Spraying trajectory optimization for redundant robots based on improved particle swarm algorithm

doi:10.3785/j.issn.1008-973X.2026.02.005

Journal of ZheJiang University (Engineering Science)

2026, Vol. 60

Issue (2): 269-278 DOI: 10.3785/j.issn.1008-973X.2026.02.005

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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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

Received: 07 February 2025 Published: 03 February 2026

CLC:

TP 241.2

Fund: 装备研制项目（GQZ2023004133）.

Corresponding Authors: Jianjun SHA E-mail: zyp_06@hrbeu.edu.cn;shajianjun_hh@163.com

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	Yipeng ZHONG
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Cite this article:

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.

URL:

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

基于改进粒子群算法的冗余机器人喷涂轨迹优化

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

Fig.1 Redundant robot spraying system

Tab.1 Denavit-Hartenberg parameters of redundant robot

Fig.2 Robot connecting rod model

Fig.3 Schematic diagram of hollow non-spherical wrist

Fig.4 Flowchart of improved particle swarm algorithm

Fig.5 Spraying simulation environment

Fig.6 Spraying path of spot-camouflage pattern

Fig.7 Schematic of oval nozzle spraying

Tab.2 Path points of linear spraying task

Fig.8 Variation curves of key parameters and fitness for algorithm

Tab.3 Comparison of comprehensive optimization performance indicators across different algorithms

Fig.9 Displacement comparison of redundant robot’s external axis before and after algorithm optimization (linear spraying task)

Tab.4 Path points of curved spraying task

Tab.5 External axis displacements of redundant robot at each path point before and after algorithm optimization

Fig.10 Base-axis displacement comparison of redundant robot before and after algorithm optimization (linear spraying task)

Fig.11 Curved spraying path

Fig.12 Displacement comparison of redundant robot’s external axis before and after algorithm optimization (curved spraying task)

Fig.13 Base-axis displacement comparison of redundant robot before and after algorithm optimization (curved spraying task)

Fig.14 Velocity comparison of redundant robot’s external axis before and after algorithm optimization (curved spraying task)

Fig.15 Base-axis velocity comparison of redundant robot before and after algorithm optimization (curved spraying task)

Fig.16 Acceleration comparison of redundant robot’s external axis before and after algorithm optimization (curved spraying task)

Fig.17 Base-axis acceleration comparison of redundant robot before and after algorithm optimization (curved spraying task)


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