基于hp伪谱同伦凸优化的火箭垂直回收在线轨迹规划方法  

Online Trajectory Planning Method for Rocket Vertical Recovery Based on hp Pseudospectral Homotopic Convex Optimization

作　　者：郭杰[1,2] 相岩 王肖 史鹏飞 唐胜景 GUO Jie;XIANG Yan;WANG Xiao;SHI Pengfei;TANG Shengjing(School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China;Key Laboratory of Dynamics and Control of Flight Vehicle,Ministry of Education,Beijing 100081,China;China Academy of Launch Vehicle Technology,Beijing 100076,China;Beijing Aerospace Automatic Control Institute,Beijing 100854,China)

机构地区：[1]北京理工大学宇航学院,北京100081 [2]飞行器动力学与控制教育部重点实验室,北京100081 [3]中国运载火箭技术研究院,北京100076 [4]北京航天自动控制研究所,北京100854

出　　处：《宇航学报》2022年第5期603-614,共12页Journal of Astronautics

基　　金：上海航天科技创新基金(SAST201711)。

摘　　要：针对可重复使用运载火箭垂直回收轨迹优化问题,提出了一种带有最优终端时间估计策略的hp伪谱同伦凸优化在线轨迹规划算法。首先,考虑状态约束和过程约束的非凸性,采用无损凸化处理推力幅值约束;然后,结合同伦方法与不动点迭代思想将气动力与非凸质量约束转化为线性时变剖面,完成问题凸化;进一步基于hp flipped Radau伪谱法对问题进行离散化处理,将最优控制问题转化为参数优化问题,进而采用原-对偶内点法求解;最后,为进一步减少燃料消耗,提升经济效益,考虑最优终端时间难以在线确定的问题,结合解析推导与二次插值法,设计了最优终端时间快速估计策略。仿真结果表明所设计的轨迹优化算法最优终端时间估计速度快,收敛性能良好,具有较高的精度和计算效率,具备在线应用的潜力。For the trajectory optimization problem of reusable launch vehicle vertical recovery, an online trajectory planning algorithm with optimal terminal time estimation strategy is proposed based on the hp-pseudospectral homotopic convex optimization method. Firstly, considering the non-convexity of the state constraints and process constraints, the lossless convexification is used to deal with the thrust magnitudes constraint. Then, the aerodynamic and non-convex mass constraint are transformed into linear time-varying profile by combing the homotopic approach and fixed point iteration ideas to complete the problem convexification. The control problem is further discretized based on the hp flipped Radau pseudospectral method, and is transformed into a parameter optimization problem, which is then solved by the primal-dual interior point method. Finally, in order to further reduce fuel consumption and improve economic efficiency, considering the problem that the optimal terminal time is difficult to be determined online, a fast estimation strategy for the optimal terminal time is designed by combining analytical derivation and quadratic interpolation method. The simulation results show that the designed trajectory optimization algorithm has fast speed of optimal terminal time estimation, excellent convergence performance, high accuracy and computational efficiency, and has the potential for online application.

关 键 词：运载火箭 垂直回收 轨迹优化 无损凸化 同伦方法 伪谱法 

分 类 号：V448.1[航空宇航科学与技术—飞行器设计]