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基于变阻抗控制的冗余驱动并联机器人多目标内力优化

梁旭 苏婷婷 侯增广 刘圣达 章杰 何广平

梁旭, 苏婷婷, 侯增广, 刘圣达, 章杰, 何广平. 基于变阻抗控制的冗余驱动并联机器人多目标内力优化. 自动化学报, 2023, 49(5): 1099−1115 doi: 10.16383/j.aas.c210963
引用本文: 梁旭, 苏婷婷, 侯增广, 刘圣达, 章杰, 何广平. 基于变阻抗控制的冗余驱动并联机器人多目标内力优化. 自动化学报, 2023, 49(5): 1099−1115 doi: 10.16383/j.aas.c210963
Liang Xu, Su Ting-Ting, Hou Zeng-Guang, Liu Sheng-Da, Zhang Jie, He Guang-Ping. A multi-objective internal preload optimization method of redundantly actuated parallel robots based on variable impedance control. Acta Automatica Sinica, 2023, 49(5): 1099−1115 doi: 10.16383/j.aas.c210963
Citation: Liang Xu, Su Ting-Ting, Hou Zeng-Guang, Liu Sheng-Da, Zhang Jie, He Guang-Ping. A multi-objective internal preload optimization method of redundantly actuated parallel robots based on variable impedance control. Acta Automatica Sinica, 2023, 49(5): 1099−1115 doi: 10.16383/j.aas.c210963

基于变阻抗控制的冗余驱动并联机器人多目标内力优化

doi: 10.16383/j.aas.c210963
基金项目: 国家自然科学基金 (62003005, 62103007, 62203442), 北京市教育委员会科学研究计划项目(KM202110009009, KM202210009010), 北京市自然科学基金 (L202020, L222058, 4204097), 国家重点研发计划 (2020AAA0105800), 北京市科技计划(Z211100007921021),中国博士后科学基金 (2021M693404), 北方工业大学毓优人才支持计划, 复杂系统管理与控制国家重点实验室开放课题 (20210103), 北京市教委基本科研业务费资助
详细信息
    作者简介:

    梁旭:北方工业大学机械与材料工程学院讲师. 主要研究方向为医疗康复机器人, 骨科手术机器人和人机交互控制. E-mail: liangxu2013@ia.ac.cn

    苏婷婷:北京工业大学信息学部讲师. 主要研究方向为轨迹规划, 机器人技术和智能控制系统. 本文通信作者. E-mail: sutingting37@163.com

    侯增广:中国科学院自动化研究所复杂系统管理与控制国家重点实验室研究员. 主要研究方向为机器人与智能系统, 康复机器人和微创介入手术机器人.E-mail: zengguang.hou@ia.ac.cn

    刘圣达:中国科学院自动化研究所复杂系统管理与控制国家重点实验室博士后. 主要研究方向为微分方程, 最优控制和康复机器人. E-mail: shengda.liu@ia.ac.cn

    章杰:北方工业大学机械与材料工程学院助理研究员. 主要研究方向为接触动力学. E-mail: zhangjie@ncut.edu.cn

    何广平:北方工业大学机械与材料工程学院教授. 主要研究方向为机器人动力学与控制, 微机电系统. E-mail: hegp55@ncut.edu.cn

A Multi-objective Internal Preload Optimization Method of Redundantly Actuated Parallel Robots Based on Variable Impedance Control

Funds: Supported by National Natural Science Foundation of China (62003005, 62103007, 62203442), R&D Program of Beijing Municipal Education Commission (KM202110009009, KM202210009010), Natural Science Foundation of Beijing (L202020, L222058, 4204097), National Key Research and Development Program of China (2020AAA0105800), Beijing Sci&Tech Program (Z211100007921021), China Postdoctoral Science Foundation (2021M693404), Yuyou Talent Support Project of North China University of Technology, Open Research Fund of the State Key Laboratory for Management and Control of Complex Systems (20210103), and Fundamental Research Funds for Beijing Municipal Universities
More Information
    Author Bio:

    LIANG Xu Lecturer at the School of Mechanical and Materials Engineering, North China University of Technology. His research interest covers rehabilitation robots, orthopedic robots, and human-robot interaction control

    SU Ting-Ting Lecturer at the Faculty of Information Technology, Beijing University of Technology. Her research interest covers trajectory planning, robotics, and intelligent control systems. Corresponding author of this paper

    HOU Zeng-Guang Professor at the State Key Laboratory for Management and Control of Complex Systems, Institute of Automation, Chinese Academy of Sciences. His research interest covers intelligent robotic systems, rehabilitation and surgery robots

    LIU Sheng-Da Postdoctor at the State Key Laboratory for Management and Control of Complex Systems, Institute of Automation, Chinese Academy of Sciences. His research interest covers differential equations, optimal control, and rehabilitation robots

    ZHANG Jie Assistant research fellow at the School of Mechanical and Materials Engineering, North China University of Technology. His main research interest is contact-impact dynamics

    HE Guang-Ping Professor at the School of Mechanical and Materials Engineering, North China University of Technology. His research interest covers dynamics and control of robots and micro-electromechanical devices

  • 摘要: 由于冗余驱动的存在, 冗余驱动并联机器人系统逆动力学模型存在无限组可跟踪期望轨迹的控制力矩解, 这使得机器人在运行过程中具有完成附加任务的能力. 以实现骨科机器人的安全精准操控为目的, 提出了基于变阻抗控制的冗余驱动并联机器人多目标内力优化方法. 首先, 采用支链分解法对冗余驱动并联机器人的动力学进行建模. 其次, 为实现机器人的安全操作, 设计了冗余驱动并联机器人时变阻抗控制器, 利用李雅普诺夫理论分析了系统的稳定性; 在此基础上, 以消除冗余驱动并联机器人运动过程中的传动间隙为附加任务, 提出了一种以力矩传递性能、驱动功率和控制力为优化目标的多目标融合驱动力优化方法. 最后, 通过仿真实验与对比分析, 验证了所提方法的有效性, 实现了机器人系统传动间隙的消除.
  • 图  1  平面二自由度冗余驱动并联机器人结构简图

    Fig.  1  Schematic of the planar 2-DOF redundantly actuated parallel robot

    图  2  本文所提方法控制框图

    Fig.  2  The control block diagram of the proposed method

    图  3  机器人末端位置曲线

    Fig.  3  Position curve of the robot in cartesian space

    图  4  机器人关节空间位置曲线

    Fig.  4  Position curve of the robot in joint space

    图  5  机器人关节空间速度曲线

    Fig.  5  Velocity curve of the robot in joint space

    图  6  $s = (1,1,1)$时预载力矩优化参数曲线

    Fig.  6  Internal preload optimization parameter curve when $s = (1,1,1)$

    图  7  $s = (1,1,1)$时机器人主动关节力矩曲线

    Fig.  7  Torque curve of the robot in joint space when $s = (1,1,1)$

    图  8  $s = (-1,-1,-1)$时预载力矩优化参数曲线

    Fig.  8  Internal preload optimization parameter curve when $s = (-1,-1,-1)$

    图  9  $s = (-1,-1,-1)$时机器人主动关节力矩曲线

    Fig.  9  Torque curve of the robot in joint space when $s = (-1,-1,-1)$

    图  10  本文所提方法与固定阻抗控制方法的机器人末端位置误差曲线

    Fig.  10  Position error curve of the robot of the proposed method and the fixed impedance control method

    图  11  本文所提方法与固定阻抗控制方法的机器人末端交互力曲线

    Fig.  11  Interaction force curve of the robot of the proposed method and the fixed impedance control method

    图  12  时变阻抗控制方法的机器人主动关节力矩曲线

    Fig.  12  Torque curve of the robot in joint space based on time-varying impedance control method

    图  13  未考虑消除传动间隙的机器人主动关节力矩曲线

    Fig.  13  Torque curve of the robot in joint space without consideration of elimination of backlash

    图  14  $s = (1,1,1)$时多目标加权归一化内力优化方法下预载力矩优化参数曲线

    Fig.  14  Internal preload optimization parameter curve under the multi-objective weighted normalized optimization method when $s = (1,1,1)$

    图  15  $s = (1,1,1)$时多目标加权归一化内力优化方法下机器人主动关节力矩曲线

    Fig.  15  Torque curve of the robot in joint space under the multi-objective weighted normalized optimization method when $s = (1,1,1)$

    图  16  $s = (-1,-1,-1)$时多目标加权归一化内力优化方法下预载力矩优化参数曲线

    Fig.  16  Internal preload optimization parameter curve under the multi-objective weighted normalized optimization method when $s = (-1,-1,-1)$

    图  17  $s = (-1,-1,-1)$时多目标加权归一化内力优化方法下机器人主动关节力矩曲线

    Fig.  17  Torque curve of the robot in joint space under the multi-objective weighted normalized optimization method when $s = (-1,-1,-1)$

    图  18  传动间隙模型

    Fig.  18  Backlash model

    图  19  $s = (-1,-1,-1)$时多目标加权归一化内力优化方法下机器人笛卡尔空间位置曲线

    Fig.  19  Position curve of the robot in Cartesian space under the multi-objective weighted normalized optimization method when $s = (-1,-1,-1)$

    图  20  $s = (-1,-1,-1)$时多目标加权归一化内力优化方法下机器人关节空间位置曲线

    Fig.  20  Position curve of the robot in joint space under the multi-objective weighted normalized optimization method when $s = (-1,-1,-1)$

    图  21  $s = (-1,-1,-1)$时本文所提方法与串联机器人时变阻抗控制方法的机器人末端位置曲线

    Fig.  21  Position curve of the robot of the method proposed in this paper and the time-varying impedance control method of the serial robot when s = (−1, −1, −1)

    表  1  冗余驱动并联机器人物理参数

    Table  1  Physical parameters of redundantly actuated parallel robots

    $m_{i1}$$m_{i2}$$l_{i1}$$l_{i2}$$r_{i1}$$r_{i2}$${I_{i1}} = {m_{i1}}r_{i1}^2$${I_{i2}} = {m_{i2}}r_{i2}^2$
    2.0 kg 2.0 kg0.50 m0.60 m0.25 m0.30 m$0.125\;{\rm{kg} } \cdot {\rm{m} }^2$$0.180\;{\rm{kg} } \cdot {\rm{m} }^2$
    下载: 导出CSV

    表  2  本文所提方法误差对比分析

    Table  2  Comparison and analysis of the error of the proposed method

    轨迹(m)${\bar q_e}\;(\text{m})$${\dot {\bar q}_e}\;({\text{m/s}})$${F_e}\;({\text{N}})$${\bar d_x}\;(\text{m})$${\bar d_y}\; (\text{m})$$\text{RMSE}\; (\text{m})$$\text{JRMSE}\; (\text{rad})$
    式(34)${[ {0.03} \;\;{ - 0.02} ]^{\rm{T}}}$${[{0.10}\;\;{ - 0.10}]^{\rm{T}}}$式(33)0.01480.00900.02170.1141
    式(37)${[ {0.03}\;\;{ - 0.02} ]^{\rm{T}}}$${[ {0.10}\;\;{ - 0.10} ]^{\rm{T}}}$式(33)0.01480.00900.02170.1113
    式(34)${[ {-0.02}\;\;{0.01} ]^{\rm{T}}}$${[{ - 0.05}\;\;{0.05}]^{\rm{T}}}$式(33)0.01230.00690.01760.0954
    式(37)${[ {-0.02}\;\;{0.01} ]^{\rm{T}}}$${[ { - 0.05}\;\;{0.05} ]^{\rm{T}}}$式(33)0.01230.00690.01760.0835
    式(34)${[ {0.05}\;\;{-0.03} ]^{\rm{T}}}$${[ { 0.20}\;\;{-0.15} ]^{\rm{T}}}$式(33)0.01930.01100.02940.1508
    式(37)${[ {0.05}\;\;{-0.03} ]^{\rm{T}}}$${[ { 0.20}\;\;{-0.15} ]^{\rm{T}}}$式(33)0.01930.01100.02940.1708
    式(34)${[ {0.03}\;\;{ - 0.02} ]^{\rm{T}}}$${[ {0.10}\;\;{ - 0.10} ]^{\rm{T}}}$式(38)0.01070.00550.01660.0809
    式(37)${[ {0.03}\;\;{ - 0.02} ]^{\rm{T}}}$${[ {0.10}\;\;{ - 0.10} ]^{\rm{T}}}$式(38)0.01070.00550.01660.0927
    式(34)${[ {0.03}\;\;{ - 0.02} ]^{\rm{T}}}$${[ {0.10}\;\;{ - 0.10} ]^{\rm{T}}}$式(39)0.00920.00540.01610.0770
    式(37)${[ {0.03}\;\;{ - 0.02} ]^{\rm{T}}}$${[ {0.10}\;\;{ - 0.10} ]^{\rm{T}}}$式(39)0.00920.00540.01610.0898
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-10-13
  • 录用日期:  2023-01-18
  • 网络出版日期:  2023-02-20
  • 刊出日期:  2023-05-20

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