机械臂运动学和动力学的李群表述  

Lie Group Representation of Kinematics and Dynamics of Manipulators

作　　者：董玫君 周焕银[1] 房鹏程 DONG Mei-jun;ZHOU Huan-yin;FANG Peng-cheng(School of Mechanical and Electronic Engineering,East China University of Technology,Nanchang 344000,China)

机构地区：[1]东华理工大学机械与电子工程学院,南昌344000

出　　处：《科学技术与工程》2024年第14期5872-5881,共10页Science Technology and Engineering

基　　金：国家自然科学基金(62063001);江西省科技厅重点基金(20224ACB204022)。

摘　　要：D-H参数法已经被广泛应用到机械手运动建模及分析中,但其所描述的运动都是围绕着x轴和z轴,而不能反映出y轴的运动。为了解决这个问题,采用旋量理论的方法,用旋量来表述出将机械臂的位置和姿态,并进一步分析机械臂的运动学和动力学。相较于传统的D-H法计算运动学正解,旋量理论是从整体上对机械臂的运动进行表述,且不需要中间参考系,几何意义清晰。利用Paden-Kahan子问题分析肘机械臂的逆运动学问题,计算出其运动学逆解,并利用旋量理论和李群-李代数,通过Newton-Euler法建立了高效的递归动力学模型。最后对于用旋量理论求出的肘机械臂运动学逆解进行仿真验证,并计算出其工作空间,结果表明用旋量理论的方法更加简洁、精确、高效。The D-H parameter method has found extensive application in the analysis of manipulator motion.However,it primarily describes motions along the x and z axes,neglecting the y-axis motion.To address this limitation,the screw theory method was emploied to represent the manipulator's position and orientation as a screw,conducting an in-depth analysis of its kinematics and dynamics.In contrast to the traditional D-H approach for forward kinematics,screw theory offers a holistic depiction of the robot arm's motion,eliminating the necessity for an intermediate reference system with explicit geometric significance.To tackle the inverse kinematic problem of the elbow robotic arm,the Paden-Kahan subproblem was applied,resulting in the computation of an inverse kinematics solution.Leveraging screw theory and Lie group-Lie algebra,the Newton-Euler approach was employed to construct an efficient recursive dynamic model.Ultimately,the manipulator's inverse kinematic solution derived through the screw theory was subjected to simulation and verification,with its workspace calculation revealing that the screw theory method offers a more concise,accurate,and effective approach.

关 键 词：旋量理论 机械臂 运动学 动力学 工作空间 

分 类 号：TP241.2[自动化与计算机技术—检测技术与自动化装置]