This study developed a high-precision paint deposition model that considers the position and direction of a spray-painting gun. Our angle-specific paint deposition model focused on the change in paint deposition due to the change in the painting angle; however, there was a problem with its versatility. We analyzed this problem, and the solution was achieved by separately modeling changes in the film thickness distribution using impact angle and spray distance, which were previously modeled together. For higher accuracy, a special function was proposed to convert the three-dimensional vector into two-dimensional coordinate values in the distribution function upper plane. To confirm the validity of our model, a painting test on an L-shaped surface was conducted, and the measured and predicted values were compared. The L-shaped surface is a typical shape in which the film thickness distribution changes with the angle; a complex path with varying distances and angles was employed. The results confirmed that the predicted values agreed well with the measured values in the L-shaped surface painting test, validating the developed model.

In the present study, we used computational fluid dynamics to analyze the sag caused by spray painting, considering the change in paint shape due to flow. We focused on the paint adhering to the target surface because this behavior has not been previously examined. The particle method was adopted for the calculation because it enabled a stable analysis of the paint droplets and the complex uneven surface of the paint film. A high-speed camera and image analysis were used to capture the spray painting and identify the parameter values. Using the developed model, we analyzed the change in the film thickness distribution for painting on a flat plate in the vertical direction. It was confirmed that the numerical and experimental data correlated for two conditions of the target distance. In addition, we proposed a new index, Degree of Sagging (DSG), to evaluate the amount of sag based on the physical properties of the paint rheology and the geometry of the target. In the painting tests on flat plates with different angles, a strong positive correlation of 0.95 was observed between the sum of the calculated DSG values and the measured paint flow distance due to sag. In the painting tests on L-shaped surfaces, the predicted sag appearance by DSG agreed with the measured results at 14 of the 15 measurement points under all conditions. Overall, a computational model was developed for field implementation that could predict painting thickness distribution and sag occurrence. Note to Practitioners—The present work is motivated by the problem that teaching painting robots in a painting site is particularly time consuming. To address this problem, off-line programming methods have been proposed to computationally predict paint quality and film thickness and determine the painting route. Conventional approaches have approximated the paint deposition model with a function, which determines the paint thickness distribution, or simulated this model with high accuracy by considering electrostatic forces and wind velocity fields using computational fluid dynamics (CFD) modeling methods. However, two major problems exist in the field implementation of these studies: The first problem is the inability to predict defects, including sagging, that may occur after painting. In the conventional approach, the behavior of the paint after it adheres to the target is outside the scope of the calculation. The second problem is the high computational resource cost of CFD simulation, which renders its application to robotic painting challenging. In painting sites, the painting thickness must be accurately predicted and routed in a short period of time. In this paper, we present a method for analyzing film thickness distributions by considering time series changes of flow and propose a function-based model for predicting sagging based on the simulation results. The model for sag prediction was shown to be computationally inexpensive enough to be implemented in the field. The results of several painting experiments with a real robot confirmed the validity of the predictions made by this method. Our method could be implemented in the near future as a prediction system for off-line evaluation of painting routes, which could significantly reduce teaching cost. Since the target in this paper was a flat plate, it is necessary to conduct evaluation tests using various target shapes and painting conditions. Also, integration with the painting route optimization method has not yet been achieved, which is a topic that will be addressed in the future.

Equivalence structure (ES) extraction can allow for finding correspondence relations between different sequential datasets. A K -dimensional ES is a set of K -tuples to specify K -dimensional sequences that are considered equivalent. Whether or not two K -dimensional sequences are equivalent is decided based on comparisons of all of their subsequences. ES extraction can be used for preprocessing for transfer learning or imitation learning, as well as an analysis of multidimensional sequences. A recently proposed method called incremental search (IS) was much faster than brute-force search. However, IS can still take a long time to obtain ESs, because ESs obtained by IS can be subsets of other ESs and such subsets must be removed in the process. In this paper, we propose a new fast method called pairwise incremental search (PIS). In the process of PIS, the aforementioned problem about subsets of ESs does not exist, because the elements of ESs are searched pairwise. As shown by results of two experiments we conducted, PIS was 48 times faster than IS in an experiment using synthetic datasets and 171 times faster in an experiment using motion capture datasets.