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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (7): 1256-1263    DOI: 10.3785/j.issn.1008-973X.2020.07.002
    
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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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     
Received: 17 January 2020      Published: 05 July 2020
CLC:  TP 11  
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Jian-ming XU
Zhi-peng ZHAO
Jian-wei DONG
Cite this article:

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.

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


连杆侧无传感器下机器人柔性关节系统的零力控制

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 
Fig.1 Structure of robot joint
Fig.2 Block diagram of force-free control strategy
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 ? ?
Tab.1 Technical characteristics of experimental setup in Fig.3
Fig.3 Experimental setup of robot joint
Fig.4 Fitting results of experimental data points of upper branch with different degree of polynomials
Fig.5 NoR of experimental data points fitting with different degree of polynomials
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
Tab.2 Coefficients of two-segment quartic polynomial
${T_{\rm{l}}},{\dot T_{\rm{l}}}$ $\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
Tab.3 Inverse mapping ${{\psi }^{{ - 1}}}{:}{{T}_{\rm{l}}} \to {\delta }$
Fig.6 Fitting results of two-segment quartic polynomial
Fig.7 Experimentally measured data of friction torque and Stribeck curve obtained by fitting
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 ? ?
Tab.4 Parameters of LuGre friction model
Fig.8 Angular displacement response for step torque signal and its fitting curve
Fig.9 Schematic of drag teaching experiment
Fig.10 Speed and contact torque curve during drag teaching experiment
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