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平面四索机器人运动平台定位误差与优化

夏硕 辛玉红 章永年 汪小旵

夏硕,辛玉红,章永年, 等. 平面四索机器人运动平台定位误差与优化[J]. 机械科学与技术,2021,40(11):1695-1702 doi: 10.13433/j.cnki.1003-8728.20200277
引用本文: 夏硕,辛玉红,章永年, 等. 平面四索机器人运动平台定位误差与优化[J]. 机械科学与技术,2021,40(11):1695-1702 doi: 10.13433/j.cnki.1003-8728.20200277
XIA Shuo, XIN Yuhong, ZHANG Yongnian, WANG Xiaochan. Positioning Error and Optimization of Plane Four-cable Robot Motion Platform[J]. Mechanical Science and Technology for Aerospace Engineering, 2021, 40(11): 1695-1702. doi: 10.13433/j.cnki.1003-8728.20200277
Citation: XIA Shuo, XIN Yuhong, ZHANG Yongnian, WANG Xiaochan. Positioning Error and Optimization of Plane Four-cable Robot Motion Platform[J]. Mechanical Science and Technology for Aerospace Engineering, 2021, 40(11): 1695-1702. doi: 10.13433/j.cnki.1003-8728.20200277

平面四索机器人运动平台定位误差与优化

doi: 10.13433/j.cnki.1003-8728.20200277
基金项目: 国家重点研发计划项目(2019YFE0125200)、中央高校基本科研业务费专项(KYXK2021001)、江苏省农业科技自主创新资金项目(CX(21)3148)及江苏省重点研发计划项目(BE2021016)
详细信息
    作者简介:

    夏硕(1999−),硕士研究生,研究方向为柔索并联机器人,871624945@qq.com

    通讯作者:

    章永年,副教授,博士,hczyn@njau.edu.cn

  • 中图分类号: TP242

Positioning Error and Optimization of Plane Four-cable Robot Motion Platform

  • 摘要: 忽略平面柔索并联机器人的末端运动平台的姿态会造成定位误差。在考虑平台姿态的前提下,构建了机器人运动学模型并对末端平台进行静力学分析,再以各柔索张力的最小方差为优化目标,提出张力均匀化优化算法并利用罚函数、梯度法计算得到满足最优索力分布条件下的位姿,然后分析了静平台出绳点布置形状、平台形状等因素对定位精度的影响规律。MATLAB的仿真试验表明:张力均匀化优化算法定位误差小于${10^{ - 6}}\;{\text{mm}}$,张力大小满足预期要求,考虑运动平台姿态的模型可修正偏转角度$6^\circ $以上,不同的出绳点布置引起偏转角误差最大可达$4.5^\circ $,运动平台长度和宽度相差越大,其对姿态影响也越大。样机实验表明:优化算法具有较高的精确度和可行性,对实现柔索并联机器人运动平台高精度定位具有重要意义。
  • 图  1  柔索并联机器人

    图  2  柔索并联机器人模型

    图  3  运动平台的α倾角

    图  4  运动平台中心点分布图

    图  5  不同位置索长关系

    图  6  正、逆解误差大小$\delta $

    图  7  各柔索张力变化

    图  8  偏转角误差

    图  9  优化前后柔索长度差

    图  10  各出绳点位置关系

    图  11  不同矩形出绳点的偏转角

    图  12  平台形状对偏转角的影响

    图  13  运动平台目标轨迹曲线

    图  14  优化前后实际曲线精度对比

    表  1  ${}^O{A_i}$坐标实际值表

    坐标值${}^O{{\boldsymbol{A}}_1}$${}^O{{\boldsymbol{A}}_2}$${}^O{{\boldsymbol{A}}_3}$${}^O{{\boldsymbol{A}}_4}$
    X/mm590670−590−940
    Y/mm−670850430−580
    下载: 导出CSV

    表  2  ${}^D{{\boldsymbol{B}}_i}$坐标实际值表

    坐标值${}^D{{\boldsymbol{B}}_1}$${}^D{{\boldsymbol{B}}_2}$${}^D{{\boldsymbol{B}}_3}$${}^D{{\boldsymbol{B}}_4}$
    X/mm$a/2$$a/2$$ - a/2$$ - a/2$
    Y/mm$ - b/2$$b/2$$b/2$$ - b/2$
    下载: 导出CSV

    表  3  正方形1坐标${}^O{\dot {\boldsymbol{A}}_i}$实际值表

    坐标值${}^O{\dot {\boldsymbol{A} }_1}$${}^O{\dot {\boldsymbol{A} }_2}$${}^O{\dot {\boldsymbol{A} }_3}$${}^O{\dot {\boldsymbol{A} }_4}$
    X/mm504504−756−756
    Y/mm−739521521−739
    下载: 导出CSV

    表  4  矩形2坐标${}^O{\ddot {\boldsymbol{A}}_i}$实际值表

    坐标值${}^O{\ddot {\boldsymbol{A}}_1}$${}^O{\ddot {\boldsymbol{A}}_2}$${}^O{\ddot {\boldsymbol{A}}_3}$${}^O{\ddot {\boldsymbol{A}}_4}$
    X/mm682682−933−933
    Y/mm−739521521−739
    下载: 导出CSV

    表  5  矩形3坐标${}^O{\dddot {\boldsymbol{A}}_i}$实际值表

    坐标值${}^O{\dddot {\boldsymbol{A}}_1}$${}^O{\dddot {\boldsymbol{A}}_2}$${}^O{\dddot {\boldsymbol{A}}_3}$${}^O{\dddot {\boldsymbol{A}}_4}$
    X/mm866866−1118−1118
    Y/mm−739521521−739
    下载: 导出CSV

    表  6  机器人实验参数

    组成部分选用参数
    控制器 Arduino MEGA2560开发板
    驱动电机 飞特SM60-360M舵机
    运动平台 50*50(mm)亚克力板
    电源 开关电源
    柔索 普通钢丝
    绕线轮 特制3D打印组件
    静平台 铝型材及铝合金板
    其他 黑色马克笔和A3纸
    下载: 导出CSV

    表  7  轨迹曲线偏差

    曲线所在区域与目标轨迹曲线最大偏差/mm
    优化前优化后
    16.50.1
    21.80.2
    32.20.2
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-06-11
  • 网络出版日期:  2022-03-02
  • 刊出日期:  2021-11-05

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