基于广义乘子法的月球软着陆轨道快速优化设计  

Rapid Optimization of Lunar Soft Landing Trajectory Based on Generalized Lagrange Multiplier

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：《科技导报》2008年第20期50-54,共5页Science & Technology Review

摘　　要：从探月器质心运动方程组出发,以探月器环绕月心的旋转角速度为中间变量,通过积分变换,将其对时间变量的积分转化为对状态变量的积分,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,将软着陆轨道优化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软着陆轨道。Soft landing is an important prerequisite of lunar exploration. Without air on the lunar surface, the velocity of lander must be reduced with thrust. The reduction of fuel consumption is a main consideration in increasing payload. So the fuel optimal lunar soft landing is an optimal control problem with variable final time. This paper develops a rapid optimization method for lunar soft landing trajectory based on integral transformation, Generalized Lagrange Multiplier （GLM） and quasi-Newton method. Through integral transformation, the negative angle velocity of lander corresponding to the lunar center is first introduced to replace the time in the motion equations, and the original optimal lunar soft landing problem is transformed into a fixed final integral variable optimal control problem. Then, by direct discretization of the control variable, the fixed final integral variable optimal control problem is converted into a Nonlinear Programming （NLP） with 4th Admas predict-modification scheme for integration. Finally, GLM is used to deal with constraints in the NLP, and the obtained unconstrained NLP is solved with quasi-Newton method. The solutions are compared with that obtained from Pontryagin＇s Maximal Principle （PMP）. The effect of initial penalty factor on the robustness of this approach is analyzed. Simulation results show good accuracy, rapid convergence （time consumption of less than 1 s）, and robustness with initial values of this approach, which means that it can used to generate an optimal soft landing trajectory through the onboard computer of the lander.

关 键 词：月球软着陆 快速优化 积分变换 广义乘子法 拟牛顿法 

分 类 号：V476.3[航空宇航科学与技术—飞行器设计]