Uniform Coverage of Simple Surfaces Embedded in R3 for Auto-Body Painting

We develop a procedure for automated trajectory generation for robotic spray painting applications. Painting requires that the spray gun deposit paint at each point on the target surface such that the variation of the resultant paint deposition is within acceptable limits; we term this the uniform coverage problem. To understand the key issues in the uniform coverage problem, we consider surface patches that are geodesically convex and topologically simple to represent realistic automotive surfaces. Our goal is to understand the relationship between the spray gun trajectory and the following output characteristics: deposition uniformity, cycle time, and paint waste. Our planning approach decomposes the coverage trajectory generation problem into three subproblems: selection of the start curve, selection of the speed profiles along each pass, and selection of the spacing between the passes. Using concepts such as area magnification, the Gauss-Bonnet theorem from differential geometry, and standard optimization procedures, we present procedures to solve each subproblem independently of the others. Finally, we demonstrate our trajectory planning procedures in simulation as well as experimentally on simple surfaces that approximate real automobile surfaces.