Research Article Open Access

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

Andrés G. García1
  • 1 Universidad Tecnológica Nacional, Argentina
Journal of Mechatronics and Robotics
Volume 4 No. 1, 2020, 1-7

DOI: https://doi.org/10.3844/jmrsp.2020.1.7

Published On: 17 January 2020

How to Cite: García, A. G. (2020). Asymptotic Stability of Unicycle-Like Robots: The Bessel’s Controller. Journal of Mechatronics and Robotics, 4(1), 1-7. https://doi.org/10.3844/jmrsp.2020.1.7

Abstract

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.

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Keywords

  • Nonholonomic Dynamics
  • Brockett’s Condition
  • Kinematic Model
  • Closed-Loop
  • Closed-Form Solution