Asymptotic Stability of Unicycle-Like Robots: The Bessel’s Controller

Asymptotic stability of unicycle-like robots proved to be involved due to Brockett's condition. By using a smooth, time-invariant controller constructed out of Bessel’s functions, in this paper unicycle-like robots are uniformly-exponentially stabilized to the origin. The pure feedback controller obtained provides closed-form trajectories with the possibility of a simple and feasible (hardware) non-linear observer construction from posture angle measurements solely. Two examples are presented: Asymptotic steering of a unicycle to the origin using gyros and a perfect non-linear observer reconstruction states along with conclusions and future work.