基于自动微分与伪谱法的小推力借力轨道设计

Low-thrust, gravity-assist trajectory optimization via pseudospectral method and automatic differentiation

摘要:

针对小推力借力轨道设计问题,给出一种基于自动微分与伪谱法的优化方法. 借力模型采用B平面模型,提高了轨迹优化设计的鲁棒性. 用高斯伪谱法对整个小推力借力轨道进行离散,将发射时间的搜索包含在同一计算框架内,避免了传统混合方法中随机搜索算法收敛慢、精度低的缺点. 将得到的大规模非线性规划(NLP)问题采用序列二次规划(SQP)法进行求解,为实现NLP问题的快速收敛,提出了串联优化以及弹性约束策略. SQP需要的导数信息通过自动微分获得,保证了计算的高精度和快速收敛. 对地球-金星-火星小推力借力轨道进行了优化设计,验证了本文方法的正确性和有效性.

Abstract:

An approach for low-thrust and gravity-assist trajectory optimization is presented in this paper based on automatic differentiation and pseudospectral method. The B-plane model is used to increase robustness of the trajectory optimization problem. A Gauss pseudospectral method is applied to the parameterization of the entire trajectory, which includes the search of launch date in the same calculation framework to avoid the slow convergence rate and poor precision caused by stochastic search algorithms. A sequential quadratic programming (SQP) method is adopted as the solver of the resulting large scale nonlinear programming (NLP) problem. Strategies of serial optimization and elastic constraints are proposed in order that the NLP problem converges rapidly. The derivatives required by the SQP method are obtained by automatic differentiation to ensure high accuracy and a rapid convergence rate. Taking the optimization of Earth-Venus-Mars low-thrust gravity-assist trajectory as an example, the results verify the correctness and validity of the proposed method.