Balancing and Velocity Control of a Unicycle Robot Based on the Dynamic Model

This paper presents a dynamic-model-based control scheme for the balancing and velocity control of a unicycle robot. Unicycle robot motion consists of a pitch that is controlled by an in-wheel motor and a roll that is controlled by a reaction wheel pendulum. The unicycle robot lacks an actuator for yaw-axis control, which makes the derivation of the dynamics relatively simple although it may limit the motion control. The Euler-Lagrange equation is applied to derive the dynamic equations of the unicycle robot to implement dynamic speed control. To achieve real-time speed control, a sliding-mode control and a nonzero set-point linear quadratic regulator (LQR) are utilized to guarantee stability while maintaining the desired speed-tracking performance. In the roll controller, a sigmoid-function-based sliding-mode controller has been adopted to minimize switching-function chattering. An LQR controller has been implemented for pitch control to drive the unicycle robot to follow the desired velocity trajectory in real time using the state variables of pitch angle, angular velocity, wheel angle, and angular velocity. The control performance of the two control systems using a single dynamic model has been experimentally demonstrated.