Task curve planning for painting robots. I. Process modeling and calibration

This paper reports the first phase of a project whose aim is the automatic generation of tool center trajectories for robots engaged in spray painting of arbitrary surfaces. The first phase consists of proposing a mathematical model for the paint flux field within the spray cone. We have called this quantity the paint flux field partly to emphasize that it is a vector field and partly to distinguish it from a paint flux distribution function, which describes the angular variation of the flux field within the spray cone. It is shown that this flux field can be derived from experimental measurements performed by robots, of coverage profiles of paint strips on flat plates by solving a singular integral equation. This flux field is derived both for published experimental data as well as two sets of data from experiments performed by the authors. The correctness of the model is demonstrated by using the underlying distribution function to predict coverage profiles for other experiments in which the spray gun is no longer vertical to the plane surface.