欠驱动柔性机械臂的动力学建模与控制

武殿博

摘  要： 针对欠驱动柔性机械臂建模、控制困难的问题，文中采用在第一关节安装轻质弹簧的方法来表示机械臂的柔性，从而得到柔性臂的简化模型。将其应用到两连杆欠驱动柔性机械臂中，建立欠驱动柔性机械臂的系统模型，并利用拉格朗日函数法，对该系统进行动力学建模。同时通过构造基于系统能量和驱动杆狀态的李雅普诺夫函数，设计该欠驱动柔性机械臂系统的控制律。最后，使用Matlab对该系统及所设计的控制律进行数值仿真。仿真结果表明，所构建的动力学模型以及设计的控制规则具有良好的有效性，且同时具备响应速度快、控制输入小的优点。

关键词： 欠驱动; 柔性机械臂; 动力学建模; 控制律设计; Matlab仿真; 结果分析

中图分类号： TN876?34; TP24                    文献标识码： A                      文章编号： 1004?373X（2020）06?0093?04

Dynamics modeling and control of under?actuated flexible mechanical arm

WU Dianbo

（School of Mechanical Engineering， Yangzhou University， Yangzhou 225127， China）

Abstract： For the problems of modeling and control difficulties of the under?actuated flexible mechanical arm， the method of installing the lightweight spring on the first joint is used to represent the flexibility of the mechanical arm， so as to obtain the simplified model of the flexible arm. This simplified model is applied to the two?link under?actuated flexible mechanical arm to establish its system model. The dynamics modeling of the system is performed by means of the Lagrangian function method. The control law of the under?actuated flexible mechanical arm system is designed by constructing the Lyapunov function based on system energy and actuating rod state. The numerical simulations of the system and the designed control law are carried out by means of Matlab. The results show that the constructed dynamics model and the designed control law have good effectiveness， and also have the advantages of fast response and low control input.

Keywords： underactuation; flexible mechanical arm; dynamics modeling; control law design; Matlab simulation; result analysis