择流形出口，在日-火系统中选择流形入口，并将其作为轨道转移的初末状态；然后基于Gauss伪谱法将最优控制问题离散化为非线性规划(NLP)问题，并采用基于逆多项式的形状算法给出了NLP初值的计算方法；最后对该轨道转移问题进行了数学仿真。仿真结果表明：Gauss伪谱法可有效用于小推力日-火Halo轨道转移的优化，且采用逆多项式形状算法得到的初值具有初始误差小，使得NLP收敛速度快的特点。

Optimization of Low Thrust Transfer Trajectory for the Sun Mars Halo Orbit Based on Gauss Pseudospectral Method

A method for optimizing of low thrust transfer trajectory from Sun Earth halo orbit to Sun Mars halo orbit based on invariant manifolds and gauss pseudospectral method (GPM) is proposed. Frist, the optimization model of low\|thrust trajectory is established in heliocentric inertial coordinate system, and the principle for choosing the entrance and the exit in transfer trajectory based on the theory of invariant manifolds is given, by the use of this principle, the entrance of Sun Earth invariant manifolds and the exit of Sun Mars invariant manifolds is chosen for both initial state and final state of the transfer trajectory. Then, the optimal control problem is discretized into a nonlinear programming (NLP) problem based on the GPM, and the initial value of the NLP problem is given by using the inverse polynomial shape based approach. The numerical simulation is proposed at last and is used to demonstrate that the GPM for optimizing of low thrust transfer trajectory is valid, in addition, the initial error obtained from the inverse polynomial shape based algorithm is small and make the NLP has fast convergence characteristics.