Search

In this paper, stabilization of a 2-degrees-of-freedom (2-DOF) inverted pendulum using an omnidirectional mobile platform (OMP) is studied. The inverted pendulum is a rod that rotating around a universal joint structure with 2-DOF. The OMP consists of platform and three omnidirectional wheels that are moving on x y  plane and keeping the rod balance. The dynamic modeling of the 2-DOF inverted pendulum and the OMP are presented. From the dynamic equation, an adaptive backstepping control method is proposed to keep the rod balance with an assumption that 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.

This paper proposes a controller design for an omnidirectional mobile platform (OMP) with three wheels using adaptive backstepping control. A kinematic modeling and a dynamic modeling of the system with disturbance and friction are presented. Based on the dynamic modeling, an adaptive backstepping controller (ABC) is designed to stabilize the OMP with parameter variations and uncertainties caused by friction and slip to follow a desired path. The controller and update laws are designed based on an adaptive backstepping control theory. It includes two steps: firstly, a virtual state and a stability function are introduced. Secondly, Lyapunov functions for the system are chosen and an adaptive backstepping controller to make the system stabilisable and the update laws to estimate the unknown parameters are obtained. The system stability is guaranteed by the Lyapunov stability theory. The simulation and experimental results are presented to demonstrate the effectiveness of the proposed controller and update laws.