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浙江大学学报(工学版)
浙江大学学报(工学版)  2026, Vol. 60 Issue (2): 269-278    DOI: 10.3785/j.issn.1008-973X.2026.02.005
能源工程、机械工程     
基于改进粒子群算法的冗余机器人喷涂轨迹优化
钟艺鹏1,2(),沙建军1,2,*(),张一飞1,2,杨汶龙1,2,殷婷1,2,马祥龙1,2
1. 哈尔滨工程大学 智能科学与工程学院，黑龙江 哈尔滨 150001
2. 哈尔滨工程大学 青岛创新发展基地，山东 青岛 266000
Spraying trajectory optimization for redundant robots based on improved particle swarm algorithm
Yipeng ZHONG1,2(),Jianjun SHA1,2,*(),Yifei ZHANG1,2,Wenlong YANG1,2,Ting YIN1,2,Xianglong MA1,2
1. College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China
2. Qingdao Innovation Development Base, Harbin Engineering University, Qingdao 266000, China
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摘要：

针对大型部件自动喷涂过程中冗余机器人耦合度低造成的轨迹不平滑、关节冲击问题，提出新的喷涂轨迹优化方法. 建立冗余机器人模型，结合分站式定位逆解和阻尼最小二乘法求逆运动学解. 采用改进粒子群算法优化冗余机器人外部轴轨迹，引入自适应惯性权重和非线性学习因子，增强算法搜索能力，提高算法的求解精度与寻优速度. 仿真实验表明，与原轨迹、GA-PSO算法优化后的轨迹和改进模拟退火遗传算法优化后的轨迹相比，采用改进粒子群算法优化后，机器人在直线喷涂任务中整体能量损耗分别降低了35.4%、1.3%和2.8%，外部轴运动幅度分别降低了32.6%、0.4%和2.3%；在曲线喷涂任务中整体能量损耗分别降低了26.8%、2.8%和7.3%，外部轴运动幅度分别降低了58.7%、17.8%和21.0%.
关键词： 冗余机器人;  机器人喷涂;  轨迹优化;  阻尼最小二乘法;  粒子群算法    
Abstract:

A new spraying trajectory optimization method was proposed to eliminate the unsmooth trajectory and joint impact that occurred when a redundant robot exhibited poor point-coupling performance during the automatic spraying of large parts. A redundant robot model was established, and an inverse kinematics solution was obtained by combining an inverse solution of stationary localization and the damped least squares method. An improved particle swarm algorithm was used to optimize the trajectory of the redundant robot’s external axes, the adaptive inertia weights and nonlinear learning factors were introduced to enhance the algorithm’s searching ability, and to increase the solving accuracy and optimization search speed of the algorithm. In simulation, the improved particle swarm algorithm scheme was compared with the original trajectory and with those generated by the GA-PSO algorithm and by the improved simulated annealing genetic algorithm. For the linear spraying task, it cut overall energy loss by 35.4%, 1.3% and 2.8%, and reduced the amplitude of the external axis motion by 32.6%, 0.4% and 2.3%, respectively. The corresponding reductions for the curved spraying task were 26.8%, 2.8% and 7.3% in energy, and 58.7%, 17.8% and 21.0% in axis motion.
Key words: redundant robot    robot spraying    trajectory optimization    damped least squares method    particle swarm algorithm
收稿日期: 2025-02-07 出版日期: 2026-02-03
CLC:  TP 241.2  
基金资助: 装备研制项目（GQZ2023004133）.
通讯作者: 沙建军     E-mail: zyp_06@hrbeu.edu.cn;shajianjun_hh@163.com
作者简介: 钟艺鹏（1999—），男，硕士生，从事工业机器人运动规划控制研究. orcid.org/0009-0005-2041-1354. E-mail：zyp_06@hrbeu.edu.cn
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引用本文:

钟艺鹏,沙建军,张一飞,杨汶龙,殷婷,马祥龙. 基于改进粒子群算法的冗余机器人喷涂轨迹优化[J]. 浙江大学学报(工学版), 2026, 60(2): 269-278.

Yipeng ZHONG,Jianjun SHA,Yifei ZHANG,Wenlong YANG,Ting YIN,Xianglong MA. Spraying trajectory optimization for redundant robots based on improved particle swarm algorithm. Journal of ZheJiang University (Engineering Science), 2026, 60(2): 269-278.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2026.02.005    或    https://www.zjujournals.com/eng/CN/Y2026/V60/I2/269

图 1  冗余机器人喷涂系统
$ A_i $$ {\theta }_{i} $/rad$ {d}_{i} $/mm$ {L}_{i-1} $/mm$ {\varphi }_{i-1} $/(°)
A1$ {\theta }_{1} $00$ {\varphi }_{0} $
A2$ {\theta }_{2} $00$ {\varphi }_{1} $
A3$ {\theta }_{3} $00$ {\varphi }_{2} $
A4$ {\theta }_{4} $0$ {L}_{3} $$ {\varphi }_{3} $
A5$ {\theta }_{5} $$ {d}_{5} $0$ {\varphi }_{4} $
A6$ {\theta }_{6} $$ {d}_{6} $0$ {\varphi }_{5} $
A7$ {\theta }_{7} $$ {d}_{7} $0$ {\varphi }_{6} $
A8$ {\theta }_{8} $$ {d}_{8} $0$ {\varphi }_{7} $
表 1  冗余机器人的Denavit-Hartenberg参数
图 2  机器人连杆模型
图 3  中空非球形手腕示意图
图 4  改进粒子群算法流程图
图 5  喷涂仿真环境
图 6  斑点迷彩图案喷涂路径
图 7  椭圆形喷嘴喷涂示意图
路径点序号x/mmy/mmz/mm
11500?3001400
2150020001400
表 2  直线喷涂路径点
图 8  算法关键参数和适应度变化曲线
算法${n_{\mathrm{c}}}$${\bar S_{{\mathrm{b}}}}$${E_{{\mathrm{s}}}}$/J
文献[9]180.27161159.9
文献[14]200.27201177.9
本研究120.27111145.3
表 3  不同算法的综合优化性能指标对比
图 9  算法优化前后冗余机器人外部轴位移对比（直线喷涂）
路径点x/mmy/mmz/mm$ {\theta _y} $/（°）
11 70001 00090
21 8004001 40060
32 0008001 70045
42 1001 2001 9000
52 1501 6002 0000
62 1002 0001 8500
71 9002 4001 50030
81 8002 2001 10045
91 7002 0001 00060
101 6001 80090090
表 4  曲线喷涂路径点
路径点Δx/mm
文献[9]文献[14]本研究
1561.4553.1594.2
2804.9651.8871.8
31 003.5796.71 082.1
41 213.1951.51 356.4
51 385.31 357.41 479.1
61 569.61 649.21 607.7
71 884.41 913.51 811.3
81 811.81 803.31 788.5
91 698.21 705.21 788.5
101 698.21 705.21 788.5
表 5  算法优化前后各路径点对应的冗余机器人外部轴位移
图 10  算法优化前后冗余机器人本体轴位移对比 (直线喷涂)
图 11  曲线喷涂路径
图 12  算法优化前后冗余机器人外部轴位移对比 (曲线喷涂)
图 13  算法优化前后冗余机器人本体轴位移对比 (曲线喷涂)
图 14  算法优化前后冗余机器人外部轴速度对比 (曲线喷涂)
图 15  算法优化前后冗余机器人本体轴速度对比 (曲线喷涂)
图 16  算法优化前后冗余机器人外部轴加速度对比 (曲线喷涂)
图 17  算法优化前后冗余机器人本体轴加速度对比 (曲线喷涂)
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