Dynamics and stabilization of a spherical inverted pendulum on a wheeled cart

This paper studies a stabilization problem of an inverted spherical pendulum on a wheeled cart assuming that pure rotation of cart cannot move support of pendulum. It is shown that in spite of nonholonomic constraints of wheels and the above geometric condition on pendulum support the pendulum can be locally stabilizable at a certain non-static equilibrium point by applying a standard linearization approach. Furthermore it is shown that equilibrium points can be chosen to make cart move to a given location. Numerical simulations are performed to confirm theoretical findings and illustrate interesting dynamics of closed loop pendulum system.