A self-balancing unicycle robot, which has a wheel for balancing and moving in the longitudinal plane (pitch angle), a vertical flywheel for balancing in the lateral plane (roll angle), and a flywheel in the horizontal plane(yaw angle) for yaw control is studied in this paper. The non-linear dynamic equations of the unicycle robot on level surface are analyzed using the Kane dynamic formulation, then a linear model of the robot is derived at the equilibrium point, and linear quadratic regulators (LQR) are designed to control the robot to change its yaw angle from 0° to 45° . Simulation results validated that the unicycle robot can achieve good performance in static standing and in dynamic moving.
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