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

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

肖帆^1,,
李光^1, ,,
杨加超¹,
章晓峰¹,
马祺杰¹,
袁鹰²

1.
湖南工业大学机械工程学院，湖南株洲 412007
2.
娄底技师学院，湖南娄底 417000

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
计量
- 文章访问数: 700
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- PDF下载量: 39
- 被引次数: 0
出版历程
- 收稿日期: 2019-04-16
- 刊出日期: 2020-06-05

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

1.
College of Mechanical Engineering, Hunan University of Technology, Hu'nan Zhuzhou 412007, China
2.
Loudi Technician Institute, Hu'nan Loudi 417000, China

摘要

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10⁻⁵mm级别，单次平均求解时间约为14.1 ms。
- CMA-ES /
- 7自由度仿人臂 /
- 逆运动学 /
- 实时 /
- 高精度
Abstract: This paper proposes an improved CMA-ES algorithm. Firstly, the original algorithm randomly generates the initial mean point, which is modified to the weighted sum of excellent individuals in good point sets. Then, the cross-border sensitivity factor and step-size scaling factor are added to adjust step size updates, when the new individuals have cross-border behaviour. Taking the 7-DOF humanoid arm as an example, the inverse kinematic solution is obtained with the improved CMA-ES algorithm. The simulation results show that the improved CMA-ES algorithm can solve the inverse kinematics of 7-DOF humanoid arm in real-time and with high-precision. In point-to-point motion, the single solution time is about 9.7 ms, and the fitness function is stable at the 10⁻⁸ level. In the continuous trajectory of workspace, the position tracking error is stable at the 10⁻⁵ mm level, and the single average solution time is about 14.1 ms.
- covariance matrix adaptation evolution strategy /
- 7-DOF humanoid arm /
- inverse kinematics /
- real-time /
- high-accuracy

HTML全文

图 1 CMA-ES进化过程简示图

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图 2 情形1

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图 3 情形2

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图 4 佳点集产生的初始种群

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图 5 拟人臂运动学模型

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图 6 3种算法单次求解进化曲线图

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图 7 两算法独立运行1 000次求得的关节角值

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图 8 轨迹位姿的求解结果

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表 1 拟人臂的连杆参数

连杆i	关节角θ_i/(°)	扭角α_i−1/(°)	长度a_i−1/mm	偏置d_i/mm
1	θ₁	180	0	0
2	θ₂	−90	0	0
3	θ₃	90	0	d₃
4	θ₄	−90	0	0
5	θ₅	90	0	d₅
6	θ₆	−90	0	0
7	θ₇	90	0	0

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表 2 关节角取值范围（°）

关节	θ₁	θ₂	θ₃	θ₄	θ₅	θ₆	θ₇
上限	−170	−170	−170	0	−120	−120	−170
下限	170	170	170	180	120	120	170

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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/mm	2.089 6×10⁻⁶	2.316 4×10⁻⁶
最大值/mm	2.121 9×10⁻⁵	2.128 6×10⁻⁵
平均值/mm	1.092 7×10⁻⁵	1.172 3×10⁻⁵
标准差/mm	4.735 9×10⁻⁶	4.975 6×10⁻⁶
平均求解时间/s	0.014 1	0.021 6

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