Learning-Based Polynomial Approximation of Minimum-Time Low-Thrust Transfers to Geostationary Orbit

This article proposes a learning-based approach to rapidly and accurately estimate the minimal time of low-thrust transfer from any elliptical orbit in a certain range to the geostationary orbit with arbitrary low-thrust propulsion parameters. It is difficult for traditional indirect methods of low-thrust trajectory optimization to obtain plenty of globally optimal trajectories as the training dataset. To address this issue, this article focuses on the following two contributions. First, a concise relationship between the minimum-time transfer problem and its optimal solution is identified, which reveals that the equivalent velocity increment can be approximately determined by only four initial orbital elements. The training samples are randomly generated based on this relationship, and the sample quantity needed by the estimation is greatly decreased. Second, a set of polynomial regression models are developed to approximate the initial costates and transfer time of the indirect method and supply good initial guesses to achieve better solutions. This predictor-corrector method promotes all the locally optimal trajectories in the training dataset to near the global optimum efficiently. Another polynomial regression model is trained on the promoted training dataset and is regarded as the estimator. Additionally, a continuation technique is developed to gradually find the globally optimal solutions. These solutions are used as the test dataset to verify the accuracy of the trained estimator. The results show that the estimator has a mean relative error of 0.075%. Meanwhile, its computational efficiency is as high as analytical expressions.