FAST SOLUTION TECHNIQUES FOR A CLASS OF OPTIMAL TRAJECTORY PLANNING PROBLEMS WITH APPLICATIONS TO AUTOMATED SPRAY COATING

Optimal trajectory planning problems are often formulated as constrain ed variational problems, In general, solutions to variational problems are determined by appropriately discretizing the underlying objective functional and solving the resulting nonlinear differential equation( s) and/or nonlinear programming problem(s) numerically, These general solution techniques often require a significant amount of time to be c omputed, and therefore are of limited value when optimal trajectories need to be frequently computed and/or recomputed, In this paper, a rea listic class of optimal trajectory planning problems is defined for wh ich the existence of fast numerical solution techniques are demonstrat ed, To illustrate the practicality of this class of trajectory plannin g problems and the proposed solution techniques, three optimal traject ory planning problems for spray coating applications are formulated an d solved, Based on the proposed discretization technique, it is shown that these problems can be reduced to either a linear program or a qua dratic program, which are readily solved, In contrast, using the stand ard discretization of these problems generally leads to nonconvex nonl inear programming problems that require a significant amount of comput ation to arrive at a (possibly) locally optimal solution.