基于联立法的运载火箭上升段轨迹优化研究  

Research on Trajectory Optimization Based on Simultaneous Method in Launch Vehicles Ascent Stage

作　　者：黄繁 冀四梅[1] 郭杰[1] 唐胜景[1] HUANG Fan;JI Simei;GUO Jie;TANG Shengjing(Key Laboratory of Dynamics and Control of Flight Vehicle,Ministry of Education,School of Aerospace Engineering,Beijing Institute of Technology,Beijing,100081)

机构地区：[1]北京理工大学宇航学院,飞行器动力学与控制教育部重点实验室,北京100081

出　　处：《导弹与航天运载技术（中英文）》2024年第6期21-27,共7页Missiles and Space Vehicles

摘　　要：针对运载火箭大气层内复杂多约束的上升段轨迹优化问题,提出一种基于联立法的轨迹优化方法。该方法采用联立框架下的直接法求解,通过有限元正交配置法离散状态变量和控制变量,再用内点法求解离散后的非线性规划问题,从而平衡了计算效率和求解精度,提高轨迹优化的自主性和任务适应能力。针对离散后非线性规划问题规模越大梯度矩阵计算耗时越多的问题,充分利用偏导数矩阵的稀疏性,将非线性规划(NonlinearProgramming,NLP)梯度中非零项的求解转化为原最优控制问题偏导数的求解,从而进一步提高轨迹优化的效率。仿真结果表明,该方法能很好地完成飞行任务,满足约束条件。Aiming at the trajectory optimization problem of the ascending stage of launch vehicle in the atmosphere with complex and multi constraints,a trajectory optimization method based on simultaneous method is proposed.The method adopts the direct method under the simultaneous framework,discretizes the state variables and control variables through the finite element orthogonal collocation method,and then solves the discrete nonlinear programming problem by the interior point method,so as to balance the calculation efficiency and solution accuracy,and improve the autonomy and task adaptability of trajectory optimization.Aiming at the problem that the larger the scale of the discrete nonlinear programming problem is,the more time-consuming the gradient matrix calculation is,making full use of the sparsity of the partial derivative matrix,the solution of the non-zero term in the NLP gradient is transformed into the solution of the partial derivative of the original optimal control problem,so as to further improve the efficiency of trajectory optimization.The simulation results show that this method can complete the flight mission well and meet constraints.

关 键 词：联立框架 有限元正交配置法 内点法 梯度矩阵 稀疏性 

分 类 号：V448.1[航空宇航科学与技术—飞行器设计]