# Multi-Revolution Low-Thrust Trajectory Optimization Using Symplectic Methods

## TL;DR

This paper introduces a high-precision symplectic method combined with iterative linear-quadratic control techniques to optimize complex low-thrust, multi-revolution orbital transfers with improved accuracy and computational efficiency.

## Contribution

It presents a novel symplectic approach for solving multi-revolution low-thrust trajectory optimization problems using iterative linear-quadratic sub-problems.

## Key findings

- High accuracy in trajectory solutions
- Efficient convergence with modified equinoctial elements
- Effective handling of multi-revolution transfers

## Abstract

Optimization of low-thrust trajectories that involve a larger number of orbit revolutions is considered a challenging problem. This paper describes a high-precision symplectic method and optimization techniques to solve the minimum-energy low-thrust multi-revolution orbit transfer problem. First, the optimal orbit transfer problem is posed as a constrained nonlinear optimal control problem. Then, the constrained nonlinear optimal control problem is converted into an equivalent linear quadratic form near a reference solution. The reference solution is updated iteratively by solving a sequence of linear-quadratic optimal control sub-problems, until convergence. Each sub-problem is solved via a symplectic method in discrete form. To facilitate the convergence of the algorithm, the spacecraft dynamics are expressed via modified equinoctial elements. Interpolating the non-singular equinoctial orbital elements and the spacecraft mass between the initial point and end point is proven beneficial to accelerate the convergence process. Numerical examples reveal that the proposed method displays high accuracy and efficiency.

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Source: https://tomesphere.com/paper/1901.02881