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%.