On the geometric construction of a stabilizing time-invariant state feedback controller for the nonholonomic integrator

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Abstract

The paper presents a rather natural and elementary geometric construction of a stabilizing time-invariant state feedback law for the nonholonomic integrator. The key features of the particular construction are the direct inclusion of certain classical optimality considerations pertaining to the geodesics of the nonholonomic integrator, the confinement of all discontinuities in the feedback law to the z-axis, as well as a uniform exponential convergence result for the closed-loop system. The results of this treatment also have interesting implications for the control of nonholonomic systems in general, e.g., they highlight that for nonholonomic systems even the most natural seeming stabilizing feedback laws may not be amenable to a closed-form expression and may need to be formulated in more elaborate and implicit terms.

Original languageEnglish
Article number110073
JournalAutomatica
Volume136
DOIs
StatePublished - Feb 2022

Keywords

  • Feedback stabilization
  • Nonholonomic systems
  • Nonlinear control

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