小推力轨道转移快速优化设计

Rapid Optimization of Low-Thrust Orbit Transfer

在研究电推进系统中,为满足小推力转移轨道高精度在线生成的要求,伪光谱方法在电推进小推力轨道转移优化设计中的应用。首先对小推力航天器轨道转移最优控制问题模型进行无量纲化处理,以提高优化算法求解精度。然后采用基于勒让德-高斯-兰伯特配置点的勒让德伪光谱方法,将最优控制问题离散成约束参数优化问题,再利用适于求解大尺度非线性规划问题的TOMLAB/SNOPT优化软件包进行求解。通过数值仿真计算,求解生成了满足各类约束条件的小推力转移轨道,并利用余向量映射定理及极小值原理验证了所得轨道转移控制量的最优性。结果表明,勒让德伪光谱优化算法具有对初始猜测值不敏感、收敛速度快、精度高等优点。

High - accuracy rapid optimization of low - thrust electric - propulsion orbit transfer by a Legendre pseudospectral method is studied in this paper. Firstly the equations of motion of the low - thrust orbit transfer optimal control problem are normalized through a non - dimensionalization method to improve solution accuracy. Then the Legendre pseudospectral method based on interpolating functions on Legendre - Gauss - Lobatto quadrature nodes is used to transform the optimal control problem into a constrainted parameter optimization problem, which is solved using TOMLAB/SNOPT. Low - thrust trajectories generated by this method can satisfy various constraints and optimality is validated through the Covector Mapping Theorem and Pontryagin＇s Minimum Principle. Simulation results demonstrate that pseudospectral optimization method is a promising method for real -time trajectory optimization.