Stabilizing a spherical pendulum on a quadrotor

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.