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改进鲸鱼优化算法在机械臂时间最优轨迹规划的应用

赵晶 祝锡晶 孟小玲 吴霄

赵晶,祝锡晶,孟小玲, 等. 改进鲸鱼优化算法在机械臂时间最优轨迹规划的应用[J]. 机械科学与技术,2023,42(3):388-395 doi: 10.13433/j.cnki.1003-8728.20200596
引用本文: 赵晶,祝锡晶,孟小玲, 等. 改进鲸鱼优化算法在机械臂时间最优轨迹规划的应用[J]. 机械科学与技术,2023,42(3):388-395 doi: 10.13433/j.cnki.1003-8728.20200596
ZHAO Jing, ZHU Xijing, MENG Xiaoling, WU Xiao. Application of Improved Whale Optimization Algorithm in Time-optimal Trajectory Planning of Manipulator[J]. Mechanical Science and Technology for Aerospace Engineering, 2023, 42(3): 388-395. doi: 10.13433/j.cnki.1003-8728.20200596
Citation: ZHAO Jing, ZHU Xijing, MENG Xiaoling, WU Xiao. Application of Improved Whale Optimization Algorithm in Time-optimal Trajectory Planning of Manipulator[J]. Mechanical Science and Technology for Aerospace Engineering, 2023, 42(3): 388-395. doi: 10.13433/j.cnki.1003-8728.20200596

改进鲸鱼优化算法在机械臂时间最优轨迹规划的应用

doi: 10.13433/j.cnki.1003-8728.20200596
基金项目: 国家自然科学基金项目(51975540)与山西省研究生教育创新项目(2019BY102)
详细信息
    作者简介:

    赵晶(1994−),博士研究生,研究方向为智能装备制造,1250912956@qq.com

    通讯作者:

    祝锡晶,教授 ,博士生导师,zxj161501@nuc.edu

  • 中图分类号: 中国分类图号:TB142

Application of Improved Whale Optimization Algorithm in Time-optimal Trajectory Planning of Manipulator

  • 摘要: 针对机械臂时间最优轨迹规划问题,提出一种改进鲸鱼优化算法的最优轨迹规划方法。首先把机械臂各个关节的角度、角速度、角加速度作为约束参数,在关节空间中采用五次多项式插值构造机械臂的轨迹,然后建立以机械臂运行时间最优为目标的目标函数,采用改进的鲸鱼优化算法(IWOA)来对时间进行优化,提高机械臂的运行效率。最后通过MATLAB进行仿真,结果表明,改进的鲸鱼优化算法相较于其它同类算法求解精度更高,收敛速度更快,并且经过IWOA和轨迹优化结合得到的机械臂的位移、速度和加速度曲线都是平滑的且没有明显的突变,验证了该轨迹规划方法的有效性。
  • 图  1  权重变化曲线

    图  2  4种函数求解6个测试函数的收敛曲线图

    图  3  6个关节优化后运动轨迹

    表  1  4种算法实验参数设置

    算法参数
    WOA
    IWOA 种群规模为30;最大迭代次数为500;
    空间维度为30;k = 0.4
    GWO a=[2,0]
    PSO wmax=0.9,wmin=0.4,c1=c2=2.0
    下载: 导出CSV

    表  2  6个基准测试函数

    函数表达式维数定义域理论最优值
    $ {f_1}(x) = \displaystyle\sum\limits_{i = 1}^d {x_i^2} $30$ [ - 100,100] $0
    $ {f_2}(x) = \displaystyle\sum\limits_{i = 1}^d {\left| {{x_i}} \right|} + \prod _{i = 1}^d\left| {{x_i}} \right| $30$ [ - 10,10] $0
    $ {f_3}(x) = \displaystyle\sum\limits_{i = 1}^d {[100(} {x_{i + 1}} - x_i^2{)^2} - {({x_i} - 1)^2}] $30$ [ - 10,10] $0
    $\begin{gathered} {f_4}(x) = - 20\exp \left( { - 0.2\sqrt {\dfrac{1}{d}\displaystyle\sum\limits_{i = 1}^d {x_i^2} } } \right) - \exp \left( {\dfrac{1}{d}\displaystyle\sum\limits_{i = 1}^d {\cos (2\text{π} {x_i})} } \right) + 20 + e \\ \end{gathered}$30$ [ - 32,32] $0
    ${f_5}(x) = \dfrac{1}{ {4\;000} }\displaystyle\sum\limits_{i = 1}^d {x_i^2 - \prod\limits_{i = 1}^d {\cos \left(\dfrac{ { {x_i} } }{ {\sqrt i } }\right)} } + 1$30$ [ - 600,600] $0
    ${f_6}(x) = x_i^2 - 10\cos (2\text{π} {x_i}) + 10$30$ [ - 5.12,5.12] $0
    下载: 导出CSV

    表  3  基准测试函数优化结果

    指标算法f1f2f3f4f5f6
    Best WOA 2.58×10−87 6.52×10−58 2.78×101 4.44×10−15 0.00×100 0.00×100
    IWOA 2.94×10−289 1.59×10−149 2.41×101 8.88×10−16 0.00×100 0.00×100
    GWO 6.21×10−29 2.38×10−17 2.58×101 6.84×10−14 0.00×100 5.68×10−14
    PSO 7.56×10−5 8.89×10−1 2.21×101 1.80×10−3 2.61×10−5 1.23×102
    Mean WOA 2.56×10−80 4.32×10−53 2.80×101 6.31×10−15 0.00×100 2.84×10−15
    IWOA 4.01×10−282 2.12×10−145 2.47×101 8.88×10−16 0.00×100 0.00×100
    GWO 1.01×10−27 4.03×10−17 2.71×101 1.21×10−13 3.93×10−3 2.32×102
    PSO 4.12×10−4 4.15×101 1.99×102 6.36×100 3.15×10−1 3.58×102
    Worst WOA 2.26×10−74 1.04×10−50 2.88×101 8.88×10−15 0.00×100 5.68×10−14
    IWOA 8.44×10−280 1.37×10−141 2.49×101 8.88×10−16 0.00×100 0.00×100
    GWO 3.85×10−27 2.72×10−16 2.79×101 1.36×10−13 3.26×10−2 5.68×102
    PSO 3.12×10−2 2.24×102 5.21×102 1.21×101 5.93×10−1 1.05×102
    Std. WOA 4.04×10−80 9.12×10−59 2.34×101 4.89×10−16 0.00×100 8.07×10−15
    IWOA 3.32×10−283 3.12×10−146 1.56×101 4.56×10−17 0.00×100 0.00×100
    GWO 1.36×10−28 3.57×10−18 7.08×10−1 1.72×10−14 8.13×10−2 3.78×102
    PSO 5.26×10−4 6.36×101 4.32×101 7.42×100 4.09×10−1 4.32×102
    下载: 导出CSV

    表  4  路径点序列

    路径点关节1/(°)关节2/(°)关节3/(°)关节4/(°)关节5/(°)关节6/(°)
    11015455106
    27525120603040
    3130−4515110−6080
    4100−70−102010−10
    5−10−10100605030
    6−501050−100−4020
    下载: 导出CSV

    表  5  机械臂关节约束条件

    关节速度/(°·s−1 )加速度/(°·s−2)加加速度/(°·s−3 )
    11004560
    2954060
    31007555
    41507070
    51309075
    61108070
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-03-23
  • 网络出版日期:  2023-04-21
  • 刊出日期:  2023-03-25

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