Planning spatial paths for automated spray coating applications

Automated spray coating is an important component of finishing operations in many industries. Robotic manipulators are used in such units to traverse around the object to be coated. This paper describes a framework for determining a good spatial path for the manipulator, in order to achieve uniform deposition over the surface and reduce wastage of coating material outside the surface. By imposing an arc-length based conditioning, the formulated variational problem is shown to be well-posed. The variation in deposition rate, the deposition outside the surface, and the arc length are minimized in a weighted combination. The necessary conditions for a minimizing spatial path are given by a set of nonlinear differential equations that are numerically solved.