3D point cloud-based trajectory planning method for personalized pattern spraying on complex surfaces

doi:10.3785/j.issn.1008-973X.2026.11.006

Journal of ZheJiang University (Engineering Science)

2026, Vol. 60

Issue (11): 2364-2372 DOI: 10.3785/j.issn.1008-973X.2026.11.006

3D point cloud-based trajectory planning method for personalized pattern spraying on complex surfaces

Zeyi YANG(

),Zhengdong ZHOU*(

),Xiaoxi YUAN,Zhi CAI,Mengyao YUAN

State Key Laboratory of Mechanics and Control for Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

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Abstract

To improve the accuracy and uniformity of personalized spraying on complex surfaces, a spraying trajectory planning and optimization method integrating raster and spiral trajectories was proposed. A coating accumulation prediction model for complex surfaces was first constructed based on the elliptical double-β model. Then, a high-precision hybrid spraying trajectory suitable for complex surfaces was designed by combining the respective advantages of raster and spiral trajectories. On this basis, the spraying spacing and spraying speed of the raster trajectory, as well as the spraying speed of the spiral trajectory, were optimized using sequential quadratic programming and an improved grey wolf optimization algorithm (IGWO). Simulation results show that the optimized hybrid trajectory provides excellent edge accuracy and coating uniformity for heart-shaped, square, and circular patterns. For the heart-shaped pattern, the edge error was reduced by 59.36%, and the coating thickness variation was reduced by 15.33% compared with the traditional raster trajectory, while the coating thickness variation was reduced by 75.87% compared with the spiral trajectory. The proposed method exhibits consistent and stable performance across patterns with different geometric features, demonstrating its universality and effectiveness for personalized spraying on complex surfaces.

Key words： trajectory planning 3D point cloud complex surface spraying robot patterned spray coating

Received: 16 September 2025 Published: 16 October 2026

CLC:

TP 391

Fund: 国家自然科学基金资助项目（52375570）；中国航空研究院首批揭榜挂帅项目（F2021109）；上海航天科技创新基金资助项目（SAST2019-121）；南京航空航天大学研究生科研与实践创新计划项目（xcxjh20240110）；江苏高校优势学科建设工程资助项目（PAPD）.

Corresponding Authors: Zhengdong ZHOU E-mail: yzy123@nuaa.edu.cn;zzd_msc@nuaa.edu.cn

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Cite this article:

Zeyi YANG,Zhengdong ZHOU,Xiaoxi YUAN,Zhi CAI,Mengyao YUAN. 3D point cloud-based trajectory planning method for personalized pattern spraying on complex surfaces. Journal of ZheJiang University (Engineering Science), 2026, 60(11): 2364-2372.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2026.11.006 OR https://www.zjujournals.com/eng/Y2026/V60/I11/2364

基于3D点云复杂曲面的个性化图案喷涂轨迹规划方法

为了提高复杂曲面个性化图案喷涂的精度与均匀性，提出融合栅格型轨迹与螺旋型轨迹的喷涂轨迹规划及优化方法. 基于椭圆双β模型构建复杂曲面涂料堆积分布预测模型. 结合栅格轨迹与螺旋轨迹各自的优势，设计适用于复杂曲面的高精度混合喷涂轨迹. 运用序列二次规划法与改进的灰狼优化算法（IGWO），分别对栅格型轨迹的喷涂间距与喷涂速度以及螺旋型轨迹的喷涂速度进行优化. 仿真实验结果表明：优化后的混合轨迹在心形、方形及圆形等复杂图案中均表现出优异的边缘精度与涂层均匀性，其中心形图案的图案边缘误差相比传统栅格轨迹降低59.36%，涂层厚度变异降低15.33%，相比螺旋轨迹涂层厚度变异降低75.87%. 所提方法在不同几何特征图案中均表现出一致且稳定的性能，验证了其在复杂曲面个性化喷涂中的普适性与有效性.

关键词： 轨迹规划, 3D点云, 复杂曲面, 喷涂机器人, 图案喷涂

Fig.1 Freeform surface spraying model

Fig.2 Elliptical double-β distribution

Fig.3 Trajectory type diagram

Fig.4 Schematic diagram of hybrid trajectory

Fig.5 Edge points before and after processing

Fig.6 Schematic diagram of point cloud slice

Fig.7 Adjacent spraying trajectories

Fig.8 Local slice area

Fig.9 Schematic diagram of multi-color pattern decomposition

Fig.10 Comparison of spraying trajectories

Fig.11 Spray coating effects of different trajectories

Fig.12 Spray coating effects of hybrid trajectory

Fig.13 Coating thickness distribution after optimization

Fig.14 Comparison of best fitness values of different grey wolf optimizer algorithms

Fig.15 Coating simulation results for circular and square patterns using three trajectories

Tab.1 Comparison of coating overall performance for different trajectory planning methods under various patterns


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