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

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

doi: 10.21656/1000-0887.400363
Funds:  The National Key R&D Program of China(2018YFB1308400);The National Natural Science Foundation of China(51905140)
  • Received Date: 2019-11-29
  • Rev Recd Date: 2020-03-01
  • Publish Date: 2020-11-01
  • 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.
  • loading
  • [1]
    姜峣, 李铁民, 王立平. 过约束并联机构动力学建模方法[J]. 机械工程学报, 2013,49(17): 123-129.(JIANG Yao, LI Tiemin, WANG Liping. Research on the dynamic model of an over-constrained parallel mechanism[J]. Chinese Journal of Mechanical Engineering,2013,49(17): 123-129.(in Chinese))
    [2]
    白志富, 韩先国, 陈五一. 基于Lagrange方程三自由度并联机构动力学研究[J]. 北京航空航天大学学报, 2004,30(1): 51-54.(BAI Zhifu, HAN Xianguo, CHEN Wuyi. Study of a 3-DOF parallel manipulator dynamics based on Lagrange’s equation[J]. Journal of Beijing University of Aeronautics and Astronautics,2004,30(1): 51-54.(in Chinese))
    [3]
    YIU Y K, CHENG H, XIONG Z H, et al. On the dynamics of parallel manipulators[C]//IEEE International Conference on Robotics & Automation.Seoul, 2001.
    [4]
    CHENG H, YIU Y K, LI Z X. Dynamics and control of redundantly actuated parallel manipulators[J]. IEEE/ASME Transactions on Mechatronics,2003,8(4): 483-491.
    [5]
    GEIKE T, MCPHEE J. Inverse dynamic analysis of parallel manipulators with full mobility[J]. Mechanism and Machine Theory,2003,38(6): 549-562.
    [6]
    WU J, WANG J S, WANG L P. Dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy[J]. Mechanism and Machine Theory,2009,44(4): 835-849.
    [7]
    WANG L P, WU J, WANG J S. Dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy[J]. Robotics and Computer-Integrated Manufacturing,2010,26(1): 67-73.
    [8]
    张国伟, 宋伟刚. 并联机器人动力学问题的Kane方法[J]. 系统仿真学报, 2004,16(7): 1386-1391.(ZHANG Guowei, SONG Weigang. A Kane formulation for the inverse dynamic of stewart platform manipulator[J]. Journal of System Simulation,2004,16(7): 1386-1391.(in Chinese))
    [9]
    杨建新, 汪劲松, 郁鼎文. 空间并联机构运动学与动力学逆解的模块化计算方法[J]. 机械工程学报, 2005,41(5): 104-107.(YANG Jianxin, WANG Jingsong, YU Dingwen. Modular calculation method for kinematics and dynamics inverse solution of spatial parallel mechanism[J]. Journal of Mechanical Engineering,2005,41(5): 104-107.(in Chinese))
    [10]
    李永泉, 宋肇经, 郭菲. 多能域过约束并联机器人系统动力学建模方法[J]. 机械工程学报, 2016,52(21): 17-20.(LI Yongquan, SONG Zhaojing, GUO Fei. Dynamic modeling method for overconstrained multi-energy domain parallel manipulator[J]. Chinese Journal of Mechanical Engineering,2016,52(21): 17-20.(in Chinese))
    [11]
    李永泉, 单张兵, 王立捷. 4-DOF混联机器人多能域动力学全解模型及试验[J]. 机械工程学报, 2017,53(23): 92-100.(LI Yongquan, SHAN Zhangbing, WANG Lijie. Multi-energy domain dynamic full solution model and experiment for the 4-DOF hybrid robot[J]. Chinese Journal of Mechanical Engineering,2017,53(23): 92-100.(in Chinese))
    [12]
    UDWADIA F E, KALABA R E. Analytical Dynamics: a New Approach [M]. New York: Cambridge University Press, 1996.
    [13]
    赵韩, 赵晓敏, 姜建满. 基于Udwadia-Kalaba理论的Hamel嵌入法研究[J]. 应用数学和力学, 2017,38(6): 696-707.(ZHAO Han, ZHAO Xiaoming, JIANG Jianman. Study on Hamel’s embedding method via the Udwadia-Kalaba theory[J]. Applied Mathematics and Mechanics,2017,38(6): 696-707.(in Chinese))
    [14]
    ZHAO X M, CHEN Y H, ZHAO H. Udwadia-Kalaba equation for constrained mechanical systems: formulation and applications[J]. Chinese Journal of Mechanical Engineering,2018,31(6): 11-24.
    [15]
    ZHAO H, ZHEN S C, CHEN Y H. Dynamic modeling and simulation of multi-body systems using the Udwadia-Kalaba theory[J]. Chinese Journal of Mechanical Engineering,2013,26(5): 839-850.
    [16]
    张新荣, CHEN Y H, 平昭琪. 基于Udwadia和Kalaba方程的机械臂轨迹跟踪控制[J]. 长安大学学报(自然科学版), 2014, 34(1): 115-119.(ZHANG Xinrong, CHEN Y H, PING Zhaoqi. Mechanic manipulator tracking control based on Udwadia and Kalaba equation[J]. Journal of Chang’an University (Natural Science Edition),2014, 34(1): 115-119.(in Chinese))
    [17]
    SUN H, ZHAO H, ZHEN S C, et al. Application of the Udwadia-Kalaba approach to tracking control of mobile robots[J]. Nonlinear Dynamics,2015,83(1/2): 1-12.DOI: 10.1007/s11071-015-2335-3.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1420) PDF downloads(376) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return