  This paper focuses on the development of minimum time control profiles for
point-to-point motion of a gantry crane system in the presence of uncertainties
in modal parameters. Assuming that the velocity of the trolley of the crane can
be commanded and is subject to limits, an optimal control problem is posed to
determine the bang-off-bang control profile to transition the system from a
point of rest to the terminal states with no residual vibrations. Both undamped
and underdamped systems are considered and the variation of the structure of
the optimal control profiles as a function of the final displacement is
studied. As the magnitude of the rigid body displacement is increased, the
collapse and birthing of switches in the optimal control profile are observed
and explained. Robustness to uncertainties in modal parameters is accounted for
by forcing the state sensitivities at the terminal time to zero. The
observation that the time-optimal control profile merges with the robust
time-optimal control is noted for specific terminal displacements and the
migration of zeros of the time-delay filter parameterizing the optimal control
profile are used to explain this counter intuitive result. A two degree of
freedom gantry crane system is used to experimentally validate the observations
of the numerical studies and the tradeoff of increase in maneuver time to the
reduction of residual vibrations is experimentally illustrated.
