关键词: 一子级可重复使用火箭, 双层优化框架, 轨迹优化, 代理模型, 运载能力

Abstract:

The joint optimization of ascent and return trajectories for first-stage reusable rockets involves highly nonlinear multi-stage trajectory planning， posing significant challenges to be solved. To enhance the reliability and optimality of the joint optimization of ascent and return trajectories， this paper proposes a bi-level optimization framework consisting of inner-layer trajectory optimization and outer-layer mission parameter optimization. By synergistically combining trajectory optimization’s constraint-handling capability with surrogate model optimization’s efficiency in black-box function minimization， this framework effectively reduces nonlinearity in trajectory planning and complexities of parametric optimization. For the inner-layer trajectory optimization， we solve the ascent trajectory using an existing convex-optimization-based method. The first-stage return trajectory， which comprises powered deceleration， atmospheric reentry， and powered landing phases， poses greater challenges to be solved. To ensure reliable inner-layer solutions， we develop a convergence-guaranteed trajectory optimization algorithm for first-stage return flight. By analyzing the characteristics of the optimal control profile and parametrizing it， the algorithm designs analytical parameter iteration equations， requiring solving only two parameters to obtain the optimal trajectory， with theoretical convergence guarantees. For the outer-layer mission parameter optimization， we adopt surrogate-model-based optimization algorithm to solve optimal mission parameters， including stage separation states and the mass of each rocket stage， thereby obtaining the optimal trajectory solution that maximizes the payload mass. Simulation results show that， compared with existing methods， the proposed bi-level optimization framework improves payload mass by approximately 25%. Furthermore， the first-stage return trajectory optimization algorithm achieves high computational efficiency， with a runtime of less than 50 ms， demonstrating both reliability and efficiency.

Key words: first-stage reusable rockets, bi-level optimization framework, trajectory optimization, surrogate model, launch capacity