Optimal trajectory planning for spray coating

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. For each surface point and for each feasible position and orientation of the applicator, a value for the instantaneous rate of film accumulation 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.<>