Development of an optimal trajectory model for spray painting on a free surface

Generally, trajectory planning problems are often formulated as constrained variational problems. This paper develops an optimal trajectory model to optimize the trajectory planning on a free surface to achieve uniform deposition over painted surface and reduce wastage of coating materials. Numerical solution techniques consider geometric characteristics on a free surface, rate of film accumulation, and position and orientation of spray guns in uniformity coating and painting duration. Given a specified spatial path and functions of film accumulation rates for an infinite range model and a beta distribution model, some results are obtained by using nonlinear programming techniques based difference quasi-Newton method over cone surfaces. It provides objective functions that can be used to minimize the thickness variation of the paint spraying of a specified spatial path. These results also give an evaluation along the average velocity trajectory and the optimal trajectory to demonstrate the feasibility of the proposed methods. The formulated optimization methods can be applied to solve the same class of nonlinear planning problems.