Robust LQ control for parallel wheeled inverted pendulum

In this study, we consider a controller of the parallel wheeled inverted pendulum named Beauto Balancer Duo. The mathematical model of the inverted pendulum is derived by using the Euler Lagrange formula. Kinetic coefficients of the motor are derived from a specification sheet. The inverted pendulum has an uncertain viscous friction coefficient around the wheel, that causes perturbation of the dynamics. Therefore, an upper bound and a lower bound of the viscous friction coefficient are estimated by several experiments. Two controllers are synthesized in order to compare by simulations and experiments. One controller provides optimal performance only for a nominal model, and other controller has a robustness for the range of the viscous friction coefficient. From comparing two controllers, an accuracy of the derived mathematical model and an accuracy of the estimated viscous friction coefficient are verified.