Global path following for the unicycle and other results

We address the maneuver regulation of the kinematic unicycle to a circle. Our control approach is passivity-based, and we frame the control design objective as a set stabilization problem. We present two main results. First, we provide a smooth, time-invariant, static feedback that globally asymptotically stabilizes the motion on the circle in a desired direction and constant velocity. Second, we provide a smooth time-varying feedback that almost globally asymptotically stabilizes the set of configurations corresponding to the unicycle centre of mass on the circle with desired heading on the circle.