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Udwadia-Kalaba方程构建操作臂名义模型的违约消除

吕桂志 刘荣

吕桂志, 刘荣. Udwadia-Kalaba方程构建操作臂名义模型的违约消除[J]. 北京航空航天大学学报, 2018, 44(11): 2305-2311. doi: 10.13700/j.bh.1001-5965.2018.0076
引用本文: 吕桂志, 刘荣. Udwadia-Kalaba方程构建操作臂名义模型的违约消除[J]. 北京航空航天大学学报, 2018, 44(11): 2305-2311. doi: 10.13700/j.bh.1001-5965.2018.0076
LYU Guizhi, LIU Rong. Violation elimination of nominal models for manipulators constructed with Udwadia-Kalaba equation[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(11): 2305-2311. doi: 10.13700/j.bh.1001-5965.2018.0076(in Chinese)
Citation: LYU Guizhi, LIU Rong. Violation elimination of nominal models for manipulators constructed with Udwadia-Kalaba equation[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(11): 2305-2311. doi: 10.13700/j.bh.1001-5965.2018.0076(in Chinese)

Udwadia-Kalaba方程构建操作臂名义模型的违约消除

doi: 10.13700/j.bh.1001-5965.2018.0076
详细信息
    作者简介:

    吕桂志  男, 博士研究生, 讲师。主要研究方向:工业机器人动力学及控制

    刘荣  男, 博士, 教授, 博士生导师。主要研究方向:工业机器人、爬壁机器人

    通讯作者:

    刘荣, E-mail:rliu@buaa.edu.cn

  • 中图分类号: TH113

Violation elimination of nominal models for manipulators constructed with Udwadia-Kalaba equation

More Information
  • 摘要:

    采用Udwadia-Kalaba方程构建的操作臂轨迹跟踪控制器名义模型中,初始条件难以满足约束方程,数值求解过程产生误差累积造成的约束违约是亟待解决的问题。通过在数值求解过程所产生位置和速度项上添加修正项直接消除违约误差的方法,对该问题进行了研究。根据Udwadia-Kalaba建模思想,构建了期望轨迹下三杆操作臂的动力学名义模型并进行轨迹跟踪仿真。分别利用传统的Baumgarte约束稳定法与所提出误差直接消除法对仿真数值结果进行了修正。结果显示,所提误差直接消除法可更加快速直接地将约束违约控制在更小范围,更适用于操作臂动力学名义模型修正的使用。

     

  • 图 1  三杆空间操作臂

    Figure 1.  Three-link spatial manipulator

    图 2  操作臂各关节角度随时间变化曲线

    Figure 2.  Curves of each manipulator joint's angle changing with time

    图 3  操作臂各关节角速度随时间变化曲线

    Figure 3.  Curves of each manipulator joint's angular velocity changing with time

    图 4  操作臂末端在Cartesian空间运动轨迹

    Figure 4.  Motion trajectories of end point of manipulator in Cartesian space

    图 5  修正后工作空间操作臂末端轨迹

    Figure 5.  Corrected trajectories of end point of spatial manipulator

    图 6  给定值和求解值之间的空间距离

    Figure 6.  Spatial distance of position given values and solution values

  • [1] LIANG X, WAN Y, ZHANG C.Task space trajectory tracking control of robot manipulators with uncertain kinematics and dynamics[J].Mathematical Problems in Engineering, 2017(2017):4275201. http://ieeexplore.ieee.org/document/7484342/
    [2] SAEED K, MEHDI F M.Uncertainty estimation in robust tracking control of robot manipulators using the Fourier series expansion[J].Robotica, 2015, 35(2):310-336. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=1348c074ff62b7cd2bd1ceea8dbc5269
    [3] XIAO B, YIN S, KAYNAK O.Tracking control of robotic manipulators with uncertain kinematics and dynamics[J].IEEE Transactions on Industrial Electronics, 2016, 63(10):6439-6449. doi: 10.1109/TIE.2016.2569068
    [4] YAO J, DENG W.Active disturbance rejection adaptive control of uncertain nonlinear systems:Theory and application[J].Nonlinear Dynamics, 2017, 89(3):1611-1624. doi: 10.1007/s11071-017-3538-6
    [5] GALICKI M.Robust task space finite-time chattering-free control of robotic manipulators[J].Journal of Intelligent and Robotic Systems Theory and Applications, 2017, 85(3-4):471-489. doi: 10.1007/s10846-016-0387-3?view=classic
    [6] UDWADIA F E, KALABA R E.A new perspective on constrained motion[J].Proceedings Mathematical and Physical Sciences, 1992, 439(1906):407-410. doi: 10.1098/rspa.1992.0158
    [7] UDWADIA F E, KALABA R E.Equations of motion for mechanical systems:A unified approach[J].Journal of Aerospace Engineering, 1996, 9(3):64-69. doi: 10.1061/(ASCE)0893-1321(1996)9:3(64)
    [8] UDWADIA F E, PHOHOMSIRI P.Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics[J].Proceedings:Mathematical, Physical and Engineering Sciences, 2006, 462(2071):2097-2117. doi: 10.1098/rspa.2006.1662
    [9] SCHUTTE A, UDWADIA F.New approach to the modeling of complex multibody dynamical systems[J].Journal of Applied Mechanics, 2011, 78(2):856-875. http://adsabs.harvard.edu/abs/2011JAM....78b1018S
    [10] PETERS J, MISTRY M, UDWADIA F, et al.A unifying framework for robot control with redundant DOFS[J].Autonomous Robots, 2008, 24(1):1-12. doi: 10.1007/s10514-007-9051-x
    [11] UDWADIA F E, MYLAPILLI H.Constrained motion of mecha-nical systems and tracking control of nonlinear systems:Connections and closed-form results[J].Nonlinear Dynamics and Systems Theory, 2014:15(1):73-89. https://www.researchgate.net/publication/273135173_Constrained_Motion_of_Mechanical_Systems_and_Tracking_Control_of_Nonlinear_Systems_Connections_and_Closed-form_Results
    [12] UDWADIA F E, KOGANTI P B.Optimal stable control for nonlinear dynamical systems:An analytical dynamics based app-roach[J].Nonlinear Dynamics, 2015, 82(1-2):547-562. doi: 10.1007/s11071-015-2175-1
    [13] 刘佳, 刘荣.双臂协调机械手动力学建模的新方法[J].北京航空航天大学学报, 2016, 42(9):1903-1910. http://bhxb.buaa.edu.cn/CN/abstract/abstract13723.shtml

    LIU J, LIU R.New approach for dynamics modeling of dual-arm cooperating manipulators[J].Journal of Beijing University of Aeronautics and Astronautics, 2016, 42(9):1903-1910(in Chinese). http://bhxb.buaa.edu.cn/CN/abstract/abstract13723.shtml
    [14] 徐亚茹, 刘荣.一种爬壁机器人动力学建模方法[J].北京航空航天大学学报, 2018, 44(2):280-285. http://bhxb.buaa.edu.cn/CN/abstract/abstract14323.shtml

    XU Y R, LIU R.An approach for dynamics modeling of climbing robot[J].Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(2):280-285(in Chinese). http://bhxb.buaa.edu.cn/CN/abstract/abstract14323.shtml
    [15] UDWADIA F E, WANICHANON T.Control of uncertain nonlinear multibody mechanical systems[J].Journal of Applied Mechanics, 2014, 81(4):041020. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=9452dd09b883548366cb09f49a1da0a1
    [16] WANICHANON T, CHO H, UDWADIA F E.An approach to the dynamics and control of uncertain multi-body systems[C]//IUTAM Symposium on Dynamical Analysis of Multibody Systems with Design Uncertainties.Amsterdam: Elsevier, 2015: 43-52. https://www.sciencedirect.com/science/article/pii/S2210983815000140
    [17] KOGANTI P B, UDWADIA F E.Dynamics and precision control of uncertain tumbling multibody systems[J].Journal of Guidance, Control, and Dynamics 2017, 40(5):1176-1190. doi: 10.2514/1.G002212
    [18] LIU J, LIU R.Simple method to the dynamic modeling of industrial robot subject to constraint[J].Advances in Mechanical Engineering, 2016, 8(4):1687814016646511. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=Doaj000004724974
    [19] UDWADIA F E.A new perspective on the tracking control of nonlinear structural and mechanical systems[J].Proceedings Mathematical Physical and Engineering Sciences, 2003, 459(2035):1783-1800. doi: 10.1098/rspa.2002.1062
    [20] CHO H, UDWADIA F E.Explicit control force and torque determination for satellite formation-keeping with attitude requirements[J].Journal of Guidance, Control, and Dynamics, 2013, 36(2):589-605. doi: 10.2514/1.55873
    [21] 张新荣, 孟为来.基于虚位移分解与伺服轨迹约束的机械系统跟踪控制[J].机械工程学报, 2015, 51(3):45-50. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=jxgcxb201503007

    ZHANG X R, MENG W L.Trajectory tracking control of mechanical systems based on virtual displacement decomposition and servo constraint following[J].Journal of Mechanical Engineering, 2015, 51(3):45-50(in Chinese). http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=jxgcxb201503007
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出版历程
  • 收稿日期:  2018-02-08
  • 录用日期:  2018-04-27
  • 网络出版日期:  2018-11-20

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