Asymptotic Stability of Unicycle-Like Robots: The Bessel’s Controller
- 1 Universidad Tecnológica Nacional, Argentina
Copyright: © 2020 Andrés G. García. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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.
- Nonholonomic Dynamics
- Brockett’s Condition
- Kinematic Model
- Closed-Form Solution