With the increasing use of robotic manipulators the requirements of their abilities are also increasing. An essential part in design and application of robots is their dynamic behaviour. The discussion of optimal trajectories within the context of path planning and optimal design of parameters leads to the optimal control problems discussed in this paper.
Several methods for solving optimal point-to-point trajectory problems of robotic manipulators have been suggested and applied, e. g., in [7], [13], [14], [15], [23], to cite only a few of many papers.
As an extension to the previous cited work
we investigate a non academic, highly nonlinear model of a
commercially available robot, discuss several objectives
for optimal trajectories and consider
state constraints on the angular velocities that
play an important role in the time optimal motion.
In our approach, we combine a direct collocation and an indirect
multiple shooting method in an hybrid approach (cf. [28])
with a large domain of convergence and highly accurate solutions.
The direct collocation method is easily capable to
treat a wide variety of objectives and constraints
on the state and control variables.