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DSC 2017 EuropeVR Van der El et al.
Measuring and Modeling Driver Steering Behavior:
From Compensatory Tracking to Curve Driving
Kasper van der El1, Daan M. Pool1, and Max Mulder1
(1) Delft University of Technology, Faculty of Aerospace Engineering, Control and Simulation section, Kluyver-
weg 1, 2629HS Delft, The Netherlands, e-mail: {k.vanderel, d.m.pool, m.mulder}@tudelft.nl
Abstract - Drivers rely on a variety of cues from different modalities while steering, but which exact cues are
most important and how these different cues are used is still mostly unclear. The goal of our research project is
to increase understanding of driver steering behavior; through a measuring and modeling approach we aim to
extend the validity of McRuer et al.’s crossover model for compensatory tracking to curve driving tasks. As part of
this larger research project, this paper first analyzes the four main differences between compensatory tracking and
curve driving: 1) pursuit and preview, 2) viewing perspective, 3) multiple feedback cues, and 4) boundary-avoidance
strategies due to available lane width. Second, this paper introduces multiloop system identification as a method
for explicitly disentangling the driver’s simultaneous responses to various cues, which is subsequently applied to
two sets of human-in-the-loop experimental data from a preview tracking and a curve driving experiment. The
results suggest that recent human modeling advances for preview tracking can be extended to curve driving, by
including the human’s adaptation to viewing perspective, multiple feedback cues, and lane width. Such a model’s
physically interpretable parameters promise to provide unmatched insights into between-driver steering variations,
and facilitate the systematic design of novel individualized driver support systems.
Keywords: curve driving, compensatory tracking, driver modeling, preview, system identification
Introduction
Today, driving is still a manual control task that re-
quires continuous attention and control from the hu-
man driver. Drivers manipulate the gas pedal, brakes,
and gears to change the vehicle’s forward velocity
(longitudinal control), and they use the steering wheel
to negotiate curves, change lanes, and supress dis-
turbances like wind gusts (lateral control). To ef-
fectively design individualized systems for autono-
mous driving or driver assistance, as currently pur-
sued [Abb11, Sal13, Gor15], it is essential to un-
derstand driver control behavior. However, humans
exhibit an extremely versatile set of control skills,
and it is safe to say that, today, many aspects of
driver control behavior are still poorly understood.
Even for lateral steering control in isolation (i.e., at
constant forward velocity), a wide variety of plau-
sible theories exist about drivers’ use of preview,
motion feedback, and path prediction. This is re-
flected by the fundamental differences in available
control-theoretic models of driver steering behavior
[McR77, Mac81, Hes90, Odh06, Sen09, Boe16].
Ideally, it would be desirable to have a universal mo-
del for driver steering behavior, similar to McRuer
et al.’s crossover model for compensatory tracking
tasks [McR67]. The crossover model has inputs and
control dynamics that resemble those of the actual
human. Its physically interpretable parameters can
be intuitively adapted, or explicitly estimated from ex-
perimental data, to predict human behavior in new
situations, to design human-machine interfaces, to
quantify human skill, and to explain observed beha-
vior. Unfortunately, the crossover model is only appli-
cable to the extremely limited single-axis, visual com-
pensatory tracking task (error-minimization). Drivers
likely adopt a complex internal control organization,
integrating a variety of cues from different modalities.
Moreover, opposed to continuous error-minimization,
driving is a boundary-avoidance task where, in prin-
ciple, any lateral position in-between the lane mar-
kings can be considered acceptable [McR77].
A fundamental issue in understanding and modeling
driver behavior is to determine which combination of
cues, or even sensory modalities (e.g., visual, vesti-
bular, proprioceptive) guide steering. Four fruitful ap-
proaches are: 1) eye-tracking to determine the dri-
ver’s visual focus of attention [Lan94, Kan09]; 2) re-
moval of cues (e.g., visual occlusion) in a simulator
environment to measure driver use of the remaining
cues in isolation [Don78, Lan95]; 3) theoretical as-
sessment to rank the usefulness of available cues
using control theory [Wei70] and visual field geome-
try [Wan00]; and 4) directly measuring the driver’s
control dynamics (i.e., input-output relation) using
system identification [McR75, Ste11]. All these me-
thods have their own strengths, but only multiloop
system identification allows for unambiguously disen-
tangling the driver’s simultaneous lumped response
to various cues, while also most directly providing
an experimentally validated mathematical model. To
date, multiloop system identification has never been
applied to study driver steering.
The goal of our research project is to obtain the much
needed fundamental insight into driver steering be-
havior, using a combination of all the four mentioned
approaches. We aim to quantify these new insights
-1-
K. van der El, D. M. Pool, and M. Mulder,
“Measuring and Modeling Driver Steering Behavior: From Compensatory Tracking to Curve Driving,”
Transportation Research Part F: Psychology and Behaviour , 2017.
DOI: 10.1016/j.trf.2017.09.011
Measuring and Modeling Driver Steering Behavior DSC 2017 EuropeVR
in a structurally-isomorphic model that extends the
validity of McRuer et al.’s crossover model to curve
driving tasks. As part of this larger research project,
in this paper we will explain the differences between
compensatory tracking and curve driving, and de-
monstrate the strength of multiloop system identifi-
cation for studying driver steering behavior.
First, we review McRuer et al.’s crossover model, to-
gether with the system identification techniques that
were used to obtain that model. Second, we explain
how we plan to move from compensatory tracking
to curve driving tasks, by stepwise introducing pre-
view, perspective viewing, visual rotational cues, op-
tic flow, vestibular motion, and two lane boundaries
(opposed to line-tracking). Next, we introduce a mul-
tiloop system identification technique, which is re-
quired to separately measure the multiple, simulta-
neously present human responses in these more ela-
borate tasks. Finally, we present experimental data
from two tasks with various preview times, to de-
monstrate the new, fundamental insight that our ap-
proach can provide about driving. The first task invol-
ved preview tracking, and the second task involved
full field-of-view visual curve driving.
Measuring and Modeling
Compensatory Tracking
Behavior
The Crossover Model
In compensatory tracking tasks, only a single task-
specific, instantaneous error is available to the hu-
man, for example representing the difference bet-
ween a vehicle’s desired and actual lateral position.
When the desired trajectory is unpredictable, humans
can only adopt a single-loop control organization,
known as compensatory tracking behavior [McR67],
see Fig. 1 and Fig. 2. In compensatory tasks, the
human’s control dynamics can be approximated with
a simple linear time-invariant model; nonlinear and
time-varying contributions are relatively small, and
are accounted for by a remnant “signal” (nin Fig. 1).
The crossover model is given by [McR67]:
Hoe(jω)Hce(jω) = ωc
jω e−j ωτe,(1)
and states that the human and vehicle dynamics
(Hoeand Hce, respectively) combined resemble an
integrator with a time delay τearound the crosso-
ver frequency ωc. A set of “Verbal Adjustment Ru-
les” quantifies the adaptation of the crossover mo-
del’s variables, τeand ωc, to task variables like the
vehicle dynamics and the forcing functions’ band-
width [McR67]. From Eq. 1 it follows that the human’s
control dynamics in the crossover region are:
Hoe(jω) = Ke
1 + TL,ejω
1 + Tl,ejω e−jω τe,(2)
with Kehumans’ control gain, and TL,e and Tl,e their
lead and lag equalization time constants, respecti-
vely, which are adapted to achieve the crossover mo-
del’s integrator dynamics around the crossover fre-
quency. Extensions of the crossover model to lo-
wer and higher frequency ranges typically include
a separate model for the neuromuscular system dy-
namics [McR68, Hes80]. The model parameters are
physically interpretable, which facilitates their intuitive
adaptation to predict behavior in new situations. Mo-
reover, the crossover model provides explicit quan-
titative insights into human adaptation and skill de-
velopment. Since its development in the 1960’s, the
crossover model has become an essential tool in the
research, design, and evaluation of human-machine
systems (e.g., see [McR69, Hes90, Poo16]).
System Identification
Measuring the human’s control dynamics in compen-
satory tracking tasks is relatively straightforward, be-
cause the human is organized as a single input (the
visual error) and single output (the steering wheel
rotations) controller. McRuer et al. [McR67] used
an instrumental variable, frequency-domain system
identification method to estimate the linear part of the
human’s control dynamics. This method relies on a
multisine external input signal (or forcing function),
the instrumental variable, which consists of a limited
number N(typically around 10) sine waves:
ft(t) =
N
X
i=1
Aisin(ωit+φi),(3)
with Aithe amplitude, ωithe frequency, and φithe
phase of the ith sinusoid. ftcorresponds to the desi-
red trajectory forcing function in Fig. 1, which can be
thought of as the road’s trajectory to be followed in
driving tasks. Alternatively, it is also possible to use a
multisine disturbance signal fd, which may resemble
wind gusts. At the input frequencies ωi, remnant is
negligibly small compared to the human’s response
to the forcing function, and the human’s linear control
dynamics can be approximated with:
ˆ
Hoe(jωi) = Sftu(jωi)
Sfte(jωi),(4)
with Sthe cross-power spectral density estimate of
the respective subscripted signals. The Nestimated
Fourier coefficients ˆ
Hoe(jωi)allowed for an explicit
look into the Hoeblock in Fig. 1, and enabled McRuer
et al. [McR67] to propose the crossover model.
From Compensatory Tracking to
Curve Driving
McRuer et al.’s [McR67] single-axis, visual compen-
satory tracking task is equivalent to a driving task
from which only the current lateral position error with
respect to the road’s center-line is perceived by the
driver. Clearly, drivers may additionally respond to
many other cues while negotiating curves. In our re-
search project we will stepwise introduce elements
from a curve driving task into the compensatory tra-
cking task, which is schematically shown in Fig. 2.
The four main differences between compensatory
tracking and curve driving will be discussed in detail
in this section: 1) pursuit and preview, 2) perspective
viewing, 3) multiple feedback cues, and 4) boundary
avoidance.
Step 1: Pursuit and Preview
In contrast with compensatory tracking tasks, dri-
vers that negotiate curves perceive cues that contain
-2-
DSC 2017 EuropeVR Van der El et al.
Hoe
Hot
Hox
+
−
+ +
+ +
+
pursuit pathways
−
+
compensatory loop
steer wheel
state, u
remnant, n
error, e
desired
trajectory, ftvehicle
dynamics
disturbances, fd
vehicle state, x
driver
Figure 1: Driver-vehicle control diagram that illustrates the possible driver responses, based on [McR67]. The single-loop
compensatory control organization is shown in black, while additional pursuit pathways are shown in gray. The driver’s possible
(proprioceptive) pursuit response on the steering wheel state uis not shown, because it is not considered in this paper.
e
τp
Step 1:
pursuit and
preview
t
τp
Step 2:
linear
perspective
t
State-of-the-Art:
compensatory
tracking
Step 3:
multiple feedback
cues
Step 4:
boundary
avoidance
Figure 2: Stepwise introduction of elements from a curve driving task (far right) into a compensatory tracking task (far left).
information about the desired trajectory ftand the
vehicle states x. Drivers can directly respond to
these signals, which is reflected by the Hotand
Hoxblocks in Fig. 1, and which is known as pur-
suit tracking [All79, Hes81]. Moreover, drivers can ty-
pically preview the road for some part ahead, yiel-
ding information about the future desired trajectory
ft([t, t +τp]), up to a certain preview time τp. The
additional information allows for an extremely wide
variety of acceptable steering behaviors, which is an
important reason why driver behavior is still poorly
understood.
First, with preview, drivers can anticipate the de-
sired trajectory, which allows them to compensate
for both their own response delays and other lags,
like those of the vehicle dynamics [Ito75, El17]. In
fact, with sufficient preview, drivers follow a desired
trajectory nearly perfectly [McL73, Mil76]. However,
how drivers exactly use preview has long remained
unclear, which is reflected by the many fundamen-
tally different ways in which driver models incorpo-
rate preview. Well-known driver models use either
one [McR77, Don78, Mac81], two [Sal04, Sal13], or
many [Mac81, Odh06] points from the previewed tra-
jectory ahead as input, together with any function
(e.g., lateral position, heading, or curvature) of that
desired trajectory.
Second, in pursuit tasks, drivers can also predict their
vehicle’s trajectory, because they have knowledge of
both the vehicle’s states and their own control in-
puts [Mac81, Odh06]. Similar as for driver use of pre-
view, it is yet unclear if, and how, drivers predict their
vehicle’s trajectory, which is again reflected by the
many different prediction mechanisms incorporated
in current driver models. Proposed driver prediction
mechanisms range from simple linear extrapolation
[Kon68, Wei70, Hes90] to elaborate optimization of
the driver’s own control inputs over a certain future
time span, using a model of the vehicle’s dynamics
[Mac81, Odh06].
In the first step of our research project, we investigate
pursuit and preview control behavior in laboratory tra-
cking tasks that closely resemble compensatory tra-
cking (see Fig. 2, Step 1). A plan-view of the pre-
viewed trajectory is shown together with the vehicle’s
lateral position. Using multiloop system identification
(explained in the next section), we estimate the hu-
man’s Hotand Hoxblocks; Hotshows how humans
use preview, while Hoxreveals if and how humans
predict the vehicle’s trajectory. Experimental results
of this task were recently published in [El16b, El17],
and will be reviewed in the final section of this paper.
Step 2: Perspective Viewing
The viewing perspective in normal driving tasks dif-
fers markedly from the plan-view preview tracking
task (Step 1). In driving, linear perspective introduces
anonlinear mapping between the visual cues on the
one hand, and the vehicle states and the desired tra-
jectory on the other hand; a plan-view display (ortho-
graphic projection) only involves a linear scaling, or
“gain”. This has two important consequences. First,
due to linear perspective the previewed trajectory
in driving tasks appears smaller with increasing dis-
tance ahead (see Fig. 2, Step 2), such that tracking
errors close ahead are visually emphasized. It has
never been explicitly investigated if and how linear
perspective evokes adaptations in human preview
control behavior, because this first requires a better
understanding of human preview control (Step 1).
Second, while the vehicle state (lateral position) is ex-
plicitly visible on the display in the plan-view tracking
-3-
Measuring and Modeling Driver Steering Behavior DSC 2017 EuropeVR
wheel
rotations, u
desired
trajectory, ft
vehicle
dynamics
disturbances, fd
vehicle
state, x
driver
perspective
cues, Φ
display /
perspective
Figure 3: Illustration of steering with perspective viewing.
tasks, a driver’s perspective view only shows this in-
formation implicitly, through the scenery ahead (like
in Step 3 in Fig. 2). Drivers must cognitively recons-
truct the vehicle’s lateral position relative to the road
using the perspective visual cues from the scenery
ahead, or, alternatively, directly use certain perspec-
tive visual cues to control their vehicle. For example,
a straight road’s perspective splay angle is directly re-
lated to the vehicle’s lateral deviation from the center-
line [Don78, Mul05]. For small deviations this rela-
tion is approximately proportional, so the splay angle
simply replaces the explicit lateral position cue that
is shown on the pursuit display in Step 1. For large
deviations, or on curved roads, the relation between
visual cues and the vehicle’s states is strongly nonli-
near [Mul04].
In perspective tasks, the assumption in Fig. 1 that
drivers respond directly to the vehicle states and the
desired trajectory is thus not necessarily valid. Ins-
tead, cues from the perspective visual scene are the
input to the human, and these are related to the
vehicle states by a (nonlinear) perspective transfor-
mation [Mul04, Mul05], see Fig. 3. Multiloop system
identification can still be applied to estimate the Hot
and Hoxblocks in Fig. 1, but yields the lumped dyna-
mics of the human and the perspective transforma-
tion together. The estimated lumped dynamics may
reveal which perspective cues are used by the hu-
man, as was shown in piloting tasks [Swe99]. Addi-
tional measurements (e.g., eye-tracking) can provide
supporting evidence for the actual inputs and control
organization adopted by the driver.
In the second step of our research project, we will
only investigate the effects of linear perspective on
human use of preview information. To do so, we will
perform the same preview tracking task as in Step 1,
but with a perspectively transformed previewed tra-
jectory (see Fig. 2, Step 2). In our research project
we will thus not pinpoint which perspective cues (like
splay angle) are actually used by the human; instead,
we will consider the lumped human and perspective
transformation dynamics together, essentially assu-
ming that humans have direct knowledge of the ve-
hicle states.
Step 3: Multiple Feedback Cues
The tasks discussed in Steps 1 and 2 involved only
visual lateral position feedback. Indeed, lateral po-
sition in the lane is a likely cue that guides stee-
ring during curve driving [Wei70, Lan95]. However,
most road vehicles have dynamics – from steering
input to lateral position – that consist of more than
two integrators [Raj11], such that continuous stabili-
zing control is required from the human, through lead
wheel
rotations
desired trajectory, ftdisturbances, fd
acceleration (vestibular)
path / heading (visual)
outer-loop response
(lateral position)
vehicle
dynamics
inner-loop
response
lateral position
driver
Figure 4: Illustration of a multiloop control organization.
equalization [McR67]. Weir and McRuer [Wei70] sho-
wed that the human can, and will, close an additio-
nal inner-loop to ease the (lead equalization) requi-
rements on the lateral-position outer-loop (see Fig. 4
for an illustration). Any cue that includes information
about the vehicle’s lateral velocity (i.e., lead on the
lateral position) or acceleration can be used as inner-
loop. Vestibular, proprioceptive, auditory and rotatio-
nal visual cues (e.g., path/heading angle and rate)
all contain such lead information. Note that none of
these cues are present in the tasks in Steps 1 and 2.
With multiloop system identification (see the next
section), the driver’s inner- and outer-loop control dy-
namics can in theory be explicitly measured and di-
sentangled, but this has never been done to date. As
such, in curve driving tasks, the exact roles of visual
cues like path and heading angle, and of non-visual
cues like motion feedback, are still poorly unders-
tood. In the third step of our research project, we in-
vestigate three situations that possibly evoke drivers
to close additional inner loops: 1) presence of physi-
cal motion feedback in the lateral position, plan-view
preview tracking task from Step 1; 2) introduce “ca-
mera” rotations that correspond to the vehicle’s hea-
ding changes, yielding visual heading and path cues
(see Fig. 2, Step 3); 3) increase the strength of the
path cues by increasing the visual flow (i.e., the tex-
ture density) to a level similar as in real driving tasks.
Step 4: Boundary Avoidance
The tasks up to Step 3 all required the human to fol-
low a well-defined signal, which is called tracking. Dri-
vers do not typically aim to continuously keep their
vehicle on the lane’s center-line, but instead steer
only when the vehicle laterally approaches the roa-
d’s edges [God86, Boe16]. This is called boundary
avoidance, and is known to evoke less aggressive
and intermittent (or “satisficing”) driver steering be-
havior [McR77, Boe16]. In the final step of our re-
search project we will extend the multiloop, perspec-
tive preview tracking task from Step 3 to a boundary-
avoidance, curve driving task (see Fig. 2, Step 4.
Due to drivers’ possibly intermittent steering beha-
vior, multiloop system identification (which assumes
time-invariant behavior) alone may not suffice to re-
veal all the subtle differences between tracking and
boundary-avoidance behavior. We intent to perform
additional time-domain analyses, and to take advan-
tage of recent advances in the modeling of intermit-
tent human steering behavior [Mar17].
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DSC 2017 EuropeVR Van der El et al.
Multiloop System Identification
The introduction of elements from curve driving tasks
allows humans to respond to multiple cues, or si-
gnals, instead of the single error signal in compen-
satory tracking tasks. To separately estimate the dy-
namics of multiple, simultaneously active human res-
ponse blocks, the single-loop system identification
technique, used by McRuer et al. [McR67] to derive
the crossover model, has been extended to multiloop
applications [Sta67, Paa98]. The maximum number
of human response blocks that can be estimated is
equal to the number of uncorrelated external forcing
functions. For example, to estimate both the human’s
Hotand Hoxpursuit blocks, two forcing functions are
needed. Realistic forcing functions can be a desired
trajectory ft(e.g., a winding road) and disturbances
fd(e.g., wind gusts). The correlation between the
driver’s steering output and each uncorrelated for-
cing function then allows for disentangling the two
driver response blocks. Two forcing functions can be
constructed to be uncorrelated by using multisines
(see Eq. 3) with mutually exclusive frequencies com-
ponents ωi[Sta67, Paa98].
Consider the scheme in Fig. 1, but without the dri-
ver’s possibly active Hoeresponse (at the end of this
section we explain why this simplification poses no
assumption on the actual driver’s behavior). The re-
sulting control diagram is given in Fig. 5. Neglecting
the human remnant at the multisine forcing function
input frequencies, we can write:
U(jωi) = Hot(jωi)Ft(jωi)−Hox(jωi)X(jωi),(5)
with capitals indicating the Fourier transform of the
respective signals. A second equation is needed to
solve Eq. 5 for the two unknown dynamics Hot(jωi)
and Hox(jωi). First, evaluate Eq. 5 only at the desi-
red trajectory’s input frequencies, ωt. Then, interpo-
late the signals U(jωd),Ft(jωd), and X(jωd)in the
frequency domain from the neighboring disturbance
signal input frequencies ωdto ωt, yielding ˜
U(jωt),
˜
Ft(jωt), and ˜
X(jωt), to obtain the following set of
equations:
U(jωt)
˜
U(jωt)=Ft(jωt)−X(jωt)
˜
Ft(jωt)−˜
X(jωt)Hot(jωt)
Hox(jωt),(6)
which can be solved for Hot(jωt)and Hox(jωt). Si-
milarly, after interpolating all signals from ωtto ωd,
Eq. 6 can also be evaluated at the disturbance signal
input frequencies to obtain Hot(jωd)and Hox(jωd).
Example multiloop system identification results are
shown in Fig. 5 and will be discussed in the next sec-
tion.
There are three situations in which not all driver res-
ponse pathways can be disentangled with multiloop
system identification. First, because the number of
meaningful forcing functions that can be defined is
limited, the number of driver response blocks that
can be separated is also limited. Second, blocks that
have the same input can never be disentangled; for
example, a simultaneous visual and vestibular res-
ponse to (derivatives of) the vehicle’s lateral position
can only be estimated together, as a lumped res-
ponse. Finally, due to the interdependency between
e,ftand x(e=ft−x), it is never possible to simulta-
neously estimate all three response blocks, Hot,Hox,
and Hoe. In any of these situations, more driver path-
ways are active than can be disentangled, and the
10-1 100101
10-1
100
101
near-viewpoint
far-viewpoint
ω, rad/s
|Hot|, -
10-1 100101
-360
-180
0
180
ω, rad/s
∠Hot, deg
10-1 100101
10-1
100
101
pursuit, non-par.
preview, non-par
ω, rad/s
|Hox|, -
10-1 100101
-360
-180
0
pursuit, model
preview, model
ω, rad/s
∠Hox, deg
ft(t)u(t)x(t)
n(t)fd(t)
+
+
vehicle
dynamics
+
−
Hox
Hot
driver
Figure 5: Illustration of estimated multiloop human
controller dynamics for a single subject in pursuit and
preview tracking tasks (gray/black markers), together with
the fitted preview model (solid lines), adapted from [El16b].
estimated driver dynamics will be lumped combina-
tions of all the actually active driver response blocks.
The active pathways that are not present in the iden-
tified model structure are not assumed to be absent,
but instead appear as “contamination” in the estima-
ted control dynamics. As we will see in the next sec-
tion, this limitation is not always problematic, because
the lumped estimate of the driver’s response dyna-
mics may reveal which modality, or pathway, was ac-
tive or dominant. Moreover, by our stepwise intro-
duction of driving-task elements into a compensa-
tory task, additional driver responses occur only gra-
dually, which facilitates the study of many separate
driver responses in isolation.
Results
In this section, we demonstrate the usefulness of
multiloop system identification for studying driver
steering behavior. First, we review results of a pursuit
and preview tracking experiment (Step 1), which were
recently published in [El16b]. Second, we present our
first data from a simulator-based curve driving expe-
riment (Step 4).
Preview Tracking (Step 1)
Only recently, multiloop system identification was ap-
plied for the very first time to measure the human’s
Hot(jω)and Hox(jω)control dynamics in pursuit and
preview tracking tasks [El16b]. Subjects were pre-
sented with the display in Fig. 2, Step 1 (10 cm outer
radius), on a screen directly in front of them, while
control inputs were given with a side stick. Tasks
involved 0 s (pursuit) and 1 s of preview, both of
-5-
Measuring and Modeling Driver Steering Behavior DSC 2017 EuropeVR
e⋆(t)
ft(t+τn)
u(t)x(t)
n(t)
fd(t)
ft(t+τf)
f⋆
t,f (t)
f⋆
t,f
ft(t)
e⋆(t)
+
+
+
+
+
−
x(t)
τ
Knjω
1+Tl,nj ω
Kf1
1+Tl,f jω
equalization physical
limitations
human controller / driver
Hoe⋆
delay and
neuromuscular
vehicle
dynamics
use of preview
“compensatory” model
near viewpoint
far viewpoint
Kf= far-viewpoint gain
Tl,f = far-viewpoint lag time-constant
τf= far-viewpoint look-ahead time
Hoe⋆=Ke⋆
1+TL,e⋆jω
1+Tl,e⋆jω
e⋆= internal error
ft,f⋆= filtered far-viewpoint
Kn= near-viewpoint gain
Tl,n = near-viewpoint lag time-constant
τn= near-viewpoint look-ahead time
Figure 6: Control diagram for preview tracking tasks, derived using multiloop system identification in [El16b].
which were repeated with gain, single- and double-
integrator vehicle dynamics. The desired trajectory
and disturbance signals had a bandwidth of 1.5 rad/s
and a highest frequency components of 16 rad/s.
Multiloop identification results for a single subject
are reproduced in Fig. 5. The observed dynamics in
each response block were first modeled separately
[El16b], after which common elements were regrou-
ped and the block diagram was rearranged to obtain
a novel model that reflects human controllers’ most
likely control organization (see Fig. 6).
This new model for preview tracking tasks extends
McRuer et al.’s model for compensatory tracking
tasks with two responses to the previewed trajec-
tory ahead. A far viewpoint, located τfs ahead (ty-
pically 0.6-2 s), provides a preshaped, smoothed tra-
jectory input to a “compensatory” error response.
The “error” e⋆responded to by the human is thus
not the true error, but a time advanced, cognitively
determined internal error signal. Humans use the
far-viewpoint response mechanism only to track the
low frequencies (i.e., slow changes) in the desired
trajectory, so the model includes a low-pass smoo-
thing filter, characterized by time constant Tl,f (typi-
cally 0-1 s). Gain Kf(typically 0.5-1.2) reflects the
human’s priority to track the previewed trajectory;
when Kf=0 the human completely ignores the de-
sired trajectory and focuses only on stabilizing the
vehicle, while high values of Kfindicate a high prio-
rity for trajectory-tracking. The near viewpoint, loca-
ted τns ahead (typically 0.1-0.9 s), is the input to an
open-loop feedforward response. Humans can use
this near-viewpoint response to better track the hi-
gher frequencies (quick changes) in the desired tra-
jectory [El17], which are not followed well with the
far-viewpoint response mechanism. However, not all
Table 1: Experimental preview times τpand the human’s
estimated far-viewpoint look-ahead times τf.
preview tracking curve driving
[El16a] [Ste11]
τp, s τf, s τp, s τf, s
0.00 0.05 0.36 0.03
0.25 0.18 0.72 0.82
0.50 0.38 1.08 1.14
1.00 1.01 7.20 1.50
subjects were found to apply a near-viewpoint res-
ponse, and the near-viewpoint response is less pro-
nounced when less preview is available, or when the
order of the vehicle dynamics increases [El17].
Following the development of this new preview mo-
del, we performed a second preview tracking expe-
riment to investigate how humans adapt their control
behavior to the preview time τp[El16a]. This expe-
riment was preformed only with integrator vehicle dy-
namics, and with six preview times between 0 and 1 s
(of which four are reproduced here, see Tab. 1). Fig. 7
shows the multiloop system identification results for
Hot(jω)and Hox(jω), together with the least-squares
fit of the model to the measurement data. Higher pre-
view times clearly evoke more phase lead in the hu-
man’s response to the desired trajectory, which is
captured in the model mainly by the far-viewpoint
look-ahead time τf. Tab. 1 shows that the estima-
ted value of τfindeed increases when more preview
becomes available. The human subject kept the far
viewpoint approximately at the end-point of the pre-
viewed trajectory, regardless of the amount of pre-
view available. Note that the estimated far viewpoint
position is occasionally slightly beyond the available
preview limit, because the estimated values are affec-
ted by the noise in the system (i.e., human remnant).
Curve Driving (Step 4)
As a start to Step 4, we recently performed a first
curve driving experiment, also with various preview
times [Ste11]. The driving task was performed at
a constant forward velocity of 50 km/h, in a fixed-
base simulator with a 180 deg field-of-view visual
screen. Moreover, opposed to the preview tracking
task from Step 1, the task involved perspective vie-
wing, visual yaw rotational cues (i.e., path and hea-
ding), “bicycle model” vehicle dynamics, and two lane
edges (boundary avoidance); control inputs were gi-
ven with a steering wheel, and the highest frequency
component in the desired trajectory and disturbance
signals was 6.5 rad/s. Fig. 2, Step 4 shows the pre-
sented visuals.
Because, at this point, we lack understanding of hu-
man adaptation to the discussed differences bet-
ween our curve driving and preview tracking task, we
fit exactly the same preview tracking model to the
curve driving data. Note that the bicycle model ve-
hicle dynamics used in [Ste11], which approximate a
double integrator from steering wheel inputs to late-
ral position, required substantial lead equalization in
-6-
DSC 2017 EuropeVR Van der El et al.
10-1 10010110-1 10010 1
10-1
100
101
ω, rad/s
|Hot|, -
curve driving (CD)
preview tracking (PT)
10-1 10010110-1 10010 1
10-1
100
101
ω, rad/s
|Hox|, -
curve driving (CD)
preview tracking (PT)
10-1 10010110-1 10010 1
-180
0
180
360
ω, rad/s
∠Hot, deg
PT: τp=0.00 s, CD: τp=0.36 s
PT: τp=0.25 s, CD: τp=0.72 s
PT: τp=0.50 s, CD: τp=1.08 s
PT: τp=1.00 s, CD: τp=7.20 s
curve driving (CD)
preview tracking (PT)
10-1 10010110-1 10010 1
-360
-180
0
ω, rad/s
∠Hox, deg
curve driving (CD)
preview tracking (PT)
Figure 7: Estimated multiloop human control dynamics for a single subject, together with fits of the preview model, for a preview
tracking (PT) [El16b] and a curve driving (CD) task [Ste11].
the human’s internal error response Hoe⋆(jω)to ob-
tain integrator open-loop dynamics around crossover
[McR67, El16b]. The near-viewpoint response was
excluded from the model, as the desired-trajectory
forcing function did not contain the high-frequency
components at which the near-viewpoint response is
active in preview tracking tasks [El16b].
The estimated Hot(jω)and Hox(jω)dynamics in the
driving task are shown in Fig. 7, together with the
model fits. Longer preview times evoke a highly si-
milar adaptation of the Hot(jω)response dynamics
as seen in preview tracking tasks; namely, more
phase lead and a lower response magnitude at the
higher input frequencies. More phase lead shows
that the subject better anticipates the desired tra-
jectory, while a lower response magnitude indicates
that more of the trajectory’s high frequencies are
ignored (i.e., trajectory smoothing or corner cutting).
Tab. 1 shows that the estimated value of τfincreases
with increasing preview time (similar as for preview
tracking), and stabilizes around 1.5 s when abun-
dant preview is available. This suggests that drivers
do not use preview information beyond 1.5 s ahead
(about 20 m at 50 km/h), which is consistent with the
control theoretical optimum [Mil76], empirical findings
that use occlusion [McL73, Lan95] and eye-tracking
data [Kon68, Lan94].
Fig. 7 also shows that the preview model does not
perfectly capture the shape of the estimated driver
dynamics. The estimated Hot(jω)and Hox(j ω)dy-
namics in the driving task are likely a lumped com-
bination of multiple driver responses. While the mul-
tiloop system identification results do show exactly
how curve driving behavior differs from preview tra-
cking behavior, separate experiments are needed to
attribute these adaptations to the viewing perspective
(Step 2), additional feedback cues (Step 3), the lane
width (Step 4), or even other, more subtle differences
between the two tasks. Nonetheless, the effect of
preview time on driver behavior is already captured
quite well by the preview tracking model. The model’s
τfparameter, which reflects the human’s look-ahead
time, allows for unique quantitative insight into driver
adaptation, as well as a direct comparison to tracking
data. We expect that extending the preview model to
curve driving tasks will further add to this insight.
Conclusions
In this paper, we presented an approach to bring
the applicability of the crossover model for human
compensatory tracking behavior to curve driving
tasks. Differences between compensatory tracking
and curve driving were divided into four main catego-
ries: 1) pursuit and preview, 2) viewing perspective, 3)
multiple feedback cues, and 4) boundary avoidance.
Multiloop system identification was shown to be a
valid method to separately measure multiple, simul-
taneously present human responses, which recently
led to the extension of the crossover model to pur-
suit and preview tracking tasks. The preview tracking
model provides new insight into driver adaptation to
the preview time in curve driving tasks, but, in its cur-
rent form, does not fully capture driver steering dyna-
mics. We aim to extend the preview model to curve
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Measuring and Modeling Driver Steering Behavior DSC 2017 EuropeVR
driving in future work, by studying human adaption to
the viewing perspective, multiple feedback cues, and
boundary avoidance. This new model’s physically in-
terpretable parameters can yield unmatched insights
into between-driver steering variations, and facilitate
the systematic design of novel individualized driver
support systems.
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