基于分层种群策略的机器人静刚度位姿优化

doi:10.3969/j.issn.1004-132X.2026.09.018

摘要/Abstract

摘要：

提出了一种面向精密磨抛场景的刚度性能指标，基于分层自适应遗传算法优化位姿以提高机器人刚度。构建了机器人运动学与静刚度模型，并通过关节刚度辨识实验获取操作刚度矩阵；以机器人磨削点处的柔度椭球为依据，结合磨抛路径上的机器人刚度及其稳定性，设计了适用于磨抛工况的综合刚度性能指标；引入适应度驱动的参数调整和种群分层机制，针对种群不同层使用差异化遗传策略，对磨削点位姿进行优化。实验结果表明，在不改变机器人结构和材料的情况下，变形量降低了约80%，机器人刚度得到有效提高。

关键词: 机器人磨抛, 刚度辨识, 综合刚度性能指标, 分层种群策略, 磨削点位姿优化

Abstract:

A stiffness performance index for precision grinding and polishing scene was proposed， and the robot stiffness was improved based on hierarchical adaptive genetic algorithm. The kinematics and static stiffness models of the robots were constructed， and the operational stiffness matrix was obtained through the joint stiffness identification experiments. Based on the flexibility ellipsoid at the grinding points of the robots， combined with the stiffness and stability of the robots on the grinding and polishing paths， a comprehensive stiffness performance index was designed for grinding and polishing conditions. Fitness-driven parameter adjustment and population stratification mechanism were introduced， and differentiated genetic strategies were used to optimize the grinding point posture for different layers of the population. The experimental results show that， without changing the structure and material of the robots， the deformation amounts reduce by 80%， and the robot stiffness is effectively improved.

Key words: robot grinding and polishing, stiffness identification, comprehensive stiffness performance index, hierarchical population strategy, grinding point posture optimization

中图分类号:

TP242.2

潘彬晖, 杨建中, 黄思, 吴浩天, 宁晓. 基于分层种群策略的机器人静刚度位姿优化[J]. 中国机械工程, 2026, 37(9): 2259-2267.

PAN Binhui, YANG Jianzhong, HUANG Si, WU Haotian, NING Xiao. Robot Static Stiffness Pose Optimization Based on Hierarchical Population Strategy[J]. China Mechanical Engineering, 2026, 37(9): 2259-2267.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2026.09.018

https://www.cmemo.org.cn/CN/Y2026/V37/I9/2259

图/表 16

图1 HSR-605机器人运动学模型

Fig.1 The kinematic model of the HSR-605 robot

表1 HSR-JR605机器人标准DH参数

Tab.1 The standard DH parameters of the HSR-JR605 robot

关节i	关节转角θ/（°）	d/mm	a/mm	α/（°）
1	0	0	0	-90
2	-90	0	360	0
3	180	0	-90	90
4	0	376.5	0	-90
5	0	0	0	90
6	0	119	0	0

图2 机器人磨抛场景

Fig.2 Robotic polishing and grinding scenario

图3 柔度椭球变换及法向刚度指标示意图

Fig 3 Ellipsoidal transformation of flexibility and schematic diagram of normal stiffness index

图4 叶片磨抛过程

Fig.4 Blade polishing and grinding process

表2 优化变量取值范围

Tab.2 The range of optimization variables

	x/mm	y/mm	z/mm	$γ$ /（°）
最大值	700	200	700	120
最小值	500	-200	500	60

表2 优化变量取值范围

Tab.2 The range of optimization variables

	x/mm	y/mm	z/mm	$γ$ /（°）
最大值	700	200	700	120
最小值	500	-200	500	60

图5 分层自适应遗传算法求解过程

Fig.5 The solving process of the hierarchical adaptive genetic algorithm

图6 位姿优化流程图

Fig.6 Pose optimization flow chart

图7 实验软硬件平台

Fig.7 Experimental software and hardware platform

表3 5种算法优化结果

Tab.3 Optimization results of five algorithms

	粒子群	$变异先行$	$交叉先行$	传统遗传	分层遗传
G_en	6	20	20	20	4
t/s	6.4860	5.9843	6.3187	5.9823	5.5434
f_best	1	0.9923	0.9660	0	1
f_ave	1	0	0.0272	0.0425	0.1783

表3 5种算法优化结果

Tab.3 Optimization results of five algorithms

	粒子群	$变异先行$	$交叉先行$	传统遗传	分层遗传
G_en	6	20	20	20	4
t/s	6.4860	5.9843	6.3187	5.9823	5.5434
f_best	1	0.9923	0.9660	0	1
f_ave	1	0	0.0272	0.0425	0.1783

表4 算法相同部分参数设置

Tab.4 Parameter settings for the same part of the algorithm

	$变异先行$	$交叉先行$	传统遗传	分层遗传
最初种群数目	100	100	100	100
最终种群数目	50	50		50
变异概率上限/下限	0.1/0.01	0.1/0.01		0.1/0.01
交叉概率上限/下限	0.9/0.6	0.9/0.6		0.9/0.6

表4 算法相同部分参数设置

Tab.4 Parameter settings for the same part of the algorithm

	$变异先行$	$交叉先行$	传统遗传	分层遗传
最初种群数目	100	100	100	100
最终种群数目	50	50		50
变异概率上限/下限	0.1/0.01	0.1/0.01		0.1/0.01
交叉概率上限/下限	0.9/0.6	0.9/0.6		0.9/0.6

图8 实验环境

Fig.8 Experimental environment

表5 不同位姿的关节转角 (°)

Tab.5 Joint angle of different poses

	$θ 1$	$θ 2$	$θ 3$	$θ 4$	$θ 5$	$θ 6$
位姿1	-15.92	-94.74	181.05	174.17	17.954	-77.74
位姿2	-33.04	-85.74	164.29	107.48	44.938	8.0564
位姿3	-15.92	-90.95	193.80	167.28	38.127	-48.47
位姿4	-5.681	-96.92	184.24	170.30	19.210	-51.46
位姿5	-32.60	-93.26	200.27	128.91	64.083	-35.19
位姿6	9.295	-111.7	205.07	57.339	-49.90	38.19

表5 不同位姿的关节转角 (°)

Tab.5 Joint angle of different poses

	$θ 1$	$θ 2$	$θ 3$	$θ 4$	$θ 5$	$θ 6$
位姿1	-15.92	-94.74	181.05	174.17	17.954	-77.74
位姿2	-33.04	-85.74	164.29	107.48	44.938	8.0564
位姿3	-15.92	-90.95	193.80	167.28	38.127	-48.47
位姿4	-5.681	-96.92	184.24	170.30	19.210	-51.46
位姿5	-32.60	-93.26	200.27	128.91	64.083	-35.19
位姿6	9.295	-111.7	205.07	57.339	-49.90	38.19

表6 负载信息

Tab.6 Load information

	第1组	第2组	第3组	第4组	第5组	第6组
负载/N	0	9.8	14.7	16.66	19.6	29.4

图9 末端法向线位移变形与法向刚度评价指标关系

Fig.9 Relationship between displacement and deformation of end normal line and evaluation index of normal stiffness

图10 位姿优化前后法向线位移变形量对比

Fig.10 Comparison of displacement and deformation of normal line before and after pose optimization

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