Tracking control method for an underactuated unicycle robot using an equilibrium state

We have developed an underactuated unicycle robot consisting of a body, a disk rotated by a DC motor, and a wheel driven by another DC motor to move the body. There is no direct force for changing the yaw direction of the robot. In the present paper, we propose a tracking control method for the unicycle robot by analogy with a rolling coin. In the absence of an external force, a rolling coin follows a circular trajectory. Similarly, the unicycle robot has an equilibrium state. First, the equation of equilibrium state of the robot is derived. This equation reveals that the yaw rate depends on the roll angle and the wheel angular velocity. Simulation results reveal the validity of the derived equation. Next, the desired tangential velocity and the angular velocity of the robot for tracking a target trajectory are derived by Kanayama´s method; and then the derived values are converted into the desired roll angle and the desired wheel velocity by using the derived equation of equilibrium state. Control inputs are set to control the roll angle and the wheel velocity to the converted desired values. Finally, the control method is applied to a control for tracking a circular orbit.