基于解析梯度的微推进转移轨道优化方法

 研究基于离散脉冲策略的行星际微推进转移轨道优化问题,为改善收敛性和计算效率,提出了一种解析的梯度矩阵计算方法。首先,基于离散脉冲思想建立了行星际微推进转移轨道优化模型,通过对速度脉冲矢量进行参数变换,避免了传统优化模型初值猜测和搜索域难以界定的缺点;然后,基于变分原理分析了离散脉冲模型中轨道状态转移矩阵与状态变分之间的关系,并给出了多种轨道特征条件下状态变分的计算方法,该方法可扩展到多次状态不连续情况;在此基础上,推导了离散脉冲轨道优化模型中性能指标与轨道约束对寻优参数梯度矩阵的解析表达式。以地球-火星的燃料最省微推进转移为例对所提解析梯度方法进行了仿真验证。数值结果表明：本文推导的解析梯度矩阵是正确的,与传统数值梯度计算方法相比,解析梯度矩阵可有效改善寻优算法的收敛特性,并能够提高计算效率约47%。

Analytical Gradient-based Optimization Method for Low-thrust Transfer Trajectories

The optimization of interplanetary low-thrust transfer trajectory is studied based on discrete impulsive strategy, and an analytical gradient matrix approach is proposed to improve the convergence property and efficiency of optimization algorithm. First, the optimization model for interplanetary low-thrust transfer is established based on the idea of discrete impulsive. A parameter transfer is used to overcome the difficulty in primary guess and searching field selection for impulsive vector of traditional optimization model. Then, the relationship between state transition matrix and state variation for optimization model is analyzed, and the computation method for state variation is proposed with different orbit characteristics, which can be expanded to multi-discontinuity case in orbit state. On this basis, the analytical gradient matrixes are derived for performance index and trajectory constraints. The proposed analytical gradient matrix algorithm is validated by finding fuel-optimal Earth to Mars trajectories that use low-thrust engine. The numerical results demonstrate that the derived analytical gradient matrixes are correct. Compared to traditional numerical algorithm, the analytical gradient matrix algorithm can improve the convergence property and computation efficiency by about 47%.