一子级可重复使用火箭上升和返回轨迹联合优化涉及多阶段非线性轨迹优化，直接求解难度大。为提高上升和返回轨迹联合优化的可靠性和最优性，提出一种由内层轨迹优化和外层任务参数优化组成的双层优化框架，结合轨迹优化方法易于处理约束和基于代理模型的优化方法能求解黑箱函数最小值的优势，显著降低轨迹优化的非线性和任务参数优化问题的复杂度。内层轨迹优化中，上升段采用已有基于凸优化的轨迹优化方法，而一子级返回段因包含动力减速、大气再入、动力着陆三个过程，轨迹优化难度大。为确保内层轨迹优化可靠高效，设计了能够保证收敛的返回段轨迹优化算法。该算法通过分析最优控制剖面的特征并将其参数化，设计解析的参数迭代方程，仅求解两个参数即可得到最优轨迹，理论保证轨迹优化的可靠性。外层任务参数优化中，采用基于代理模型的优化方法求解最优任务参数（包括各阶段交接班参数和火箭各部分质量），得到最大化有效载荷质量的最优飞行方案。仿真结果表明，相比于现有方法，本文提出的双层优化框架将有效载荷质量提升约25%；一子级返回段轨迹优化算法计算耗时小于50 ms，算法可靠高效。
The joint optimization of ascent and return trajectories for first-stage reusable rockets involves highly nonlinear multistage 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 milliseconds, demonstrating both reliability and efficiency.
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