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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2021, Vol. 55 Issue (5): 801-809    DOI: 10.3785/j.issn.1008-973X.2021.05.001
    
Identification of improved friction model for robot based on hybrid genetic algorithm
Tie ZHANG(),Liang-liang HU,Yan-biao ZOU
School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, China
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Abstract  

Aiming at the problem that the Coulomb and viscous friction model cannot really reflect the nonlinear characteristics of friction in the process of robot motion, an improved Stribeck friction model was used to describe the joint friction, and a method of model parameter identification based on the combination of hybrid genetic algorithm and cosine trajectory was proposed. First, different cosine trajectories were used to excite the robot joints, and the friction torque of the joints was determined using the known dynamic equations of the robot, so as to establish the mapping relationship between the robot joint velocity and the joint friction torque. Second, the simulated annealing hybrid genetic algorithm was used to identify the friction parameters. Finally, a multi-joint series robot was used as the research object, and the friction parameter identification experiments were carried out to verify the effectiveness of the proposed method. Experimental results indicate that compared with the traditional Coulomb and viscous friction model, the improved Stribeck friction model can reduce the calculation error of the joint torque by 17.7% to 33.6%, and can further improve the accuracy of the robot dynamic model.

Key words： robot dynamic model      joint torque      Stribeck friction model      hybrid genetic algorithm      parameter identification     
Received: 28 June 2020      Published: 10 June 2021
CLC:  TP 242.2  
Fund:  国家科技重大专项资助项目（2015ZX04005006）；广东省科技计划资助项目（2019B040402006）；中山市科技重大专项资助项目（2016F2FC0006，2018A10018）
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Tie ZHANG
Liang-liang HU
Yan-biao ZOU
Cite this article:

Tie ZHANG,Liang-liang HU,Yan-biao ZOU. Identification of improved friction model for robot based on hybrid genetic algorithm. Journal of ZheJiang University (Engineering Science), 2021, 55(5): 801-809.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2021.05.001     OR     http://www.zjujournals.com/eng/Y2021/V55/I5/801


基于混合遗传算法的机器人改进摩擦模型辨识

为了解决机器人运动过程中库伦+黏性摩擦模型不能真实反映关节摩擦的非线性特性的问题，采用改进Stribeck摩擦模型对机器人关节摩擦进行建模，提出基于混合遗传算法与余弦轨迹的模型参数辨识方法. 采用不同的余弦轨迹对机器人关节进行激励，利用已知的机器人动力学方程确定关节摩擦力矩，从而建立机器人关节速度与关节摩擦力矩之间的映射关系，并利用模拟退火混合遗传算法对摩擦参数进行辨识. 为了验证所提方法的有效性，以多关节串联型机器人为研究对象，进行摩擦参数辨识实验. 实验结果表明，与传统的库伦+黏性摩擦模型相比，改进的Stribeck摩擦模型可以减少17.7%~33.6%的关节力矩计算误差，并能够进一步提高机器人动力学模型的准确性.


关键词： 机器人动力学模型,  关节力矩,  Stribeck摩擦模型,  混合遗传算法,  参数辨识 
Fig.1 Improved Stribeck friction model
Fig.2 Fitting curve of Stribeck friction model
Fig.3 Flow diagram of simulated annealing and hybrid genetic algorithm
Fig.4 Robotic experimental platform
Fig.5 Effect of joint 2 and joint 3 at different positions on friction torque of joint 1
Fig.6 Diagram of actual friction torque and velocity of joint 1 for single trajectory
辨识方法 ${f_{\rm{C}}}/$ $\left( {{\rm{N}} \cdot {\rm{m}}} \right)$ ${f_{\rm{S}}}/$ $\left( {{\rm{N}} \cdot {\rm{m}}} \right)$ $v_{\rm{s}}/$ $\left( {{\rm{rad}} \cdot {{\rm{s}}^{{\rm{ - 1}}}}} \right)$ ${f_{\rm{V}}}/$ $\left( {{\rm{N}} \cdot {\rm{m}} \cdot {\rm{s}} \cdot {\rm{ra}}{{\rm{d}}^{{\rm{ - 1}}}}} \right)$ $\displaystyle\sum{{e^2} }/({\rm{N} } \cdot {\rm{m} })^2$
最小二乘法 10.76 19.66 0.0385 24.03 251
遗传算法 10.75 19.73 0.0384 24.05 252
混合遗传算法 10.76 19.68 0.0385 24.04 251
Tab.1 Dentification results of three algorithms
Fig.7 Fitting curve of friction torque of joint 1
Fig.8 Optimization of objective function $J$
算法 使用条件 计算效率 参数之间关联性
最小二乘法 要求目标函数连续可微，故只适用于同一速度方向下的摩擦参数辨识 计算速度较快，但是计算程序较复杂 先通过求根法得到中间变量，再依次求出其余摩擦参数，各摩擦参数的准确性直接受中间变量的影响
遗传算法 无特殊要求，实用范围广泛 计算量大，须进行大量无效迭代，故计算速度较慢 同时初始化各摩擦参数，在辨识过程中参数彼此之间相互独立
混合遗传算法 同遗传算法 每代种群的进化时间增加，但所需进化代数大大减少，
故在效率方面相对遗传算法有所提升 		同遗传算法
Tab.2 Comparison of three friction parameter identification algorithms
Fig.9 Diagram of actual friction torque and velocity of joint 1 for compositing two trajectories
Fig.10 Fitting curve of improved Stribeck friction model
关节 ${f_{\rm{C}}}/$
$\left( {{\rm{N}} \cdot {\rm{m}}} \right)$ 		${f_{\rm{S}}}/$
$\left( {{\rm{N}} \cdot {\rm{m}}} \right)$ 		$v_{\rm{s}}/$
$\left( {{\rm{rad}} \cdot {{\rm{s}}^{{\rm{ - 1}}}}} \right)$ 		$\gamma $ ${f_{\rm{V}}}/$
$\left( {{\rm{N}} \cdot {\rm{m}} \cdot {\rm{s}} \cdot {\rm{ra}}{{\rm{d}}^{{\rm{ - 1}}}}} \right)$ 		${f_{\rm{P}}}/$
$\left( {{\rm{N}} \cdot {\rm{m}}} \right)$ 		${\dot q_0}/$
$\left( {{\rm{rad}} \cdot {{\rm{s}}^{{\rm{ - 1}}}}} \right)$
1 11.64 23.19 0.02767 2 27.88 0.47 0.010
2 39.93 73.24 0.01292 2 89.24 ?3.34 0.005
3 38.53 53.78 0.01557 2 89.49 ?4.74 0.010
Tab.3 Parameter identification of improved Stribeck friction model
Fig.11 Torque fitting curve of each joint
机器人
关节 		$\displaystyle\sum \varepsilon^2 $/ ${({\rm{N}} \cdot {\rm{m}})^2}$ Δ/%
库伦+黏性摩擦模型 原始Stribeck摩擦模型 改进Stribeck摩擦模型 改进Stribeck相对于库伦+黏性 改进Stribeck相对于原始Stribeck
1 629 537 449 28.6 16.3
2 26873 25076 22103 17.7 11.8
3 5881 4725 3909 33.6 17.3
Tab.4 Torque residual sum of squares at different friction models
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