Trajectory Optimization for Spacecraft Using a Second-Order Gauss Pseudo Spectral Method

다국어 초록 (Multilingual Abstract)

An optimal control problem for the trajectory of spacecraft under nonlinear constraints is presented. The second-order Gauss pseudo spectral method（GPM） is described for solving the problem numerically. Based on the first-order GPM, the differential matrix of the second-order GPM is derived. The dynamic equations and its constraints are approximated by the two methods. The terminal state constraints of the second-order GPM are converted to two constraints: terminal state variables and the first-order derivative constraints. The first-order GPM and second-order GPM are compared in terms of the accuracy of the state and control, the number of variables in NLP, the convergence time. A key feature of the second-order method is that it provides a more accurate and efficient way than the first-order method, due to reducing the number of variables in the nonlinear programming problem that is transcribed. A numerical example is used to identify the key differences between the two methods. The results of this study indicate that the first-order and second-order Gauss methods are very similar in accuracy, while the computational efficiency of the two methods is significantly different, for the numerical solution of nonlinear optimal control problems.

목차 (Table of Contents)

• Abstract
• 1. Introduction
• 2. Optimal Control
• 2.1. Optimal Control Problem
• 2.2. Second-Order GMP for Optimal Control Problem
• 3. Numerical Example
• 4. Conclusions
• Acknowledgements
• References