摘要
以平面冗余驱动并联机器人为研究对象,利用Udwadia-Kalaba(U-K)方法,将并联机构的物理连接抽象成系统约束,建立了平面2自由度冗余驱动并联机器人的闭链运动方程.首先,将2自由度冗余驱动并联机器人分割成3个无约束开链子系统,子系统的动力学方程由Lagrange法获得;然后,采用运动学约束来描述各子系统和末端执行器、子系统与基座之间的物理连接.对约束进行微分,并转化为二阶Pfaffian标准微分形式,通过应用U-K方程,可以获得满足该物理约束的约束力的解析解.根据U-K理论,将该约束力附加到无约束开链系统方程即可建立平面冗余驱动并联机器人的动力学模型.在轨迹跟踪控制器设计中,将期望的位置或者速度轨迹抽象成虚拟约束,并将约束条件转化为Pfaffian标准微分形式,再通过U-K方程求解各驱动关节满足给定轨迹约束所需要的输出力矩.该方法不需要Lagrange乘子或伪广义速度等辅助变量,并可以同时处理完整约束和非完整约束.数值模拟和分析结果表明,该建模与控制方法能够高效、系统、快速地建立平面2自由度冗余驱动并联机器人的动力学解析解耦模型,实现给定轨迹的高精度跟踪控制.
The redundantly driven parallel robots were considered.The Udwadia-Kalaba(U-K)method was used to formulate the physical connections of the parallel mechanism as system constraints,and the closed-chain motion equations for the planar 2-DOF redundantly driven parallel robot were established.Firstly,the 2-DOF robot was divided into 3 unconstrained open-chain subsystems.The dynamic equations for the subsystems were obtained with the Lagrangian method.Then,the kinematic constraints were used to describe the physical connections between each subsystem and the end effector,and between each subsystem and the base.The constraint was differentiated and transformed into a 2nd-order Pfaffian standard differential form.With the U-K equations,the analytical solution satisfying the physical constraints was given.According to the U-K theory,the constraints can be added to the unconstrained open-chain system equations to establish the dynamics model for the planar redundantly driven parallel robot.In the trajectory tracking controller design,the desired position or velocity trajectory was formulated as a virtual constraint,and the constraint condition was transformed into a standard Pfaffian differential form.Then the U-K equations were used to solve the output torque required for each driving joint to satisfy a given trajectory constraint.This method does not require auxiliary variables such as Lagrangian multipliers or pseudo-generalized speeds,and can handle both holonomic and non-holonomic constraints.The numerical simulation and analysis results show that,the modeling and controlling method can effectively,systematically and quickly establish the dynamic analytical decoupling model for the planar 2-DOF redundantly driven parallel robot,and realize the high-precision tracking control along a given trajectory.
作者
韩江
汪鹏
董方方
夏链
陈珊
卢磊
HAN Jiang;WANG Peng;DONG Fangfang;XIA Lian;CHEN Shan;LU Lei(School of Mechanical Engineering,Hefei University of Technology,Hefei 230009,P.R.China)
出处
《应用数学和力学》
CSCD
北大核心
2020年第11期1183-1196,共14页
Applied Mathematics and Mechanics
基金
国家重点研发计划(2018YFB1308400)
国家自然科学基金(51905140)
安徽省科技重大专项(17030901036)。
作者简介
韩江(1963-),男,教授,博士生导师(E-mail:jianghan@hfut.edu.cn);汪鹏(1995-),男,硕士生(E-mail:1549122090@qq.com);通讯作者:董方方(1988-),男,副教授,硕士生导师(E-mail:fangfangdong@hfut.edu.cn).
