The problem of how to optimally traverse a spray applicator around a surface to be coated is formulated as a type of optimization problem known as a constrained variational problem. An optimal trajectory for a spray applicator is defined to be one that results in minimal variation in accumulated film thickness on the surface. The trajectory for an applicator is characterized by a six-dimensional vector function that specifies the position and orientation of the applicator at each instant of time. The surface to be coated is represented with a function. For each surface point and fclr each feasible position and orientation of the applicator, a value for the instantaneous rate of film accumulat'lon is assumed to be known. Empirical data and/or estimates for these values can be readily incorporated in the formulation. By making realistic approximations, the proposed constrained variational problem is transformed into a finite dimensional constrained optimization problem. Numerical studies are included that illustrate the utility of the problem formulation and the effectiveness of applying standard nonlinear programming techniques for determining solutions.

Date of this Version

September 1993