Balancing of a Spherical Inverted Pendulum with an Omni-directional Mobile Robot

A spherical inverted pendulum is a rod connected to a universal joint, which is attached to a horizontal movable base. The movable base is free to move on the plane acted on by a planar control force. It is a two-dimensional inverted pendulum. An omni-directional mobile robot is a special type of wheeled mobile robot that can perform translational movement along any desired path combined with any rotational movement. In this paper, we consider the problems of balancing a spherical inverted pendulum that is driven by an omni-directional mobile robot. A detailed dynamic model of the system is given for the control design and simulation study. By retaining the predominant nonlinear terms and neglecting the high-order coupling terms, the spherical inverted pendulum system model is simplified to two decoupled one-dimensional inverted pendulum systems. A stabilizing controller based on sliding mode control is designed for each decoupled system. In addition, a linear-quadratic regulator controller based on a linearized system model is also designed for performance comparison. The performance of the two control strategies is investigated through experimental studies.