机械臂动力学分析及关节非线性摩擦模型建立

doi:10.3901/JME.2020.09.018

机械工程学报 ›› 2020, Vol. 56 ›› Issue (9): 18-28.doi: 10.3901/JME.2020.09.018

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机械臂动力学分析及关节非线性摩擦模型建立

段书用^1,2, 李昌洛^1,2, 韩旭^1,2, 刘桂荣³

1. 省部共建电工装备可靠性与智能化国家重点实验室(河北工业大学) 天津 300131;
2. 河北工业大学机械工程学院天津 300131;
3. 辛辛那提大学航空工程和机械工程系辛辛那提 45221 美国

收稿日期:2019-05-28 修回日期:2019-09-25 出版日期:2020-05-05 发布日期:2020-05-29
通讯作者: 韩旭(通信作者),男,1968年出生,教授,博士研究生导师。主要研究方向为计算反求技术、机器人可靠性、优化理论与算法。E-mail:xhan@hebut.edu.cn
作者简介:段书用,女,1984年出生,博士,副教授,硕士研究生导师。主要研究方向为机器人动力学、机器人可靠性和计算反求技术。E-mail:duanshuyong@hebut.edu.cn
基金资助:
国家重点研发计划（2017YFB1301300）和国家自然科学基金青年基金（11902110）资助项目。

Forward-inverse Dynamics Analysis of Robot Arm Trajectories and Development of a Nonlinear Friction Model for Robot Joints

DUAN Shuyong^1,2, LI Changluo^1,2, HAN Xu^1,2, LIU Guirong³

1. State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300131;
2. School of Mechanical Engineering, Hebei University of Technology, Tianjin 300131;
3. Aeronautical Engineering and Mechanical Engineering, University of Cincinnati, Cincinnati 45221, USA

Received:2019-05-28 Revised:2019-09-25 Online:2020-05-05 Published:2020-05-29

摘要/Abstract

摘要： 现有研究大多采用分段线性组合而成的拟非线性摩擦模型来描述机械臂各关节摩擦力矩大小及其分布，忽略了低速区关节摩擦的实际非线性变化，而该非线性变化恰恰是影响机械臂轨迹精度及稳定性的关键因素之一。基于此，着重研究机械臂关节非线性摩擦模型及其对机械臂末端轨迹的影响。对多关节机械臂进行几何机构建模，对任意设定的机械臂理想运动轨迹，通过机构运动学分析得到各关节的角位移、角速度和角加速度。考虑非线性摩擦，建立高可靠性的关节非线性摩擦的一般模型。对给定的理想运动轨迹下的角位移、角速度和角加速度进行Newton-Euler反向动力学分析，从而得到各关节的非线性驱动力矩。基于一般非线性摩擦模型，将得到的驱动力矩代入正向动力学模型中得到机械臂末端实际的运动轨迹。通过上述分析步骤，深入研究各关节在不同类型驱动力矩组合条件下对机械臂末端运动轨迹、及各关节角位移的影响。研究结果表明机械臂各关节的不同摩擦形式对末端运行轨迹影响显著，各关节驱动力矩的变化对其相邻关节的角位移也有明显影响。

关键词: 机械臂, 非线性摩擦模型, 动力学建模, Newton-Euler法, 正-反向动力学, 机械臂运动学, 运动轨迹

Abstract: Piecewise linear friction in the joints is often used to model dynamic behavior of robot arms. Nonlinear friction has been, however, found as one of the key factors to determine the dynamic jitter trajectory of robot arm tips. It is studied that the nonlinear friction model of the robot joints and its influence on the dynamic trajectory of robots. A kinematic model is established for multi-joint robots, using which the angular displacement, velocity and acceleration of joints are obtained for any planned trajectory. The Newton-Euler inverse dynamics analysis is then carried out to find out the forces and torques at the joints considering nonlinear frictions, for a given trajectory at the arm-tip. These forces and torques are substituted applied into the forward dynamics model to obtain the actual trajectory of the arm-tip. Using our analysis procedure, the influence of different driving torques on the trajectory and the angular displacement of each joint are studied in great detail. The results show that the nonlinear friction has a significantly influence on the trajectory of the arm-tip. The present forward and inverse dynamic analysis procedure and the nonlinear friction model proposed in this work provide a useful analytic and modeling tool for the development of high-precision robots.

Key words: robot arm, nonlinear friction model, dynamic modeling, Newton-Euler methods, forward-inverse dynamics, robot arm kinematics, motion trajectory

中图分类号:

TP242

段书用, 李昌洛, 韩旭, 刘桂荣. 机械臂动力学分析及关节非线性摩擦模型建立[J]. 机械工程学报, 2020, 56(9): 18-28.

DUAN Shuyong, LI Changluo, HAN Xu, LIU Guirong. Forward-inverse Dynamics Analysis of Robot Arm Trajectories and Development of a Nonlinear Friction Model for Robot Joints[J]. Journal of Mechanical Engineering, 2020, 56(9): 18-28.

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机械臂动力学分析及关节非线性摩擦模型建立

Forward-inverse Dynamics Analysis of Robot Arm Trajectories and Development of a Nonlinear Friction Model for Robot Joints

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