Up: Publications of Oskar von Stryk
of the Industrial Robot Manutec r3
Minimum time and minimum energy point-to-point
trajectories for an industrial robot
of the type Manutec r3
are computed subject to state constraints
on the angular velocities.
The numerical solutions of these optimal control
problems are obtained in an efficient way by a combination
of a direct collocation and an indirect multiple shooting
This combination links the benefits of both
approaches: A large domain of convergence
and a highly accurate solution.
The numerical results show that the
constraints on the angular velocities become active
during large parts of the time optimal motion.
But the resulting stress on the links can be significantly reduced
by a minimum energy trajectory that is only about ten percent
slower than the minimum time trajectory.
As a by-product, the reliability of the direct collocation
method in estimating adjoint variables and the
efficiency of the combination of direct collocation and
multiple shooting is demonstrated.
The highly accurate solutions reported in this paper may also
serve as benchmark problems for other methods.
Oskar von Stryk
Fri Apr 5 21:57:02 MET DST 1996