Modeling with Euler-Lagrang Equation and Cybernetical Analysis for a Unicycle Robot

In this paper we study the dynamic modeling of a unicycle robot composed of a wheel, a frame and a disk. The unicycle can reach longitudinal stability by appropriate control to the wheel and lateral stability by adjusting appropriate torque imposed by the disk. The dynamic modeling of the unicycle robot is derived by Euler-Lagrange method. The stability and controllability of the system are analyzed according to the mathematic model. Independent simulation using MATLAB and ODE methods are then proposed respectively. Through the simulation, we confirm the validity of the two obtained models of the unicycle robot system, and provide two experimental platforms for the designing of the balance controller.