Efficient Machine Learning Method for Co-state Estimation of Low-thrust Optimal Trajectories

For initial values of co-state variables guessing problem in the indirect optimization of the low-thrust trajectory with variable specific impulse, a method based on machine learning is proposed to estimate the initial values of co-state variables with high accuracy and efficiency. Firstly, based on the continuation of the nominal optimal trajectory, a data set generation method under the condition of high perturbation upper limit of the state variable boundary value is established and the influence of the upper limit of the perturbation on solving efficiency is analyzed. Then, an artificial neural network (ANN) mapping relationship based on the combined inputs of position, velocity, the orbital elements and the modified equinoctial elements is constructed. The neural network structure is analyzed and optimized. The proposed method is applied to the scenarios of low-thrust transfers in deep space exploration. Simulation results indicate that the method effectively improves the solution convergence rate compared with the data set generation method with direct perturbation of nominal trajectory and the artificial neural network mapping method with a single form of states input, and it can efficiently and accurately estimate the initial values of co-state variables to achieve fast trajectory optimization. © 2022, Editorial Dept. of JA. All right reserved.