HYBRID VARIABLE STRUCTURE PATH TRACKING CONTROL
OF ARTICULATED VEHICLES
Antonella Ferrara and Lorenza Magnani
Dipartimento di Informatica e Sistemistica
University of Pavia
via Ferrata 1, 27100 Pavia, Italy
{antonella.ferrara, lorenza.magnani}@unipv.it
Keywords: Hybrid vehicles, sliding-mode control,
vehicle dynamics, variable structure systems
ABSTRACT
This paper presents a path-tracking hybrid controller for
articulated vehicles. It is based on the approximation of
the desired path with lines and arcs. Suitable controllers
are designed for tracking lines and others for tracking
arcs. The control objective is attained by switching
among the different controllers. Each controller is
designed using time scale transformation and partial
linearization methods, as well as variable structure
control theory. Relying on the proposed hybrid control
approach it is possible to prove that, starting from the set
of feasible vehicle configurations, the driving point
tracks any desired path.
INTRODUCTION
This paper presents a hybrid path-tracking controller
which makes an articulated vehicle follow a desired path
consisting of lines and arcs, as the vehicle moves forward
and/or backward.
The path tracking control of articulated vehicles is a
challenging problem (Altafini et al. 2001) and (Samson
1995): many industrial applications require automatic
guidance of articulated vehicles. In the past years, many
approaches have been followed: local linearization
(Sampei et al. 1995), fuzzy control (Kong and Kosko
1992), neural network (Nguyen and Widrow 1990),
genetic algorithms and expert systems (Koza 1992), as
well as Lyapunov methods (Astolfi et al. 2001).
In the present work the control strategy consists in
approximating the desired path with lines and arcs,
design suitable controllers for tracking lines and others
for tracking arcs, and then switching among the different
controllers according to a prespecified logic. The control
laws associated with the various controllers are designed
using a time scale transformation (Sampei and Furuta
1986), partial linearization (Su 1982), and variable
structure control theory (Utkin 1992) and (De Carlo et al.
1998). The overall control strategy makes the articulated
vehicle follow any chosen path accurately. Indeed, each
controller guarantees that the corresponding reference
line or arc is tracked asymptotically, starting from the set
of feasible vehicle configurations. This set, which will be
specified in the paper, does not contain only peculiar
configurations, such as, for instance, that characterized
by the tractor perpendicular to the trailer, or that for
which the trailer is perpendicular to the line to be
tracked.
The controlled vehicle can be viewed as an hybrid
system by virtue of the switch between the two types of
controllers. In the present formulation, the switches are
driven by events which, though asynchronous, can be
pre-scheduled, in the sense that they depend on the
subdivision into lines and arcs of the a-priori known
reference path. Yet, the sequence of the switches, in
contrast to the sequence of the events, cannot be a-priori
scheduled. In fact, the occurrence of a switch between a
line tracking controller and an arc tracking controller is
constrained by the fact that the vehicle steering angle is
required to be a continuous variable. Then, the time
instant where the switch between two different types of
controllers takes place can be different from the time
instant when the event consisting of the passage from a
line to an arc of the reference path is scheduled.
Taking into account these considerations, the
proposed control system can be regarded as a true hybrid
control system, in which the controller switches are
asynchronous and non predictable a-priori, as discussed
in the next sections.