行星际小推力转移轨道分层初始设计方法

针对小推力转移轨道设计问题,提出了一种结合切比雪夫多项式拟合和离散脉冲策略的分层初始设计方法.基于曲线拟合思想采用切比雪夫多项式对小推力轨道进行逼近,建立起轨道状态与时间的关系,避免了传统曲线拟合策略中时间约束的解算并舍去了速度方向假设;在全局搜索中利用低阶多项式求解边界约束得到降维解空间中的全局最优解;在此基础上,增加切比雪夫多项式的自由度并局部优化;通过脉冲离散并进一步优化求解出引入路径约束的小推力轨道.以地火交会轨道及地-火-木星借力交会轨道为例对所提方法进行了仿真验证,结果表明此方法可有效地对交会、借力轨道进行快速全局初始设计.

A Layered Initial Design Method for Interplanetary Low-Thrust Transfer Trajectories

To implement the interplanetary low-thrust transfer trajectory, a layered initial design method is proposed based on the Chebyshev polynomial theory and the multiple impulse design strategy. First, the Chebyshev polynomial is used to approach the orbital states of low-thrust orbit by fitting curve and the relationship between the states and time in three-dimensional space is established, accordingly avoiding the calculation of time constraint and having no assumption on the direction of velocity. Then, to reduce the difficulty of initial guess, low-level Chebyshev polynomial is used to solve boundary constraints in the global search. On this basis, the order of the Chebyshev polynomials is increased to improve the solution space dimension and the sequential quadratic programming is used for optimization of initial search results. Finally, adopting impulse discretization to process the consequence of the curve fitting, the low-thrust transfer trajectory design is described as a multi-variable optimization problem for solving the low-thrust orbit involving path constraint. The proposed layered method is demonstrated for an earth-Mars transfer trajectory and an earth-Mars-Jupiter transfer trajectory. Numerical results show that the method could be applied effectively to the rapid global initial design of low-thrust trajectories.