欠驅動柔性機械臂的動力學建模與控制

武殿博

摘? 要： 針對欠驅動柔性機械臂建模、控制困難的問題，文中采用在第一關節安裝輕質彈簧的方法來表示機械臂的柔性，從而得到柔性臂的簡化模型。將其應用到兩連桿欠驅動柔性機械臂中，建立欠驅動柔性機械臂的系統模型，并利用拉格朗日函數法，對該系統進行動力學建模。同時通過構造基于系統能量和驅動桿狀態的李雅普諾夫函數，設計該欠驅動柔性機械臂系統的控制律。最后，使用Matlab對該系統及所設計的控制律進行數值仿真。仿真結果表明，所構建的動力學模型以及設計的控制規則具有良好的有效性，且同時具備響應速度快、控制輸入小的優點。

關鍵詞： 欠驅動; 柔性機械臂; 動力學建模; 控制律設計; Matlab仿真; 結果分析

中圖分類號： TN876?34; TP24? ? ? ? ? ? ? ? ? ? 文獻標識碼： A? ? ? ? ? ? ? ? ? ? ? 文章編號： 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