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基于平板标定工具的机器人工具中心点标定方法

韩奉林 李鹏 谭冬和 李单 邵冬世 严宏志

韩奉林, 李鹏, 谭冬和, 李单, 邵冬世, 严宏志. 基于平板标定工具的机器人工具中心点标定方法[J]. 西南交通大学学报, 2020, 55(1): 60-67. doi: 10.3969/j.issn.0258-2724.20180807
引用本文: 韩奉林, 李鹏, 谭冬和, 李单, 邵冬世, 严宏志. 基于平板标定工具的机器人工具中心点标定方法[J]. 西南交通大学学报, 2020, 55(1): 60-67. doi: 10.3969/j.issn.0258-2724.20180807
HAN Fenglin, LI Peng, TAN Donghe, LI Dan, SHAO Dongshi, YAN Hongzhi. Method of Using Flat Plate as Calibration Tool for Robot Tool Center Point Calibration[J]. Journal of Southwest Jiaotong University, 2020, 55(1): 60-67. doi: 10.3969/j.issn.0258-2724.20180807
Citation: HAN Fenglin, LI Peng, TAN Donghe, LI Dan, SHAO Dongshi, YAN Hongzhi. Method of Using Flat Plate as Calibration Tool for Robot Tool Center Point Calibration[J]. Journal of Southwest Jiaotong University, 2020, 55(1): 60-67. doi: 10.3969/j.issn.0258-2724.20180807

基于平板标定工具的机器人工具中心点标定方法

doi: 10.3969/j.issn.0258-2724.20180807
基金项目: 湖南省战略性新兴产业科技攻关类项目(2016GK4031);国家自然科学基金(51405518);湖南省创新平台与人才计划(2016TP2022)
详细信息
    作者简介:

    韩奉林(1983—),男,博士,副教授,研究方向为机器人技术,E-mail:hanfl@csu.edu.cn

  • 中图分类号: TP242.2

Method of Using Flat Plate as Calibration Tool for Robot Tool Center Point Calibration

  • 摘要: 为在工业现场便捷、准确地获取工具中心点(tool center point,TCP)参数,降低机器人末端工具的定位误差,提出了一种基于平板标定工具的机器人TCP标定方法. 利用机器人TCP与平板多次触碰所形成的空间触点应共面的约束条件,建立了机器人TCP参数标定模型;针对TCP名义参数未知和已知的情况,分别提出了基于粒子群算法的TCP直接求解和线性化的偏差求解算法. 通过数值仿真和标定试验验证所提出方法的可行性和准确性,结果表明:TCP直接求解和偏差求解算法求解的结果与传统四点标定法相比,误差分别在0.5 mm和1.0 mm以内.

     

  • 图 1  标定系统组成

    Figure 1.  Schematic diagram of calibration system composition

    图 2  TCP求解流程

    Figure 2.  Flow chart of solving TCP

    图 3  TCP偏差求解流程

    Figure 3.  Flow chart of solving TCP deviation

    图 4  末端工具

    Figure 4.  End of arm tooling

    图 5  标定平板

    Figure 5.  Flat plate for calibration

    图 6  采用直接求解法得到的触点距各自拟合平面距离

    Figure 6.  Distance between contact points obtained by direct solution algorithm and fitting plane

    图 7  采用TCP偏差算法计算的触点距各自拟合平面距离

    Figure 7.  Distance between contact points obtained by TCP deviation solution algorithm and fitting plane

    表  1  TCP与标定平板上的6个点重合时机器人各关节转角

    Table  1.   Rotation angles of each robot joint when TCP coincides with the six points on flat plate (°)

    $j$$\theta _1^{(j)}$$\theta _2^{(j)}$$\theta _3^{(j)}$$\theta _4^{(j)}$$\theta _5^{(j)}$$\theta _6^{\left( j \right)}$
    1 4.592 3.883 40.894 93.418
    2 −16.360 −69.026 3.156 3.766 39.137 133.812
    3 −18.966 −72.777 7.720 15.494 51.803 170.749
    4 −15.545 −72.356 10.098 30.897 27.092 129.078
    5 −17.059 −76.277 13.533 30.244 33.174 28.440
    6 −16.637 −72.496 8.437 33.510 43.938 50.159
    下载: 导出CSV

    表  2  KUKA-KR5 arc六轴机械手D-H参数

    Table  2.   D-H parameters of KUKA-KR5 arc six-axis manipulator

    i连杆扭角
    ${\alpha _{i - 1}}$/(°)
    连杆长度
    ${{\rm{\alpha }}_{i - 1}}$/mm
    连杆偏距
    ${d_i}$/mm
    关节变量
    ${\theta _i}$/(°)
    关节变量
    范围/(°)
    1 −180 0 −400 ${\theta _1}$ $ \pm 155$
    2 90 180 0 ${\theta _2}$ 65 ~ −180
    3 0 600 0 ${\theta _3} - 90$ 158 ~ −15
    4 90 40 −620 ${\theta _4}$ $ \pm 350$
    5 −90 0 0 ${\theta _5}$ $ \pm 130$
    6 90 0 −80 ${\theta _6}$ $ \pm 350$
    下载: 导出CSV

    表  3  带尖端的工具TCP与标定平板触碰10次机器人各关节转角

    Table  3.   Rotation angles of each robot joint when TCP of pointed tool touches flat plate for ten times (°)

    $j$$\theta _1^{(j)}$$\theta _2^{(j)}$$\theta _3^{(j)}$$\theta _4^{(j)}$$\theta _5^{(j)}$$\theta _6^{\left( j \right)}$
    1 2.620 −97.869 106.089 −42.201 53.464 53.897
    2 3.405 0 −98.277 109.043 −50.821 53.495 67.413
    3 −8.362 −99.114 109.047 −42.222 43.170 54.233
    4 −2.599 −95.747 107.063 −46.442 44.167 49.021
    5 −19.339 −93.316 98.347 2.277 44.676 −6.206
    6 −4.734 −81.491 80.254 −7.669 72.043 5.501
    7 −16.592 −94.005 100.254 12.081 41.775 10.819
    8 −15.702 −94.978 109.910 −13.487 16.745 10.065
    9 −8.751 −87.764 92.296 −2.780 48.022 −17.819
    10 −10.505 −86.340 87.267 5.413 60.768 −18.097
    下载: 导出CSV

    表  4  随机选取的五组点

    Table  4.   Randomly selected five sets of points

    组数点的组合
    第1组 1,4,5,7,9,10
    第2组 1,2,4,6,8,9
    第3组 2,4,5,7,9,10
    第4组 3,5,6,7,8,10
    第5组 2,3,4,6,8,9
    下载: 导出CSV

    表  5  采用TCP直接求解算法计算的TCP数值及触点距拟合平面距离参数

    Table  5.   TCP value calculated by the TCP direct solution algorithm and distance from contact points to fitting plane mm

    算法6PTCP${\delta _{{\rm{av}}}}$${\delta _{{\rm{max}}}}$${\delta _{{\rm{min}}}}$
    xyz 四点法 (77.051,17.549,424.403) 0.054 700 44 0.198 660 20 0.002 9713 34
    平板法 第1组 (77.261,17.963,424.182) 0.019 577 00 0.036 198 00 0.001 1571 61
    第2组 (77.302,17.892,424.212) 0.020 623 99 0.056 222 38 0.004 9632 50
    第3组 (77.164,17.965,424.105) 0.020 089 88 0.040 741 77 0.002 9905 96
    第4组 (77.174,17.916,424.232) 0.022 560 21 0.054 562 15 0.001 6164 12
    第5组 (77.009,17.960,424.041) 0.022 746 09 0.060 353 03 0.002 5718 00
    下载: 导出CSV

    表  6  采用TCP偏差求解算法计算的TCP数值及触点距拟合平面距离参数

    Table  6.   TCP value calculated by TCP deviation solution algorithm and distance from contact points to fitting plane mm

    分组d6PTCP r${\delta _{{\rm{av}}}}$/
    × 10−2
    ${\delta _{{\rm{max}}}}$/
    × 10−2
    ${\delta _{{\rm{min}}}}$/
    × 10−2
    1 ${\left[ {\begin{array}{*{20}{c}} {{\rm{ - 0}}{\rm{.961}}} \\ {{\rm{ - 0}}{\rm{.236}}} \\ {{\rm{ - 1}}{\rm{.043}}} \end{array}} \right]}$ ${\left[ {\begin{array}{*{20}{c}} {{\rm{ 77}}{\rm{.039}}} \\ {{\rm{17}}{\rm{.764}}} \\ {{\rm{423}}{\rm{.957}}} \end{array}} \right]}$ 2.638 10.116 0.046
    2 ${\left[ {\begin{array}{*{20}{c}} {{\rm{ - 1}}{\rm{.639}}} \\ {{\rm{ - 0}}{\rm{.141}}} \\ {{\rm{ - 1}}{\rm{.617}}} \end{array}} \right]}$ ${\left[ {\begin{array}{*{20}{c}} {{\rm{76}}{\rm{.361}}} \\ {{\rm{17}}{\rm{.860}}} \\ {{\rm{423}}{\rm{.383}}} \end{array}} \right]}$ 3.140 10.719 0.157
    3 ${\left[ {\begin{array}{*{20}{c}} {{\rm{ - 1}}{\rm{.179}}} \\ {{\rm{ - 0}}{\rm{.041}}} \\ {{\rm{ - 1}}{\rm{.357}}} \end{array}} \right]}$ ${\left[ {\begin{array}{*{20}{c}} {{\rm{76}}{\rm{.821}}} \\ {{\rm{17}}{\rm{.959}}} \\ {{\rm{423}}{\rm{.643}}} \end{array}} \right]}$ 2.242 5.130 0.479
    4 ${\left[ {\begin{array}{*{20}{c}} {{\rm{ - 0}}{\rm{.160}}} \\ {{\rm{0}}{\rm{.060}}} \\ {{\rm{ - 0}}{\rm{.390}}} \end{array}} \right]}$ ${\left[ {\begin{array}{*{20}{c}} {{\rm{77}}{\rm{.840}}} \\ {{\rm{18}}{\rm{.059}}} \\ {{\rm{424}}{\rm{.609}}} \end{array}} \right]}$ 2.689 5.529 0.592
    5 ${\left[ {\begin{array}{*{20}{c}} {{\rm{0}}{\rm{.341}}} \\ {{\rm{ - 0}}{\rm{.299}}} \\ {{\rm{0}}{\rm{.612}}} \end{array}} \right]}$ ${\left[ {\begin{array}{*{20}{c}} {{\rm{78}}{\rm{.341}}} \\ {{\rm{17}}{\rm{.701}}} \\ {{\rm{425}}{\rm{.612}}} \end{array}} \right]}$ 4.189 5.287 0.272
    下载: 导出CSV
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出版历程
  • 收稿日期:  2018-09-21
  • 修回日期:  2019-03-11
  • 网络出版日期:  2019-07-16
  • 刊出日期:  2020-02-01

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