LQR control for a self-balancing unicycle robot

A self-balancing unicycle robot, which has a wheel for balancing and movement in the longitudinal plane (pitch angle) as well as a flywheel for balancing in the lateral plane (roll angle), is studied in this paper. The non-linear dynamic equations of the unicycle robot on a slope are analyzed using the Lagrangian dynamic formulation, then a linear model of the robot is derived at the equilibrium point, and 3 linear quadratic regulators (LQR) are designed to control the robot on slopes with the angle of inclination varying from -11°to 11°. Simulation results validated that the unicycle robot can achieve good performance both on level plane and on slope.