Application of discretization methods in the online trajectory optimization of six-degree-of-freedom landing for reusable vehicles

离散化方法在可重复使用飞行器六自由度着陆在线轨迹优化问题中的应用

¹ School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China
² Research and Development Center, China Academy of Launch Vehicle Technology, Beijing 100076, China
³ School of Aeronautics and Astronautics, Sun Yat-Sen University, Shenzhen 518107, China
⁴ School of Systems Science and Engineering, Sun Yat-Sen University, Guangzhou 510275, China
⁵ Unmanned System Technology Research Institute, Northwestern Polytechnical University, Xi'an 710072, China

Received: 18 September 2024

Abstract

The process of vertical soft landing for reusable vehicles presents challenges such as model deviations and sensitivity to the initial reference trajectory. To address these difficulties, this paper first establishes a six-degree-of-freedom(6-DOF) dynamics model for the attitude motion during the flipping landing phase. Subsequently, the study focuses on two critical evaluation metrics for optimization in numerical simulations: solution accuracy and computational efficiency. Then, a comparative analysis of three discretization methods-trapezoidal, pseudospectral, and first-order hold discretization-is conducted in terms of solution accuracy and computational efficiency in simulation experiments. Ultimately, the first-order hold discretization method, with better overall performance, is selected. An iterative convex optimization algorithm is designed to solve the vertical landing trajectory optimization problem, and its results are verified using integration methods. This approach provides an effective solution for the demands of efficiency and accuracy in real-time trajectory optimization.

摘要

可重复使用飞行器垂直软着陆过程中存在模型偏差和初始参考轨迹敏感等问题, 针对相关难点, 建立考虑飞行器姿态运动的六自由度翻转着陆阶段动力学模型, 关注仿真实验中求解精度和计算效率这2个优化问题求解的重要评价指标, 重点对比分析了梯形离散、伪谱离散和一阶保持离散3种处理原问题动力学方程的离散化方法。选取综合表现更好的一阶保持离散方法, 针对可重复使用飞行器垂直着陆轨迹优化问题特性, 设计了迭代凸优化算法并使用积分方法验证其优化结果的正确性, 为在线求解轨迹优化的效率和准确性需求提供了解决方案。