Fast solver for J2-perturbed Lambert problem using deep neural network

TL;DR

This paper introduces a rapid, neural network-based solver for the J2-perturbed Lambert problem, combining an intelligent initial guess generator with differential correction, outperforming classical methods in speed while maintaining accuracy.

Contribution

The paper develops a novel deep neural network approach integrated with differential correction to efficiently solve the J2-perturbed Lambert problem, significantly improving speed over traditional methods.

Findings

The neural network provides accurate initial guesses for the Lambert problem.

The combined method is significantly faster than classical shooting and homotopy methods.

Performance validated on a multi-revolution J2-perturbed problem in the Jupiter system.

Abstract

This paper presents a novel and fast solver for the J2-perturbed Lambert problem. The solver consists of an intelligent initial guess generator combined with a differential correction procedure. The intelligent initial guess generator is a deep neural network that is trained to correct the initial velocity vector coming from the solution of the unperturbed Lambert problem. The differential correction module takes the initial guess and uses a forward shooting procedure to further update the initial velocity and exactly meet the terminal conditions. Eight sample forms are analyzed and compared to find the optimum form to train the neural network on the J2-perturbed Lambert problem. The accuracy and performance of this novel approach will be demonstrated on a representative test case: the solution of a multi-revolution J2-perturbed Lambert problem in the Jupiter system. We will compare the performance of the proposed approach against a classical standard shooting method and a homotopy-based perturbed Lambert algorithm. It will be shown that, for a comparable level of accuracy, the proposed method is significantly faster than the other two.