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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 4259869, 10 pages
Research Article

Trajectory Optimization of Spray Painting Robot for Complex Curved Surface Based on Exponential Mean Bézier Method

1School of Electronics and Information, Jiangsu University of Science and Technology, Zhenjiang 212003, China
2School of Automation, Southeast University, Nanjing 210096, China
3School of Science, Jiangsu University, Zhenjiang 212013, China

Correspondence should be addressed to Yang Tang

Received 22 May 2017; Revised 24 August 2017; Accepted 11 September 2017; Published 20 November 2017

Academic Editor: Shoudong Huang

Copyright © 2017 Wei Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Automated tool trajectory planning for spray painting robots is still a challenging problem, especially for a large complex curved surface. This paper presents a new method of trajectory optimization for spray painting robot based on exponential mean Bézier method. The definition and the three theorems of exponential mean Bézier curves are discussed. Then a spatial painting path generation method based on exponential mean Bézier curves is developed. A new simple algorithm for trajectory optimization on complex curved surfaces is introduced. A golden section method is adopted to calculate the values. The experimental results illustrate that the exponential mean Bézier curves enhanced flexibility of the path planning, and the trajectory optimization algorithm achieved satisfactory performance. This method can also be extended to other applications.