Non-linear stable inversion-based output tracking control for a spherical inverted pendulum

Abstract

We design an exact output tracking control law for a four degree of freedom spherical inverted pendulum based on the non-linear stable inversion tool proposed by Devasia et al. (1989). The pendulum is a slim cylindrical beam attached to a horizontal plane via a universal joint; the joint is free to move in the plane under the influence of a planar force. The upright position is an unstable equilibrium of the uncontrolled system because of gravity. The objective is to design a controller so that the pendulum can be steered to track some smooth desired translational trajectories while keeping the pendulum tightly around the upright position. The design proceeds in three steps: 1. identificatio..