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多切断点分离-重构技术推导非球型手腕6R机器人逆解公式

肖帆 曾克俭

肖帆,曾克俭. 多切断点分离-重构技术推导非球型手腕6R机器人逆解公式[J]. 机械科学与技术,2022,41(4):559-565 doi: 10.13433/j.cnki.1003-8728.20200380
引用本文: 肖帆,曾克俭. 多切断点分离-重构技术推导非球型手腕6R机器人逆解公式[J]. 机械科学与技术,2022,41(4):559-565 doi: 10.13433/j.cnki.1003-8728.20200380
XIAO Fan, ZENG Kejian. Deriving the Inverse Solution Formula of 6R Robot with Non-spherical Wrist with Multi-cut Point Separation and Reconstruction Technique[J]. Mechanical Science and Technology for Aerospace Engineering, 2022, 41(4): 559-565. doi: 10.13433/j.cnki.1003-8728.20200380
Citation: XIAO Fan, ZENG Kejian. Deriving the Inverse Solution Formula of 6R Robot with Non-spherical Wrist with Multi-cut Point Separation and Reconstruction Technique[J]. Mechanical Science and Technology for Aerospace Engineering, 2022, 41(4): 559-565. doi: 10.13433/j.cnki.1003-8728.20200380

多切断点分离-重构技术推导非球型手腕6R机器人逆解公式

doi: 10.13433/j.cnki.1003-8728.20200380
详细信息
    作者简介:

    肖帆(1988−),硕士研究生,研究方向为机器人智能控制,297067972@qq.com

    通讯作者:

    曾克俭,教授,硕士生导师,zengkejian@126.com

  • 中图分类号: TP242.2

Deriving the Inverse Solution Formula of 6R Robot with Non-spherical Wrist with Multi-cut Point Separation and Reconstruction Technique

  • 摘要: 本文提出一种利用多切断点分解—重构技术求解非球型手腕机器人逆解新方法,简化了该类机器人逆运动学公式的推导过程。首先利用指数积公式的变形,说明了n自由度机器人的可分解性,以及重构连接的通用几何约束;然后以一款手腕前端偏置型机器人为例,给出了针对常见非球型手腕机器人的分解方法及重新连接的几何约束条件。以满足约束条件为目的,得到了只含θ6的非线性封闭方程,以及其它关节角关于θ6的求解公式,推导过程具有更直观的物理几何意义。最后使用二分法求解,算法约2 ms可得到目标位姿所有解,计算位姿误差在10−12 mm以内。
  • 图  1  n自由度机器人

    图  2  机器人分解图

    图  3  MOTOMAN-EA140机器人结构简图

    图  4  MOTOMAN-EA140机器人分解图

    图  5  位姿T对应的f(θ6)曲线

    表  1  各关节螺旋轴参数

    iωiri
    1 [0 0 1]T [0 0 0]T
    2 [0 −1 0]T [l2 0 l1]T
    3 [0 −1 0]T [l2 0 l1+l3]T
    4 [1 0 0]T [l2+l5 0 l1+l3+l4]T
    5 [0 −1 0]T [l2+l5 0 l1+l3+l4]T
    6 [0 0 −1]T [l2+l5+l6 0 l1+l3+l4-l7]T
    下载: 导出CSV

    表  2  目标位姿T的12组逆解

    θ1 /radθ2 /radθ3 /radθ4 /radθ5 /radθ6 /rade /mm
    2.25038889−1.49034188−1.339933870.00270934−4.601716191.625958163.6×10−12
    2.10476338−1.51441021−1.26985578−2.044470811.421145283.617699041.1×10−12
    2.25113961−1.53222813−1.240448423.134323471.517721734.777810018.3×10−12
    2.39481362−1.51464078−1.269620762.049109341.422693485.917709681.9×10−12
    2.249986191.60871108−2.40742833−0.00070966−0.350089631.628242591.7×10−12
    2.249894051.75768624−2.506915363.14077780−2.742014954.769723902.9×10−12
    −0.73193189−2.52178659−1.077662021.78079767−1.718972300.335807391.3×10−12
    −0.89041575−2.50228309−1.117298763.13409508−1.626797791.621487851.2×10−12
    −1.05141999−2.52193887−1.07750491−1.77807632−1.720375722.923799623.6×10−12
    −0.89084055−2.54228100−1.014749440.00490210−1.577347894.775294331.1×10−12
    −0.891692010.99331192−2.630062333.140798170.356035201.628727888.3×10−12
    −0.891604331.10799726−2.73261364−0.00071240−3.509761874.770335921.9×10−12
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-06-04
  • 录用日期:  2021-12-16
  • 刊出日期:  2022-09-05

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