Transverse Function control of a class of non-invariant driftless systems. Application to vehicles with trailers

The paper addresses the stabilization of reference trajectories for a class of nonlinear driftless systems. The proposed method is based on the so-called Transverse Function approach, a control design method initially developed by the authors for driftless systems invariant with respect to a Lie group operation. The present work shows how the approach can be generalized to a larger class of systems, not necessarily invariant. This possibility is illustrated with the control of unicycle-type (or car-like) vehicles with an arbitrary number of trailers, and with simulation results in the case of two trailers.