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浙江大学学报(工学版)
浙江大学学报(工学版)  2020, Vol. 54 Issue (7): 1256-1263    DOI: 10.3785/j.issn.1008-973X.2020.07.002
自动化技术、计算机技术     
连杆侧无传感器下机器人柔性关节系统的零力控制
徐建明(),赵智鹏,董建伟
浙江工业大学 信息工程学院，浙江 杭州 310023
Free-force control of flexible robot joint system without sensors on link side
Jian-ming XU(),Zhi-peng ZHAO,Jian-wei DONG
College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China
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摘要：

针对机器人直接示教应用场景，提出机器人柔性关节系统在连杆侧无传感器下的零力控制方法. 引入动态LuGre摩擦模型进行关节摩擦力矩估计，采用2段四次多项式建立柔性关节系统刚度模型，基于广义动量观测关节力矩. 该方法利用刚度逆模型以及关节力矩估算谐波减速器扭转位移，结合谐波减速器运动传递特性估计连杆侧角度并计算重力矩，利用连杆动力学方程估计接触力矩. 构建期望的电机驱动力矩（包含估计的重力矩、摩擦力矩与接触力矩），通过对该期望电机驱动力矩的跟踪实现零力控制. 在搭建的机器人柔性关节系统实验平台上进行实验. 实验结果表明，完成相同的拖动示教过程时，该方法所需要的接触力矩约为1.8 N·m. 基于重力矩与摩擦力矩补偿的零力控制方法需要接触力矩约为3.4 N·m. 功率级脱离示教所需要的接触力矩约为14 N·m，验证了所提方法的实际效果.
关键词： 人机交互;  零力控制;  摩擦补偿;  重力补偿;  柔性关节    
Abstract:

A free-force control method of the flexible robot joint system without sensors on link side was proposed aiming at the application of robot direct teaching. The dynamic LuGre model was introduced to estimate the joint friction. Two-segment quartic polynomial was adopted to describe the stiffness of the flexible robot joint system. The joint torque was observed based on the generalized momenta. The torsional displacement of the harmonic drive was estimated through the inverse stiffness model and the joint torque among the algorithm. The gravity and angle on link side were figured out by combining torsional angle with motion transmission characteristics. The contact torque was obtained by utilizing the kinetic equation on link side. Then a desired motor driving torque was constructed comprising the gravity, joint friction and the contact torque. The free-force control was realized by tracking this desired motor torque. The experiments were conducted on the laboratory setup of the flexible robot joint system. The experimental results show that the contact torque is about 1.8 N·m when accomplishing the same drag teaching process. The free-force control method based on the compensation of gravity and friction requires a contact torque of about 3.4 N·m. The contact torque required for the power stage off teaching is approximately 14 N·m. The experimental results verify that the proposed method has a practical effect.
Key words: human-robot interaction    free-force control    friction compensation    gravity compensation    flexible joint
收稿日期: 2020-01-17 出版日期: 2020-07-05
CLC:  TP 11  
基金资助: 国家自然科学基金-浙江省自然科学基金联合基金两化融合项目（U1709213）；国家自然科学基金资助项目（61374103）
作者简介: 徐建明（1970—），男，教授，博导，从事机器人控制技术、电机伺服控制技术、迭代学习控制等研究.orcid.org/0000-0001-9745-7901. E-mail： xujm@zjut.edu.cn
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徐建明
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引用本文:

徐建明,赵智鹏,董建伟. 连杆侧无传感器下机器人柔性关节系统的零力控制[J]. 浙江大学学报(工学版), 2020, 54(7): 1256-1263.

Jian-ming XU,Zhi-peng ZHAO,Jian-wei DONG. Free-force control of flexible robot joint system without sensors on link side. Journal of ZheJiang University (Engineering Science), 2020, 54(7): 1256-1263.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2020.07.002    或    http://www.zjujournals.com/eng/CN/Y2020/V54/I7/1256

图 1  机器人关节系统结构图
图 2  零力控制策略框图
参数 数值 参数 数值
${ {{J} }_{\rm{l} } }/({\rm{kg} } \cdot { {\rm{m} }^{2} })$ 0.128 3 ${ {{J} }_{\rm{m} } }/({\rm{kg} } \cdot { {\rm{m} }^{2} })$ $2.196\;5 \times {10^{ {\rm{ - } }3} }$
m/kg 1.142 9 ${ {{K} }_{\rm{e} } }/({\rm{N} } \cdot {\rm{m} } \cdot { {\rm{A} }^{ - 1} })$ 0.53
h/m 0.3 ${{N} }$ $80$
${{g} }/({\rm{N} } \cdot {\rm{k} }{ {\rm{g} }^{ { - 1} } })$ 9.8 ? ?
表 1  图3实验装置的机械参数
图 3  机器人关节系统实验装置
图 4  不同次数多项式对上支实验数据点的拟合效果
图 5  不同次数多项式对实验数据进行拟合的残差模
多项式系数 数值 多项式系数 数值
${\rm{\varepsilon }}_{0}^{ + }$ ?4.577 1 ${\rm{\varepsilon }}_{0}^{ - }$ 2.664 8
${\rm{\varepsilon }}_{1}^{ + }$ 1.019 1 ${\rm{\varepsilon }}_{1}^{ - }$ ?5.268 1
${\rm{\varepsilon }}_{2}^{ + }$ ?47.385 1 ${\rm{\varepsilon }}_{2}^{ - }$ 21.634 6
${\rm{\varepsilon }}_{3}^{ + }$ 117.303 9 ${\rm{\varepsilon }}_{3}^{ - }$ 113.517 2
${\rm{\varepsilon }}_{4}^{ + }$ 143.58 ${\rm{\varepsilon }}_{4}^{ - }$ ?76.850 7
表 2  2段4次多项式系数表
${T_{\rm{l}}},{\dot T_{\rm{l}}}$ $\delta $
${T_{\rm{l}}} = - 30.73,{\dot T_{\rm{l}}} \geqslant 0$ ?0.630 0
${T_{\rm{l}}} = - 30.72,{\dot T_{\rm{l}}} \geqslant 0$ ?0.629 7
$ \vdots $ $ \vdots $
${T_{\rm{l}}} = 29.21,{\dot T_{\rm{l}}} \geqslant 0$ 0.630 0
${T_{\rm{l}}} = 29.20,{\dot T_{\rm{l}}} < 0$ 0.629 9
$ \vdots $ $ \vdots $
${T_{\rm{l}}} = - 30.92,{\dot T_{\rm{l}}} < 0$ ?0.630 0
表 3  逆映射 ${{\psi }^{{ - 1}}}:{{T}_{\rm{l}}} \to {\delta }$
图 6  2段4次多项式对实验数据的拟合效果
图 7  摩擦力矩实验数据测量点及拟合得到的Stribeck曲线
参数 数值 参数 数值
${ {{T} }_{\rm{c} } }$ 0.106 7 ${{\rm{\sigma }}_{2}}$ 0.017 2
${ {{T} }_{\rm{s} } }$ 0.175 5 ${{\rm{\sigma }}_{0}}$ 1.436 3
${{\rm{\dot \theta }}_{\rm{s}}}$ 0.664 8 ${{\rm{\sigma }}_{1}}$ 0.129 96
${\rm{\alpha }}$ 2.208 4 ? ?
表 4  LuGre摩擦模型参数
图 8  角位移对阶跃力矩信号的响应及其拟合曲线
图 9  拖动示教实验示意图
图 10  拖动示教实验过程中速度曲线与接触力矩曲线
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