火箭返回着陆问题高精度快速轨迹优化算法
High precision rapid trajectory optimization algorithm for launch vehicle landing

针对垂直起降可重复使用运载火箭子级返回着陆问题, 提出一种高精度快速轨迹优化算法. 算法将凸化技 术与伪谱离散方法有机结合, 将非凸、非线性优化问题转化为凸优化问题, 进而充分利用凸优化求解快速性、收敛 确定性以及伪谱法离散精度高的理论基础. 在优化精度方面, 建立了高保真优化模型, 分析了发动机开机/终端时刻 值设计对轨迹最优性的影响; 采用flip-Radau谱法对连续最优控制问题进行离散, 并利用伪谱法的独特离散时域映 射, 将开机和终端时刻设计为特殊控制变量, 提高了优化结果的精度和最优性. 在快速性方面, 为利用凸优化方法 求解非凸问题, 基于一种新的信赖域更新策略, 提出了改进序列凸化算法, 减少了算法迭代次数, 提高了算法收敛性 能. 数值实验验证了算法的有效性. 高精度的优化结果和较高的计算速度, 使得算法具有发展为在线最优制导方法 的潜力.
Aiming to solve the precision landing problem of vertical takeoff-vertical landing reusable rockets, a high accuracy rapid trajectory optimization algorithm is proposed. The non-convex and nonlinear problem is transformed into convex problem through a proper combination of convexification techniques and pseudospectral discretization, so the fast and deterministic convergence properties of convex optimization theory as well as the high discretization accuracy of pseudospectral methods can be taken advantage of. In terms of optimization accuracy, a high-fidelity optimization model is built, and the effects of the design of ignition and terminal time on the optimality of the trajectory are analyzed. The flip- Radau pseudospectral discretization is adopted, and its unique time domain mapping is utilized to transform the ignition and terminal time into special control variables, so the accuracy and optimality of the trajectory are improved. For rapidness, in order to solve the non-convex problem by convex optimization methods, an improved successive convexification algorithm is proposed based on a novel online trust-region update strategy, thus the number of iterations is decreased and the convergence property is enhanced. The effectiveness of the proposed algorithm is demonstrated by numerical experiments. With high accuracy results and a high computing speed, the algorithm has the potential to develop into an online optimal guidance method.