  In this article we design a backstepping control law based on geometric
principles to swing up a spherical pendulum mounted on a moving quadrotor. The
available degrees of freedom in the control vector also permit us to position
the plane of the quadrotor parallel to the ground. The problem addressed here
is, indeed, novel and has many practical applications which arise during the
transport of a payload mounted on top of a quadrotor. The modeling and control
law are coordinate-free and thus avoid singularity issues. The geometric
treatment of the problem greatly simplifies both the modeling and control law
for the system. The control action is verified and supported by numerical
experiments for aggressive manoeuvres starting very close to the downward
stable equilibrium position of the pendulum.
