Fast Estimation of Initial Costate for Time-Optimal Trajectory Based on Surrogate Model

Abstract

This study investigated the time-optimal low-thrust interplanetary transfer problem, and proposes a fast estimation method for guessing the initial costate and optimal transfer time based on a surrogate model, and applied it to the problem of the 11th Global Trajectory Optimization Competition (GTOC 11). Two core methods are proposed in this paper: (1) a fast generation method called the neighbor point iteration algorithm (NPIA) is presented for rapidly generating low-thrust databases with high efficiency and accuracy; and (2) deep neural networks (DNNs) are adopted to learn the state–costate pairs of low-thrust databases, and the surrogate network can quickly estimate the initial costate and optimal transfer time of the low-thrust interplanetary problem. Experiments verified the proposed method and investigated the influence of network structure, learning rate, and loss function on the accuracy of network estimation. The effects of database generation and network estimation were compared based on three transfer scenarios: coplanar, non-coplanar, and arbitrary orbital transfer. In addition, the application case study showed that the proposed method can quickly obtain the time-optimal low-thrust solution to GTOC 11’s interplanetary transfer, which achieves high precision and meets the terminal constraints.