  In this work we present the optimization-based design and control of a
fully-actuated omnidirectional hexarotor. The tilt angles of the propellers are
designed by maximizing the control wrench applied by the propellers. This
maximizes (a) the agility of the UAV, (b) the maximum payload the UAV can hover
with at any orientation, and (c) the interaction wrench that the UAV can apply
to the environment in physical contact. It is shown that only axial tilting of
the propellers with respect to the UAV's body yields optimal results. Unlike
the conventional hexarotor, the proposed hexarotor can generate at least 1.9
times the maximum thrust of one rotor in any direction, in addition to the
higher control torque around the vehicle's upward axis. A geometric controller
on SE(3) is proposed for the trajectory tracking problem for the class of fully
actuated UAVs. The proposed controller avoids singularities and complexities
that arise when using local parametrizations, in addition to being invariant to
a change of inertial coordinate frame. The performance of the controller is
validated in simulation.
