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Due to linear perspective, the visual stimulus provided by a previewed reference trajectory reduces with increasing distance ahead. This paper investigates the effects of linear perspective on human use of preview in manual control tasks. Results of a human-in-the-loop tracking experiment are presented, where the linear perspective's horizontal and vertical deformations along the previewed trajectory were applied separately and combined, or were absent (plan-view task). Measurements are analyzed with both nonparametric and parametric system identification techniques, in combination with a quasi-linear human controller model for plan-view preview tracking tasks. Results show that reduced visual stimuli in perspective tasks evoke less aggressive control behavior, but that the human's underlying control mechanisms are still accurately captured by the model. We conclude that human controllers use preview information similar in plan-view and perspective tasks.
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IEEE TRANSACTIONS ON HUMAN-MACHINE SYSTEMS 1
Effects of Linear Perspective on
Human Use of Preview in Manual Control
Kasper van der El, Student Member, IEEE, Daan M. Pool, Member, IEEE,
Marinus (Ren´
e) M. van Paassen, Senior Member, IEEE, and Max Mulder
Abstract—Due to linear perspective, the visual stimulus pro-
vided by a previewed reference trajectory reduces with increasing
distance ahead. This paper investigates the effects of linear per-
spective on human use of preview in manual control tasks. Results
of a human-in-the-loop tracking experiment are presented, where
the linear perspective’s horizontal and vertical deformation along
the previewed trajectory were applied separately and combined,
or were absent (plan-view task). Measurements are analyzed
with both nonparametric and parametric system identification
techniques, in combination with a quasi-linear human controller
model for plan-view preview tracking tasks. Results show that
reduced visual stimuli in perspective tasks evoke less aggressive
control behavior, but that the human’s underlying control mech-
anisms are still accurately captured by the model. We conclude
that human controllers use preview information similar in plan-
view and perspective tasks.
Index Terms—Linear perspective, man-machine systems, man-
ual control, parameter estimation, preview, system identification
I. INT ROD UC TI ON
HUMANS rely heavily on visual information in many
manual control tasks. An important visual cue is pre-
view, information about the future reference trajectory, or
target, to follow. Examples of preview include the road ahead
when driving [1]–[3] or cycling [4], and an artificially dis-
played tunnel-in-the-sky when piloting a helicopter [5] or
aircraft [6]. Preview enables humans to apply feedforward
control to anticipate upcoming trajectory changes [7].
To study the human controller’s (HC) use of preview
information, simplified tracking tasks are often performed with
a plan-view (i.e., two-dimensional or top down) display [8]–
[12]. Removal of all other control-related cues, like physical
motion and optic flow, then allows for explicit measuring and
identification of the HC’s response to preview information.
Recent modeling efforts [11] and subsequent analysis [12]
suggested that HCs apply a dual-mode control strategy: open-
loop control based on a point on the target close ahead, the
“near” viewpoint, and closed-loop control based on a point
farther ahead, the “far” viewpoint.
The novel preview model from [11] extends McRuer et
al.’s [13], [14] famous crossover model for compensatory
tracking; as such, it may facilitate a similar structured, quanti-
tative approach to design and evaluate human-machine systems
(e.g., interfaces), but for more realistic control tasks. However,
general vehicle control tasks differ markedly from the preview
The authors are with the Control and Simulation section, Faculty of
Aerospace Engineering, Delft University of Technology, 2629 HS Delft, The
Netherlands. Corresponding author: k.vanderel@tudelft.nl
tracking experiments in [8]–[12], as the target trajectory is
often viewed from a point within the visual scene, like a
camera on a remote vehicle or the human eye. First, due to
linear perspective, the previewed target trajectory appears in-
creasingly compressed with distance ahead, while the target in
the plan-view tracking experiments is displayed equally large
nearby and far ahead. Second, the visual flow field provides
additional cues of the viewpoint’s rotations and translations
[15], [16]. The HC’s excellent adaptive capabilities [13], [17]
make it difficult to predict if and how these two factors affect
HC behavior.
In this paper, we focus on the effects of linear perspective,
because the reducing visual stimuli from the target farther
ahead, and the corresponding magnification of parts nearby,
may severely affect the near- and far-viewpoint responses
adopted by the HC. On the one hand, it was shown in
compensatory tracking tasks that smaller visual stimuli evoke
less aggressive control behavior and larger response time-
delays [18], [19]. This would suggest that the HC’s response to
preview far ahead, which is strongly affected by perspective,
will be weaker in perspective tasks (compared to plan-view
tasks). On the other hand, perception research has shown that
the human’s visual system compensates visual stimuli with
simultaneously sensed depth cues [20]; as such, HC perception
(and hence control) of a previewed target might still be equal
in plan-view and perspective tasks.
Perspective displays have been extensively studied, and
applied, as they allow for intuitive three-dimensional spatial
information transfer (e.g., see [21]–[23]). Unfortunately, these
studies did not measure – and thus did not increase our
understanding of – the HC’s underlying control behavior. The
HC’s control dynamics were measured in other perspective
control tasks, like driving and flying, but these tasks lacked
preview information [18], [24], or did not explicitly reveal
the effects of linear perspective on the HC’s near- and far-
viewpoint responses [1], [2], [4], [6], [25].
The goal of this paper is to explicitly quantify how lin-
ear perspective affects HC use of preview information, and
specifically the near- and far-viewpoint response mechanisms.
Measurements from a human-in-the-loop experiment are an-
alyzed, in which eight subjects performed a tracking task
with integrator controlled element (CE) dynamics, and 2 s of
preview. The preview was shown either in plan-view, or with
the horizontal and vertical perspective deformations along the
previewed trajectory applied separately, as well as combined.
First, objective measures are calculated to quantify tracking
performance, control activity, and coherence. Next, a non-
K. van der El, D. M. Pool, M. M. van Paassen, and M. Mulder,
“Effects of Linear Perspective on Human Use of Preview in Manual Control,”
IEEE Trans. on Human-Machine Systems, 2017.
DOI: 10.1109/THMS.2017.2736882
2 IEEE TRANSACTIONS ON HUMAN-MACHINE SYSTEMS
Xw
Yw
Zw
a
b
U
V
CE output xd(t)
previewed
target
current target fd
t(t)
τ
p
ub
va
τ
a,
(a)
Xw
Yw
Zw
a
b
U
V
CE output xd(t)
previewed
target
current target fd
t(t)
τ
p
ub
va
τ
a
(b)
90°
10°
220 m
60 m
30 m / 2 s
Xw
Yw
Zw
viewpoint / COP
viewing axis / Xv
previewed target
side view
(c)
Fig. 1. Plan-view (a) and perspective (b) preview displays, obtained by viewing the target from points “90/220 m” and “10/60 m”, respectively (c).
parametric, multiloop, frequency-domain system identification
method is applied [26], and the parameters of the HC model
for plan-view preview tracking tasks from [11] are estimated.
The obtained HC dynamics and model parameters explicitly
characterize how HCs adapt their control behavior between
plan-view and perspective tasks.
This paper is structured as follows. In Section II we in-
troduce the preview control task and linear perspective. In
Sections III and IV we elaborate on our methods: the HC
model for plan-view preview tracking tasks from [11], the
applied system identification techniques, and the performed
experiment. Results are presented in Section V, followed by a
discussion and our main conclusions in the final two sections.
II. PR EV IE W TRAC KI NG A ND LI NE AR PE RS PE CT IV E
A. The Control Task
In this paper, we consider a single-axis, lateral position
tracking task. The HC is required to minimize the lateral
tracking error e(t), which is the difference between the target
signal ft(t)and the CE output x(t):
e(t) = ft(t)x(t),(1)
at current time t. The HC gives control inputs u(t)to the
CE, which is simultaneously perturbed by a disturbance signal
fd(t). The task, illustrated in Figs. 1 and 2, is thus two-fold:
target tracking and disturbance rejection.
In preview tracking tasks, the target ahead ft([t,t+
τ
p]) is
visible up to preview time
τ
p. A plan-view of the previewed
target is shown in Fig. 1a; this view corresponds to looking
straight down from a point high above the previewed tar-
get (i.e., 90elevation in Fig. 1c). Due to the viewpoint’s
movement parallel to world frame axis Xw, the previewed
ed(t)u(t)x(t)
fd(t)
fd
t([t, t +τp])
xd(t)
ft(t)human
controller side-stick controlled
element
display
Fig. 2. The HC in a target-tracking and disturbance-rejection task.
target moves down over the screen and forces the current
target (cross) left and right. Note that, in a forced-pace
(fixed velocity) task as we consider, time and distance are
linearly related, so all signals can be written with time as the
independent variable without loss of generality.
The same scene observed from 10elevation yields a
perspective view (see Fig. 1b). Viewed from this particular
point, the displayed target trajectory is compressed in verti-
cal display direction Vand magnified in horizontal display
direction U. Vertical display coordinate vais much smaller on
the perspective display than on the plan-view display, for the
same point aon the previewed target
τ
as ahead. Horizontally,
the display coordinate ubis larger on the perspective display
for any arbitrary point bon the previewed target. Clearly, the
displayed signals ( fd
t,ed, and xdin Fig. 2), hence the visual
stimuli from the previewed target, are markedly different in
plan-view and perspective tasks.
B. Perspective Projection Method
Central projection is a technique to map a three-dimensional
visual scene to a two-dimensional display surface [27]. The
basic principle is similar to that of a camera, which produces
a picture (i.e., a two-dimensional representation) of a three-
dimensional visual scene. The center of projection (COP),
or viewpoint, is the location from which the visual scene is
supposedly observed (see Fig. 3). Light rays, or projectors,
emanate from each point in the visual scene to converge
in the COP. When a certain viewplane is defined at finite
distance
κ
from the COP, the intersection of passing light-
rays with this viewplane yields a two-dimensional image:
the perspective projection. Alternatively, when
κ
is infinite, a
parallel projection is obtained, yielding a plan-view. The COP
is the origin of the view reference frame (superscript v), with
the central viewing axis Xvdefining the viewing direction. The
boundaries of the visualized volume are characterized by the
horizontal and vertical field of view (FOV):
HFOV =2arctan w
2
κ
,VFOV =2arctan h
2
κ
,(2)
VAN DER EL et al.: EFFECTS OF LINEAR PERSPECTIVE ON HUMAN USE OF PREVIEW IN MANUAL CONTROL 3
viewplane
U
VXv
Yv
Zv
Ow
Ow
Xw
Yw
Zw
COP
COP
VRP
VRP
κ
κ
h
h
w
w
a
a
ad
ad
Xw,Yw,Zw
Xv,Yv,Zv
U,V
world frame origin
world frame axis
view frame axis
display axis
center of projection
view reference point
distance COP-VRP
viewplane width
viewplane height
arbitrary point
displayed point
Fig. 3. The perspective projection method and its principal terminology.
with wand hthe viewplane’s width and height, respectively.
For an arbitrary point ain the visual scene, the corresponding
viewplane coordinates uaand vaare obtained from:
ua=
κ
yv
a
xv
a
,va=
κ
zv
a
xv
a
,(3)
with xv
a,yv
aand zv
athe coordinates of point ain the view
reference frame.
C. Perspective Display Gains
HC task performance depends on the appearance of a
perspective scene, as demonstrated by Kim et al. [21] for
three-axis pursuit tracking tasks. It is possible to use the
perspective projection’s parameters (like FOV and elevation)
to compare the appearances of perspective scenes; however,
when analyzing HC behavior, it is more convenient to express
perspective deformations as display scaling gains, as a function
of time
τ
along the previewed trajectory ahead. In horizontal
display direction, we define display gain Kd,u(
τ
)as the ratio
of the display and world coordinates of an arbitrary point ain
the visual scene:
Kd,u(
τ
) = ua(
τ
)
yw
a(
τ
).(4)
In vertical display direction, we define gain Cd,v(
τ
)as the ratio
of the displayed and real (i.e., in world coordinates) lengths
of an element with length d
τ
as:
Cd,v(
τ
) = va(
τ
+d
τ
)va(
τ
)
yw
a(
τ
+d
τ
)yw
a(
τ
).(5)
Notations Kand Care adopted to emphasize the task’s
controlled and non-controlled directions: HCs can only control
the CE laterally, so in horizontal display direction.
As an example, consider the situation in Fig. 1c: a target
trajectory is visible for 30 m ahead, corresponding to 2 s of
preview at a velocity of 15 m/s. Fig. 4 shows the display
gains for all four COP’s, for a
κ
of 75 cm. Looking straight
down from 220 m height, each point on the previewed target
is approximately equally far away from the COP, yielding a
near-uniform scaling in both horizontal and vertical display
directions with a ratio of 1:
κ
/220, or 1:0.0035 (black solid
lines in Fig. 4). This projects the 30 m of preview to about
10 cm on the display, which corresponds roughly to the plan-
view preview tracking task in [11] and [12]. Fig. 4 shows that a
0 0.5 1 1.5 2
0.000
0.005
0.010
0.015
0.0
0.5
1.0
τ
, s
relative Kd,u, -
absolute Kd,u, -
(a)
0 0.5 1 1.5 2
0.000
0.005
0.010
0.015
τ
, s
90/220 m
90/60 m
10/220 m
10/60 m
immersed
tethered
absolute Cd,v, -
(b)
Fig. 4. Horizontal (a) and vertical (b) display scaling gains for various
viewpoints, as a function of time
τ
along the previewed trajectory ahead.
smaller object distance (i.e., moving the COP down vertically)
yields higher display gains in both directions (gray solid line).
For large object distances this magnification is nearly uniform,
as all points of the previewed target remain approximately
equally far from the COP.
Viewed from a non-vertical elevation, the object distance to
the nearer part of the previewed target (small
τ
) is smaller than
that of far parts (large
τ
). Therefore, the horizontal and vertical
display gains will be larger for near points compared to far
points, as illustrated for an elevation angle of 10in Fig. 4
(black and gray dashed lines). This effect is more pronounced
when the COP is closer to the previewed target, because the
relative difference in object distance between near and far parts
increases.
Fig. 4 also shows the display gains for an immersed and a
tethered viewpoint, for a
κ
of 5 cm. The immersed viewpoint
corresponds to a view from a car or bicycle, at 1 m height
above the start of the previewed target (at
τ
=0 s), yielding
display gains that are a strong nonlinear function of
τ
(black
dash-dotted line). The display gains increase asymptotically
to infinity for points close ahead (small
τ
), as these parts
are outside the (forward aimed) viewing volume. A tethered
viewpoint located 3.5 m above and behind the start of the
previewed target yields similar display gains, but with the near
points still in sight (gray dash-dotted line). Our experiment
will include the display gains from this tethered view. For
comparison, the right axis in Fig. 4a shows the horizontal
display gains relative to that of the tethered view at
τ
=0 s.
III. HUM AN CO NT ROL LE R MOD EL IN G AN D SYS TE M
IDE NT IFI CATI ON
To investigate how linear perspective affects HC use of
preview information, we analyze the experimental data with
system identification techniques, in combination with a quasi-
linear cybernetic model. This approach is explained here.
A. HC Model for Plan-view Preview Tracking Tasks
The HC model for plan-view preview tracking tasks
from [11] is shown in Fig. 5, together with a display model.
The display gains Kd,u(
τ
)scale the previewed target horizon-
tally at the indicated time
τ
ahead. The relative display gains
are used, such that the CE output x(t)(located at
τ
=0 s) has
unity scaling, as Kd,u(0)=1. It is mathematically equivalent to
4 IEEE TRANSACTIONS ON HUMAN-MACHINE SYSTEMS
e(t)u(t)
n(t)
human controller
Hnmseτv
Hof
Hon
Hoe
+
+
+
+
+
use of
preview
controlled
element
equalization
physical
limitations
Kd,u(τn)
display
fd
t(t+τn)
fd
t(t+τf)
xd(t)
Kd,u(τf)
1
ft(t+τn)
ft(t+τf)
x(t)
Fig. 5. Control diagram of the HC model for preview tracking tasks, adapted from [11] and augmented with a simple display model.
use the absolute display gains from Fig. 4, but this changes
the interpretation of the gains in the HC model and makes
comparisons with previous work less straightforward.
The HC model extends McRuer et al.’s [13], [14] crossover
model for compensatory tracking tasks, with two viewpoints
on the previewed target as inputs. It was found that this
two-viewpoint model structure is sufficient to account for
the HC’s total response to a previewed target [11], [12].
A far-viewpoint ft(t+
τ
f)is the input to a feedback model
for compensatory control behavior (similar as in the model
by Modjtahedzadeh & Hess [28]), while a near-viewpoint
ft(t+
τ
n)is the input to a parallel, additive open-loop response.
The near- and far-viewpoints are located
τ
nand
τ
fs ahead on
the previewed target, respectively. The model is quasi-linear,
so linear functions describe most of the HC’s behavior. Neither
nonlinear and time-varying behavior, nor perception and motor
noise are explicitly modeled; these are injected together as
filtered white noise through the remnant n(t).
Central to the model is the feedback response to an internal
error e(t): a hypothetical, cognitively calculated signal, which
cannot be measured. Fig. 5 shows that e(t)is the difference
between the target in the far viewpoint, low-pass filtered by
Hof(j
ω
), and the CE output:
E(j
ω
) = Hof(j
ω
)Fd
t(
τ
f,j
ω
)Xd(j
ω
).(6)
The signals written in capitals denote the Fourier transform
of the respective time domain signals, and Hof(j
ω
)is the
following low-pass filter:
Hof(j
ω
) = Kf
1
1+Tl,fj
ω
.(7)
The time constant Tl,fcharacterizes the bandwidth of the far-
viewpoint response. It models the HC’s cognitive elimination
of the target signal’s high frequencies from the far-viewpoint
response, facilitated by the preview [12]. Gain Kfreflects
the HC’s ability to respond relatively more aggressive to the
target (Kf>1) or to the CE output (Kf<1). When Kf=1 and
Tl,f=
τ
f=0 s, (6) and (7) show that e(t) = e(t), so that the
HC responds to the real error.
The internal error response Hoe(j
ω
)is identical to McRuer
et al.’s [14] simplified precision model:
Hoe(j
ω
) = Ke1+TL,ej
ω
1+Tl,ej
ω
,(8)
with Kethe error response gain, and TL,eand Tl,ethe lead
and lag equalization time constants, respectively. In compen-
satory tracking tasks, humans apply only proportional control
when the CE has integrator dynamics [13] (as considered in
this paper); however, estimated human control dynamics in
preview tasks point to some low-frequency lag-lead equaliza-
tion [11], [12].
At the target signal’s high frequencies the far-viewpoint
response is attenuated by the low-pass filter in Hof(j
ω
). Here,
HCs predominantly apply open-loop control, which is captured
in the model by the near-viewpoint response Hon(j
ω
). A gain
Knwith a differentiator generally suffices to describe these
control dynamics [12]:
Hon(j
ω
) = Knj
ω
.(9)
A near-viewpoint response is not always clearly present in
preview tasks, and some HCs do not apply this control
mechanism at all [11], [12].
The model also includes the HC’s main physical limi-
tations. Visual response time-delay
τ
vcombines perceptual,
cognitive and transport delays, while Hnms(j
ω
)represents the
combined side-stick and HC neuromuscular system (NMS)
dynamics [29]:
Hnms(j
ω
) =
ω
2
nms
(j
ω
)2+2
ζ
nms
ω
nms j
ω
+
ω
2
nms
,(10)
with
ω
nms and
ζ
nms the natural frequency and damping ratio.
B. Nonparametric System Identification
The HC dynamics can be objectively estimated without
making any assumptions, besides the model’s inputs and
outputs, using a nonparametric system identification method
based on Fourier coefficients [26]. The resulting estimates,
called describing functions, can validate the parametric model
structure from the previous section.
1) Forcing Functions: Nonparametric system identification
allows for the estimation of an equal number of describing
functions as there are uncorrelated external inputs, called
forcing functions [30]. To closely resemble common control
tasks, only two forcing functions can be inserted in the
considered preview tracking task: a target and a disturbance.
By choosing multisine forcing functions (here with 20 sines
each) high signal-to-noise ratio’s are obtained at the input
frequencies:
ft(t) =
20
i=1
At[i]sin(
ω
t[i]t+
φ
t[i]),(11)
fd(t) =
20
i=1
Ad[i]sin(
ω
d[i]t+
φ
d[i]),(12)
VAN DER EL et al.: EFFECTS OF LINEAR PERSPECTIVE ON HUMAN USE OF PREVIEW IN MANUAL CONTROL 5
with amplitude A[i], frequency
ω
[i]and phase
φ
[i]of the ith
sinusoid (see Section IV for the values used in the experiment).
Selecting different input frequencies for the target and distur-
bance is sufficient for these two signals to be uncorrelated.
2) Model Restructuring: The two forcing functions allow
for the identification of only two describing functions, so the
model in Fig. 5 must first be converted to a two-channel model.
The structure in Fig. 6 is convenient, as it separates the target-
to-control dynamics Hu
ft(j
ω
)from the CE-output-to-control
dynamics Hu
x(j
ω
)[11], [12]. These dynamics can be expressed
in terms of the HC dynamics and the display gains using block
diagram algebra (for details, see [11]):
Hu
ft(j
ω
) =Kd,u(
τ
f)Hof(j
ω
)Hoe(j
ω
)e
τ
fj
ω
+Kd,u(
τ
n)Hon(j
ω
)e
τ
nj
ω
Hnms(j
ω
)e
τ
vj
ω
,(13)
Hu
x(j
ω
) =Hoe(j
ω
)Hnms(j
ω
)e
τ
vj
ω
.(14)
Note that the HC dynamics and the display gains must be
lumped in (13) and (14), as the visual stimulus provided by the
perspectively transformed, displayed target fd
tis unsuitable for
linear frequency-domain analysis. The HC and display gains
in (13) can be lumped together into effective gains:
Kn,e f f =Kd,u(
τ
n)Kn,Kf,e f f =Kd,u(
τ
f)Kf,(15)
to easily compare results from plan-view and perspective tasks.
3) Multiloop Describing Function Estimation: Using
Fig. 6, the control output can be written as:
U(j
ω
) = Hu
ft(j
ω
)F
t(j
ω
)Hu
x(j
ω
)X(j
ω
) + N(j
ω
).(16)
A second equation is required to solve for the two unknown
describing functions. Evaluating (16) only at the target signal
input frequencies
ω
t, a second equation can be obtained by
interpolating the measured signals (U,F
t,X) in the frequency
domain from the disturbance input frequencies
ω
dto these
same
ω
t(indicated by ˜
U,˜
F
t,˜
X). Neglecting the remnant,
which is small compared to the HC’s response to the forcing
functions at the input frequencies, it follows that [11], [26]:
U(j
ω
t)
˜
U(j
ω
t)=F
t(j
ω
t)X(j
ω
t)
˜
F
t(j
ω
t)˜
X(j
ω
t)Hu
ft(j
ω
t)
Hu
x(j
ω
t).(17)
Solving (17) for Hu
ft(j
ω
t)and Hu
x(j
ω
t)yields the describing
function estimates at
ω
t. Replacing
ω
tby
ω
din (17), and
interpolating all signals from
ω
tto
ω
d, yields the describing
functions at
ω
d. The method’s complete derivation was pub-
lished in [11], [26], [30]; examples of successful identification
of HC behavior are found in [11], [12], [16], [30].
ft(t)
x(t)
Hce
fd(t)
u(t)
n(t)
+
+
+
+
+
Hu
ft
Hu
xdisplay &
human
Fig. 6. Two-channel model used for system identification purposes; the
display and HC models are lumped.
C. Parameter Estimation and Model Fitness
1) Parameter Estimation: The HC model’s parameters can
be estimated in the frequency domain by minimizing a crite-
rion Jthat is based on the difference between the measured
and the modeled control outputs [12]:
J(ˆ
Θ) =
Nl
l=1
|U(j
ω
l)ˆ
U(j
ω
l|Θ)|2.(18)
The modeled output ˆ
U(j
ω
l|Θ)is given by (16) with
remnant N=0; the model parameter vector Θis
[Kf,e f f
τ
fTl,fKn,e f f
τ
nKeTL,eTl,e
τ
v
ω
nms
ζ
nms]T.
Nlis the number of measured frequencies below a chosen
cut-off frequency, here 25 rad/s. A Nelder-Mead simplex
algorithm is often used to minimize J, constrained only
to avoid solutions with negative parameters. Selecting the
best solution from many randomly initialized optimizations
(here we use 100) yields a high chance to find the global
minimum. In a second step, the display gains Kd,u(
τ
)can be
calculated at the estimated
τ
nand
τ
f, which can then be used
to calculate the HC gains Knand Kfwith (15).
2) Variance Accounted For (VAF): The VAF is a measure
for the similarity of two signals; its maximum, 100%, indicates
that two signals are equal. When applied to compare the
measured and the modeled control output the VAF inherently
quantifies the model’s ability to describe the measured HC
behavior [31]. Because a signal’s variance is equal to its
integrated power-spectral density, the VAF can be calculated
as follows:
VAF =
1
Ns1
l=0
P
ε
u
ε
u(l
ω
b)
Ns1
l=0
P
uu(l
ω
b)
×100%,(19)
with Nsthe number of samples in the measured time-traces
and
ω
bthe fundamental radial frequency. Pis the estimated
periodogram of the subscripted signals, and
ε
uis the difference
between the measured and modeled control outputs:
ε
u(j
ω
) = U(j
ω
)ˆ
U(j
ω
|Θ).(20)
3) Coherence: The coherence is a measure for the linear
relationship between two signals. A high coherence between
the external input signals and the HC’s control output can jus-
tify using a quasi-linear HC model to analyze the experimental
data [31]. The value of the coherence is always between 0 (no
linear relation) and 1 (perfect linear relation). The coherence
Γftubetween the target signal and the control output is given
by:
Γftu(˜
ω
t) = s|˜
Pftu(˜
ω
t)|2
˜
Pftft(˜
ω
t)˜
P
uu(˜
ω
t),(21)
The tilde indicates the average periodogram between the
neighboring frequencies in a double band of input frequen-
cies [31]. The coherence between the disturbance input signal
and the HC output is calculated similarly.
6 IEEE TRANSACTIONS ON HUMAN-MACHINE SYSTEMS
IV. THE EX PE RI ME NT
A. Independent Variables
The experiment had two independent variables, namely hor-
izontal and vertical display scaling. Each had two levels: con-
stant (plan-view) and perspective scaling. This design allows
to investigate the difference in HC behavior between plan-view
and perspective tasks, while separating the individual effects
of horizontal and vertical perspective deformations. The full
factorial of the two independent variables was tested, yielding
four conditions: 1) constant scaling, or no perspective (NP),
2) horizontal perspective with constant vertical scaling (HP),
3) vertical perspective with constant horizontal scaling (VP),
and 4) horizontal and vertical perspective combined (HVP).
The applied perspective scaling was in accordance with
the tethered view in Fig. 4, so the entire previewed target
was visible on the display. The plan-view’s vertical scale was
set to 5.08 cm/s of preview, which was similar as in [11]
and [12], and corresponds to the “90/220 m” condition in
Fig. 4. The plan-view had unity horizontal scaling, equal to
the tethered view at
τ
=0 s (see Fig. 4), yielding an equally
large displayed error ed(t)in all four conditions; thereby, any
measured changes in control behavior must be due to linear
perspective. Pictures of all four displays are shown in Fig. 7,
video’s that further illustrate the conditions are available at
http://ieeexplore.ieee.org.
B. Control Variables
1) Controlled Element: The CE had integrator dynamics,
Hce(j
ω
)=1.5/s, with its gain of 1.5 tuned such that the
operator could give accurate inputs, but would not reach the
stick deflection limits during a normal run.
(a) (b)
(c) (d)
Fig. 7. Layout of the four experimental displays: NP (a), HP (b), VP (c), and
HVP (d); the grid was not visible during the experiment.
2) Display: The display showed the previewed target tra-
jectory and the CE output in white, on a brown background.
Grid lines, as included in Fig. 7 for clarification, were not
shown. The CE output (circle) was a two-dimensional overlay,
so subjects could only distinguish between conditions from the
previewed target.
3) Preview Time: The visual preview time
τ
pwas set to 2
s, well beyond reported critical preview times for integrator
CE dynamics [8]–[10].
4) Forcing Functions: The target and disturbance signals’
input frequencies were chosen such that an integer number
kof their sinusoid periods exactly fitted the measurement
time of 120 s. Double bands of input frequencies were used,
to allow calculation of the coherence. The bandwidth of
both signals was approximately 1.5 rad/s, above which the
sinusoids’ amplitudes were attenuated 20 dB. The target and
disturbance signals standard deviations were 1.27 cm and
0.508 cm, respectively. Five different realizations of the target
signal were used during the experiment to prevent subjects
from remembering it, after repeated exposure. All forcing
function parameters are given in Table I.
C. Apparatus
The experiment was conducted in the fixed-base part-task
simulator at TU Delft, Faculty of Aerospace Engineering.
Subjects were seated directly in front of the screen on which
the display was shown, at a distance of approximately 75
cm. The screen was 36 by 29.5 cm, had a resolution of
1280 by 1024 pixels, and an update rate of 100 Hz. The
image generator time delay was in the order of 20-25 ms.
To generate control inputs, subjects used an electro-hydraulic
servo-controlled side-stick, positioned at their right-hand side.
It had a moment arm of 9 cm and could only rotate around its
roll axis. The side-stick’s torsional stiffness was 3.58 Nm/rad,
its torsional damping 0.20 Nm·s/rad, its mass moment of
inertia 0.01 kg·m2, and its gain 0.44 cm/deg.
D. Subjects and Experimental Procedure
The experiment was performed by eight motivated, male
volunteers; their tracking experience ranged from novice to
experienced. We explained that the experimental goal was to
investigate the effect of linear perspective on HC behavior,
without giving further information about the individual con-
ditions. Subjects were simply instructed to track the target as
well as possible, hence to always minimize the current tracking
error e(t). They were informed of their rights and agreed to
these by signing a consent form.
The experiment was divided in two sessions of two con-
ditions. Each session took place on a different day to reduce
fatigue effects. To get subjects accustomed with the task and
the displays, each condition was practiced at least twice before
the measurements were started. Then the conditions were
presented to the subjects in an order dictated by a balanced
Latin-Square design. When stable performance was achieved
in a condition, generally after three to eight (128 s long) runs,
the five actual measurement runs were recorded, after which
subjects moved on to the next condition. On the second day,
VAN DER EL et al.: EFFECTS OF LINEAR PERSPECTIVE ON HUMAN USE OF PREVIEW IN MANUAL CONTROL 7
TABLE I
FOR CIN G FU NCT IO NS PAR AME TER S,FI VE TAR GET S IG NAL S AND O NE D IST URB ANC E SI GNA L.
target signals ftdisturbance signal fd
i, - kt, - At, cm
ω
t, rad/s
φ
t,1, rad
φ
t,2, rad
φ
t,3, rad
φ
t,4, rad
φ
t,5, rad kd, - Ad, cm
ω
d, rad/s
φ
d, rad
1 2 0.630 0.105 5.017 5.185 2.676 4.473 4.483 5 0.252 0.262 0.939
2 3 0.630 0.157 4.313 0.570 1.602 1.772 2.604 6 0.252 0.314 2.487
3 8 0.630 0.419 0.000 1.297 3.207 0.721 4.614 11 0.252 0.576 5.016
4 9 0.630 0.471 3.158 4.984 5.360 0.904 4.954 12 0.252 0.628 1.985
5 14 0.630 0.733 6.193 4.283 5.540 1.954 0.557 18 0.252 0.942 1.359
6 15 0.630 0.785 0.044 2.953 4.250 2.709 3.057 19 0.252 0.995 1.105
7 26 0.630 1.361 0.257 5.641 4.175 0.208 4.215 31 0.252 1.623 4.734
8 27 0.630 1.414 0.650 2.567 6.001 5.051 5.770 32 0.252 1.676 1.821
9 40 0.063 2.094 3.791 4.138 2.878 1.891 3.604 58 0.025 3.037 4.937
10 41 0.063 2.147 0.290 6.022 5.151 2.129 3.005 59 0.025 3.089 5.563
11 78 0.063 4.084 2.651 1.896 3.165 0.190 5.865 93 0.025 4.869 4.183
12 79 0.063 4.136 2.236 4.554 6.094 5.892 1.513 94 0.025 4.922 0.350
13 110 0.063 5.760 4.384 4.724 3.065 1.727 2.292 128 0.025 6.702 5.330
14 111 0.063 5.812 2.281 1.166 4.500 1.281 4.865 129 0.025 6.754 4.830
15 148 0.063 7.749 2.039 3.571 0.499 4.448 1.819 158 0.025 8.273 6.123
16 149 0.063 7.802 4.257 0.384 2.712 1.652 1.398 159 0.025 8.325 3.631
17 177 0.063 9.268 3.665 4.293 4.570 5.477 1.165 193 0.025 10.105 5.327
18 178 0.063 9.320 1.511 4.202 2.161 0.959 2.601 194 0.025 10.158 5.996
19 220 0.063 11.519 2.355 0.843 4.464 4.042 2.919 301 0.025 15.760 2.593
20 221 0.063 11.572 1.286 5.611 3.022 1.221 2.209 302 0.025 15.813 3.733
all four conditions were practiced once before the final two
conditions were tested.
After each run the subjects were informed of the root-mean-
square of their tracking error in that run, to motivate them to
optimize their performance. The total experiment lasted about
3.5 hours per subject, approximately evenly distributed over
the two sessions. In-between each two conditions a 15 minute
break was taken to further reduce fatigue effects.
The time-traces of the error e(t), the CE output x(t), and
the operator’s control actions u(t)were recorded during the
experiment with a sampling frequency of 100 Hz. From the
128 s of each of the recorded time-traces only the last 120 s
were used for our analysis; the first 8 s, which contained most
of the subjects’ transient response, were used as run-in time.
E. Dependent Measures
First, time-traces of the control output were used to compare
control behavior between conditions. Second, the variances of
the error
σ
2
eand the control output
σ
2
uwere used as measures
for tracking performance and control activity, respectively.
Third, the coherence was used as a measure for the linearity
of the subjects’ response. Fourth, the nonparametric describing
functions were used to compare HC behavior in the frequency
domain. Fifth, the describing functions were compared to
the model fits to validate the model’s ability to describe
the measured HC dynamics. Sixth, the VAF was used as a
second measure for the model’s fitness. Finally, the subjects’
control behavior was quantified using the estimated model
parameters, the response gains Knand Kf, and the vertical
display coordinate vresponded to.
F. Data Processing
The error and control output variances and the coherence
were calculated per run. Before applying system identifica-
tion, all signals were averaged over the five runs in the
frequency domain to reduce the remnant contribution in the
estimates [26]. Statistics were used to test for significant
effects on the error and control output variances, and the
model parameters. To reflect within-subject effects only, 95%
confidence intervals were calculated after removing between-
subject variability, by compensating each subject’s data both
with that subject’s mean over the four condition and the
grand mean over all subjects. A repeated-measures two-way
ANOVA was used to deal with the experiment’s two cate-
gorical independent variables: horizontal and vertical display
scaling. Each dependent measure was analyzed with a separate
test. For some measures, the collected samples in specific
conditions were not normally distributed, thereby violating
the normality assumption for parametric statistical tests. With
no nonparametric equivalent test for a two-way repeated-
measured ANOVA, and ANOVAs’ known robustness against
violations of the normality assumption [32], the ANOVA was
still performed.
G. Hypotheses
Due to linear perspective, the previewed target trajectory
ahead is horizontally compressed by Kd,u(
τ
)(see Section II).
Considering that the task involves lateral control, HCs can
adapt to horizontal perspective by increasing their control
gains Knand Kf. Although ideally the HC inverts the display
gains (so the closed-loop dynamics remain equal as in plan-
view tasks), subjects in compensatory control tasks increased
their control gains insufficiently to compensate for smaller
displayed errors, while also increasing their response delay
τ
v[18], [19]. Therefore, we hypothesize that:
I: From constant to perspective horizontal scaling, HCs
increase their response gains Knand Kf, but insufficiently
8 IEEE TRANSACTIONS ON HUMAN-MACHINE SYSTEMS
to invert the display gain (Kn,e f f and Kf,e f f decrease);
HCs also increase their response delay
τ
v[18], [19].
Due to linear perspective, the previewed target ahead is also
compressed vertically, by Cd,v(
τ
). Assuming that this vertical
compression does not affect perception, we hypothesize that:
II: With and without vertical perspective scaling HC behav-
ior is similar: subjects select the same two viewpoints
on the previewed target ahead (characterized by
τ
nand
τ
f); due to the perspective transformation, however, these
correspond to other vertical display coordinates v.
V. EXPERIMENTAL RES ULTS
A. Nonparametric Results
1) Control Output: Fig. 8 shows representative time-traces
of the measured control outputs. At low frequencies (slow,
large amplitude oscillations) the control outputs are similar in
all conditions, but at high frequencies (fast, small amplitude
oscillations) the control outputs have different amplitudes and
are out-of-phase.
2) Performance and Control Activity: Fig. 9 shows the
tracking performance and control activity, the corresponding
ANOVA results are given in Table II. Overall, task perfor-
mance is good, considering that the target signal’s variance
was 1.61 cm2. The total tracking performance decreases signif-
icantly when either horizontal or vertical perspective is added
to the plan-view task (NP). However, when horizontal perspec-
tive is already present and vertical perspective is added (HP to
HVP), performance improves (significant interaction effect).
The total control activity is slightly lower when horizontal
perspective is present (not significant).
At the disturbance input frequencies (black bars in Fig. 9),
both performance and control activity are identical in all condi-
tions (although some differences are significant, see Table II).
At the target and remnant frequencies performance drops
markedly with horizontal perspective, while control activity
decreases at the target frequencies and increases at the remnant
frequencies (all significant effects); this suggests that subjects
apply a less consistent and less effective control strategy.
Similar as for the total performance, vertical perspective has
a negative effect on performance at the target and remnant
frequencies when added to plan-view tasks (NP to VP), but a
positive effect when horizontal perspective is already present
(HP to HVP; significant interaction effect).
52 54 56 58 60 62
-12
-6
0
6
12
t, s
u(t), deg
NP
HP
VP
HVP
Fig. 8. Measured control outputs for a representative subject, single run data.
0.00
0.05
0.10
0.15
0.20
NP HP VP HVP
σ
2
e, cm2
target
disturbance
remnant
(a)
0
2
4
6
8
10
NP HP VP HVP
σ
2
u, deg2
(b)
Fig. 9. Variances of the error (a) and the control output (b), mean of all
subjects; errorbars indicate 95% confidence intervals.
TABLE II
ERRO R AN D CON TRO L OUT PU T ANOVA RE SULT S.1
horizontal vertical hor.×vert.
NV F sig. F sig. F sig.
total 0 174 ** 8.04 * 180 **
target 1 29.0 ** 21.4 ** 30.4 **
disturb. 0 1.04 - 0.01 - 6.28 *
error, e
remnant 1 49.6 ** 2.04 - 36.5 **
total 2 4.18 - 0.44 - 6.55 *
control target 0 49.0 ** 0.40 - 1.97 -
output, udisturb. 0 2.47 - 21.5 ** 11.0 *
remnant 3 49.0 ** 0.40 - 1.97 -
1NV is the number of samples that violate the Lilliefors normality test
(p< .05). Symbols **, *, and - indicate the result is highly significant
(p< .01), significant (p< .05), and not significant ( p> .05), respectively.
Degrees of freedom (df) is always (1,7).
3) Coherence: The average coherence (Fig. 10) between
the input signals and the control output is often close to 1,
and always above 0.7. The closed-loop human-machine system
is thus predominantly linear, even in perspective tasks, which
justifies using a quasi-linear model to analyze the experimental
data. Especially at frequencies below 2 rad/s the coherence
is high. Here, the input signals’ amplitudes were large (see
Section IV) and well visible, allowing for little observation
noise. At higher frequencies, the input signals’ amplitudes
were 10 times smaller; consequently, more observation noise is
present and the coherence drops. With horizontal perspective
scaling, the displayed excursions are attenuated even more
along the previewed target ahead, yielding a lower coherence
10−1 100101
0.7
0.8
0.9
1.0
ω
, rad/s
Γftu, -
(a)
10−1 100101
0.7
0.8
0.9
1.0
ω
, rad/s
NP
HP
VP
HVP
Γfdu, -
(b)
Fig. 10. Coherence between the target (a) and disturbance (b) input forcing
functions, and the HC control outputs; mean of all subjects.
VAN DER EL et al.: EFFECTS OF LINEAR PERSPECTIVE ON HUMAN USE OF PREVIEW IN MANUAL CONTROL 9
10-1 100101
10-1
100
101
NP
HP
VP
HVP
HNP
ox+1/Hce
ω
, rad/s
|Hu
ft(j
ω
)|, -
10-1 100101
10-1
100
101
ω
, rad/s
|Hu
x(j
ω
)|, -
10-1 100101
-180
-90
0
90
180
ω
, rad/s
6Hu
ft(j
ω
), deg
10-1 100101
-270
-180
-90
0
90
ω
, rad/s
6Hu
x(j
ω
), deg
Fig. 11. Nonparametric describing function estimates, mean of all subjects.
in the HP and HVP conditions. In these conditions where the
coherence is low, the remnant is typically large (see Fig. 9b).
4) Describing Functions: Fig. 11 shows the nonparametric
describing function estimates. Hu
x(j
ω
)is similar in all con-
ditions over the full input frequency range, which indicates
that subjects hardly adapted their neuromuscular dynamics,
response time delay, and internal-error feedback dynamics,
see (14). In plan-view tasks (NP), Hu
ft(j
ω
)approximates
the dynamics that result in perfect target-tracking (gray line;
Hu
x(j
ω
)+ 1/Hce(j
ω
), see [12]). Because Hu
x(j
ω
)is identical
in all conditions (see Fig. 11b and d), the perfect target-
tracking dynamics are also similar. With horizontal perspective
(HP and HVP) the phase and magnitude required to perfectly
track the target signal are matched less well, especially at
high frequencies. This corresponds to a lower target-tracking
performance in these conditions (see Fig. 9a).
B. Modeling Results
1) Model Fits: Fig. 12 shows both the nonparametric de-
scribing function estimates (markers) and the model fits (lines)
for a representative subject. The full model fits (including lag-
lead equalization) coincide well with the estimated describing
functions, which indicates that the model captures most of
the subject’s control dynamics, also in perspective tasks. A
fit with the original model from [11], which lacked lag-lead
equalization in integrator tasks (i.e., Hoe(j
ω
) = Ke), clearly
lacks the capacity to match the describing functions, and has
a consistently lower VAF than the full model.
2) Variance Accounted For: For most subjects, the model
VAFs (Fig. 13a) are between 80% and 95%, which is higher
than in similar manual control modeling attempts [11], [12],
[33]. In the HP condition the VAFs are slightly lower, which is
in line with the larger remnant (see Fig. 9b). The consistently
high VAFs indicate that the model describes all subjects’
control behavior well, even in perspective tasks.
3) Model Parameters: Fig. 13 also shows the estimated
model parameters, corresponding ANOVA results are given in
10−1 100101
10−1
100
101
NP describing function
HVP describing function
ω
, rad/s
|Hu
ft(j
ω
)|, -
10−1 100101
10−1
100
101
NP red. model, VAF = 90.7%
NP model, VAF = 93.7%
HVP model, VAF = 91.7%
ω
, rad/s
|Hu
x(j
ω
)|, -
10−1 100101
−180
−90
0
90
180
ω
, rad/s
6Hu
ft(j
ω
), deg
10−1 100101
−270
−180
−90
0
90
ω
, rad/s
6Hu
x(j
ω
), deg
Fig. 12. Estimated describing functions and model fits, single subject data.
The reduced model lacks the internal error response lead-lag equalization.
Table III. The far-viewpoint response gain Kf,e f f (Fig. 13d)
is most consistently affected by linear perspective; this was
expected, as perspective deformations are largest far ahead.
Kf,e f f is substantially lower with horizontal perspective (sig-
nificant effect). The smaller visual stimulus in control direction
thus evokes less aggressive control behavior, similar as in
compensatory tracking tasks [18], [19]. Vertical perspective
results in a higher Kf,e f f , but only when horizontal perspective
is already present (HP to HVP; significant interaction effect).
Higher values of Kf,e f f correspond closely to a better tracking
performance (see Fig. 9a). Effects of linear perspective on the
effective near-viewpoint gain Kn,e f f (Fig. 13e) are similar to
Kf,e f f , but due to larger between-subject variations the statis-
tical results are less pronounced. No systematic adaptation is
visible for the near- and far-viewpoint look-ahead times,
τ
n
and
τ
f(Figs. 13h and 13g), nor for the low-pass filter time-
constant Tl,f(Fig. 13j).
The internal-error response gain Ke(Fig. 13f) is slightly
lower in all three perspective tasks (compared to NP), but this
effect is only significant for vertical scaling. The lead and lag
equalization time constants, TL,eand Tl,e(Figs. 13b and 13c),
are both significantly lower with horizontal perspective. The
lag time constant is always about twice as large as lead time
constant, reflecting the low-frequency lag-lead equalization
visible in Fig. 12. The response time-delay
τ
v(Fig. 13i) is
slightly, but not significantly, higher in all conditions with
perspective scaling, compared to the NP condition, which is
similar as in compensatory tracking tasks where the error is
displayed smaller [18], [19]. Finally, subjects also adapt the
properties of their neuromuscular system, but only to horizon-
tal perspective; here, the neuromuscular break frequency
ω
nms
is significantly higher (Fig. 13k), while the neuromuscular
damping ratio
ζ
nms (Fig. 13l) is significantly lower.
C. Human Controller Adaptation
1) Horizontal Display Direction: The effective gains Kn,ef f
and Kf,e f f (Figs. 13e and 13d) are lumped combinations of the
10 IEEE TRANSACTIONS ON HUMAN-MACHINE SYSTEMS
70
80
90
100
NP HP VP HVP
VAF, %
(a)
0.0
0.5
1.0
1.5
NP HP VP HVP
TL,e, s
(b)
0.0
1.0
2.0
3.0
NP HP VP HVP
Tl,e, s
(c)
0.8
0.9
1.0
1.1
NP HP VP HVP
Kf,e f f , -
(d)
0.0
0.1
0.2
0.3
0.4
NP HP VP HVP
Kn,ef f , -
(e)
1.0
2.0
3.0
4.0
5.0
NP HP VP HVP
Ke, -
(f)
0.0
0.2
0.4
0.6
0.8
NP HP VP HVP
τ
f, s
(g)
0.0
0.3
0.6
0.9
NP HP VP HVP
τ
n, s
(h)
0.0
0.1
0.2
0.3
NP HP VP HVP
τ
v, s
(i)
0.0
0.1
0.2
0.3
0.4
0.5
NP HP VP HVP
Tl,f, s
(j)
10
12
14
16
NP HP VP HVP
ω
nms, rad/s
(k)
0.0
0.1
0.2
0.3
NP HP VP HVP
ζ
nms, -
(l)
Fig. 13. Estimated model parameters: raw individual subject data (gray
lines), and means with 95% confidence intervals corrected for between-subject
variability (errorbars).
TABLE III
EST IMATE D PARA ME TER S ANOVA RE SU LTS.1
horizontal vertical hor.×vert.
NV F sig. F sig. F sig.
Kf,e f f 0 80.7 ** 3.77 - 17.6 **
τ
f1 0.01 - 1.67 - 0.65 -
Tl,f1 0.00 - 2.60 - 0.47 -
Kn,ef f 0 17.2 ** 0.21 - 1.23 -
τ
n0 3.54 - 5.54 - 2.93 -
Ke2 5.50 - 6.34 * 0.08 -
TL,e1 7.90 * 0.23 - 0.46 -
Tl,e0 8.53 * 0.06 - 0.47 -
τ
v1 3.28 - 0.81 - 0.53 -
ω
nms 1 11.2 * 1.26 - 3.04 -
ζ
nms 0 15.2 ** 0.32 - 1.85 -
1NV is the number of samples that violate the Lilliefors normality
test (p< .05). Symbols **, *, and - indicate the result is highly
significant (p< .01), significant ( p< .05), and not significant
(p> .05), respectively. Degrees of freedom (df) is always (1,7).
HC and the display gains, see (15). To better illustrate HCs’
control adaptation to horizontal perspective, Fig. 14 shows the
separate contributions of the far-viewpoint gains Kf,Kf,e f f ,
and Kd,u(
τ
f), which are most strongly affected by perspective.
HCs more than double their response gain Kf(black markers)
to compensate for the reduced display gains (white markers)
with horizontal perspective. In other words, subjects respond
much more aggressively to the reduced visual stimulus. This
0.0
1.0
2.0
3.0
NP HP VP HVP
Kf,e f f
Kd,u(
τ
f)
Kf
K, -
Fig. 14. Estimated far-viewpoint response gain adaptation.
−6
−3
0
3
6
NP HP VP HVP
v, cm
near viewpoint
far viewpoint
displayed preview
current time t,
τ
=0 s
vertical screen center,
τ
=1 s
maximum preview,
τ
=
τ
p=2 s
Fig. 15. Vertical location of the near- and far-viewpoints on the display.
adaptation is still less than required to fully invert the display
gains, as the combined gain Kf,e f f is consistently lower with
horizontal perspective (HP and HVP conditions). Results for
the near-viewpoint gains are similar, see also Fig. 13.
2) Vertical Display Direction: Due to the perspective trans-
formation, the same point on the previewed target ahead
corresponds to a different vertical display location in plan-
view and perspective conditions. Fig. 15 shows the points on
the display that subjects responded to, which clearly illustrates
the substantial adaptation required to compensate for vertical
perspective deformations. With the introduction of vertical
perspective (NP and HP to VP and HVP), subjects shift their
near-viewpoint from about 3.5 to 1.5 cm below the screen
center, and their far-viewpoint from about 3 to 0.5 cm below
the screen center. Moreover, the viewpoints’ locations shift
from about 25% above the start of the previewed target (at
τ
=0 s in Fig. 15) to about 25% below the end of the previewed
target (at
τ
=2 s).
VI. DISCUSSION
In the experiment, we measured how linear perspective
affects HC use of preview information. With horizontal per-
spective scaling, we indeed found the hypothesized increase of
the response gains Knand Kf(H.I). Subjects thus responded
more aggressively to lower amplitude of the displayed target
ahead, but, as expected, not aggressively enough to completely
invert the display gain (Kn,e f f and Kf,e f f were lower than in
the plan-view task). HCs also slightly increased their response
time-delay
τ
v, confirming H.I. HC adaptation to perspective
scaling of a previewed target trajectory appears to be similar
VAN DER EL et al.: EFFECTS OF LINEAR PERSPECTIVE ON HUMAN USE OF PREVIEW IN MANUAL CONTROL 11
to their adaptation to a reduced scaling of the visual error
in compensatory tracking tasks, which also evokes a less
aggressive, and more delayed response [18], [19]. Due to
the wider variety of HC behavior compared to compensatory
tracking, we recommend future preview tracking investigations
to test more than the eight subjects used here, to avoid
normality violations and improve confidence in the results.
We further hypothesized that vertical perspective scaling
would not affect HC behavior (H.II). Indeed, subjects selected
approximately the same viewpoints
τ
nand
τ
fs ahead on
the previewed target in conditions with and without vertical
perspective, despite their different vertical locations von the
display. However, H.II cannot be fully confirmed, as our
results point to a substantial interaction between horizontal
and vertical perspective. When vertical perspective is added
to a task where horizontal perspective is already present
(HP to HVP), subjects reduce their remnant, respond with a
higher gain Kf,e f f , and improve their tracking performance.
Comparison of the displays in Figs. 7b and 7d yields a possible
explanation: the “unnatural” exponential magnification of the
approaching previewed target in the HP condition is likely
more difficult to anticipate on than the familiar full linear
perspective in the HVP condition.
The results in the plan-view condition differ from those
in [12], where a similar experiment was performed. Compared
to the experiment in [12], our forcing functions contained
less high-frequency power, and the displayed signals were
magnified horizontally (to keep the target far ahead well visible
in perspective conditions). Amongst others, this resulted in a
much more aggressive internal error response, as visible from
the magnitude of Hu
x(j
ω
), which is about two times higher
than in [12]. Likely, the higher horizontal display scaling
evoked the more aggressive control behavior, which again
emphasizes the importance of proper display scaling in manual
control tasks. However, future work should also investigate the
effects of forcing function characteristics on human control
behavior in preview tracking tasks, as these have not been
quantified to date.
The model for plan-view preview tracking tasks from [11]
accurately described the measured behavior, also in our per-
spective tasks. For such perspective tasks, it is convenient
to lump the linear perspective transformation and the HC
dynamics, so the model is mathematically equivalent as for
plan-view tasks. Although the lumped model’s inputs are
no longer the visual stimuli as sensed by the HC, but the
actual target and CE output signals before the perspective
transformation, the effective gains can be interpreted similar
as the HC gains in plan-view tasks.
All subjects were found to apply lag-lead equalization at the
lower frequencies, opposed to the pure proportional control
strategy often observed in compensatory tracking tasks with
integrator CE dynamics [13]. While it was not yet recognized
as such, similar lag-lead equalization is visible in the preview
tracking results in [11]. Preview information seems to evoke
such behavior, which is perhaps best explained as “waiting”
(i.e., lagging) for the low-frequency portion of the cognitively
calculated, internal error to build up, before more aggressively
responding to it. Future investigations into preview tracking
tasks with integrator CE dynamics can include the lag-lead
equalization in the error response model.
The estimated describing functions showed that HCs use
similar control mechanism in perspective and plan-view pre-
view tracking tasks, for perspective transformations that ap-
proximate the view on the road during driving or cycling.
Unfortunately, several other aspects of HC behavior in such
vehicle control tasks are not yet fully understood. For example,
the viewing direction generally rotates with the vehicle’s
attitude. The resulting optical flow can be used by HCs to
close an inner feedback-loop [3], [25], which can alleviate
the requirements on the outer-loop position control, as tested
here. Furthermore, instead of tracking a line, it is generally
acceptable to keep a vehicle between two boundaries, like the
road’s edges. We intend to investigate and model the effects
of these elements on HC behavior in our future work.
VII. CONCLUSION
This paper quantified how linear perspective affects human
use of preview information in manual control tasks, using
experimental results and both nonparametric and parametric
system identification techniques. The compression of the tra-
jectory ahead due to linear perspective evokes less aggressive
control behavior and inferior task performance, mainly due to
reduced visual stimuli in the control direction (i.e., horizontal
perspective scaling). Perspective deformations in the non-
controlled (vertical) direction affect human control behavior
only marginally. We conclude that humans use preview infor-
mation similarly in plan-view and perspective tracking tasks.
The validity of the previously derived quasi-linear model for
preview tracking tasks is extended to perspective tasks, and can
thereby be used to design and evaluate man-machine systems
in more realistic control tasks.
REF ER EN CE S
[1] R. A. Hess and A. Modjtahedzadeh, “A preview control model of driver
steering behavior,” in Proc. 1989 IEEE Int. Conf. Systems, Man, and
Cybernetics, Cambridge, MA, 1989, pp. 504–509.
[2] S. D. Keen and D. J. Cole, “Bias-free identification of a linear model-
predictive steering controller from measured driver steering behavior,”
IEEE Trans. Systems, Man, and Cybernetics - Part B: Cybernetics,
vol. 42, no. 2, pp. 434–443, Apr. 2012.
[3] L. Saleh, P. Chevrel, F. Claveau, J. F. Lafay, and M. F., “Shared steering
control between a driver and an automation: stability in the presence of
driver behavior uncertainty,” IEEE Transactions on Intelligent Trans-
portation Systems, vol. 14, no. 2, pp. 974–983, Jun. 2013.
[4] R. A. Hess, J. K. Moore, and M. Hubbard, “Modeling the manually
controlled bicycle,” IEEE Trans. Systems, Man, and Cybernetics - Part
A: Systems and Humans, vol. 42, no. 3, pp. 545–557, May 2012.
[5] A. J. Grunwald, J. B. Robertson, and J. J. Hatfield, “Experimental eval-
uation of a perspective tunnel display for three-dimensional helicopter
approaches,” Journal of Guidance, Control, and Dynamics, vol. 4, no. 5,
pp. 623–631, Nov.-Dec. 1981.
[6] M. Mulder and J. A. Mulder, “Cybernetic analysis of perspective flight-
path display dimensions,” Journal of Guidance, Control, and Dynamics,
vol. 28, no. 3, pp. 398–411, May-Jun. 2005.
[7] T. B. Sheridan, “Three models of preview control,IEEE Trans. Human
Factors in Electronics, vol. 7, no. 2, pp. 91–102, Jun. 1966.
[8] L. D. Reid and N. H. Drewell, “A pilot model for tracking with preview,”
in Proc. 8th Ann. Conf. Manual Control, Ann Arbor, MI, 1972, pp. 191–
204.
[9] M. Tomizuka and D. E. Whitney, “The preview control problem with
application to man-machine system analysis,” in Proc. 9th Ann. Conf.
Manual Control, Cambridge, MA, 1973, pp. 429–441.
12 IEEE TRANSACTIONS ON HUMAN-MACHINE SYSTEMS
[10] K. Ito and M. Ito, “Tracking behavior of human operators in preview
control systems,” Electrical Eng. in Japan, vol. 95, no. 1, pp. 120–127,
1975, (Transl.: D.K. Ronbunshi, vol. 95C, no. 2, Feb. 1975, pp 30-36).
[11] K. van der El, D. M. Pool, H. J. Damveld, M. M. van Paassen, and
M. Mulder, “An empirical human controller model for preview tracking
tasks,” IEEE Trans. on Cybernetics, vol. 46, no. 11, pp. 2609–2621,
Nov. 2016.
[12] K. van der El, D. M. Pool, M. M. van Paassen, and M. Mulder, “Effects
of preview on human control behavior in tracking tasks with various
controlled elements,” IEEE Trans. on Cybernetics, 2017, online preprint
available.
[13] D. T. McRuer and H. R. Jex, “A review of quasi-linear pilot models,”
IEEE Trans. Human Factors in Electronics, vol. 8, no. 3, pp. 231–249,
May 1967.
[14] D. T. McRuer, D. Graham, E. S. Krendel, and W. J. Reisener, “Human
pilot dynamics in compensatory systems, theory models and experiments
with controlled element and forcing function variations,” Air Force
Flight Dynamics Laboratory, Wright-Patterson Air Force Base, OH,
Tech. Rep. AFFDL-TR-65-15, 1965.
[15] J. J. Gibson, “Visually controlled locomotion and visual orientation in
animals,” British Journal of Psychology, vol. 49, no. 3, pp. 182–194,
Aug. 1958.
[16] P. M. T. Zaal, F. M. Nieuwenhuizen, M. M. van Paassen, and M. Mulder,
“Modeling human control of self-motion direction with optic flow and
vestibular motion,IEEE Trans. on Cybernetics, vol. 43, no. 2, pp. 544–
556, Apr. 2013.
[17] L. R. Young, “On adaptive manual control,” IEEE Trans. Man-Machine
Systems, vol. 10, no. 4, pp. 292–331, Dec. 1969.
[18] W. H. Levison and R. Warren, “Use of linear perspective scene cues in
a simulated height regulation task,” in Proc. 20th Ann. Conf. Manual
Control, Sunnyvale, CA, 1984, pp. 467–490.
[19] S. W. Breur, D. M. Pool, M. M. van Paassen, and M. Mulder, “Effects
of displayed error scaling in compensatory roll-axis tracking tasks,” in
Proc. AIAA Guidance, Navigation, and Control Conf., Toronto, Canada,
2010.
[20] S. Murray, H. Boyaci, and D. Kersten, “The representation of percieved
angular size in human primary visual cortex,” Nature Neuroscience,
vol. 9, no. 3, pp. 429–434, Mar. 2006.
[21] W. S. Kim, S. R. Ellis, M. E. Tyler, B. Hannaford, and L. W. Stark,
“Quantitative evaluation of perspective and stereoscopic displays in
three-axis manual tracking tasks,” IEEE Trans. Systems, Man, and
Cybernetics, vol. 17, no. 1, pp. 61–72, Jan. 1987.
[22] I. D. Haskell and C. D. Wickens, “Two- and three-dimensional displays
for aviation: A theoretical and empirical comparison,” The International
Journal of Aviation Psychology, vol. 3, no. 2, pp. 87–109, 1993.
[23] S. Zhai, P. Milgram, and A. Rastogi, “Anisotropic human performance
in six degree-of-freedom tracking: An evaluation of three-dimensional
display and control interfaces,” IEEE Trans. Systems, Man, and Cyber-
netics - Part A: Systems and Humans, vol. 27, no. 4, pp. 518–528, Jul.
1997.
[24] B. T. Sweet, “A model of manual control with perspective scene
viewing,” in AIAA Modeling and Simulation Technologies (MST) Conf.,
Boston, MA, 2013.
[25] D. T. McRuer, D. H. Weir, H. R. Jex, R. E. Magdaleno, and R. W.
Allen, “Measurement of driver-vehicle multiloop response properties
with a single disturbance input,” IEEE Transactions on Systems, Man,
and Cybernetics, vol. 5, no. 5, pp. 490–497, Sep. 1975.
[26] M. M. van Paassen and M. Mulder, “Identification of human oper-
ator control behaviour in multiple-loop tracking tasks,” in Proc. 7th
IFAC/IFIP/IFORS/IEA Symposium on Analysis, Design and Evaluation
of Man-Machine Systems, Kyoto, Japan, 1998, pp. 515–520.
[27] J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer
Graphics. Principle and Practice., 2nd ed. Reading, MA: Addison-
Wesley, 1992.
[28] A. Modjtahedzadeh and R. A. Hess, “A model of driver steering control
behavior for use in assessing vehicle handling qualities,Journal of
Dynamic Systems, Measurement, and Control, vol. 115, no. 3, pp. 456–
464, 1993.
[29] D. T. McRuer, R. E. Magdaleno, and G. P. Moore, “A neuromuscular
actuation system model,” IEEE Trans. Man-Machine Systems, vol. 9,
no. 3, pp. 61–71, Sep. 1968.
[30] R. L. Stapleford, D. T. McRuer, and R. E. Magdaleno, “Pilot describing
function measurements in a multiloop task,” IEEE Trans. Human Factors
in Electronics, vol. 8, no. 2, pp. 113–125, Jun. 1967.
[31] F. C. T. Van der Helm, A. C. Schouten, E. De Vlugt, and G. G. Brouwn,
“Identification of intrinsic and reflexive components of human arm
dynamics during postural control,” Journal of Neuroscience Methods,
vol. 119, no. 1, pp. 1–14, Sep. 2002.
[32] E. Schmider, M. Ziegler, E. Danay, L. Beyer, and M. B¨
uhner, “Is it really
robust? Reinvestigating the robustness of ANOVA against violations of
the normal distribution assumption,” Methodology, vol. 6, no. 4, pp.
147–151, 2010.
[33] F. M. Drop, D. M. Pool, H. J. Damveld, M. M. van Paassen, and M. Mul-
der, “Identification of the feedforward component in manual control with
predictable target signals,” IEEE Trans. Cybernetics, vol. 43, no. 6, pp.
1936–1949, Dec. 2013.
Kasper van der El (S’15) received the M.Sc. degree
in aerospace engineering (cum laude) from TU Delft,
The Netherlands, in 2013, for his research on manual
control behavior in preview tracking tasks. He is
currently pursuing the Ph.D. degree with the section
Control and Simulation, Aerospace Engineering, TU
Delft. His Ph.D. research focuses on measuring and
modeling human manual control behavior in general
control tasks with preview. His current research in-
terests include cybernetics, mathematical modeling,
and system identification and parameter estimation.
Daan M. Pool (M’09) received the M.Sc. and Ph.D.
degrees (cum laude) from TU Delft, The Nether-
lands, in 2007 and 2012, respectively. His Ph.D.
research focused on the development of an objective
method for optimization of flight simulator motion
cueing fidelity based on measurements of pilot con-
trol behavior. He is currently an Assistant Professor
with the section Control and Simulation, Aerospace
Engineering, TU Delft. His research interests include
cybernetics, manual vehicle control, simulator-based
training, and mathematical modeling, identification,
and optimization techniques.
Marinus (Ren´
e) M. van Paassen (M’08, SM’15)
received the M.Sc. and Ph.D. degrees from TU Delft,
The Netherlands, in 1988 and 1994, respectively,
for his studies on the role of the neuromuscular
system of the pilot’s arm in manual control. He
is currently an Associate Professor at the section
Control and Simulation, Aerospace Engineering, TU
Delft, working on human-machine interaction and
aircraft simulation. His work on human-machine in-
teraction ranges from studies of perceptual processes
and manual control to complex cognitive systems. In
the latter field, he applies cognitive systems engineering analysis (abstraction
hierarchy and multilevel flow modeling) and ecological interface design to
the work domain of vehicle control.
Dr. van Paassen is an Associate Editor of the I EEE TR AN SAC TIO NS ON
HUM AN- MAC HIN E SYS TEM S.
Max Mulder (M’14) received the M.Sc. degree and
Ph.D. degree (cum laude) in aerospace engineer-
ing from TU Delft, The Netherlands, in 1992 and
1999, respectively, for his work on the cybernetics
of tunnel-in-the-sky displays. He is currently Full
Professor and Head of the section Control and
Simulation, Aerospace Engineering, TU Delft. His
research interests include cybernetics and its use in
modeling human perception and performance, and
cognitive systems engineering and its application in
the design of “ecological” interfaces.
... Broad investigations in this area were carried out at Delft University [3][4][5][6][7][8][9][10] for the gain coefficient and simple/double integrator controlled element dynamics, for a rectangular power spectrum input with different bandwidths ( . i 1 5   rad/s). ...
... The parameters of these characteristics were obtained from the preliminary measurements of two pilot describing functions, one describing the pilot response to the input signal ( ) prev i t T  and the other describing the pilot response to the error signal ( ) e t . The methodology of these measurements and calculations is given in [6,7]. All these studies exposed the effect of preview on pilot behavior characteristics and its potential for improving task performance, and the influence of the input signal bandwidth and controlled element dynamics on all these regularities. ...
... As a matter of fact, the current state of technology has allowed to realize a display with a 3D presentation of the planned trajectory on the screen. This technology has caused a number of studies in defining the best way of presenting the information [2][3][4][5][6]12]. Finally, the so-called "tunnel in the sky" display was proposed [12]. ...
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