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

Mathematical Problems in Engineering, Nov 2017

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.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

http://downloads.hindawi.com/journals/mpe/2017/4259869.pdf

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

Trajectory Optimization of Spray Painting Robot for Complex Curved Surface Based on Exponential Mean Bézier Method Wei Chen,1,2 Junjie Liu,1 Yang Tang,3 Jian Huan,1 and Hao Liu1 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; nc.ude.sju@711008yt 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. Abstract 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. 1. Introduction Spray painting robot is an important advanced paint production equipment, which is widely used in the paint production line of automotive. The complex shape of the workpiece in the actual industrial production is often encountered. The basic steps of the existing method in the trajectory optimization for spray painting on this kind of complex curved surface are as follows: After obtaining the CAD (Computer Aided Design) data of the workpiece surface, triangulation is directly performed on the surface. And the surface is modeled by the corresponding method. After patching the complex curved surface according to the surface topology, each patch is approximated as a plane. Then the spray painting trajectory is optimized on each patch. The spray painting trajectory at the junction between patches is optimized. It needs to be optimized according to the geometric position relation of the painting path on every two patches: PA-PA (parallel-parallel), PA-PE (parallel-perpendicular), and PE-PE (perpendicular-perpendicular) [1–3]. Perform the tool trajectory optimal integration on each patch. Specifically, we can use ant colony algorithm or genetic algorithm. In general, such trajectory optimization method for spray painting on a complex curved surface can basically meet the requirement of spray painting. However, this method has many steps to perform, and it needs to undergo three optimization operations such as the trajectory optimization on patch, optimization for spray painting trajectory at the junction of every two patches, and the tool trajectory optimal integration on each patch in actual process [4–6]. The operation will be more troublesome, and a lot of system time will be consumed. In addition, when the area of complex curved surface is larger or with more patches, the following two problems will occur: It is necessary to combine the optimized trajectories at the junction between the patches after the optimization for the painting path. The error will be larger, which will make the uniformity of the paint thickness at the junction of the patches worse. What is more, a lot of system execution time will be consumed in this process [7]. When the number of patches is large, the population size (this is the concept of ant colony algorithm) will increase when performing the tool trajectory optimal integration on each patch. In this case, the convergence speed of genetic algorithm or ant colony algorithm is slow, and the algorithm is easy to fall into different local optimum fields, which leads to poor spray painting effect and lower spray painting efficiency [8–10]. Because of the existence of the problems above, the spray painting effect of the complex workpiece surface is still not very satisfactory in the current spray painting operations. Under this background, a new trajectory optimization method on curved surface based on Bézier surface is proposed in this paper. The specific idea for this method is after modeling the complex curved surface by using the Bézier triangular surface modeling technique, the discrete point array on the equidistant surface of the complex curved surface is found by the calculation method for discrete point array on equidistant surface of Bé (...truncated)


This is a preview of a remote PDF: http://downloads.hindawi.com/journals/mpe/2017/4259869.pdf

Wei Chen, Junjie Liu, Yang Tang, Jian Huan, Hao Liu. Trajectory Optimization of Spray Painting Robot for Complex Curved Surface Based on Exponential Mean Bézier Method, Mathematical Problems in Engineering, 2017, 2017, DOI: 10.1155/2017/4259869