月球着陆轨道的一种快速优化方法  

A Rapid Approach for Lunar Landing Trajectory Optimization

作　　者：赵吉松[1] 谷良贤[1] 

机构地区：[1]西北工业大学航天学院,西安710072

出　　处：《宇航学报》2009年第4期1564-1568,共5页Journal of Astronautics

摘　　要：提出一种基于积分变换,广义乘子法和拟牛顿法的月球着陆轨道快速优化方法。从探月器质心运动方程组出发,通过积分变换,将其对时间变量的积分转化为对状态变量(探月器环绕月心的旋转角速度)的积分,使得原问题转化为终端积分变量固定型最优控制问题。在此基础上,通过优化变量的直接离散化和四阶Admas预测-校正数值积分方法,将月球最优着陆问题转化为有约束非线性规划问题。采用广义乘子法处理约束条件,采用拟牛顿法求解处理后的无约束最优化问题。仿真结果表明:此方法收敛速度快(耗时小于1s),优化精度高(接近理论最优解),对初始控制量不敏感、鲁棒性好,可用于探月器机载计算机实时生成着陆轨道。A rapid approach, based on integral transformation, generalized Lagrange muhiplier （GLM） , and quasi- Newton＇s method was proposed for lunar landing trajectory optimization. Through integral transformation, a state variable was introduced in stead of time in the motion equations of the lander, and the optimal landing problem was transformed into a fixed final integral variable optimal control problem. By direct diseretization of the control variable, the obtained new problem was converted into nonlinear programming （NLP） with 4th Admas predict-modification scheme as integrating procedure. Generalized Lagrange multiplier was used to dispose of constraints in NLP, and the obtained unconstrained NLP was solved with quasi-Newton＇ s method. Simulation results demonstrate good accuracy （nearly identical with theoretical solutions） , rapid convergence （time consumption less than 1 second） , and rnbustness with initial values of this approach, which make it a promising candidate for on-line generating a feasible landing trajectory on the onboard computer.

关 键 词：月球着陆 快速优化 积分变换 广义乘子法 拟牛顿法 

分 类 号：V412.4[航空宇航科学与技术—航空宇航推进理论与工程]