Sight Distance of Automated Vehicle Considering Highway Vertical Alignments and Its Implications for Speed Limits

Abstract

Most existing road infrastructures were constructed before the emergence of automated vehicles (AVs) without considering their operational needs. Whether and how AVs could safely adapt to as-built highway geometry are questions that remain inconclusive, and a plausible concern is a challenge from vertical alignments. To fill this gap, this study uses a virtual simulation to investigate the available sight distance (ASD) of AVs on vertical alignments subject to the current highway geometric design specification and its implications for speed limits. According to the scenario generation framework, several scenarios featuring vertical geometric elements and lidar sensors were created and tested. Moreover, the maximum speed for adequate ASD is calculated to determine the AV speed limit, considering safe sight distance and speed consistency requirements. The results indicate that crest curves are not disadvantaged in ASD compared with either sag curves or tangent grades. Only equipped with multichannel lidar and advanced perception algorithms enabling a lower detection threshold would a level 4 AV be compatible with the as-built vertical alignment with a design speed (Vd) of 100 km/h. However, a level 3 AV can only adapt to the vertical profile with Vd = 60 km/h. The findings of this study should be of interest to the road-oriented operational design domain and support road administrators in regulating AV safe speeds.

Full text

1939-1390/24©2024IEEEIEEE INTELLIGENT TRANSPORTATION SYSTEMS MAGAZINE • 2 • MONTH 2024
Sight Distance of
Automated Vehicles
Considering Highway
Vertical Alignments and
Its Implications for
Speed Limits
XXXXXXX
Dig ital Obj ect Ide ntif ier 10.1109/MITS .2023.3334769
Dat e of curre nt versio n: 8 December 2023
Shuyi Wang †
Is with the College of Civil Engineering, Fuzhou University,
Fuzhou 350108, China. E-mail: syw@fzu.edu.cn
Yang Ma †
Is with the School of Automotive and Transportation Engineering, Hefei University of
Technology, Hefei 230000, China. E-mail: mayang@hfut.edu.cn
Said M. Easa
Is with the Department of Civil Engineering, Toronto Metropolitan University,
Toronto, ON M5B 2K3, Canada. E-mail: seasa@torontomu.ca
Hao Zhou
Is with the Department of Civil Engineering, University of South Florida,
Tampa, FL 33620 USA. E-mail: haozhou1@usf.edu
Yuanwen Lai*
Is with the College of Civil Engineering, Fuzhou University, Fuzhou 350108, China.
E-mail: laiyuanwen@fzu.edu.cn
Weijie Chen
Is with the School of Transportation, Southeast University, Nanjing,
211189, China. E-mail: chenweijie@seu.edu.cn
*Corresponding author
†Corst author
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Introduction
The International Society of Automotive Engineers has
classified driving automation into six levels [1], i.e.,
from no driving automation (level 0 [L0]) to full driv-
ing automation (L5). Over the past few years, many
features of lower automation levels have been available in
the automobile market (e.g., the L2 Tesla). In the mean-
time, many features of higher levels are being tested on
public roads (e.g., the L4 Baidu). According to the China
automobile market statistics report [2], general automation
is developing from L2 to L3. In other words, it is maturing
from advanced driver-assist systems to automated driving
systems (ADS).
Recent studies have revealed signif icant differences in
the performance and features between automated vehicles
(AVs) (i.e., vehicles equipped with ADS) and traditional hu-
man-driven vehicles (HVs), particularly in the perception-
related functions (e.g., [3] and [4]). However, most as-built
road infrastructures, especially their road geometry, were
designed only considering the characteristics of human
drivers or HVs [5]. In this regard, the compatibility of AVs
with as-built roads is gaining increasing interest from aca-
demia and industry.
As stated in previous studies (e.g., [6]), specifying the
operational design domain (ODD) of AVs is essential to
safely deploy them on as-built roads. The ODD refers
to an AV’s needed operating conditions, including envi-
ronmental, traff ic, and roadway characteristics, among
others [1]. However, only the less detailed ODD require-
ments regarding roadway characteristics were specified,
such as merely mentioning the allowable road type w ith-
out the speed limit for the specific geometric conditions.
This might lead to consumer overreliance, suspicion, or
confusion [7], [8]. In addition, it is very challenging to ad-
dress a lack of ODD standardization or elaborate on nu-
merous conditions for every vehicle [9]. These limitations
hinder road administrators’ application of this vehicle-
based ODD concept for road design, management, and
maintenance.
Since many road infrastructures were constructed
before the emergence of AVs, it could be cost-effective
for road administrators to adapt AVs to as-built roads.
Therefore, it is necessary to adjust or improve the ODD
concept from the road perspective—that is, offering such
a road-oriented ODD concept by stating the specific road
condition (e.g., the road geometry) and its matching AV
operation (e.g., the driving speed). As García et al. [9]
proposed, the road-oriented ODD concept can be defined
as the operational road section. Previous studies focused
mostly on horizontal alignments. They (e.g., [10]) high-
lighted the perception-related limitations of AVs and jus-
tified the available sight distance (ASD) for exploring AV
compatibilit y. The ASD refers to the longest path distance
at which a stationary obstruction along the roadway ge-
ometry can be detected. Given the limited angular resolu-
tion, range, and object detection threshold of AV sensors,
AVs might not have sufficient ASD to ensure safe driv ing at
high speeds on horizontal curved roads.
Due to vertical curves, vertical alignment s may be sub-
ject to the same concerns as horizontal alignments. Al-
though Wang et al. [10] demonstrated that either a higher
sensor mounting height or a larger upward ver tical field
of view ( VFoV) would induce a milder requirement of
vertical alignments for AVs, sightline obstructions might
be caused by the crest and sag-curve pavement profile, as
depicted in Figure 1. Such obstructions reduce the ASD
and the corresponding maximum safe speed [11], [12],
[13]. However, the results on vertical alignments were
Abstract—Most existing road infrastructures were constructed before the emergence of automated vehicles (AVs)
without considering their operational needs. Whether and how AVs could safely adapt to as-built highway geometry
are questions that remain inconclusive, and a plausible concern is a challenge from vertical alignments. To fill this
gap, this study uses a virtual simulation to investigate the available sight distance (ASD) of AVs on vertical align-
ments subject to the current highway geometric design specification and its implications for speed limits. According
to the scenario generation framework, several scenarios featuring vertical geometric elements and lidar sensors
were created and tested. Moreover, the maximum speed for adequate ASD is calculated to determine the AV speed
limit, considering safe sight distance and speed consistency requirements. The results indicate that crest curves
are not disadvantaged in ASD compared with either sag curves or tangent grades. Only equipped with multichannel
lidar and advanced perception algorithms enabling a lower detection threshold would a level 4 AV be compatible
with the as-built vertical alignment with a design speed (Vd) of 100 km/h. However, a level 3 AV can only adapt to the
vertical profile with Vd = 60 km/h. The findings of this study should be of interest to the road-oriented operational
design domain and support road administrators in regulating AV safe speeds.
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quite inconclusive. Only a limited number of scenarios
including crest vertical cur ves and advanced driver-as-
sist systems were investigated in field tests [11]. In addi-
tion, the analytical studies (e.g., [10]) might overestimate
the actual AV’s perception ability since some critical sen-
sor-related factors (e.g., the angular resolution) were not
considered. Given those motivations and limitations, fur-
ther extending road geometry studies to vertical align-
ments is vital.
This study investigates whether and how AVs could
safely adapt to as-built vertical alignment. In this re-
gard, two intriguing questions arise: how far can AVs
see, and how fast should they drive? A series of virtu-
al simulations featuring AVs and vertical alignments
were conducted to estimate the ASD. Based on that, we
derived the maximum speed for adequate ASD (Vmax)
according to the safe sight distance (SD) requirement.
That is, the ASD must not be less than the required
stopping SD (RSD) [14]. In addition, the Vmax-based
speed limit on vertical alignments was determined
considering speed consistency. Note that the road type
in this study refers to a highway, as only the ego vehicle
and geometric features were considered. The present
study offers thorough and feasible answers to these two
questions, which are expected to further advance the
road-oriented ODD and support road administrators in
regulating Avs’ safe speeds on as-built vertical align-
ments.
The study is organized as follows. The next section pres-
ents the literature rev iew. The “Methods” section intro-
duces the simulation design. The “Results and Discussion”
presents the simulation and analysis results, and the final
section presents concluding remarks, limitations, and fu-
ture work.
Literature Review
Related Work
Over the past few years, many efforts in the literature have
been expended on improving the ODD concept from the road
perspective and determining how AVs could safely adapt to
the as-built roadway geometry. Recent studies can be clas-
sified into four types: analytical studies, empirical studies,
computer-aided studies, and virtual simulation studies.
The analytical studies determined the required geo-
metric design controls (e.g., vertical alignment) or ODDs
(e.g., sensor range) for AVs [3], [4], [10], [11], [15], [16], [17],
[18]. However, they merely considered perception sensors’
simple 2D FoV or mounting heights, omitting other cr iti-
cal technical parameters (e.g., angular resolutions) and
object detection thresholds. That might overestimate an
actual AV’s perception ability from the roadway geometry
perspective (i.e., the ASD) and, thus, ease the geometric re-
quirement or ODD.
The empirical studies better captured AVs’ natural char-
acteristics [11], [19], [20]. Previous studies investigated the
maximum operational speeds for the automation system on
public roads. In such field tests, although they have real
alignment conditions, it is difficult to completely exclude
the effect of nongeometric factors (e.g., the traffic flow and
weather). In addition, those costly tests would limit the
sample sizes regarding various sensor configurations and
geometric design elements.
The computer-aided studies used actual lidar point
cloud data of highways [12], [21]. They created a simulation
environment and then proposed automatic ASD estimation
algorithms. Compared with analytical and empirical stud-
ies, computer-aided studies increased the FoV from two
dimensions to three, save testing time, and expanded the
AV
AV
TV
TV
TV
TV
Ver tical Curve
Sag Curve
Crest Curve
The lidar VFoV is above the pavement profile.
The lidar VFoV is occluded by the pavement profile.
The TV can be sensed by the AV.
The TV cannot be sensed by the AV.
FIG 1 Possible sightline obstructions for AVs on crest and sag vertical curves. lidar: light detection and ranging; TV: target vehicle.
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sensor-related sample size (e.g., the sensor quantity). Never-
theless, they failed to consider other sensor-related factors
(e.g., the angular resolution). Also, the sensitiv ity investiga-
tion of geometric conditions might be insufficient due to the
limited number of road scenarios modeled by the point clouds.
The virtual simulation studies avoided the mentioned
issues and limitations [13], [22]. These studies adopted a
high-fidelity simulation technology to effectively simulate
AVs’ perception processes and, thus, estimated the ASD
along different alignments. Importantly, they ascertained
that lidar’s angular resolutions and laser-point thresholds
for object detection affect the ASD substantially. Moreover,
this method is well recognized in the AV-testing domain
[23]. It can customize numerous scenarios effectively,
which include road geometry, sensors, AV features, etc.
AVs’ Lidar-Based Perception System
The lidar-based multisensor fusion and perception system
has been recognized as one of the optimal perception so-
lutions for AVs because of lidar’s advantages over cameras
and radar sensors [24]. Generally, a camera is more susc ep-
tible to adverse weather and lighting conditions [25]; radar
has a narrower FoV, especially the VFoV; a shorter range;
a coarser angular resolution; and inferior performance on
stationary target detection [26]. In addition, camera data
are mainly used for lane-marking detection, traffic sign
identification, and traffic light recognition [24].
As stated, the ASD of AVs is a critical item in previous
studies that can effectively ref lect the safety margin provid-
ed by the road alignment from the SD perspective and in-
form AV safe driving speeds [27]. As demonstrated by Wang
et al. [13], [22], the primary cause of many crashes involving
an AV colliding with a stationar y obstruction is ASD < RSD.
Furthermore, in the case of ASD test-
ing, sensing results from lidar would
play a priority role over those from
either a camera or radar mainly due
to the features of “long distance” and
“stationary obstruction,” respectively.
Therefore, referring to [13] and
[22], the AV, in this context, also de-
notes an AV equipped with a lidar-
based perception system (L AV).
Note that effective object detection is
closely related to a sufficient number
of laser points impinging on that ob-
ject, as highlighted in previous stud-
ies (e.g., [22]).
Methods
Overview
The workflow of this study is shown in
Fig ure 2. Fi rst, a cosi mulation plat form
is used to conduct virtual simulations. Then, the experiments
are designed according to the basic framework of AV driving
scenario generation (i.e., functional–logical– concrete scenari-
os), as defined in the PEGASUS project [28]. Those experiments
consider vertical alignments and lidar elements. The vertical
alignment elements are design speed (Vd), length and curva-
ture of the crest curve (LCV and RCV), length and curvature of
the sag curve (LSV and RSV), and tangent grade length (LTG).
The lidar elements are the number of vertical channels (NC),
laser-point threshold for vehicle detection (NT), and mount-
ing height (hmL). After testing each trial, the ASD of the LAV
is output. Second, “How far can the LAV see on highway ver-
tical alignments?” is answered by investigating the relation-
ships between the ASD and those variables. With the output of
the ASD, “How fast should the LAV drive on highway vertical
alignments?” is further addressed by setting the ASD equal to
the RSD of the LAV. The answer is Vmax for the LAV. Finally,
given a specific vertical alignment, Vmax related to the Vd of that
alignment is adopted as the speed limit.
Simulation Platform
As shown in Figure 2, we used the PreScan software pack-
age (version 2021.1.0) and MATLAB/Simulink (version
2018b) to establish the cosimulation platform. This plat-
form is good at physics-based calculations of perception
sensor inputs/outputs. It is highly effective on cosimula-
tions of roads, vehicle control, and AV systems [29] and has
been employed in previous studies to investigate the ASD
of LAVs (e.g., [22]).
Specifically, PreScan can offer a colossal actor data-
base of vehicles, user-defined vehicle trajectories, roads
with varied geometric characteristics, and top-notch sen-
sor models [29]. MATLAB/Simulink enables real-time data
Virtual Simulations How far can the LAV
see on highway
vertical alignments?
How fast should the LAV
drive on highway
vertical alignments?
1
2
Simulation Platform
How far? → the ASD of the LAV
How fast? →Vmax →Speed Limit
• Relationships Between
the ASD, Ve rtical Alignment,
and LIDAR Elements
• ASD = RSD of LAV
• Speed Consistency With Vd
Functional
Simulation Design
Concrete
Logical
FIG 2 The proposed workflow.
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access from PreScan through a cluster communication port-
based interface. The data herein include lidar outputs (e.g.,
the number of received laser points) and the vehicle’s path
information (e.g., the relative path distance). Based on these
data, the ASD calculation can be programmed in M ATLAB.
Note that Wang et al. [13], [22] have verified the effective-
ness of this cosimulation platform in investigating the ASD
of LAVs. They compared the v irtual ASD with the actual
data, measured by Abdo et al. [30], under the same scenario.
Experimental Design
Given the virtual simulations conducted in this study,
there is a need for a scenario-based experimental de-
sign that can reflect various variables and handle well-
designed scenarios [31]. In view of the advantages of the
scenario-based design approach, a much-cited scenario
design framework [28] was used, as shown in F igure 3.
This scenario-based design can explicitly and systemati-
cally present the infor mation required for the generation
of simulation scenarios [32].
Specifically, the functional scenario has a high degree
of abstraction, w ritten or depicted in natural language, to
clarify the scenario content, objective, and necessary com-
ponents [28]. Based on t he components defined in the func-
tional scenario, the types and value ranges (if any) of their
representative parameters or variables are further defined
in the logical scenario [28]. Finally, a concrete scenario is
established by sampling the parameters and variables de-
fined in the logical scenario [28].
Functional Scenario
Regarding t his study, t he functional scenario (see F igure 4)
can be expressed as a situation where the LAV drives along
a particular road alignment. A still target vehicle (TV), as
a fixed obstacle, is on the desired path ahead of the LAV.
Many previous findings have shown that a rear-end
collision with another vehicle is the most common type
of AV-involved crash [33]. Moreover, the vehicle is also the
representative object (or obstacle) in the HV-related ASD
analysis [5], where the object height (0.6 m) for estimating
the ASD refers to the vehicle’s taillight height. Therefore, a
TV was used in the scenario.
As shown in Figure 4, t he passenger vehicle for the LAV
and TV was selected according to the primary desig n vehicle
in the highway geometric design [5]. Also, the on-road pas-
senger vehicle is one of the most important manifestations
of automated driv ing technology [1]. The vertical align-
ments include crest and sag curves as well as the tangent
grade. In addition, a one-lane road segment was selected to
enable the LAV’s driv ing path to overlap the road centerline
completely so as to explore the direct effect of geometr y.
Logical Scenario
To serve the functional scenario defined previously, we
further defined the components, including the vehicles
(the LAV and TV), road geometry, and lidar.
Functional Scenario Logical Scenario Concrete Scenarios
• Objective: To Simulate the ASD
of the LAV
• Components:
– Vehicles
– Vertical Alignments
– Lidar
Vd
LCV/RCV
LSV/RSV
LTG
Vd
LCV/RCV
LSV/RSV
LTG
e.g., NC, NT, hmL e.g., NC, NT, hmL
: Value Space of Variable : One Variable-Value : Combination of Va riable-Values
FIG 3 The scenario design framework.
Lidar
Roadway
GeometryLAV
FoVTarget
Vehicle
(Obstacle)
Speed
Crest Curve Sag Curve Tangent Grade
Driving Path
FIG 4 The functional scenario.
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Veh icles
Specific information on vehicles includes the dimensions,
motion states, and locations. The Audi A8 vehicle model
provided by the simulation platform was adopted for both
the LAV and TV. The vehicle is 5.21 m long, 2.04 m wide,
and 1.44 m high.
When measuring the ASD of the HV, the ego vehicle is
usually set to drive at a uniform speed, closely related to the
road environment, especially the geometr y [5]. Concerning
the LAV, without external disturbances, its products (e.g.,
Tesla) usually drive at a uniform speed set by the driver’s
desire [34]. To the authors’ best knowledge, personalized
automated driving strategies [35] that can imitate an HV’s
speed character istics remain theoretical.
To maximize the safet y benefit, the LAV is primar-
ily mandated to drive with a minimal deviation from the
lane centerline [36]. This path feature is also consistent
with that required in the HV-related ASD measurement.
Therefore, a constant speed and a fixed driving path (i.e.,
the lane centerline) were used for the LAV independent of
geometric conditions.
Very few efforts were expended to measure the AV’s ac-
tual driv ing or operating speeds corresponding to various
as-built geometric conditions, which are designed main-
ly by a Vd-derived deterministic approach. In addition, to
achieve better mobility, a speed closer to the safe margin
supplied by the as-built road geometry could be the desired
speed for AVs. Therefore, Vd corresponding to the geometry
was used as the LAV’s driving speed.
Furthermore, the minimum
speed within the AV’s ODD is usu-
ally larger than 40 km/h [37]. In ad-
dition, Varotto et al. [38] found an
average speed of 107.2 km/ h from
the naturalistic driving data of AVs,
which were collected on high-type
highways and under normal driv-
ing conditions. Also, the driving risk
is rarely attributable to the limited
ASD solely when Vd is larger than
100 km /h [39]. Therefore, we adopt-
ed the driving speed (i.e., Vd herein)
for the LAV ranging from 40 to 100
km/h with an interval of 20 km/h.
As for the stationary TV, it can be po-
sitioned anywhere along the driv ing
path of the LAV from the end of the
road segment until it is detected.
Road Geometry
To investigate the ef fect of as-built
highway geometry, all adopted val-
ues of vertical geometric elements
comply with the Chinese design
specification for highway alignments [40]. Also, other
safety failure modes regarding vehicle dy namics (e.g., roll-
over) can be excluded.
■ Tangent grades: As shown in Figure 5, given a certain
relative distance between the LAV and TV, adjusting the
grade (iG) alone affects neither the relative location be-
tween vehicles nor between the TV and lidar FoV. There-
fore, the ASD under different iG values is supposed to be
the same as that on the tangent. Since the specified max-
imum iG decreases with an increase in Vd [40], an | iG | o f
4% corresponding to the maximum iG at Vd = 100 km/h
was adopted.
In addition, as mentioned, the ASD for iG = 4% is the
same as that on the tangent. Wang et al. [13] have simulat-
ed the A SD of an LAV on the ta ngent at NC = 64, hmL = 1.44 m
(referring to the roof of Audi A8), Vd = 40 –100 km /h, and
NT = 10 and 20. Their results show that the driving speed
of the LAV hardly affects the ASD on the tangent since
there is neither lateral nor vertical relative movement
between the vehicles. Based on their results, the average
ASD values over Vd = 40–100 km/h at NT = 10 and 20 are 71
and 43 m, respectively, which are much shorter than the
minimum LTG (120 m at Vd = 40 km/h) specified by [40].
Therefore, to reduce the unnecessary sample size, we ad-
opted LTG ranging from 0 to 70 m and 0 to 40 m at NT = 10
and 20, respectively, with an inter val of 10 m.
■ Vertical curves: Regarding the vertical cur ve models in
the simulation platform, the length (LV) and curvatu re
(RV) of the vertical curve are related by LV = RV ×
,~
Channel
Vertical Angular
Resolution
VFoV of Lidar
VFoV of Lidar
Range
TV
TV
LAV
LAV
Tangent Grade
Tangent
VFoV Occluded by Pavement
VFoV Occluded by Pavement
FIG 5 The relative position between the LAV, TV, and lidar VFoV under different iG values.
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where
~
is the algebraic difference in grades [40]. To
simplify the simulation, the iG before and after the
point of vertical intersection (iG0 and iG1, respectively)
is assumed to be zero (or ±4%) and ±4% (or zero), re-
spectively, and, thus, an
;;~
of 4% was used.
Furthermore, to satisfy the requirements of both LCV (or
LSV) and RCV (or RSV) specified by [40], their value ranges
were selected or calculated based on the
;;~
of 4%, as listed
in Table 1. Note that the minimum values of their ranges
should not be less than their limited minimum values (Llim_
Vmin and Rlim_Vmin) specified by [40]; the maximum values
are determined by reference to the common minimum val-
ues (Lco m_Vmi n and Rc om_Vm in) specified by [40]. The inter vals
of LV and RV are 10 and 250 m, respectively. Specifically, the
following hold:
■ The minimum LCV at Vd = 40 km/ h adopts the Llim_Vmin,
and the minimum RCV is calculated by (LCV/4%),
while the minimum RCV at Vd = 60–100 km/h uses
Rlim_Vmin, and the minimum LCV is calculated as 4%
of the RCV.
■ The minimum RSV values at Vd = 40 and 60 km/h use
Rlim_Vmin, and the minimum LSV is calculated as 4%
RSV, while the minimum LSV values at Vd = 80 and
100 km /h use Llim_Vmin, and the minimum RSV values
are calculated as LSV/4%.
■ T he maximu m LV and RV at Vd = 40–80 k m/h use those
at Vd = 100 km/h to capture as many ASD features
along the vertical alignment as possible. Therefore,
the minimum LV and RV selections at Vd = 100 km/h
also apply to its maximum LV and RV.
■ Tangent g rade and vertical curve: For the alignment
of a tangent grade followed by a vertical curve, the val-
ues of their respective geometric design elements (e.g.,
LV) are consistent with those stated earlier. In addition,
since the LAV always drives along the lane centerline,
and the lidar is mounted on the centerline of the L AV’s
width, the lane width and cross slope are not expected
to affect the ASD. Therefore, a lane width of 3.75 m and
a cross slope of 2% were adopted as per [40].
Lidar
According to the comparisons of various commercially
available lidar products [24], [25], [41], [42], [43], the most
significant difference among them is NC or vertical angu-
lar resolution (= VFoV/(NC – 1) if vertical channels are uni-
formly distributed). The frequently used NC values are 32,
64, and 128 for the multichannel lidar, which have gradu-
ally become the requisite of high-level AVs (e.g., Waymo).
On the contrary, many lidar manufacturers have
reached a consensus on the design values of other techni-
cal parameters of their lidar products. A lso, to eliminate
the possible blind spot, they pay more attention to obtain-
ing as good a horizontal-related sensing performance as
possible, e.g., a wider horizontal FoV (HFoV).
According to these comparisons, the adopted values of
the lidar technical parameters are shown in Table 2. Note
that these values were selected concerning their general
levels of current multichannel lidar products instead of
referring to a specific product. A lso, to simplify the lidar
model setting, the uniform and symmetrical distribution of
vertical channels was selected, which enables the adopted
NC to correspond to vertical angular resolutions in order.
For example, an NC of 32 corresponds to a vertical angu-
lar resolution of 0.97°. In addition, since the investigated
road segment only extends longitudinally, an HFoV of 120°
is sufficient.
Only one high-type lidar model with technical parame-
ters listed in Table 2 was employed because that is the typi-
cal lidar configuration for detecting long-distance targets
[44]. Furthermore, two widely used mounting locations
were considered: the front-end centers of t he LAV’s roof
and bumper (or headlights) [10]. Therefore, the adopted
hmL values are 1.44 and 0.6 m, corresponding to the heights
of Audi A8’s roof and headlights, respectively.
As stated in the “Introduction” section, receiving suf-
ficient laser points reflected from the target is essential for
lidar-based detection algorithms. Although
different algorithms might require more or
fewer laser points, a general-level NT could be
determined by referring to previous studies.
Specifically, Teichman et al. [45] found that the
accuracy of the proposed algorithm decreases
to approximately 80% when fewer than 50 laser
points are received. The accuracy of the algo-
rithm proposed by Suganuma et al. [46] drops to
85% when the number of points reduces to 25.
Vertical
Curve
Type Variable
Design Speed, Vd (km/h)
40 60 80 100
Crest LCV (m) [35, 400] [56, 400] [120, 400] [260, 400]
RCV (m) [875, 10,000] [1,400, 10,000] [3,000, 10,000] [6,500, 10,000]
Sag LSV (m) [35, 210] [50, 210] [80, 210] [120, 210]
RSV (m) [875, 5,250] [1,250, 5,250] [2,000, 5,250] [3,000, 5,250]
Table 1. Adopted ranges for the length and curvature of vertical curves.
Parameter Value
Range 200 m
HFoV 120° = [–60°, +60°]
VFoV 30° = [–15°, +15°]
Horizontal angular resolution 0.4°
Vertical angular resolution 0.97°, 0.48°, and 0.24°
NC 32, 64, and 128
Frame rate 20 Hz
Table 2. Adopted values for the lidar technical parameters.
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Furthermore, Abdo et al. [30] and Wang et al. [13], [22] have
investigated the effective range of lidar at many NT values,
e.g., 10, 20, etc. Therefore, to reduce the sample size, two
typical values of NT with a two-fold relation, 10 and 20, were
adopted.
Concrete Scenario
Using the pair sampling approach [32], the values of pa-
rameters or variables were selected by considering all
possible combinations within the set range according
to the user-defined categories. Due to the different ge-
ometry properties of vertical curves and tangent grades,
two categories—1) vertical curves and 2) tangent grades
and vertical curves—were considered for the concrete
scenarios.
Figure 6 shows the parameters–variables pair sampling
for concrete scenarios. As noted, to reduce the sample
size, 1) in the category of vertical curves, hmL = 0.6 m is
only paired with NC = 64, and 2) in the category of tangent
grades and vertical curves, only NC = 64 and hmL = 1.44 m
are selected in the ranges of NC and hmL, respectively. Fur-
thermore, the parameters and variables of each component
are paired (see “+” in Figure 6), and variables bet ween
each component are paired (see solid or dashed straight
arrows in Figure 6).
Experimental Process
Figure 7 shows the entire experimental process for
each trial. As noted, first, according to the scenario
design, two categories of concrete scenarios are es-
tablished in the simulation platform. After starting
the simulation, the ASD in specific geometric and li-
dar conditions is estimated by collecting Ni, compar-
ing it with NT, and outputting Li when Ni meets the
requirement. Finally, the ASD profiles for all concrete
scenarios are created. More details regarding the pro-
gramming of ASD estimation were described in previ-
ous studies [13], [22].
Results and Discussion
How Far Can the LAV See?
Vertical Curves
According to the results in the ASD profiles, Figure 8 shows
the ASD at NC = 64 and hmL = 1.44 m along vertical curves
with different RV (= LV/4%). As noted, the ASD increases lin-
early as RV increases and then fluctuates around a general
level. Specifically, the f luctuation amplitudes are about 20
and 10 m at NT = 10 and 20, respectively. Compared with
the ASD results simulated by Wang et al. [13], [22], these
fluctuations along vertical curves with different RV values
are much larger than those along the horizontal curves
with different radii (about 5 and 2 m at NT = 10 and 20, re-
spectively), but the former frequency is lower. Also, there
are considerable overlaps between ASD cur ves at different
Vd, which means that Vd has little effect on the ASD along
vertical curves.
The ASD, limited by the
;;~
of 4%, can cover the entire
LV (= 4%RV) at a small RV, but its actual features appear as RV
increases to a critical RV (RVcri ); i.e., ASD = LV if RV ≤ RVcr i. The
features mentioned are attributed to the follow ing factors:
■ Prerequisite: Instead of the horizontal angular resolu-
tion, the vertical angular resolution plays a signifi-
cant role in determining the ASD along the vertical
curves because there is no lateral movement between
the vehicles.
■ A larger fluctuation amplitude: The vertical angular
resolution is larger than the horizontal angular resolu-
tion at NC = 64, and some of the laser points are emitted
into the air or blocked by the pavement.
■ A lower f requency and insi gnif icant effect of Vd: The
pitch angle (or vertical displacement) between vehicles
on the vertical curves is smaller than the yaw angle (or
lateral displacement) on horizontal curves.
Moreover, as shown in Figure 8(a) and (b), the ASD at
NT = 10 is longer than at NT = 20, and the ASD on the crest
Parameters
Variables
: Concrete Scenarios for Vertical Curves : Concrete Scenarios for Vertical Curves + Tangent Grades
Vehicles
Vd
Road Geometry
Vehicle Model
Driving Path
Lane Width
Cross Slope
LV (RV)
LTG
NC
NT
hmL
32
64
128
1.44 m
0.6 m
Lidar
HFoV
VFoV Horizontal Angular Resolution Range
Frame Rate
FIG 6 The parameters–variables pair sampling for the concrete scenarios.
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curve is approximately the same as on the sag curve. Spe-
cifically, ASD ≈ 55–75 m and 40–50 m at NT = 10 and 20,
respectively. This means that the as-built crest-curve
pavement profile does not have a disadvantage in ASD
(i.e., blocking the laser beams) compared with the sag-
curve pavement.
Because of the insignificant effect of Vd on ASD, the
ASD at Vd = 4 0 km/ h is show n in Fig ure 9 to f urt her explore
the effects of NC and hmL. As shown in Figure 9(a) and (b),
the A SD increa ses wit h NC. Notably, more NC or less NT c an
reduce the dif ficulty of TV detection, thus increasing
the ASD, which is consistent with the previous findings
[13], [22].
Figure 9(c) and (d) show that the ASD curve at hmL = 0.6 m
is mostly above that at hmL = 1.44 m, especially when RVC or
RVS is large. Due to the limited
~
and large RV, the closer
the hmL (0.6 m) is to the middle height of the TV (1.44/2 =
0.72 m), the more the laser points can be emitted to it by the
lidar with uniformly and symmetrically distributed vertical
channels, as illustrated in Figure 10. This also aligns w ith
the finding on horizontal curves [22]. However, this would
contradict the opinion that a higher hmL does enable a lidar
to receive more target information without occlusion. To
justify that opinion, it needs to assume that the TV can be
detected once its boundary enters the lidar’s FoV or it is ap-
plied in urban streets with several vehicles between the LAV
Simulation
Platform
Scenario
Design
Scenario Establishment
Ver tical
Alignments
Vehicle Model
Lidar Model
LAV
Motion
State and
Location
Profile
Motion
State and
Location
Profile
TV
Snapshots for Concrete Scenarios From the Simulation Platform
ASD Profiles in Different
Geometric and Lidar Conditions
Where tj is the ith (i ∈N+) timestamp of the total simulation time T for each trial; ti+j is the remaining timestamp after ti
until T, i.e., j = 1, 2, ...,N and ti+j < T;Ni,Ni+j are the numbers of laser points reflected from TV at ti and ti+j, respectively.
ASD Estimation
Collect Laser Points at ti
Output: Relative Path
Distance (Li) at ti = ASD
Number of Laser Points
Reflected From TV (Ni)
(Ni≤NT) and (Ni+j > NT)?
No
Ye s
ASD
Start the Experiment
FIG 7 The experimental process.
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and TV. To trade off the pros and cons of a higher or lower
hmL, some lidar products (e.g., Velodyne’s Alpha Prime)
mounted on the vehicle roof use a VFoV w ith a downward
offset and a more concentrated resolution distribution to-
ward the road pavement, as depicted in Figure 10.
To capture the RVc ri and compare the ASD on sag curves
with that on crest curves from the average perspective,
Table 3 shows the RVc ri and the average ASD
ASD
^h
when
RV > RVcr i. Note that, due to the adopted RV interval of 250 m,
the resulting RVc ri might differ from the actual value.
As shown in Table 3, the RVc ri for crest curves is larger
than that for sag curves in all conditions except at NC = 64
and hmL = 0.6 m. Also, the
ASD
on sag curves is basically
the same as that on crest curves except that the former is
longer than the latter at NC = 64 and hmL = 1.44 m. These
indicate that a lower hmL does cause a shorter ASD on
80
70
60
50
40
30
ASD (m)
80
70
60
50
40
30
ASD (m)
875
875
3,000
6,500
10,000
1,400
1,250
2,000
3,000
5,250
RVC (m) RVS (m)
Vd = 40 NT = 10
Vd = 60 NT = 10
Vd = 80 NT = 10
Vd = 100 NT = 10
Vd = 40 NT = 20
Vd = 60 NT = 20
Vd = 80 NT = 20
Vd = 100 NT = 20
(a) (b)
FIG 8 The ASD at NC = 64 and hmL = 1.44 m: (a) crest curves and (b) sag curves.
FIG 9 The ASD at Vd = 40 km/h: (a) for crest curves, hmL = 1.44 m; (b) for sag curves, hmL = 1.44 m; (c) for crest curves, NC = 64; and (d) for sag curves, NC = 64.
100
90
80
70
60
50
40
30
ASD (m)
100
80
90
70
60
50
40
30
ASD (m)
RVC (m) RVS (m)
NC = 32 NT = 10 hmL = 1.44
NC = 64 NT = 10 hmL = 1.44
NC = 64 NT = 10 hmL = 0.6
NC = 128 NT = 10 hmL = 1.44
NC = 32 NT = 20 hmL = 1.44
NC = 64 NT = 20 hmL = 1.44
NC = 64 NT = 20 hmL = 0.6
NC = 128 NT = 20 hmL = 1.44
(a) (b)
90
80
70
60
50
40
30
ASD (m)
80
70
60
50
40
30
ASD (m)
875 87510,000 5,250
RVC (m) RVS (m)
(c) (d)
875 87510,000 5,250
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IEEE INTELLIGENT TRANSPORTATION SYSTEMS MAGAZINE • 12 • MONTH 2024
crest curves when RVC < RVcr i; a higher hmL enables the
ASD to cover a wider range of LVC, but the ASD substan-
tially decreases when RVC > RVc ri, which is explained by
Figu re 11.
As shown in Figure 11, given the same RV, the FoV above
the pavement of the crest curve is larger than that of the
sag curve according to the geometric relation. However,
on the crest curve, the laser pulses from the lower lidar
channels would be easily blocked, and most upper beams
point to the air. On the contrary, most upper laser beams
shoot to the TV on the sag curve. In addition, both verti-
cal curves approach the tangent section as RV increases. It
should be noted that the current Vd-derived design of the
crest curve cannot block the FoV of the LAV completely
due to the limited
,~
which is required by vehicle dynam-
ics safety [40]. In F igure 11, although the area of the FoV
above the pavement reduces as hmL lowers from 1.44 m to
0.6 m, the FoV can still cover the TV in the same position
ahead. Also, the actual ASD on vertical curves (see
ASD
in Table 3) is significantly shorter than the range of lidar
(200 m).
Furthermore, given the same NC, NT, and hmL conditions,
ASD
on vertical curves (see Table 3) is basically the same
as that on tangent sections [13], but it is shorter than that on
the horizontal curves [13], [22], especially for NC = 128 and
NT = 10 (shorter by about 10 m). That further demonstrates
the small effect of vertical curve pavement on the ASD.
In addition, it is noteworthy that the LAV’s FoV might be
obstructed by an overhead structure (e.g., a flyover) on sag
curves, as illustrated in Figure 12. Therefore, whether such
a structure reduces the ASD on sag curves is further ex-
amined.
Since that as-built structure must be designed to pro-
vide sufficient vertical clearance (hVC ) for the HV’s RSD,
it is convenient to calculate t he ASD and then compare it
with the ASD of the LAV. Specifically, the ASD of the LAV
would be limited to ASDunder if ASDunder ≤ ASD. Otherwise,
the structure would not obstruct the LAV’s FoV. The ASD is
given by [40] as follows:
.
R
hh
hh22
ASD
S
under
V
VC EV
CO
=
-+ -
^^hh
6
@
(1)
where ASDunder is the ASD at the undercrossing, and hE and
hO are the heights of the human driver’s eye and object,
respectively. The empirical values of hVC , hE, and hO are 4.5,
1.5, and 0.75 m, respectively [40].
Given the same RVS listed in Table 1, ASDu nder calculated
by (1) is significantly longer than the ASD of the LAV. Ac-
cordingly, the ASD would not be affected by as-built struc-
tures on sag curves.
Tangent Grade and Vertical Curve
Based on t he st ated r elat ionsh ip bet ween t he A SD a nd RV, only
four typical RV values, i.e., both minimum and maximum
values o f RV range s at Vd = 4 0 km/ h (see Table 1), were adopt-
ed to investigate the independent effect of LTG. Figure 13(a)
and (b) depicts the ASD at NC = 64 and hmL = 1.44 m along
the tangent grades and vertical curves with different LTG
values.
As shown in Figure 13(a) and (b), the ASD still fluctu-
ates with LTG. In general, with an increase in LTG, 1) when
RV adopts the maximum value, the ASD increases and
decreases at NT = 10 and 20, respectively, and 2) when RV
adopts the minimum value, the ASD still increases linearly
(ASD = LTG + LV) and then rises gradually (ASD < LTG + LV).
Regarding the road segment covered by the lidar
FoV, the overall curvature of its longitudinal profile de-
creases as the proportion of a tangent grade increases.
hmL = 0.72 m
hmL = 1.44 m
hmL = 1.44 m
hmL = 0.6 m
LAV TV
Vehicle Height = 1.44 m
Lidar’s Vertical FoV
Symmetrical
Distribution
of Vertical
Channels
Asymmetrical
Distribution
of Vertical
Channels
FIG 10 The TV coverages by the lidar’s VFoV at different hmL values. Note
that the vehicles are simplified as rectangles, and the VFoV is simplified
as a triangle.
Crest Vertical Curve Sag Vertical Cur ve
hmL = 1.44 mhmL = 0.6 m
FIG 11 A scenario comparison of the crest and sag curves under different
hmL values and the same RV.
Flyover
Ver tical Clearance
at Undercrossings
FIG 12 The s scenario at undercrossings.
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Accordingly, the relative path distance within the FoV
decreases based on the geometric relation, as with the
ASD at larger RV and NT. Given that a large RV cau ses
the longitudinal road profile to approach horizontal
alignment, this aligns with the previous finding that,
the higher the NT, the more consistent the change of
the ASD with the relative path length [13], [22]. On the
contrary, a lower NT allows a longer ASD, but that ASD
would f luctuate instead of complying with the change
of the relative path length due to sparser channels.
Furthermore, the ASD results at the minimum RV are
consistent wit h those in Figure 8(a) and (b) because
the additional tangent grade length can be considered
the increasing RV.
Table 4 further lists
ASD
when ASD < LTG + LV. As
shown in Table 4, all
ASD
re-
sults are basically the same as
those corresponding results at
NC = 64 and hmL = 1.44 m on com-
plete vertical curves (see Table 3),
except that the
ASD
(= 68.1 and
68.7 m) at NT = 10 on the ta ngent grade
and crest curve are much larger
than 61.9 m. It is necessary to high-
light such an
ASD
reduction from
a tangent grade followed by a crest
curve to a complete crest curve at
those lidar-related features.
Finally, both the ASD (see Fig-
ures 9 and 13) and
ASD
(see Tables 3
and 4) results answer, “How far can
LAV s ee?”
How Fast Should the LAV Drive?
According to [1], AV automation lev-
els that are still constricted by the
ODD include L3 and L4. As proposed
by Wang et al. [10], RSDs of L3 and L4 (RSDL3 and RSDL4,
respectively) are calculated via (2) and (3), respectively:
.
.
.
.
RSDVt Ai
V
Ait
Ait
0 278
254 981
981
2
1
981
33
2
2
LdP_LdG
d
dp
GT
dp
GT
##
!
!#
!#
=+
-
-
cc
cc
c
mm
m
m
m
;
;
E
E
(2)
.
.
Vt Ai
V
0 278
254
981
RS
D4
2
L4 dP_L
dG
d
##
!
=+
cm
;
E
(3)
where tP_L 3 and tP_L 4 are the perception–brake reaction
times of L3 and L4, respectively; tT is the driver’s takeover
time from the L3 automation system; Adp is a preset decel-
eration rate activated by the L3 automation system dur-
ing tT; and Ad is the deceleration rate. For vertical curves
(i.e., quadratic parabolic curves), iG ≈ iG0 – ASD/(2RV) on
NChmL (m) NT
RVcri (m)
a
ASD
(m)
Crest Sag Crest Sag
32 1.44 10 1,375 1,250 51.2 51.2
20 875 —
b
34.4 33.4
64 0.6 10 1,625 1,750 70.4 70.8
20 1,125 1,250 47.6 46.5
1.44 10 1,875 1,250 61.9 66
20 1,125 1,000 45.2 46.4
128 1.44 10 2,250 2,250 89.3 89.9
20 1,625 1,500 66.1 65.9
Note:
a
RVcri corresponds to the critical LV (= 4%RVcri);
b
There is no RVcri under those NC, hmL,
and NT conditions.
Table 3. The critical curvature of vertical curves and average
ASD for RV > RVcri.
Alignment Combination RV (m) NT
ASD
(m)
Tangent grade and crest curve 875 10 68.1
20 44.9
10,000 10 68.7
20 46.6
Tangent grade and sag curve 875 10 66.4
20 46.1
5,250 10 67.9
20 45.7
TABLE 4. The average available SD for ASD < LTG + LV.
30
35
40
45
50
55
60
65
70
75
80
ASD (m)
0102030
LTG (m)
(a)
40 50 60 70
30
35
40
45
50
55
60
65
70
75
80
ASD (m)
0102030
LTG (m)
(b)
40 50 60 70
NT = 10 RVC = 875 m
NT = 20 RVC = 875 m
NT = 10 RVC = 10,000 m
NT = 20 RVC = 10,000 m
NT = 10 RVS = 875 m
NT = 20 RVS = 875 m
NT = 10 RVS = 5,250 m
NT = 20 RVS = 5,250 m
FIG 13 The ASD on (a) tangent grades and crest curves and (b) tangent grades and sag curves.
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IEEE INTELLIGENT TRANSPORTATION SYSTEMS MAGAZINE • 14 • MONTH 2024
upgrades, and iG ≈ iG0 + AS D/(2RV) on downgrades [47 ].
Take “–” and “+” on upgrades and downgrades, respec-
tively. The empirical or assumed values of tP_L3 , tP_ L4 , tT,
Adp, and Ad are 4.3 s, 0.5 s, 3.8 s, 2.5 m /s2, and 3.4 m/s2,
respectively, which were adopted by Wang et al. [10]. Be-
cause of the adopted
~
of ±4% and maximum |iG| of 4%,
the minimum and maximum iG0 values are zero and 4%,
respectively, for crest curves and –4% and zero, respec-
tively, for sag curves.
As Vd has little influence on the ASD, Vmax for the LAV
under a given RV could be calculated by setting the ASD
[see (1)] equal to the RSD [see (2) or (3)]. Figu re 14(a)–(d)
show Vmax for L3 and L4 on vertical curves. Note that only
the ASD is considered at RV ≥ RVcr i due to the limited LV at
RV < RVcr i. The Vmax values at RV < RVcri can refer to those at
RV ≥ RVcr i since the actual road still has a subsequent align-
ment after a vertical curve.
As shown in Figure 14(a)–(d), Vmax for L4 is much larg-
er than that for L3 due to RSDL3 > RSDL4 given the same Vd
and geometric conditions. That is in line with the case of
horizontal alignment [10]. Also, Vma x values on upgrades
are larger than those on dow ngrades, and their differ-
ence increases with more NC. Other Vmax features related
to RV, NC, NT, and hmL are consistent with the case of ASD
features.
In addition, since the market maturity of AVs can-
not be achieved overnight [48], their driving speed on
as-bu ilt highways needs to be c omparable to that of HVs or
vehicles with lower automation levels. The Vd of a specif-
ic highway section can be tentatively regarded as a gen-
eral driving speed of most vehicles. Therefore, to ensure
speed consistency with Vd (40–100 km/h), a typical Vmax
range of (Vd – 20 km/h) to Vd [49], [50] corresponding to
the specified RV range was adopted [see Figure 14(a)–(d)].
Furthermore, given specific geometry, lidar, and auto-
mation level conditions, if Vmax > Vd and (Vd – 20 km/h)
≤ Vmax ≤ Vd, such an LAV driving wit h Vd and Vmax, respec-
tively, could satisfy both the SD and speed consistency
requirements. However, if Vmax < (Vd – 20 km/ h), the
speed consistency for the LAV driving with Vmax will
fail. As shown in Figu re 14(a)– (d), generally, Vmax for L3
and L4 at NT = 10 ranges from 30 to 55 km/h and 55 to
85 km/h, respectively, and both Vmax values for L3 and L4
reduce by 10–15 km/ h at NT = 20.
Such a fluctuating Vmax along the alignment specified by
a certain Vd could be feasible in an individual AV’s dynamic
NC
hmL
(m) NT
Driving
Automation
Level
Crest Curves:
Vd (km/h) and Specified RCV (m) Range
Sag Curves:
Vd (km/h) and Specified RSV (m) Range
40 km/h
[875,
10,000]
60 km/h
[1,400,
10,000]
80 km/h
[3,000,
10,000]
100 km/h
[6,500,
10,000]
40 km/h
[875,
5,250]
60 km/h
[1,250,
5,250]
80 km/h
[2,000,
5,250]
100 km/h
[3,000,
5,250]
32 1.44 10 L3 [34, 35] O O O 34 O O O
L4 P P [62, 65] O P [59, P] [O, 62] O
20 L3 [25, 26] O O O [24, 25] O O O
L4 P[49, 52] O O P [46, 49] O O
64 0.6 10 L3 P[43, 45] O O P [43, 44] O O
L4 P P [72, 76] O P P [70, 74] O
20 L3 [32, 33] O O O [31, 32] O O O
L4 P[58, P] [O, 61] O P [56, 59] O O
1.44 10 L3 [39, P] [O, 41] O O P [41, 42] O O
L4 P P [67, 71] O P P [68, 72] O
20 L3 [31, 32] O O O [31, 32] O O O
L4 P[57, 60] [O, 60] O P [56, 59] O O
128 1.44 10 L3 P[52, 53] O O P [51, 53] O O
L4 P P P [82, 86] P P P [80, 84]
20 L3 P[41, 42] O O P O O O
L4 P P [70, 74] O P P [68, 71] O
Note: O:
Vmax_d
and
Vmax_u
< (Vd – 20 km/h)
Vmax_d
< (Vd – 20 km/h) and
(Vd – 20 km/h) <
Vmax_u
<Vd
(Vd – 20 km/h) <
Vmax_d
and
Vmax_u
< Vd
(Vd – 20 km/h) <
Vmax_d
<
Vd and Vd <
Vmax_u
P:
Vmax_d
and
Vmax_u
> Vd.
TABLE 5. Average maximum speeds of LAV for upgrades and downgrades (Vmax_ u . Vmax_d)
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control, which improves the vehicle-based ODD. However,
Vmax might not be attractive to road administrators due to
its lack of generality. To obtain a more general Vmax for the
speed limit, the average maximum speed
V
max
^h
within
the specified RV range was further calculated, as shown in
Table 5. Note that
Vmax
was separately calculated using the
maximum speed on the upgrade
V
_maxu
^h
and downgrade
.V
_maxd
^h
As shown in Table 5,
Vmax
with an exact value (see yel-
low or light red/green cells) can be used as a speed limit
for vertical curves. In addition, the
Vmax
on the tangent
grade and vertical curve are basically the same as those
on vertical curves due to the same
ASD
except the case
at NC = 64, hmL = 1.44, and NT = 10 on the tangent grade
and crest curve. In that case, with
ASD
≈ 68 m,
Vmax
would increase by about 4 km/h. However, more atten-
tion to a smaller
Vmax
should be paid on subsequent crest
curves. Finally, the results of both Vmax (Figure 14) and
Vmax
(Table 5) answer the question, “How fast should the
LAV d r iv e? ”
Our answers to these two questions appear to fall
well short of what the general public expects for an
AV’s potential advantages—i.e., it can see farther and
drive faster. This is mainly attributed to the specific
experimental designs related to lidar adopting only
a single multichannel lidar and NT of more than one
100
90
80
70
60
50
40
30
20
Vmax (km/h)
875 1,400 3,000 6,500 10,000
875
1,250
3,000
5,250
2,000
100
90
80
70
60
50
40
30
20
Vmax (km/h)
100
90
80
70
60
50
40
30
20
Vmax (km/h)
100
90
80
70
60
50
40
30
20
Vmax (km/h)
875 1,400 3,000 6,500 10,000
RVS (m)
RVC (m) RVC (m)
(a)
(c) (d)
(b)
875
1,250
3,000
2,000
RVS (m)
Vd = 100 Vd = 100
Vd = 100
Vd = 80 Vd = 80
Vd = 80
Vd = 60 Vd = 60
Vd = 60
Vd = 40
Vd = 100
Vd = 80
Vd = 60
Vd = 40
Vd = 40 Vd = 40
5,250
NC = 32 L4
hmL = 1.44 Upgrade
NC = 32 L4
hmL = 1.44 Downgrade
NC = 64 L4
hmL = 1.44 Upgrade
NC = 64 L4
hmL = 1.44 Downgrade
NC = 64 L4
hmL = 0.6 Upgrade
NC = 64 L4
hmL = 0.6 Downgrade
NC = 128 L4
hmL = 1.44 Upgrade
NC = 128 L4
hmL = 1.44 Downgrade
NC = 32 L3
hmL = 1.44 Upgrade
NC = 32 L3
hmL = 1.44 Downgrade
NC = 64 L3
hmL = 1.44 Upgrade
NC = 64 L3
hmL = 1.44 Downgrade
NC = 64 L3
hmL = 0.6 Upgrade
NC = 64 L3
hmL = 0.6 Downgrade
NC = 128 L3
hmL = 1.44 Upgrade
NC = 128 L3
hmL = 1.44 Downgrade
40 km/h < Vmax < 20 km/h 60 km/h < Vmax < 40 km/h
80 km/h < Vmax < 60 km/h 100 km/h < Vmax < 80 km/h
Specified RVC or RVS
Range Corresponding
to Certain Vd
FIG 14 Vmax: (a) for crest curves, NT = 10; (b) for crest curves, NT = 20; (c) for sag curves, NT = 10; (d) and for sag curves, NT = 20. Note that upgrade refers to
the crest or sag curves with iG0 = 4% or zero, respectively, and downgrade refers to the crest or sag curves with iG0 = zero or –4%, respectively.
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laser point, which were justified earlier. Therefore,
how the LAV safely adapts to the as-built vertical
alignment could be solved by referring to the pro-
posed speed limits. Otherwise, to help the LAV see far-
ther and drive faster on as-built vertical alignments, it
is suggested to equip it with more lidars, incorporate
more channels, or develop algorithms with fewer NT.
In addition, we conjecture that detection capability
beyond the SD can be achieved by deploying roadside
monitoring sensors [51], which is also beneficial to im-
proving the LAV’s Vmax.
Concluding Remarks
This study adopts a vir tual simulation method and con-
ducts a scenario-based experimental design to answer
the question, “How far can the LAV see on highway verti-
cal alignments?” Then, the SD and speed consistency re-
quirements are considered to answer the question, “How
fast should it drive?” To the authors’ best knowledge, this
study is the first attempt that considers the LAV’s ASD
issues on vertical alignments and proposes the corre-
sponding speed limits. Based on the study, the following
comments are offered:
■ The answer to “How far can the LAV see on highway
vertical alignments?” depends on variables regarding
vertical geometric elements and lidar. Specifically, the
ASD increases as NT decreases, NC increases, or hmL
decreases. Importantly, the ASD on crest curves is the
same as on sag curves or tangent sections, which means
that the as-built crest-cur ve pavement profile would not
limit the ASD. Also, since lidar’s vertical angular reso-
lution is generally coarser than the horizontal, the ASD
fluctuates around
ASD
as RV increases, which is more
noticeable than horizontal curves. Consequently, these
results provide new insight into effects attributable to
the features of the vertical geometry and lidar on an
LAV’s ASD variations. They further highlight the lim-
ited perception capabilit y of current AVs from the per-
spective of road safety.
■ The answer two “How fast should it drive?’ further
depends on the LAV’s automation level besides those
variables. Specifically, ranges of Vmax for L3 and L4 are
30–55 km/h and 55– 85 km/h, respectively, at NT = 10
and 20–40 km/h and 45–75 km/h, respectively, at
NT = 20. An important practical implication of this study
is related to the proposed speed limit within the road
section, which regulates L3 and L4 safe speeds and im-
proves road-oriented ODD specifications. Also, only at
NC = 128 and NT = 10 would L4 be compatible with as-
built vertical alignment with Vd = 100 km /h. However,
even under these conditions, L3 can only adapt to the
vertical profile with Vd = 60 km/h.
■ The main limitation of this study is a lack of consid-
eration of weather effects. On the one hand, adverse
weather (e.g., rainy days) would impair lidar functions
and, thus, shorten the ASD [30]. On the other hand, the
weather might also impact the RSD due to the wet pave-
ment or longer takeover time. In addition, this study
only considers one AV type of passenger vehicle. Be-
sides the ASD, speed limits for heavy-duty AVs on verti-
cal alignment must account for their braking capacity
and truck drivers’ reaction times [10]. Therefore, exten-
sive tests that include weather effects and automated
trucks should be conducted in the future. Also, in the
future, we are interested in extending the road geom-
etry from 2D to 3D, i.e., combined alignment, which
would be more consistent regarding the reality of geo-
metric conditions.
About the Authors
Sh uy i Wa ng (syw@fzu.edu.cn) earned
his Ph.D. degree from the School of
Transportation, Southeast University,
Nanjing, China, in 2023. He is an as-
sistant professor at the College of Civil
Engineering, Fuzhou University, Fu-
zhou 35108, China. His research inter-
ests include road and traffic safety analysis for automated
vehicles.
Yang Ma (mayang@hfut.edu.cn) earned
his Ph.D. degree from the School of
Transportation, Southeast University,
Nanjing, China, in 2022. He is an
associate professor in the School of Au-
tomotive and Transportation Engineer-
ing, Hefei University of Technology,
Hefei 230000, China. His research interests include infra-
structure digitalization, point cloud data processing, and
road safety analysis.
Said M. Easa (seasa@torontomu.ca)
earned his Ph.D. degree in transporta-
tion engineering from the University of
California, Berkeley, CA, USA, in 1982.
He is a professor with the Department of
Civil Engineering, Toronto Metropolitan
University, Toronto, ON 350, Canada.
He was a recipient of numerous best paper and lifetime
achievement awards from national Canadian and U.S. orga-
nizations for his works, including The Frank M. Masters
Transportation Engineering Award from the American
Society for Civil Engineering, Sandford Fleming Award
from the Canadian Society for Civil Engineering (CSCE),
and the Award of Academic Merit from the Transportation
Association of Canada. He is a fellow of the Engineering In-
stitute of Canada, the Canadian Academy of Engineering,
and the CSCE.
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IEEE INTELLIGENT TRANSPORTATION SYSTEMS MAGAZINE • 16 • MONTH 2024 IEEE INTELLIGENT TRANSPORTATION SYSTEMS MAGAZINE • 17 • MONTH 2024
weather (e.g., rainy days) would impair lidar functions
and, thus, shorten the ASD [30]. On the other hand, the
weather might also impact the RSD due to the wet pave-
ment or longer takeover time. In addition, this study
only considers one AV type of passenger vehicle. Be-
sides the ASD, speed limits for heavy-duty AVs on verti-
cal alignment must account for their braking capacity
and truck drivers’ reaction times [10]. Therefore, exten-
sive tests that include weather effects and automated
trucks should be conducted in the future. Also, in the
future, we are interested in extending the road geom-
etry from 2D to 3D, i.e., combined alignment, which
would be more consistent regarding the reality of geo-
metric conditions.
About the Authors
Sh uy i Wa ng (syw@fzu.edu.cn) earned
his Ph.D. degree from the School of
Transportation, Southeast University,
Nanjing, China, in 2023. He is an as-
sistant professor at the College of Civil
Engineering, Fuzhou University, Fu-
zhou 35108, China. His research inter-
ests include road and traffic safety analysis for automated
vehicles.
Yang Ma (mayang@hfut.edu.cn) earned
his Ph.D. degree from the School of
Transportation, Southeast University,
Nanjing, China, in 2022. He is an
associate professor in the School of Au-
tomotive and Transportation Engineer-
ing, Hefei University of Technology,
Hefei 230000, China. His research interests include infra-
structure digitalization, point cloud data processing, and
road safety analysis.
Said M. Easa (seasa@torontomu.ca)
earned his Ph.D. degree in transporta-
tion engineering from the University of
California, Berkeley, CA, USA, in 1982.
He is a professor with the Department of
Civil Engineering, Toronto Metropolitan
University, Toronto, ON 350, Canada.
He was a recipient of numerous best paper and lifetime
achievement awards from national Canadian and U.S. orga-
nizations for his works, including The Frank M. Masters
Transportation Engineering Award from the American
Society for Civil Engineering, Sandford Fleming Award
from the Canadian Society for Civil Engineering (CSCE),
and the Award of Academic Merit from the Transportation
Association of Canada. He is a fellow of the Engineering In-
stitute of Canada, the Canadian Academy of Engineering,
and the CSCE.
Hao Zhou (z hou hao@gatech.edu)
earned his Ph.D. degree in civil engi-
neering from the Georgia Institute of
Technology in 2022. He is an assistant
professor in the Department of Civil
Engineering, University of South Flori-
da, Tampa, FL 33620 USA. His research
interests are primarily focused on traff ic flow theory, com-
plex network science, and autonomous driving.
Yuanwen Lai (laiyuanwen@fzu.edu.cn)
earned his Ph.D. degree in transporta-
tion engineering from the Beijing Uni-
versity of Technology in 2022. He is an
associate professor at the College of
Civil Engineering, Fuzhou University,
Fuzhou 350108, China. His research
interests include data mining for road and traffic safety
analysis.
Weijie Ch en (chenweijie@seu.edu.cn)
earned his M.S. degree from the School
of Transportation, Southeast University,
Nanjing, China, in 2017. He is currently
pursuing his Ph.D. degree in transpor-
tation engineering at Southeast Univer-
sity, Nanjing 211189, China. His research
interests include intelligent transportation systems.
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