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双移动机械臂空间协作动力学建模研究

董方方 喻斌 赵晓敏 陈珊

董方方,喻斌,赵晓敏,陈珊. 双移动机械臂空间协作动力学建模研究 [J]. 应用数学和力学,2022,43(8):846-856 doi: 10.21656/1000-0887.420223
引用本文: 董方方,喻斌,赵晓敏,陈珊. 双移动机械臂空间协作动力学建模研究 [J]. 应用数学和力学,2022,43(8):846-856 doi: 10.21656/1000-0887.420223
DONG Fangfang, YU Bin, ZHAO Xiaomin, CHEN Shan. Dynamic Modeling of Spatial Cooperation Between Dual-Arm Mobile Manipulators[J]. Applied Mathematics and Mechanics, 2022, 43(8): 846-856. doi: 10.21656/1000-0887.420223
Citation: DONG Fangfang, YU Bin, ZHAO Xiaomin, CHEN Shan. Dynamic Modeling of Spatial Cooperation Between Dual-Arm Mobile Manipulators[J]. Applied Mathematics and Mechanics, 2022, 43(8): 846-856. doi: 10.21656/1000-0887.420223

双移动机械臂空间协作动力学建模研究

doi: 10.21656/1000-0887.420223
基金项目: 国家自然科学基金(51905140);安徽省自然科学基金(2208085ME126)
详细信息
    作者简介:

    董方方(1988— ),男,副教授,硕士生导师(E-mail:fangfangdong@hfut.edu.cn

    赵晓敏(1986— ),女,副教授,硕士生导师(通讯作者. E-mail:zhaoxiaomin@hfut.edu.cn

  • 中图分类号: O313.3

Dynamic Modeling of Spatial Cooperation Between Dual-Arm Mobile Manipulators

  • 摘要:

    移动机械臂进行空间协作时会产生复杂的非线性耦合,使得采用Lagrange方程或Newton-Euler法直接进行建模极为繁琐。针对双移动机械臂空间协作问题,提出了一种结合Udwadia-Kalaba (U-K)方法与Lagrange方程建立动力学模型的方法。在建模过程中,将负载简化为连杆,选择负载中心断开的方式对系统进行分解,从而避免了机械臂末端关节断开导致的末端关节转角与连杆转角的约束信息缺失问题;将分割形成的两个子系统通过Lagrange方程进行建模,得到了子系统的动力学模型;再将协作系统的固有几何关系通过约束形式引入,应用U-K方法得到了协作系统动力学模型,减少了建立动力学模型所需要的计算量;最后通过数值仿真验证了该方法所得到的动力学模型的准确性。

  • 图  1  移动机械臂示意图

    Figure  1.  The schematic of the mobile manipulator

    图  2  双移动机械臂空间协作系统示意图: (a) 主视图;(b) 俯视图

    Figure  2.  The schematic of dual-system cooperative handling mobile manipulators: (a) the main view; (b) the vertical view

    图  3  断开处轨迹示意图

    Figure  3.  Trajectories at disconnection points

    图  5  移动平台位移示意图

    Figure  5.  Displacements of mobile platforms

    图  4  关节角度约束示意图

    Figure  4.  Joint angle constraints

    图  6  子系统转角示意图:(a) 左半子系统;(b)右半子系统

    Figure  6.  Rotation angles of subsystems: (a) the left subsystem; (b) the right subsystem

    表  1  系统动力学参数表

    Table  1.   Dynamic parameters of system

    objectmass
    $ m / \mathrm{k}\mathrm{g}$
    moment of inertia
    $I / (\mathrm{k}\mathrm{g}\cdot {\mathrm{m} }^{2})$
    length
    $ l / \mathrm{m} $
    mobile platform $ {v}_{1} $$ 50 $$ 0 $$ 0 $
    joint $ {r}_{1} $$ 2 $$0.062\;5$$ 0.5 $
    link $ 1 $$ 3 $$0.490\;0$$ 0.7 $
    link $ 2 $$ 4 $$0.855\;0$$ 0.8 $
    link $ 3 $$ 1 $$0.080\;0$$ 0.4 $
    mobile platform $ {v}_{2} $$ 50 $$ 0 $$ 0 $
    joint $ {r}_{2} $$ 2 $$0.062\;5$$ 0.5 $
    link $ 4 $$ 3 $$0.490\;0$$ 0.7 $
    link $ 5 $$ 4 $$0.855\;0$$ 0.8 $
    link $ 6 $$ 1 $$0.080\;0$$ 0.4 $
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-08-02
  • 修回日期:  2021-11-02
  • 网络出版日期:  2022-07-05
  • 刊出日期:  2022-08-01

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