| P. N. Atkar, A. Greenfield,
D. C. Conner, H. Choset, and A. A. Rizzi Carnegie Mellon
University, Pittsburgh, PA 15213, USA |
| 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 surfaces. |
