Robot Static Stiffness Pose Optimization Based on Hierarchical Population Strategy

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

Abstract

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

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

CLC Number:

TP242.2

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.

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.

Figures/Tables 16

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

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

Fig.2 Robotic polishing and grinding scenario

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

Fig.4 Blade polishing and grinding process

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

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

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

Fig.6 Pose optimization flow chart

Fig.7 Experimental software and hardware platform

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

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

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

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

Fig.8 Experimental environment

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

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

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

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

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

References 14

[1]	陈守欢，周婷婷，胡天亮. 六自由度铣削加工机器人刚度建模及误差补偿［J］. 计算机集成制造系统， 2023， 29（2）： 404-418.
	CHEN Shouhuan， ZHOU Tingting， HU Tianliang. Stiffness Modeling and Error Compensation Method of 6-DOF Milling Robot［J］. Computer Integrated Manufacturing Systems， 2023， 29（2）： 404-418.
[2]	HUANG Si， YANG Jianzhong， HU Pengcheng， et al. High Stiffness 6-DOF Dual-arm Cooperative Robot and Its Application in Blade Polishing［J］. IEEE Transactions on Automation Science and Engineering， 2024， 21（4）： 5929-5941.
[3]	XUE Xiangru， ZHANG Chengrui， CHEN Qizhi， et al. The Posture Optimization Method Based on Deformation Index in Robotic Milling Process［J］. The International Journal of Advanced Manufacturing Technology， 2022， 121（7）： 4999-5014.
[4]	高轲. 基于静动态刚度的铣削加工机器人姿态最优调控研究［D］. 长春：吉林大学， 2023.
	GAO Ke. Research on the Optimum Control of Milling Robot Postures Based on Static and Dynamic Stiffness［D］. Changchun： Jilin University， 2023.
[5]	CHEN Chen， PENG Fangyu， YAN Rong， et al. Stiffness Performance Index Based Posture and Feed Orientation Optimization in Robotic Milling Process［J］. Robotics and Computer-Integrated Manufacturing， 2019， 55： 29-40.
[6]	廖昭洋. 机器人曲面铣削轨迹规划方法研究［D］. 广州：华南理工大学， 2021.
	LIAO Zhaoyang. Research on Toolpath Planning Method for Robotic Surface Milling［D］. Guangzhou： South China University of Technology， 2021.
[7]	YE Congcong， YANG Jixiang， ZHAO Huan， et al. Task-dependent Workpiece Placement Optimization for Minimizing Contour Errors Induced by the Low Posture-dependent Stiffness of Robotic Milling［J］. International Journal of Mechanical Sciences， 2021， 205： 106601.
[8]	宁晓，黄思，张禛哲，等. 带有并联缓冲机构的三指机器人夹持器设计［J］. 华中科技大学学报（自然科学版）， 2024， 52（6）： 148-155.
	NING Xiao， HUANG Si， ZHANG Zhenzhe， et al. Design of Three-finger Robot Gripper with Parallel Buffer Mechanism［J］. Journal of Huazhong University of Science and Technology （Natural Science Edition）， 2024， 52（6）： 148-155.
[9]	LIAO Zhaoyang， LI Jingrong， XIE Hailong， et al. Region-based Toolpath Generation for Robotic Milling of Freeform Surfaces with Stiffness Optimization［J］. Robotics and Computer-Integrated Manufacturing， 2020， 64： 101953.
[10]	WU Haotian， YANG Jianzhong， HUANG Si， et al. Multi-objective Adaptive Trajectory Optimization for Industrial Robot Based on Acceleration Continuity Constraint［J］. Robotics and Computer-Integrated Manufacturing， 2023， 84： 102597.
[11]	孙文娟. 自适应遗传算法的改进及其在爆炸冲击响应谱时域合成优化中的应用研究［D］. 合肥：中国科学技术大学， 2019.
	SUN Wenjuan. Improvement of Adaptive Genetic Algorithm and Its Application in Time Domain Synthesis Optimization of Pyroshock Response Spectrum［D］. Hefei： University of Science and Technology of China， 2019.
[12]	CHOE K I， HUANG Xiaoxia， MA Di. Uncertain Mean-risk Index Portfolio Selection Considering Inflation： Chaos Adaptive Genetic Algorithm［J］. International Journal of Machine Learning and Cybernetics， 2024， 15（4）： 1261-1275.
[13]	FENG Tingping， LI Junmin， JIANG Hao， et al. The Optimal Global Path Planning of Mobile Robot Based on Improved Hybrid Adaptive Genetic Algorithm in Different Tasks and Complex Road Environments［J］. IEEE Access， 2024， 12： 18400-18415.
[14]	HARTENBERG R S， DENAVIT J. Kinematic Synthesis of Linkages［M］. New York： McGraw-Hill， 1964.