Reconstruction of admissible joint-references from a prescribed output-reference for the non-standard and generalized N-trailers

Abstract

A reconstruction of admissible reference signals for the inner dynamics upon a prescribed output reference of a dynamical system is a one of the key problems stated in the control theory. We address this problem with respect to a class of driftless dynamical systems representing nonholonomic kinematics of the N-trailers equipped with the on-axle and off-axle hitching, including difficult cases of the differentially non-flat and nonminimum-phase kinematics. Given a prescribed admissible reference path or trajectory for the last trailer’s posture (treated as a reference output), we analyse possible solutions to the reconstruction problem for different types of the reference output. We propose a computational procedure to reconstruct the corresponding references (in a continuous domain of some parametrizing variable) for the joint angles of the N-trailer vehicles comprising an arbitrary number of segments interconnected by any type of hitching. In particular, we show how to find an admissible solution to the reconstruction problem, that is, the one which does not exhibit a jackknife effect, by appropriate searching in a set of all the possible (at least 2N) solutions. The proposed computational method is formally explained and numerically verified for the 3-trailer kinematics equipped with various types of hitching.