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

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.