ON THE STABILIZATION OF THE UNICYCLE MODEL PROJECTING A HOLONOMIC SOLUTION

Abstract

It is shown that, adopting a polar-like kinematic description of the Cartesian unicycle nonholonomic vehicle in order to prevent Brocketts negative result, a stabilizing time-invariant feedback law can be simply obtained projecting a suitable holonomic linear velocity on the nonholonomic linear velocity axis and superimposing an angular velocity that asymptotically steers such axis parallel to the holonomic velocity vector. KEYWORDS: Nonholonomic vehicles, unicycle model INTRODUCTION The problem of feedback stabilizing the nonholonomic unicycle-like system has received a wide attention in the literature of the last years. This was due both to the concern of the robotics community dealing with the practical control of nonholonomic vehicles and to the theoretical interest inspired by the work of Brockett [1] that shows how a large class of nonholonomic systems cannot be stabilized by timeinvariant smooth state feedback. Nevertheless thanks to the results presented in [2] [3] [4] [5] it i...