Uniform Coverage of Automotive Surface Patches

In spray painting applications, it is essential to generate a spray gun trajectory such that the entire surface is completely covered and receives an acceptably uniform layer of paint deposition; we call this the “uniform coverage” problem. The uniform coverage problem is challenging because the atomizer emits a non-trivial paint distribution, thus making the relationships between the spray gun trajectory and the deposition uniformity complex. To understand the key issues involved in uniform coverage, we consider surface patches that are geodesically convex and topologically simple as representative of subsets of realistic automotive surfaces. In addition to ensuring uniform paint deposition on the surface, our goal is to also minimize the associated process cycle time and paint waste. Based on the relationships between the spray gun trajectory and the output characteristics (i.e., uniformity, cycle time and paint waste), our approach decomposes the coverage trajectory generation problem into three subproblems: (1) selecting a seed curve, (2) determining a speed profile along each pass, and (3) selecting the spacing between successive passes. Using concepts such as area magnification and the Gauss–Bonnet theorem from differential geometry, as well as standard optimization procedures, we present procedures to solve each subproblem independently from the others. We demonstrate our trajectory planning procedures by approximating real automotive surfaces by simple surfaces in simulation, and finally evaluate the effectiveness of our algorithms experimentally on real automotive