  It is wellknown that helicopters descending fast may enter the so called VRS,
a region in the velocity space where the blade's lift differs significantly
from regular regions. This may lead to instability and therefore this region is
avoided, typically by increasing the horizontal speed. This paper researches
this phenomenon in the context of small scale quadcopters. The region
corresponding to the VRS is identified by combining first principles modeling
and wind tunnel experiments. Moreover, we propose that the so called WBS or
autorotation region should also be avoided for quadcopters, which is not
necessarily the case for helicopters. A model is proposed for the velocity
constraints that the quadcopter must meet to avoid these regions. Then, the
problem of designing optimal time descend trajectories that avoid the VRS and
WBS regions is tackled. Finally, the optimal trajectories are implemented on a
quadcopter. The flight tests show that by following the designed trajectories,
the quadcopter is able to descend considerably faster than purely vertical
trajectories that also avoid the VRS and WBS.

Dynamical Systems;Optimization and Control