Control of a 2-DOF omnidirectional mobile inverted pendulum

Abstract

In this paper, stabilization of a 2-degrees-of-freedom (2-DOF) omnidirectional mobile inverted pendulum (OM-IP) is studied. The OM-IP consists of the rod that rotates around a rotary point of a universal joint which is connected at the center of the omnidirectional mobile platform (OMP). For ease of analysis, the OM-IP is decoupled into two subsystems: a 2-DOF inverted pendulum (IP) and an OMP. The IP is a rod that rotates around a universal joint with 2-DOF. The OMP is a body consisting of disk and three omnidirectional wheels that moves on plane and keeps the rod in balance. Dynamic modeling of the 2-DOF OM-IP is presented. From the dynamic equa- tion, an adaptive backstepping control method is proposed to keep the rod in balance. Update law is presented as differential equation of an unknown parameter when the distance from the center of gravity of the rod to the rotary point on the OMP is unknown. Stability of the adaptive controller is proven by using Lyapunov function. Simulation and experimental results show the effectiveness of the proposed controller.