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

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

董方方^{1, 2},
喻斌¹,
赵晓敏^3, ,,
陈珊¹

1.
合肥工业大学机械工程学院，合肥 230009
2.
安徽省智能数控技术及装备工程实验室，合肥 230009
3.
合肥工业大学汽车与交通工程学院，合肥 230009

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
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- 被引次数: 0
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

Dynamic Modeling of Spatial Cooperation Between Dual-Arm Mobile Manipulators

DONG Fangfang^{1, 2},
YU Bin¹,
ZHAO Xiaomin^{3
, ,},
CHEN Shan¹

1.
School of Mechanical Engineering, Hefei University of Technology, Hefei 230009, P.R.China
2.
Anhui Engineering Laboratory of Intelligent CNC Technology and Equipment, Hefei 230009, P.R.China
3.
School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei 230009, P.R.China

摘要

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。
- Udwadia-Kalaba方法 /
- 动力学建模 /
- 协作机械臂 /
- 移动机械臂
Abstract:
The complex nonlinear coupling in the spatial cooperation process of mobile manipulators, makes it extremely tedious to directly model the spatial cooperative systems with the Lagrange equation or the Newton-Euler method. A dynamic modeling method, combining the Udwadia-Kalaba (U-K) method with the Lagrange equation, was proposed for spatial cooperation of dual-arm mobile manipulators. The load was simplified as a connecting link during modeling. The load center was selected to be disconnected for decomposition, so that the lack of constraint information was avoided between the end joint angle and the end link angle caused by the disconnection of the manipulator end joint; the segmented 2 subsystems were modeled with the Lagrange equation, thus, the dynamic model for the subsystems was obtained. The inherent geometric relationships of the cooperative system were introduced in the form of constraints, and the U-K method was applied to obtain the dynamic model for the cooperative system. The computation for modeling was reduced. The numerical simulation verifies the accuracy of the model.
- Udwadia-Kalaba method /
- dynamic modeling /
- cooperative manipulator /
- mobile manipulator

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图 1 移动机械臂示意图

Figure 1. The schematic of the mobile manipulator

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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

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图 3 断开处轨迹示意图

Figure 3. Trajectories at disconnection points

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图 5 移动平台位移示意图

Figure 5. Displacements of mobile platforms

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图 4 关节角度约束示意图

Figure 4. Joint angle constraints

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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

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表 1 系统动力学参数表

Table 1. Dynamic parameters of system

object	mass $ 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 $

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