Chained form approximation of a driftless system. Application to the exponential stabilization of the general N-trailer system

Abstract

This paper addresses the stabilization of postures (or configurations) for the general N -trailer system, also known as the N -trailer system with 'off-axle' or 'kingpin' hitching. In general, the kinematic model of this system cannot be transformed into the chained form, so the wealth of tools developed for the latter are not directly applicable to that system. Nevertheless, it is shown here that there exists a class of systems that may be locally approximated by a chained form, and sufficient conditions for a system to be in this class are pointed out. Such a 'chained form approximation' may then be used to build a local stabilizer for the original (approximated) system. After deriving its kinematic model, it is shown in this paper that the general N -trailer system has a chained form approximation at some postures, and that these may be locally -exponentially stabilized by simple feedback controllers available in the literature. Simulation examples are given to illustrate the approach.