IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 17, NO. 1, JANUARY 2009 135
Combined Automatic Lane-Keeping and Driver’s
Steering Through a 2-DOF Control Strategy
Vito Cerone, Member, IEEE, Mario Milanese, Senior Member, IEEE, and Diego Regruto, Member, IEEE
Abstract—In this paper, we address the problem of combining
automatic lane-keeping and driver’s steering for either obstacle
avoidance or lane-change maneuvers for passing purposes or any
other desired maneuvers, through a closed-loop control strategy.
The automatic lane-keeping control loop is never opened, and no
on/off switching strategy is used. During the driver’s maneuver,
the vehicle lateral dynamics are controlled by the driver himself
through the vehicle steering system. When there is no driver’s
steering action, the vehicle center of gravity tracks the center of the
traveling lane thanks to the automatic lane-keeping system. At the
beginning (end) of the maneuver, the lane-keeping task is released
(resumed) safely and smoothly. The performance of the proposed
closed-loop structure is shown both by means of simulations and
through experimental results obtained along Italian highways.
Index Terms—automatic lane-keeping, driver’s steering, lane-
change, two-degrees-of-freedom (2-DOF) control, vehicle lateral
control.
I. INTRODUCTION
I
NTELLIGENT vehicle systems (IVSs) have recently be-
come an attractive area of research throughout the world.
The aim of the research effort is mainly that of enhancing
driving safety and reducing the driver’s workload. In [1], the
positive effect of driver assistance systems on drivers’ physical
and mental workload reduction is shown through the measure
of some vital reactions such as the electromyographic and
the electrodermal activities. In particular, automated highway
systems (AHS), which have been extensively studied at Ohio
State University since 1964 [2], are receiving renewed attention
due to fast developments in hardware/software technology that
stimulate the design of more effective control systems. Since
the mid-1980s, a larger effort is being conducted mainly in
the California PATH program. Early attempts of the project
were devoted to assess previous knowledge in the field of
automatic vehicle control providing the analytical basis for
new developments [3]. In the last several years, large efforts
have been directed to the solution of the highway automatic
steering control problem for different types of vehicles and
using different control strategies and techniques. Most of the
Manuscript received March 09, 2007; revised October 31, 2007. Manuscript
received in final form April 10, 2008. First published June 13, 2008; current
version published December 24, 2008. Recommended by Associate Editor
A. Stefanopoulou. This work was supported in part by the Italian Ministero
dell’Istruzione, dell’Università e della Ricerca (MIUR) under the plan “Control
of advanced systems of transmission, suspension, steering and braking for the
management of the vehicle dynamics” and by Centro Ricerche Fiat (CRF)
under Contract “Analisi e sintesi di nuove architetture di controllo laterale per
il mantenimento della corsia di marcia di un autoveicolo.”
The authors are with the Dipartimento di Automatica e Informatica, Po-
litecnico di Torino, 10129 Torino, Italy (e-mail: vito.cerone@polito.it; mario.
milanese@polito.it; diego.regruto@polito.it).
Digital Object Identifier 10.1109/TCST.2008.924558
contributions rely on buried magnet or electrified wires placed
along the path for the detection of the vehicle lateral position,
the so-called
look down sensing scheme. The problem, in the
case of passenger cars, was analyzed in this framework by
Patwardhan et al. in [4], where they show the fundamental
control difficulties of this approach. An interesting alterna-
tive approach, that avoids the modification of infrastructures,
involves the use of vision sensors placed on the vehicle, the
so-called look-ahead sensing scheme. A comparative study of
vision-based control strategies was presented by Ko
ˇ
seckà et
al. in [5]. A great deal of remarkable works about application
of advanced linear and nonlinear control techniques to the
automatic steering control problem were conducted, still in
the PATH program, by Tomizuka and coworkers in the case
of four wheeled vehicles in [6], heavy vehicles in [7] and [8],
and tractor–semitrailer combinations in [9], while in [10] and
[11] the problem of designing a fault-tolerant lane-keeping
controller for automated vehicles has been considered. In
recent years, the problem of steering control has attracted wide
interest also outside the PATH program. Relevant contributions
in the field of robust steering and vehicle lateral dynamics
control were also provided by Ackermann and coworkers (see,
e.g., [12] and [13]). Preliminary experimental results on robust
lateral control conducted by Byrne et al. were reported in
[14], highlighting several implementation difficulties. Adaptive
steering control for lane-keeping of a tractor–semitrailer has
been proposed by Wang et al. in [15], while a model-predictive
control strategy for lateral control of autonomous vehicles
has been considered in [16]. Other contributions based on the
look-ahead sensing scheme were provided by Hatipo
ˇ
glu et al.
in [17], where they used a digital videocamera together with a
radar system, by Broggi et al. [18], who used a stereo vision
system composed of two videocameras, and by Cerone et al.
[19]–[21], where properties of single-input two-output (SITO)
systems are exploited. Significant Japanese contributions to the
development of vision-based intelligent vehicles, given since
the mid 1970s to the early 1990s, are surveyed by Tsugawa
[22].
Some of the advanced maneuvers pertaining to vehicle lat-
eral control are lane changing for vehicle-passing purposes and
obstacle avoidance. The problem of automated lane-change ma-
neuvers is widely addressed in the literature. In [17], [23], and
[24], for example, the authors consider open-loop and closed-
loop lane-change and design time optimal steering controllers
with nonlinear constraints. First, they generate a special open-
loop lane-change steering signal which minimizes the period of
lane-change subject to constraints on the lateral acceleration and
jerk. Then, they discuss how to implement those steering com-
mands in the closed-loop system using a lane-following con-
troller previously published. We point out that autonomous lane
1063-6536/$25.00 © 2008 IEEE
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136 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 17, NO. 1, JANUARY 2009
change deals with the generation of the appropriate steering
signal to have the vehicle accomplish the task without driver
assistance.
In this paper, we address the problem of combining auto-
matic lane-keeping and driver’s steering for either obstacle
avoidance or lane-change maneuvers for passing purposes or
any other desired maneuvers through a closed-loop control
strategy. The proposed control strategy is designed assuming
that the vehicle is traveling along highway paths. First, in
Section II, we present the physical plant and derive a suit-
able simplified model focusing on the accordance between
simplification hypotheses and experimental context. Then,
in Section III, we formulate the control problem. Further, in
Section IV, we propose a two-degree-of-freedom (2-DOF)
closed-loop control strategy that gives a solution to the formu-
lated problem. The automatic lane-keeping control loop is never
opened, and no on/off switching strategy is used. During the
driver’s maneuver, the vehicle lateral dynamics are controlled
by the driver himself through the vehicle steering system.
When there is no driver steering action, the vehicle’s center
of gravity tracks the center of the traveling lane thanks to the
automatic lane-keeping system. At the beginning (end) of the
maneuver, the lane-keeping task is released (resumed) safely
and smoothly. Both simulation and experimental results along
Italian highways, obtained with the proposed 2-DOF structure
on a FIAT Brava 1600 ELX provided by Centro Ricerche Fiat,
are presented and discussed in Sections V and VI, respectively.
II. P
LANT DESCRIPTION AND
MODELING
The plant to be controlled, provided by Centro Ricerche
Fiat, consists of a Fiat Brava 1600 ELX equipped with a vision
system and a steering actuator. The vision system comprises a
single CCD videocamera and related image-processing algo-
rithms. The steering actuator system is a locally controlled dc
brushless electric motor. Both control and vision algorithms
are processed by an INTEL 486 microprocessor-based PC
for industrial applications. The sampling time of the whole
system is
ms. The described hardware is not supposed
to be modifiable by the control designer. The mathematical
modeling of such a plant was discussed in detail in [19], in
which a simplified model that is suitable for the description of
the vehicle behavior in highway experimental conditions was
presented. The equations of such a model are recalled here
for self-consistency of the paper. The interaction between the
vehicle lateral dynamics and the vision system can be modeled
by the following state space equations parameterized by the
longitudinal velocity
:
(1)
Fig. 1. Feedback signal
y
.
Fig. 2. Centerline linear approximation supplied by the vision system.
where is the so-called look-ahead distance, taken along the
longitudinal axis, from the vehicle center of gravity to a suit-
able point in the road between 3–20 m ahead of the vehicle
(see Fig. 1),
is the road curvature, i.e., the inverse of
the instantaneous curve radius at the look-ahead point,
is the
steering-wheel angle, and
and are the measurements sup-
plied by the vision system about the vehicle location on the lane,
as shown in Fig. 2. The meanings of the symbols involved are
vehicle mass;
longitudinal component of center of gravity (CG)
velocity;
transverse component of CG velocity;
vehicle yaw angle;
inertial vehicle moment around center of gravity referred
to the vertical axis;
steering-wheel angle;
front wheels angle/steering-wheel angle ratio, expressed
in rad/degrees;
: front wheels angle;
cornering stiffness of front tires;
cornering stiffness of rear tires;
distance between the rear axle and the center of gravity;
distance between the front axle and the center of gravity;
: wheelbase;
;
;
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CERONE et al.: COMBINED AUTOMATIC LANE-KEEPING AND DRIVER’S STEERING THROUGH A 2-DOF CONTROL STRATEGY 137
Fig. 3. Plant block diagram.
;
;
;
.
The steering actuator, given by Centro Ricerche Fiat, is de-
scribed by the following transfer function:
(2)
where
is the reference steering angle due to the sum of (pro-
vided by the lateral dynamics controller) and
(i.e., the effect
of the torque
applied by the driver on the steer), as can be
seen in Fig. 3. The transfer function between the torque
ap-
plied by the driver on the steer and the reference steering angle
is denoted by
(see Fig. 3). The bandwidth of is
supposed to be wider than the bandwidth of the control system
to be designed; from available data, it can be assumed that, in
the working frequency range, a static gain
can be
used to describe the behavior of
. The transfer function of
the nominal plant to be controlled is
, where
is the position error of the vehicle with re-
spect to the lane centerline measured at the look-ahead distance
(see [19] for a detailed discussion about the advantages of
using such a quantity as feedback signal in lane-keeping con-
trol systems). The value of the look-ahead distance
has to
be carefully chosen taking into account the specific behavior of
the vehicle to be controlled (e.g., understeering behavior, over-
steering behavior, neutral steering behavior, etc.). In the exper-
imental tests performed with the vehicle under consideration,
we noted that the increase of
improves comfort performances
though it tends to cause large lateral position error at the center
of gravity (CG) when a curve is approached. The experimental
results presented in this paper were obtained with
m.
Although such a value, obtained through trial and error, pro-
vides good results for the specific vehicle considered in this
study, we remark that the problem of choosing the value of
may require deeper analysis in the general case. Most of the
early contributions in the field of steering control were based on
the use of reduced-order nominal models like the one presented
above, sometimes considering the effect of the longitudinal ve-
locity variations (see, for example, [25]). In recent years, works
have been presented where the attention is focused on the model
uncertainty (see, e.g., [12], [14], [13], and [7]). Looking at the
proposed model, it can be noted that some unmodeled linear
and nonlinear dynamics are present in the actual plant like, for
example, roll, yaw, and heave effects neglected by the single
TABLE I
V
ALUES OF MODEL PARAMETERS
track model, steering gear backlash, or actuator voltage com-
mand saturation. Moreover, the system has a time-varying na-
ture due to parametric dependence on longitudinal velocity
and, finally, some parameters of the simplified model cannot be
exactly known. Thus, all of these sources of uncertainty should
be taken into account in the controller design. However, it can be
noted that unmodeled dynamics are little excited along highway
paths, which are characterized by bends with large radii re-
quiring slow steering actions, while highway longitudinal ve-
locity variations are typically slow. Thus, all considered, the
following parametric uncertainties have been considered. The
vehicle mass
can take values from 1226 kg (nominal value)
to 1626 kg, corresponding to the mass of a vehicle with five pas-
sengers, each one weighting 80 kg, on board. The inertial mo-
ment
can vary coherently from 1900 kg m to 2520 kg m .
The cornering stiffness coefficients
and range respectively
between [51000, 69000] N/rad and [81600, 110400] N/rad. Fi-
nally, the velocity is handled as an uncertain parameter whose
value belongs to [60, 120] km/h. The nominal values of the pa-
rameters
and the corresponding
parameter uncertainty intervals
are sum-
marized in Table I. The uncertain system generated by the given
parameter uncertainty intervals can be represented by the fol-
lowing model set:
(3)
where
is the vector of the uncertain
parameters and
.
III. C
ONTROL PROBLEM
FORMULATION
The problem we are dealing with in this paper is the design
of a closed-loop control system able to keep the vehicle inside
the lane along typical highway paths and to permit any interven-
tion on the side of the driver in order to override the automatic
lane-keeping system and obtain complete control of the vehicle
lateral dynamics. In other words, we aim at a combined auto-
matic lane-keeping and driver’s steering through a closed-loop
control strategy. We assume that the automatic lane-keeping
system is available (see, e.g., [19]–[21]). In the paper, the terms
driver’s steering or driver’s maneuver mean any intervention
of the driver on the vehicle steering system in order to obtain
a desired behavior of the vehicle (for example, lane change for
passing purposes or obstacle avoidance) and, in general, when
it is desired to override the automatic lane-keeping and obtain
complete control of the vehicle lateral dynamics.
In the paper, it is assumed that all of the signals in the con-
trol loop are seamless. As a matter of fact, as is well known,
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138 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 17, NO. 1, JANUARY 2009
such an assumption is not always satisfied in practice since the
nonideal behavior of the vision sensor can affect the signal in-
tegrity in some particular situations (e.g., high exposure in the
CCD camera or high contrast items on the road). In addition,
the presence of vibrations and noise on the sensing system can
deteriorate the quality of the measured signal. Although such
complications should be carefully taken into account in order to
ensure that the system will work without fail, they will not be
explicitly considered in this work whose contribution is focused
on the development of a new control strategy to combine auto-
matic lane keeping and driver’s steering.
Control problem description—The following specifications
(S1)–(S5) concur in the definition of the control problem under
consideration, i.e., the design of a closed-loop control strategy
for combined automatic lane keeping and driver’s steering.
(S1) Before the driver’s steering action, the vehicle CG
tracks the center of the traveling lane thanks to the lane-
keeping control system.
(S2) At the beginning of the driver’s maneuver, the lane-
keeping task must be released safely and smoothly.
(S3) During the driver’s maneuver, the vehicle lateral dy-
namics are controlled by the driver himself through the ve-
hicle steering system.
(S4) At the end of the driver’s maneuver, the CG tracks the
center of the lane in which the vehicle is traveling and the
lane-keeping task must be resumed safely and smoothly.
(S5) A closed-loop control strategy is sought which com-
bines the automatic lane-keeping and the driver’s maneu-
vers, which means that the automatic lane-keeping control
loop is never opened, and no on/off switching strategy is
used.
Specification (S5) is introduced to guarantee the driver’s
safety. As a matter of fact, thanks to such a specification, the
lane-keeping control loop is never physically disconnected from
the plant. Therefore, if the driver accidentally loses control of
the steering wheel while performing a maneuver, the vehicle
will be kept inside the lane by the lane-keeping control loop.
IV. C
OMBINED AUTOMATIC
LANE-KEEPING AND
DRIVER’S STEERING
A. 2-DOF Structure
It is desired that the automatic lane-keeping control loop be
never switched off, i.e., the loop control be always active. Fur-
thermore, it is also specified that the transition between the au-
tomatic lane-keeping mode and the driver’s steering mode be
actuated without on/off switching strategy. In order to meet the
above requirements, we propose the 2-DOF structure of Fig. 4.
The feedback controller
is designed in order to satisfy au-
tomatic lane keeping specifications (see, e.g., [19]–[21]), while
is designed with the aim of combining the above described
two modes in a smoothly way.
B. Design of Controller
The guidelines for the design of controller are derived
from specifications (S1)–(S4), which describe the control
problem under consideration. More precisely,
must be
designed in such a way that the following conditions hold.
Fig. 4. Combined automatic lane-keeping and driver’s steering through a
2-DOF structure.
Condition (1): the vehicle lateral dynamics are controlled
by the automatic lane-keeping system when the torque
applied by the driver on the steer is negligible and
Condition (2): when the driver’s torque
on the steer is
different from zero, the vehicle behavior perceived by the
driver is as close as possible to the one of the vehicle
without automatic lane-keeping.
It is easily seen that the 2-DOF structure shown in Fig. 4 takes
care of condition (1). As a matter of fact, when
, the pro-
posed structure simplifies to a 1-DOF structure with regulation
to a zero reference signal, i.e., the automatic lane-keeping con-
trol system. In order to take care of condition (2), the following
result is given.
Result 1: Condition (2) holds if and only if (iff)
(4)
Proof:
Condition (2) implies that the transfer function
be zero, i.e.,
(5)
which in turn implies (4).
The converse is also true. If , then ,
and the automatic lane-keeping control loop is open.
C. Implementation Issues: Stability of
As can be seen from Fig. 4, is a cascade filter, thus it
must enjoy the stability property. While
is a constant scalar
transfer function (t.f.) and
is the stable actuator t.f., unfor-
tunately
shows two integrators responsible for instability.
Thus,
cannot be implemented in the form of (4). We imple-
mented the following stable approximation of
:
(6)
As can be seen, the double integrator contained in
is re-
placed by a couple of real poles
, and is chosen in
order to get an acceptable compromise between low-frequency
behavior approximation and settling time of the control system
step response. Results presented in the paper are obtained with
.
Remark: We point out that, if controller
is given by (4),
at least in principle a null signal error
is expected when the
driver’s torque
on the steer is different from zero. However,
there are a couple of reasons which lead to a nonperfect zero
.
First, the components of
, i.e., , and , are not ex-
actly known and can only be suitably approximated. Second, as
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CERONE et al.: COMBINED AUTOMATIC LANE-KEEPING AND DRIVER’S STEERING THROUGH A 2-DOF CONTROL STRATEGY 139
discussed above, only a stable approximation of can be im-
plemented. In practice, however, the presence of an error signal
slightly different from zero when does not compromise
the desired performance of the proposed control structure. The
only resulting drawback (which indeed might not be considered
as such) is the presence of an “opposing” torque “felt” on the
steer by the driver, which actually can be considered as a simu-
lation of the load due to the steering system.
D. Implementation Issues: Lane Change Maneuver
We recall that
is the measurement supplied by the vision
system about the vehicle location on the lane, as shown in Fig. 2.
Thus, during the lane-change maneuver, the vision system is
subject to a change in the measurement reference system: before
the maneuver
is measured with respect to the current lane, at
the end of the maneuver
is measured with respect to the new
lane. The transition from one lane to the next can be handled
by properly resetting the initial condition of controller
with
respect to the new measurement reference system. This can be
simply accomplished if one notes that, when the vehicle crosses
the line between two lanes, there is no loss of continuity in the
time evolution of the state variables
, and , while there is
a discontinuity in the state variable
, as large as the width of the
lane, due to the change of the measurement reference system.
Thus, in order to reset the controller, a realization is sought in
the state variables form, four of which are just the physical state
variables (
, and ) of the plant, whose model is
part of
. It can be easily shown that the controller reset can
be achieved by changing the sign of the state variable of
corresponding to the physical state variable .
E. Robustness Issues: Stability
In order to analyze the robustness of the proposed control
system, a suitable but conservative description of the uncertainty
generated by the considered parameters perturbation is provided
by the following model set expressed in the so-called input mul-
tiplicative form:
(7)
where
is the nominal plant, is a complex function
which represents the unknown modeling error, and
is a
known function bounding the modeling error. A description of
obtained gridding the hypercube is shown in Fig. 5
together with the upper bound
. As far as robust sta-
bility is concerned, the application of the Small Gain Theorem
to the block diagram of Fig. 4 leads to the following condition.
Result 2: The control system in Fig. 4 with
is robustly stable iff
(8)
where
is the norm of a system.
Result 2 shows that robust stability of the proposed control
scheme is not affected by the design of the filter
. The lane-
keeping controller
designed in [21] satisfies (8).
Fig. 5. Uncertainty
1
and weighting function
W
(solid line).
F. Robustness Issues: Performance
As far as robust performance is concerned, we are inter-
ested in evaluating the effect of the modeling error on the
main task of the proposed approach, expressed by (2), which
is equivalent to the condition
. The plant is
assumed to be described by the following uncertain model
where
is the additive unstructured modeling error. According to
the discussion of Section IV-C, the stable approximation
is considered for the feed-
forward filter
. First of all, in order to evaluate the
performance of the controlled system in the uncertainty-free
case, let us compute the transfer function
when
. Such a transfer function, called , is given by
(9)
where
is the sensitivity function of the
lane-keeping control loop. As expected,
since the ideal
of (4) has been approximated by the filter . However,
tends to 0 when the pole moves towards 0.
Then, let us compute the transfer function
in
the presence of the additive uncertainty
. The obtained
transfer function, called
, is given by
(10)
Finally, the effect of the uncertainty
on the closed-loop per-
formance can be quantified computing the difference between
and , called ,as
(11)
Thus, (11) shows that the effects of the modeling error
are
attenuated by the sensitivity function of the feedback loop. A
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