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基于Udwadia-Kalaba方法的平面冗余并联机器人建模与轨迹跟踪控制

韩江 汪鹏 董方方 夏链 陈珊 卢磊

韩江, 汪鹏, 董方方, 夏链, 陈珊, 卢磊. 基于Udwadia-Kalaba方法的平面冗余并联机器人建模与轨迹跟踪控制[J]. 应用数学和力学, 2020, 41(11): 1183-1196. doi: 10.21656/1000-0887.400363
引用本文: 韩江, 汪鹏, 董方方, 夏链, 陈珊, 卢磊. 基于Udwadia-Kalaba方法的平面冗余并联机器人建模与轨迹跟踪控制[J]. 应用数学和力学, 2020, 41(11): 1183-1196. doi: 10.21656/1000-0887.400363
HAN Jiang, WANG Peng, DONG Fangfang, XIA Lian, CHEN Shan, LU Lei. Modeling and Control of Planar Redundant Parallel Robots Based on the Udwadia-Kalaba Method[J]. Applied Mathematics and Mechanics, 2020, 41(11): 1183-1196. doi: 10.21656/1000-0887.400363
Citation: HAN Jiang, WANG Peng, DONG Fangfang, XIA Lian, CHEN Shan, LU Lei. Modeling and Control of Planar Redundant Parallel Robots Based on the Udwadia-Kalaba Method[J]. Applied Mathematics and Mechanics, 2020, 41(11): 1183-1196. doi: 10.21656/1000-0887.400363

基于Udwadia-Kalaba方法的平面冗余并联机器人建模与轨迹跟踪控制

doi: 10.21656/1000-0887.400363
基金项目: 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)
详细信息
    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);董方方(1988—),男,副教授,硕士生导师(通讯作者. E-mail: fangfangdong@hfut.edu.cn).

  • 中图分类号: TH113

Modeling and Control of Planar Redundant Parallel Robots Based on the Udwadia-Kalaba Method

Funds: The National Key R&D Program of China(2018YFB1308400);The National Natural Science Foundation of China(51905140)
  • 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.
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出版历程
  • 收稿日期:  2019-11-29
  • 修回日期:  2020-03-01
  • 刊出日期:  2020-11-01

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