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改进CMA-ES算法及其在7自由度仿人臂逆运动学求解中的应用

肖帆 李光 杨加超 章晓峰 马祺杰 袁鹰

肖帆,李光,杨加超, 等. 改进CMA-ES算法及其在7自由度仿人臂逆运动学求解中的应用[J]. 机械科学与技术,2020,39(6):844-851 doi: 10.13433/j.cnki.1003-8728.20190162
引用本文: 肖帆,李光,杨加超, 等. 改进CMA-ES算法及其在7自由度仿人臂逆运动学求解中的应用[J]. 机械科学与技术,2020,39(6):844-851 doi: 10.13433/j.cnki.1003-8728.20190162
Xiao Fan, Li Guang, Yang Jiachao, Zhang Xiaofeng, Ma Qijie, Yuan Ying. Applying Improved CMA-ES Algorithm to Solve Inverse Kinematics of 7-DOF Humanoid Arm[J]. Mechanical Science and Technology for Aerospace Engineering, 2020, 39(6): 844-851. doi: 10.13433/j.cnki.1003-8728.20190162
Citation: Xiao Fan, Li Guang, Yang Jiachao, Zhang Xiaofeng, Ma Qijie, Yuan Ying. Applying Improved CMA-ES Algorithm to Solve Inverse Kinematics of 7-DOF Humanoid Arm[J]. Mechanical Science and Technology for Aerospace Engineering, 2020, 39(6): 844-851. doi: 10.13433/j.cnki.1003-8728.20190162

改进CMA-ES算法及其在7自由度仿人臂逆运动学求解中的应用

doi: 10.13433/j.cnki.1003-8728.20190162
基金项目: 湖南省自然科学基金项目(2018JJ4079)资助
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:

    李光,教授,硕士生导师,博士,liguang@hut.edu.cn

  • 中图分类号: TP242.2

Applying Improved CMA-ES Algorithm to Solve Inverse Kinematics of 7-DOF Humanoid Arm

  • 摘要: 提出一种改进的CMA-ES算法:将原算法随机生成初始均值点,改为由佳点集中优秀个体加权求和得到;增加越界敏感因子和步长缩放系数,用于新个体存在越界行为时,修正步长更新。以7自由度仿人臂为例,用改进的CMA-ES算法求逆运动学解,结果表明改进的CMA-ES算法可实时、高精度地求解:在点对点运动中,改进的算法单次求解时间约为9.7 ms,适应度函数稳定在10−8级别;在工作空间的连续轨迹中,位置跟踪误差稳定在10−5 mm级别,单次平均求解时间约为14.1 ms。
  • 图  1  CMA-ES进化过程简示图

    图  2  情形1

    图  3  情形2

    图  4  佳点集产生的初始种群

    图  5  拟人臂运动学模型

    图  6  3种算法单次求解进化曲线图

    图  7  两算法独立运行1 000次求得的关节角值

    图  8  轨迹位姿的求解结果

    表  1  拟人臂的连杆参数

    连杆i关节角θi/(°)扭角αi−1/(°)长度ai−1/mm偏置di/mm
    1θ118000
    2θ2−9000
    3θ3900d3
    4θ4−9000
    5θ5900d5
    6θ6−9000
    7θ79000
    下载: 导出CSV

    表  2  关节角取值范围 (°)

    关节θ1θ2θ3θ4θ5θ6θ7
    上限 −170 −170 −170 0 −120 −120 −170
    下限 170 170 170 180 120 120 170
    下载: 导出CSV

    表  3  3种算法独立运行1 000次的f1结果

    f1原CMA-ES改进的CMA-ES遗传算法
    最小值 2.262 8×10−8 6.700 5×10−9 1.873 1×10−4
    最大值 1.748 1×10−7 9.987 2×10−8 0.021 7
    平均值 7.648 7×10−8 6.939 4×10−8 0.005 8
    标准差 1.663 7×10−8 1.842 0×10−8 0.003 6
    平均求解时间/s 0.022 6 0.009 7 0.346
    下载: 导出CSV

    表  4  轨迹采样点的位置绝对误差

    位置绝对误差改进的CMA-ES原CMA-ES
    最小值/mm2.089 6×10−62.316 4×10−6
    最大值/mm2.121 9×10−52.128 6×10−5
    平均值/mm1.092 7×10−51.172 3×10−5
    标准差/mm4.735 9×10−64.975 6×10−6
    平均求解时间/s0.014 10.021 6
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-04-16
  • 刊出日期:  2020-06-05

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