R. Ramabhadran et Jk. Antonio, FAST SOLUTION TECHNIQUES FOR A CLASS OF OPTIMAL TRAJECTORY PLANNING PROBLEMS WITH APPLICATIONS TO AUTOMATED SPRAY COATING, IEEE transactions on robotics and automation, 13(4), 1997, pp. 519-530
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.