Balance Control of a Configurable Inverted Pendulum on an Omni-Directional Wheeled Mobile Robot

Abstract

This paper considers the balance control problems of a configurable inverted pendulum with an omni-directional wheeled mobile robot. The system consists of two parts. One is an inverted pendulum, and another one is an omni-directional wheeled mobile robot. The system can be configured as a rotary inverted pendulum or a spherical inverted pendulum. The objective is to control the omni-directional wheeled mobile robot to provide translational force on the plane to balance the spherical inverted pendulum and to provide the moment to balance the rotary inverted pendulum. Detailed dynamic models of these two systems are derived for the control strategy design and simulation studies. Stabilizing controllers based on the second-order sliding mode control are designed for both systems. The closed-loop stability is proved based on the passivity properties. The proposed control schemes can guarantee semi-globally asymptotical stability over the upper-half plane. In addition, the conventional sliding mode controllers proposed in our previous work and Linear-Quadratic Regulator (LQR) controllers based on the linearized system models about its upright equilibrium point are also used for performance comparison. The effectiveness of the control strategies is investigated and verified using simulation and experimental studies. In the simulation studies, different sources of uncertainty and disturbance are investigated. It is shown that the second-order sliding mode control outperforms the conventional sliding mode control and LQR control without any uncertainty and disturbance. For robustness to the matched disturbance, the simulation results show that the second-order sliding mode controller has a less significant steady-state oscillation in the pendulum’s angular displacement than other controllers. The simulation results also show that only the second-order sliding mode controller can stabilize the system with a significant initial deviation from the pendulum’s upright position. Finally, the experimental results demonstrate that second-order sliding mode control outperforms conventional sliding mode control and LQR control.