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浙江大学学报(工学版)  2026, Vol. 60 Issue (11): 2364-2372    DOI: 10.3785/j.issn.1008-973X.2026.11.006
机械工程     
基于3D点云复杂曲面的个性化图案喷涂轨迹规划方法
杨泽毅(),周正东*(),袁晓曦,蔡智,袁梦瑶
南京航空航天大学 航空航天结构力学及控制全国重点实验室,江苏 南京 210016
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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摘要:

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    
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
收稿日期: 2025-09-16 出版日期: 2026-10-16
CLC:  TP 391  
基金资助: 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).
通讯作者: 周正东     E-mail: yzy123@nuaa.edu.cn;zzd_msc@nuaa.edu.cn
作者简介: 杨泽毅(2001—),男,硕士生,从事轨迹规划研究. orcid.org/0009-0002-2608-4030. E-mail:yzy123@nuaa.edu.cn
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引用本文:

杨泽毅,周正东,袁晓曦,蔡智,袁梦瑶. 基于3D点云复杂曲面的个性化图案喷涂轨迹规划方法[J]. 浙江大学学报(工学版), 2026, 60(11): 2364-2372.

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.

链接本文:

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

图 1  自由曲面喷涂模型
图 2  椭圆双β模型
图 3  轨迹类型示意图
图 4  混合型轨迹示意图
图 5  处理前后的图案边缘点
图 6  点云切片示意图
图 7  相邻喷涂轨迹
图 8  局部切片区域
图 9  多色图案拆解示意图
图 10  喷涂轨迹对比图
图 11  不同轨迹的喷涂效果
图 12  混合型轨迹的喷涂效果
图 13  优化后的涂层厚度分布
图 14  不同灰狼算法的最佳适应度对比
图 15  圆形与方形图案在3种轨迹下的涂层仿真结果
图案类型轨迹类型$ {\overline{d}_{\text{error}}} $/mmR/μm$ \sigma $/μmCV/%
心形栅格轨迹32.2923.393.0217.08
心形螺旋轨迹13.1242.297.2559.92
心形优化混合轨迹13.1212.641.9814.46
圆形栅格轨迹27.0019.422.5922.38
圆形螺旋轨迹13.7610.781.078.99
圆形优化混合轨迹13.7615.022.1114.76
方形栅格轨迹15.395.521.789.80
方形螺旋轨迹14.2514.223.6624.74
方形优化混合轨迹14.258.161.048.61
表 1  不同轨迹规划方法在不同图案下的涂层综合性能对比
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