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ARTICLE INFO
Article ID: 13-02-01-0002
© 2021 SAE International
doi:10.4271/13-02-01-0002
History
Received: 09 Aug 2020
Revised: 05 Nov 2020
Accepted: 11 Jan 2021
e-Available: 18 Mar 2021
Keywords
Connected and automated
vehicle (CAV), Dynamic
eco-driving, Signal phase
and timing (SPaT),
Signalized corridor
Citation
Wu, G., Hao, P., Wang, Z.,
Jiang, Y. et al.,
“Eco-Approach and
Departure along Signalized
Corridors Considering
Powertrain Characteristics,”
SAE Int. J. Sust. Trans.,
Energy, Env., & Policy
2(1):2021,
doi:10.4271/13-02-01-0002.
ISSN: 2640-642X
e-ISSN: 2640-6438
Eco-Approach and Departure along
Signalized Corridors Considering
Powertrain Characteristics
Guoyuan Wu,1 Peng Hao,1 Ziran Wang,1 Yu Jiang,1 Kanok Boriboonsomsin,1 Matthew Barth,1 Michael McConnell,2
Shuwei Qiang,3 and John Stark2
1University of California Riverside, USA
2Leidos, Inc., USA
3Amazon, Inc., USA
Abstract
With the emergence of connected and automated vehicles (CAVs), numerous dynamic eco-driving
strategies have been developed all over the world. The Eco-Approach and Departure (EAD) applica-
tion is considered to bea promising solution to the relief of transportation activity-related pressure
on energy and environment. Unlike most of existing EAD strategies that utilize signal phase and
timing (SPaT) information on an intersection basis, wepropose a computationally ecient algorithm
for EAD along signalized corridors (EADSC), which can take advantage of SPaT information of all
the intersections along the corridor as a whole, and can determine the optimal (in terms of fuel
eciency) speed trajectories with the consideration of the host vehicle’s powertrain characteristics.
Both the numerical study and real-world field implementation indicate that the proposed EADSC
system shows great promise in fuel savings (e.g., ranging from 12% to 28%) without compromising
on mobility, compared to the baseline driving strategy without SPaT knowledge and other repre-
sentative EAD strategies. Wealso discuss some practical issues when deploying the proposed system
in the real-world, such as unavailability of complete knowledge on the background signal timing
plan in current SPaT messages, and handling of interactions from other trac (e.g., cut-ins).
Downloaded from SAE International by Ziran Wang, Friday, April 23, 2021
2 Wu et al. / SAE Int. J. Sust. Trans., Energy, Env., & Policy / Volume 2, Issue 1, 2021
Introduction
The uninterrupted growth in transportation activities,
for both people and goods movement, has been exer ting
a significant amount of pressure on our society,
economy, and environment. It was reported that about 28%
of total U.S. energy was consumed for transporting people
and goods from one place to another in 2018 [1]. In addition,
according to a report by U.S. Environmental Protection
Agency (USEPA), the transportation sector accounted for 28%
of total greenhouse gas (GHG) emissions in 2018, higher than
any other sector including electricity, industry, agriculture,
commercial, and residential [2].
On the other hand, emerging technologies such as
connected vehicles (CVs), transportation electrication, and
edge computing have been stimulating more and more dedi-
cated eorts by engineers, researchers, and policymakers to
tackle these transportation-related energy and environmental
problems. Good examples include the Applications for the
Environment: Real-Time Information Synthesis (AERIS)
Program initiated by U.S. Department of Transportation [3],
the eCoMove [4], and Horizon 2020 [5] funded by the
European Commission. A variety of environmentally friendly
CV applications [6], in particular those related to eco-driv ing
strategies, have been proposed, developed, and validated.
Among all eco-driving strategies, the Eco-Approach and
Departure at Signalized Intersections (EADSI) system has
shown signicant promise [7, 8, 9, 10, 11]. In this system, an
equipped vehicle can take advantage of the signal phase and
timing (SPaT) and geometric intersection description (GID)
information from the upcoming signalized intersection, and
then calculate the optimal speed prole to pass through the
intersection in green or to decelerate to a full stop in the most
energy ecient manner. Speed references may beprovided to
the driver using a driver-vehicle interface (DVI) or to the
control system that supports automated driving capabilities
(at least) longitudinally.
Due to its attractiveness, the eco-driving system has
received considerable attention from numerous studies
involved in the development and testing of various algorithms
[12, 13, 14, 15, 16 , 17, 18, 19, 20, 21]. However, many of these
algorithms are not exible enough to handle well the road
grade, customized powertrain characteristics, or interaction
with other trac. In addition, very few of them have been
designed and va lidated for eco-driving along signalized corri-
dors but only for isolated intersections [22]. eir extendibility
to handle the eco-driving along multiple signalized intersec-
tions is still questionable, mainly due to the real-
time performance.
To address the aforementioned issues, wepropose herein
an innovative algorithm for Eco-Approach and Departure
along Signalized Corridors (EADSC). Unlike EADSI, the
proposed EADSC can take full advantage of the SPaT infor-
mation from all downstream intersections (e.g., via cellular
communications) to plan the equipped vehicle’s trajectory.
More specically, it is assumed that the downstream trac
states can bereliably predicted (through the fusion of all
available sensors). is predicted information can beinte-
grated with the host vehicle’s states and characteristics (e.g.,
location, instantaneous speed, tractive power limit) to
construct the so-called reachable region (RR) at the lane level.
Based on the predicted lane-level RR, the optimal passage
cycle (in terms of energy/fuel consumption minimization with
consideration of detailed powertrain characteristics) at each
signal can bedetermined in a time-ecient manner, to guar-
antee the real-time performance of the EADSC algorithm.
Upon the determination of the target cycle at each signal along
the corridor, the RR can besignicantly reduced.
en, the trajectory planning can beformulated as a
shortest path problem within the reduced RR.
e rest of this article is organized as follows: Section 2
reviews the background information related to the proposed
EADSC system. Details of the methodology are described in
Section 3, followed by the (numerical) case study in S ection4.
e eld implementation is presented in Section 5. Section 6
discusses some practical issues for real-world deployment.
e last section summarizes this article with concluding
remarks and future work.
LiteratureReviewand
Background
In this section, werst review the status quo of research
related to EAD application, and then give a brief introduction
on the powertrain model used for fuel/energy consumption
estimation in this study.
2.1. Eco-Approach and
Departure
In the past decade, a variety of studies have been conducted
on EAD, especially from the perspective of isolated intersec-
tions. Mandava etal. [12] proposed a piecewise linear trigo-
nometric function-based vehicle trajectory planning algo-
rithm for eco-driving along urban arterials. It has been exten-
sively evaluated and validated in both simulation [23] and
eld testing (with light-duty vehicle [24] and heavy-duty truck
[25], respectively), in the form of either advanced driver assis-
tance system (ADAS) [26] or partially automated control [27],
showing good real-time performance and substantial benets
in reducing fuel consumption and ta ilpipe emissions. However,
signicant eorts are required to modify the algorithm to
accommodate customized powertrain models and to handle
rolling terrains. Based on the VT-Micro model, Rakha and
Kamalanathsharma [14] developed a constant deceleration-
based eco-driving strategy to avoid full stops at signals,
followed by further improvement using a multistage dynamic
programming and recursive path-nding principles as well
as evaluation with an agent-based model [28]. Asadi and
Vahidi [15] proposed a two-step predictive cruise control
concept, aiming to reduce fuel use and trip time by utilizing
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Wu et al. / SAE Int. J. Sust. Trans., Energy, Env., & Policy / Volume 2, Issue 1, 2021 3
trac signal status information. e rst step is to determine
the target speed based on available green window, while the
second step is to perform the optimal tracking of target speed.
Katsaros etal. [16] developed a Green Light Optimized Speed
Advisory (GLOSA) system whose goal was to minimize
average fuel consumption and average stop delay at a trac
signal. By taking into account the queue discharging process,
Chen etal. [17] devised an eco-driving algorithm for the
equipped vehicle’s approaching and leaving a signalized inter-
section to minimize the integrated metrics of emissions and
travel time, but the algorithm did not consider the roadway
grade information. Jin etal. [18] formulated the power-based
optimal eco-driving problem as a 0-1 Binary Mixed Integer
Linear Programming (MILP), which is applicable to scenarios
of signalized intersection, nonsignalized intersection, or
freeway. e approach can take into account road-grade eects
and powertrain dynamics, but has relatively low computa-
tional eciency. Li etal. [19] used the Legendre pseudospec-
tral method and knotting technique to overcome the discrete
gear ratio issue in the optimal control for eco-driving at
signalized intersections. Huang and Peng [20] adopted a
simplified powertrain model and applied the sequential
convex optimization approach to optimizing vehicle speed
trajectory at signalized intersections, which can keep a ba lance
between optimality and real-time performance.
When considering the application of EAD in a more
realistic environment, many studies took “reactive”
approaches to cope with disturbances from the downstream
trac (e.g., switching to the car-following mode control if
the host vehicle was too close to its predecessor) or assumed
trac signals were running xed-time mode [21, 29, 30]. To
address these issues, some researchers specically focused
on tackling the queuing eects for EADSI by applying the
shockwave theory [31] or data-driven techniques [32] to
predict the queue length or in essence the trajectory of the
host vehicle’s predecessor. Others were dedicated to dealing
with uncertainties in trac signal operation such as actuated
signals by improving the prediction of the SPaT information
[33] or developing more robust eco-driving strategies [34, 35,
36]. In addition, most of the existing EAD strategies were
applicable to only isolated intersection scenarios or to signal-
ized corridor scenarios, but in an intersection-by-intersection
manner which may be far from being optimal. Very few
studies were particularly focused on the eco-driving strate-
gies along multiple signalized intersections [35, 37, 38, 39],
where one of the major challenges was to balance energy
minimization against computational eciency for driving
on a long enough roadway stretch. Some recent studies tried
to address the real-time performance for dynamic eco-
driving along the signalized corridor [22, 40], but the selected
speed profiles were simplified with certain smoothness
assumptions without considering detailed powertrain char-
acteristics. In this article, wedevelop a exible algorithm for
EADSC, which can accommodate a variety of factors (e.g.,
customized powertrain, rolling terrain, disturbance from
downstream trac, and uncertainty in signal operation),
while keeping the balance between optimality and real-
time performance.
2.2. Powertrain Model and
Fuel Consumption
Estimation
One of the key questions in vehicle trajectory planning for
EAD is to identify a useful model, which directly relates the
energy consumption rate with the vehicle dynamics and other
externalities such as road grade, wind speed, and road surface
roughness. On one hand, the longitudinal vehicle dynamics
model [41] governs the relationship between the traction/
brake force (Ft) and the inertia force (Fi) as well as other road
resistances, including rolling resistance (Ff), aerodynamic
drag (Fa), and grade resistance (Fg):
Fv
aFFFFmamgf
CAvmg
tifa
gr
aDf
,,
θδθ
ρθ
()
=+++ =+
++
cos
sin
1
2
2 Eq. (1)
where m represents the vehicle mass; S is the coecient
accounting for the eect of rotating and reciprocating parts;
g is the gravity factor (m/s2); fr is the rolling resistance coef-
cient; θ is the road grade (rad); CD is the drag coecient; ρa
is the air density (kg/m3); Af is the vehicle frontal area (m2);
and v is the vehicle speed (m/s).
On the other hand, the engine eciency map or brake-
specic fuel consumption (see Figure 1 as an example) sets up
the mapping from both engine torque (τ) and engine speed
(ω) to the fuel consumption rate (Q). In this study, weuse
activity dataset collected from the test vehicle to t the energy
consumption rate (liter/h) as a quadratic function of engine
torque (N·m) and engine speed (rpm):
Qt
τω ββτβωβτω βτ βω
,
()
=+ ++ ++
12 34 5
2
6
2
Eq. (2)
where βi represents the coefficient of the ith terms
in Equation 2.
erefore, to map the fuel consumption rate with vehicle
speed, acceleration and road grade, that is, Qt(v, a, θ),
1000
800
600
400
200
0
)mN(euqrotenignE
Engine speed (rpm)
800 1200 1600 2000 2400
60
50
40
30
20
10
0
FIGURE 1 An example engine map where the maximum
engine torque-speed curve is indicated by the solid curve.
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4 Wu et al. / SAE Int. J. Sust. Trans., Energy, Env., & Policy / Volume 2, Issue 1, 2021
weapproximate both engine torque and engine speed as func-
tions of these variables. One key step is to relate the “lumped”
gear ratio as a function of vehicle speed, as both engine torque
and engine speed can beexpressed as
τθ
ηη
δθ
ρθ
=
()
=+
++
Fva
nn
ma mgfCAv mg
t
raDf
,, 11
2
2
co
ss
in
Eq. (3)
ω
=⋅nv
Eq . (4)
where η is the overall powertrain efficiency; and the
“lumped” gear ratio n = rfrt/rr is determined by the nal
drive ratio rf , the gear ratio of the transmission rt, and the
radius of wheel rr . By following the similar step in [42],
weformulate the “lumped” gear ratio as the sum of weighted
indicator functions of v where the weights are the ratios at
associated gear levels. It is also noted that if the vehicle is
operating in the coast or brake mode, that is,
dv
dt
acoast
≤, then
weassume the fuel consumption rate is a constant Qidie
which equals to the rate when idling, and
am
gf CAvmg
coastr aD f
=−
−−
−co
ss
in
θρ
θ
1
2
2 E q. (5)
ProposedMethodology
Figure 2 presents a owchart of the framework that enables
an equipped vehicle to perform dynamic eco-driving along a
signalized corridor, which includes the stages of sensing,
planning (or decision-making), and execution. In this study,
wefocus on the development and validation of three major
steps of our EADSC algorithm (i.e., planning stage): (a) RR
construction; (b) target cycle determination; and (c) vehicle
trajectory planning. e environment sensing, lane-level trac
state prediction (including sensor fusion), and execution and
state update (e.g., low-level controller design) are also impor-
tant topics, but outside the scope of this study. Before elabo-
rating the description of each step, a few major assumptions
and remarks are presented in the following:
•e trac signal controllers along the corridor are
operating in xed-time manner. erefore, the SPaT
information is deterministic and the future signal state
can bewell predicted. It is expected that actuated signal
control would present much more challenges for eco-
driving due to some uncertainties in the future SPaT, as
discussed in our previous research [34].
•Full knowledge of background signal timing (i.e., cycle
length, phase duration, phase sequence) is available for
trajectory planning. is is a widely adopted assumption
for almost all EAD-related studies. However, this
information may not beavailable in the SPaT message in
practice [43]. Further discussion on how to handle
partial knowledge of background signal timing from the
SPaT will bepresented in Section 6.
3.1. Reachable Region
Construction
In this study, wedene the lane-level “Reachable Region”
(with respect to the host vehicle) as the set of (predicted) reach-
able states in the spatiotemporal region or distance-time (D-T)
diagram, which is widely used in the transportation engi-
neering (see the “void” areas in Figure 3). e gure may
represent one ingress lane along the approach of interest at a
signalized intersection with potential disturbances from other
trac. As can be observed in the gure, the RR is usually
bounded due to both endogenous and exogenous factors. e
endogenous factors may include the host vehicles’ tractive
power limit, maximum acceleration/deceleration, and jerk
limit to guarantee driving comfort, while the exogenous
factors consider the roadway speed limit, (predicted) down-
stream trac conditions (such as queue length or predeces-
sor’s trajectory), and the upcoming trac SPaT.
Reachable region
construction
Target cycle
determination
Traffic state predictionEnvironment sensing
Execution and
state update
Vehicle trajectory
planning
GPS V2V
communication
I2V
communication Radar
Focus of this study
FIGURE 2 Flowchart of the proposed methodology.
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Wu et al. / SAE Int. J. Sust. Trans., Energy, Env., & Policy / Volume 2, Issue 1, 2021 5
For eco-driving along a signalized corridor, the major
purpose of the RR construction algorithm is to reduce the size
of feasible region for the host vehicle’s trajectory planning, in
particular the size of searching space for available green
phases (within dierent cycles) at each signalized intersection
along the corridor, by applying any aforementioned system
constraints (e.g., speed limit, no collision to preceding
vehicles). e key output of the RR construction algorithm is
a set of intervals tt
ii
minmax
,
, where
ti
min
represents the earliest
feasible crossing time at the stop line of the ith downstream
intersection, while
ti
max
is the latest feasible crossing time at
the same intersection considering a nontrivial minimum
cruising speed vmin (e.g., to avoid presenting potential safety
hazards to other trac). When the host vehicle is traveling in
trac, the crossing time of its exact proceeding vehicle
ti
′
needs
to be predicted and the minimum headway hmin should
beconsidered to estimate
ti
min
. Inspired by [39], the lane-level
RR construction algorithm is proposed to include: (1) forward
calculation of
ti
min
based on
ti−1
min
and
ti
′
and (2) backward correc-
tion of
ti
max
to avoid any constraint violation. If there is no
feasible solution (i.e., the set is empty at certain signal), then
a nonstop trajectory along the signalized corridor is very
unlikely. Also note that the algorithm is based on the assump-
tion that the host vehicle has full knowledge of all the signal
timing plans (under xed-time control) along the corridor,
and the preceding vehicle’s trajectory is well predicted.
Since the RR construction algorith m is performed at the lane
level where the queue length is already taken into account,
wecould further develop “proactive” lane selection and lane
change strategies (e.g., queue balancing or overtaking) for the
real-world situation to help the host vehicle identif y or update its
passage path (in t he D-T diagram) along the corr idor, rather than
changing the lane in a “reactive” manner (e.g., to avoid collision
or a wrecked vehicle/object). e lateral maneuver is not the focus
of this study, but can denitely beone of the future steps.
3.2. Target Cycle
Determination
Once weconstruct the RR in the D-T diagram, wediscretize
it in both space and time to nd the optimal vehicle trajectory.
For an isolated intersection, the size of RR should beaccept-
able considering the computational eciency. However, as
route length and the number of intersections along the target
corridor increase, the RR will expand dramatically, and the
real-time per formance for vehicle trajectory plan ning becomes
questionable. erefore, wedevelop t he target cycle determina-
tion step to quickly identify the target cycle that the optimal
vehicle trajectory should pass at each intersection. Since
weassume all the signal plans of downstream intersections
are available, this problem can beformulated to nd the
optimal path from the initial states (i.e., d0 and v0) at time t0
to some nal states (where df and vf are supposed to begiven,
and the knowledge of tf is optional) within the RR in a
weighted directed acyclic graph (see Figure 4).
Figure 4 illustrates an example of the case considering
roadway speed limit vLimit and nontrivial minimum cruising
speed vmin, but no other trac interaction. e node (“blue
dot”) represents feasible passage time within the green phase
of each cycle at the respective signalized intersection. In this
gure, the node is placed at the beginning of each feasible
green window. For a better approximation, more nodes (e.g.,
the mid-point and end point) can beplaced within the same
green phase. e number of candidate nodes would heavily
depend on the neness of approximation as well as real-time
performance requirement on this step.
As aforementioned, the purpose of this step is to deter-
mine which cycle the host vehicle should travel through to
achieve the minimal energy consumption in a time-ecient
manner, rather than nding the exact optimal passage time
at each intersection. Weuse parabolic speed proles (as shown
in Equations 6 and 7) to smoothly (in terms of speed and
acceleration) connect each signa lized intersection (in the D-T
diagram) along the corridor, where the vehicle speed at (t0, d0)
is v0 and the vehicle speed at (ti, di) for i = 1, 2, 3, … is
vi
f
, which
can bethe roadway speed limit vLimit, a user-dened free-ow
speed, or an intermediate value between vmin and vLimit (var ied
with intersection). More specically, the proposed parabolic
speed trajectories are as follows (t0 = 0 without loss
of generality):
Between d0 and d1:
vt
at bt ct t
()
=++∈
[
)
1
2
11 1
0
,,
Eq. (6)
where
a
tvv
dd
t
b
tvv at
cv
i
f
f
1
1
20
10
1
3
1
1
10 11
10
3
6
1
=+
()
−
−
()
=−
()
−
=
v
Limit
d
0
d
t
0
v
0
Time
Distance
Preceding vehicles’
trajectories
v
min
Reachable
region
FIGURE 3 An example of the reachable region for
approaching a signalized intersection.
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6 Wu et al. / SAE Int. J. Sust. Trans., Energy, Env., & Policy / Volume 2, Issue 1, 2021
Between di and di+1 (i = 1, 2, 3, …):
vt at bt ct tt
ii
()
=++∈
[
)
+
2
2
22 1
,,
Eq. (7)
where
a
v
tt
dd
tt
batt
cv
i
f
ii
ii
ii
ii
i
2
1
2
1
1
3
221
2
66
=−
()
−
−
()
−
()
=− −
()
=
+
+
+
+
++1
f
With the approximated speed proles, weestimate the
fuel/energy cost of each arc using the energy estimation
model described in Section 2.2. en, the problem is formu-
lated as nding the shortest path with single origin and
multiple destinations, which can besolved eciently with
the Dijkstra’s algorithm [45]. If a target arrival time is also
dened, then the problem can bereduced to a typical shortest
path problem with single origin and single destination where
more efficient algorithms (e.g., A* algorithm [46]) may
beapplied. As the determination of target passage cycle is
an approximate process, it may not benecessary to have too
many paths in real-world implementation. For example,
wemay only look at two cycles ahead from each accessible
node at each intersection (see those thicker lines in Figure
4), without much compromising in mobility. In that case,
even an enumerative searching may be computationally
acceptable in real-world deployment. In the case where the
full knowledge of signal plans of all downstream intersec-
tions is not available, the scope of graph model and the
connectivity between nodes would be significantly
constrained and need updating as new information ows in.
is issue will beelaborated in Section 6.
3.3. Vehicle Trajectory
Planning
After the determination of target passage cycle at each
downstream intersection, the potential RR is significantly
reduced. Within the reduced region (including the avail-
able green window at each intersection), wecan formulate
another weighted directed graph model G = (V, E, C) where
V, E, C represent the set of vertices, edges, and costs,
respectively, by discretizing the time and space into fixed-
time step ∆t and distance grid ∆x (therefore the speed is
discretized with the step of ∆x/∆t for consistency). This is
similar to the approach described in Section 3.2. For each
node, weassign a 3-tuple (t, x, v), which describes the
dynamic state of the host vehicle, where t∈ (0, T] is the
time (in second); x∈[0, L] is the traveled distance (in
meter) along the entire route with the length of L; and v ∈
[0, vLimit] is the speed (in m/s). The edge defines the connec-
tivity between two nodes, and eVi→Vj is created from Vi(ti,
xi, vi) to Vj(tj, xj, vj) if and only if the following rules
are satisfied:
•Consecutive in time, i.e., tj = ti + ∆t
•Consistency between distance and speed: xj = xi + vi∆t
•Boundary on acceleration and consistency between
speed and acceleration, i.e.,
avv
t
a
ji
mi
nm
ax
≤
−
≤
∆
where amin and amax are the maximum deceleration rate and
maximum acceleration rate for the host vehicle, respectively.
e jerk constraint may beapplied in a similar manner
(if any).
vLimit
d0
d1
d2
d3
t0T1
min T2
min T3
min
v0
vfvfvf
Time
Distance
df
t1
min
t2
min
t3
min
vmin>0
FIGURE 4 Possible passage cycle combinations along the signalized corridor [44].
Reprin ted with pe rmission from Re f. [44].
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Wu et al. / SAE Int. J. Sust. Trans., Energy, Env., & Policy / Volume 2, Issue 1, 2021 7
Using the model presented in Section 2.2, wecalculate
the cost cVi→Vj on edge eVi→Vj as follows:
c
Qv
vv
t
vv
ta
Qvv
t
VV
ti
ji
i
ji
coast
idle
ji
ij
→
′
=
−
−
>
−
∆∆
∆
,if
if
θ
≤≤
acoast
Eq. (8)
where the road grade θi can beestimated by the elevations
between nodes Vi and Vj.
Upon the completion of this directed graph model,
wethen apply the Dijkstra’s algorithm to solve this single
source shortest path problem with nonnegative cost. Figu re5
illustrates an example where the host vehicle traverses a road
segment (36m long) in 4 s with both the initial and nal
speed being 10 m/s. e time step ∆t is 1 s, the distance grid
∆x is 2 m, and the maximum and minimum acceleration
rates are 2 m/s2 and −2 m /s2, respectively. For a more generic
case of EADSC where the RR has extended scope in space
and time with higher resolution, the time complexity using
the Dijkstra’s algorithm is O(log(N)*E) [45], where N repre-
sents the number of nodes and E denotes the number of edges.
e pseudocode for the vehicle trajectory planning algorithm
is as follows.
NumericalSimulation
To illustrate the performance of the proposed EADSC system,
weconduct a numerical case study in this section using a
three-intersection road stretch of El Camino Real in Palo Alto,
CA, consisting of three cross-streets—Maybell Ave., Los
Robles Ave., and Ventura Ave.—from south to north. e
road-grade change is less than 1% (around 0.4%) and therefore
FIGURE 5 An example to illustrate the vehicle trajectory
planning step by constructing the graphic model and
formulating it as the shortest path problem.
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ALGORITHM Vehicle Trajectory Planning Algorithm
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8 Wu et al. / SAE Int. J. Sust. Trans., Energy, Env., & Policy / Volume 2, Issue 1, 2021
weconsider it as a at segment. As shown in Figure 6(a), the
intersection spacing within this stretch varies from 200m to
500m and the speed limit is 40 mph. e background signal
timing plans (130 s of cycle length) at these three intersections
for the northbound direction are illustrated in Figure 6(b),
which were obtained from archived document by the
California Department of Transportation (Caltrans) D4 and
implemented in the eld in July 2005.
We evaluate the performance of the proposed EADSC
system with two scenarios. In both scenarios, the host vehicle
starts o (northbound) from the landmark 207m upstream of
Maybell Ave., that is, from W. Charleston Rd. at El Camino Real,
and terminates the trip at the intersection of Ventura Ave. with
target speed of 40 mph. e starting times are Ts1 = 20 s and Ts2
= 70 s for Scenario 1 and Scenario 2, respectively (see Figure 6).
As to the SPaT at Maybell Ave., Scenario 1 represents a typical
case approaching in red (remaining time is 29 s), while Scenario
2 denotes the case approaching in green (remaining time is 33 s).
For comparison, wetotally test ve driving strategies as
described in the following (see Figure 7):
1. Baseline driving strategy without the SPaT
information (as “Baseline” in Figure 7). With this
strategy, the host vehicle attempts to cruise at or
around the speed limit unless getting close to the
signalized intersections during the red phase (slowing
down and stop if necessary).
2. Piecewise linear trigonometric function like eco-
driving strategy (as “Trigonometric EAD” in Figure 7).
Please refer to [12, 27] for more technical details.
(a) Map of the numerical case study in Palo Alto, CA (Source: Google Map).
(b) SPaT of three intersections along El Camino Real in Palo Alto, CA.
70 s
Ventura Ave. (offset = 83 s)
Los Robles Ave. (offset = 53 s)
Maybell Ave. (offset = 0 s)
Cycle length = 130 s, Speed limit = 40 mphDistance
Time
57 s
70 s 57 s
54 s 73 s
203 m
515 m
207 m
Curtner Ave.
167 m
49 s
50 s
20 s
0Ts1Ts2
W. Charleston Rd.
FIGURE 6 The three-intersection (red lines in the Google Map) corridor with detailed parameters (including spacing and signal
timing plans). Ts1 = 20 s (when the phase is red at Maybell Ave.) and Ts2 = 70 s (when the phase is green at Maybell Ave.) represent
the starting times of two testing scenarios.
© Googl e Maps
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Wu et al. / SAE Int. J. Sust. Trans., Energy, Env., & Policy / Volume 2, Issue 1, 2021 9
3. Intersection-by-intersection shortest-path-based eco-
driving strategy with priority in travel time (as “IBI-
max target speed” in Figure 7). is strategy is based
on what wepresented in the vehicle trajectory
planning step (in Section 3.3). Wedene the target
state at each intersection and consider the consistency
between the end state of an upstream section and the
initial state of the respective downstream section.
4. Corridor-wise shortest-path-based eco-driving
strategy with priority in travel time (as “Corridor time
optimal” in Figure 7). Based on the proposed EADSC
algorithm, an optimal (in terms of minimizing the
trip time) corridor-wise speed prole can
becalculated with the specied target state at the end
of the corridor.
5. Corridor-wise shortest-path-based eco-driving strategy
with priority in fuel consumption (as “Corridor fuel
optimal” in Figure 7). is strategy is also based on the
proposed EADSC algorithm in this article. Rather than
prioritizing the mobility performance, this strategy
provides the corridor-wise optimal vehicle trajectory in
terms of minimizing the fuel consumption, where
target passage cycles are determined using the
algorithm presented in Section 3.2.
It is noted that for both “Baseline” and “Trigonometric
EAD” strategies, the jerk constraint suggested by [47] has
been applied to guarantee the driving comfort. For the other
three shortest path-based strategies, that is, “IBI-max target
speed,” “corridor time optimal,” and “corridor fuel optimal,”
switching between drastic acceleration and deceleration is
discouraged by the proposed model. erefore, the jerk would
belimited by the acceleration range as aforementioned (i.e.,
−2 m/s2 ≤ accel ≤ 2 m/s2).
We estimate the trip-level fuel consumption for all the
strategies and the results are summarized in Tabl e 1. As can
beobserved in the table, all eco-driving strategies can signi-
cantly reduce fuel consumption, compared to the baseline
driving strategy. e improvement may range from 12% to
28%, depending on the scenario. Most of the eco-driving st rat-
egies (except for the corridor-wise fuel optimal eco-driving
strategy, i.e., “Cor. Fuel”) also outperform the baseline driving
strategy in mobility performance. For the corridor-wise fuel-
oriented eco-driving strategy, the host vehicle chooses the end
of green window (at the intersection of Ventura Ave.) to achieve
the fuel savings to the maximum extent in both scenarios.
Further comparison results reveal that: (a) Compared to
“Trigonometr ic EAD” strategy, “IBI-max target speed ” strategy
performs better or at least the same in terms of mobility while
the energy benets or dis-benets may vary with scenarios;
(b) “Corridor time optimal” strategy can save up to 4.3% more
fuels than “Trigonometric EAD” strategy in both scenarios,
without compromising in trip time; (c) e corridor-wise eco-
driving strategies always outperform the intersection-by-
intersection strategy in terms of fuel savings (in the range of
4-9%), and “corridor time optimal” strategy can guarantee no
penalty in mobility performance; (d) For dierent versions of
corridor-wise eco-driving strategies (i.e., time-saving vs. fuel
savings), fuel savings may befurther squeezed out by 2-3%
(around 0.01 liter in this study) but at the cost of travel time
increase by up to 20% (about 13 s for both scenarios). is may
shed some light upon the trade-os between mobility and
fuel/energy benets regarding the proposed EADSC system.
FieldImplementation
A eld implementation with a real passenger vehicle is also
conducted to validate the eect iveness of the proposed EA DSC
system. The testbed is located at the Federal Highway
(a) Scenario 1
(b) Scenario 2
FIGURE 7 Distance-time diagrams of five driving strategies
under two scenarios in numerical simulation.
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10 Wu et al. / SAE Int. J. Sust. Trans., Energy, Env., & Policy / Volume 2, Issue 1, 2021
Administration’s (FHWA) Turner-Fairbank Highway
Research Center (TFHRC) in McLean, Virginia, using the
Saxton Transportation Operations Laboratory (STOL)
Intelligent Intersections. is testbed oers a sheltered trac
environment where the eld test can be conducted with
minimal safety risk and without disrupting live
trac operations.
Figure 8 provides an overview of this testbed, specifying
the starting point (green pin) where the test vehicle can begin
test runs f rom a stop and travel through two consecutive inter-
sections (blue pins). e test corridor covers a range of approx-
imately 320m. e maximum allowable travel speed is 30
mph (13.41 m/s). Each of the two intersections is equipped
with a McCain ATC2 trac controller, which sends out SPaT
objects in the NTCIP 1202 standard. To allow the test vehicle
to receive this information, the DSRC J2735 Map and SPaT
messages are broadcasted from a Cohda MK5 RSUs mounted
at each intersection. e forwarding of the Map and SPaT
messages to the R SU is handled using the open source soware
V2XHub [48]. Both trac signal controllers are set up for
xed-time signal plans (i.e., green for 27 s, yellow for 3 s, and
red for 30 s in each cycle along the travel direction), which
removes excess all-red clearance timings and loop detector
triggers from actuating the signal.
e test vehicle is a production Cadillac SR X 2013 (shown
in Figure 9), which is outtted for automated throttle and
brake control using hardware developed by STOL and TORC
Robotics. It is additionally equipped with a TORC PinPoint
GPS unit, which integrates IMU and Dual Phase GPS solution
for accurate localization.
e algorithm implementation is built as a plugin for the
CARMA Platform (Ver. 2.8.1) soware package [49]. e
CARMA Platform is an Open Source Soware platform devel-
oped at STOL, and is designed to support research in
Cooperative Automation. e platform is built on top of the
Robot Operating System (ROS) supporting level 1 speed
control [50]. Dierent cooperative algorithms are imple-
mented as Java plugins, which provide speed commands to
FIGURE 8 Field implementation testbed at the FHWA Turner-Fairbank Highway Research Center in McLean, VA. Start and end
points are shown as green and red pins, respectively. Two intersection center points are shown as blue pins (Source: Google Map).
Map Data : © 2020 Google. Im agery: © 2020 CN ES/Airbus Comm onwealth o f
Virgin ia, Maxa r Technol ogies , Sanbo rn, U.S Geolo gical Survey
TABLE 1 Comparison in performance measures for dierent driving strategies under two scenarios
Scenario Strategy
Fuel (liter) Trip time (s)
Absolute Change (%) Absolute Change (%)
Scenario 1 Baseline 0.4641 —124 —
Trigonometry 0.3565 −23.2 119 −4.0
Int-By-Int 0.3678 −20.8 117 −5.7
Cor. Time 0.3428 −26.1 117 −5.7
Cor. Fuel 0.3359 −27. 6 130 4.8
Scenario 2 Baseline 0.4209 — 75 —
Trigonometry 0.3706 −12.0 67 −10.7
Int-By-Int 0.3595 −14.6 67 −10.7
Cor. Time 0.3545 −15.8 67 −10.7
Cor. Fuel 0.3439 −18.3 80 6.7
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Wu et al. / SAE Int. J. Sust. Trans., Energy, Env., & Policy / Volume 2, Issue 1, 2021 11
the vehicle through the CARMA Platform APIs. A diagram
of the CARMA Platform system architecture showing where
the plugins t is shown in Figu re 10.
Two representative runs from dierent directions (i.e.,
eastbound and westbound) in the eld implementation are
illustrated in Fig u res 11 and 12, respectively, where the D-T
plots and speed trajectories are presented. In Run 1, the D-T
plot (see Figure 11(a)) shows the test vehicle rst accelerates
to catch up with the end of green phase (with some safety
buer time) at the rst trac signal, thus no fu ll stop is needed
and the fuel consumption can besaved.
For the second trac signal, the vehicle cruises through
the intersection during the green phase without any speed
changes. Figure 11(b) illustrates the speed trajectories of this
scenario, where both the “commanded speed” prole and
“vehicle speed” prole are shown. e “commanded speed”
prole is calculated by the proposed algorithm with real-time
feedback update (e.g., considering cumulative errors in the
speed track ing), while the “vehicle speed” prole is the output
from the actuator.
In Run 2 as shown in Figure 12, when approaching both
trac signals, the test vehicle slightly decelerates during the
red phase, and passes both intersections at the beginning of
the green phases (with some safety buffer time). In this
manner, the test vehicle may avoid full stops and unnecessar y
idling at the intersections, and arrives just in time when the
signal turns from red to green.
Discussion
In this section, wewill further discuss some practical issues
related to the real-world deployment of the proposed corridor-
wise EAD application.
6.1. Availability of Signal
Timing Plan
Most of the existing studies on EAD have assumed that the
equipped vehicle has the knowledge about the signal timing
plan at the intersection, including c ycle length, phase duration,
and sequence, which is not readily available in the SPaT
message. is would give rise to additional challenges for the
implementation of EAD application.
FIGURE 9 The test vehicle running the algorithm using the
CARMA Platform (Source: FHWA).
Reprin ted from Fe deral Highway Adm inistration
FIGURE 10 High-level CARMA Platform v2.8.1 architecture (Source: FHWA).
Reprin ted from Re f. [x]
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12 Wu et al. / SAE Int. J. Sust. Trans., Energy, Env., & Policy / Volume 2, Issue 1, 2021
In the UnitedStates, the art-of-the-practice trac signal
control organizes phases by grouping them into rings and
separating the conicting trac streams either by mak ing the
movements sequential or adding barriers in between [51].
Figure 13 presents an example of the ring-and-barrier diagram
to illustrate the time sequence of phases. At each time step,
the available information from SPaT messages includes the
current phase (i.e., green, yellow, red, or maybe all-red clear-
ance) and minimum/maximum time of change to the next
phase [43]. For example (see Figure 13), assuming that the host
vehicle is approaching the intersection along the through lane
(i.e., Movement #2) at time t0, it knows the current phase
through movement being green, and can obtain the time
instances of all movements when the associated next phases
start or T2Ni’s (where i represents the movement index). With
this limited information, the host vehicle is able to know the
(exact) end time of current green and a lower bound of
time-to-next-green (i.e., T2NG2). Unless it keeps tracking the
SPaT for a certain period, the host vehicle would not have a
complete knowledge of all the downstream signal timings to
plan well its trajectory even under xed-time signal control.
To mitigate this issue, the signal timing plan should bebroad-
cast, or a separate on-board module needs to bedeveloped to
learn the background signal control parameters and predict
the operation of signal controllers.
Toward this end, wemay modify the way to construct the
RR (in a conservative manner) for an isolated intersection based
on the partial knowledge of signal plan. Here, wetake an
example where the host vehicle approaches the intersection in
green (at time t0). Based on the on-board radar detection (with
the range Rr), wecan construct the reliable RR (assuming no
cut-ins by other vehicles). In addition, a predicted RR can
beconstructed based on the information available (if any) from
the V2I communication range Rc (assuming a limited
FIGURE 11 Distance-time plot and speed trajectory of Run 1.
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Wu et al. / SAE Int. J. Sust. Trans., Energy, Env., & Policy / Volume 2, Issue 1, 2021 13
communication range). If the vehicle is predicted to beable to
pass through the intersection in current green (constrained by
the host vehicle’s maximum power/acceleration and predicted
trajectories of other vehicles), then the predicted RR w ill include
area in the downstream of the intersection. Otherwise, the
predicted RR will berestricted to the upstream of the intersec-
tion as shown in Figure 14, where the length of red phase is
unk nown and is assumed to belong (or at least longer than T2N4
in Figure 13). e detected preceding (nonconnected) vehicles
are predicted to bestopped in the queue or at the stop line.
6.2. Other Trac Interaction
In this article, we mainly focus on the description of the
EADSC, comparative results with other algorithms and
prototyping eorts in idealized scenarios. Although the RR
construction module may cover some practical issues (e.g.,
with downstream trac detection and prediction), more
delicate interaction with other trac such as cut-ins and
wrecks would further complicate the proposed system. In
these unexpected situations, the ego-vehicle may need to apply
emergency stops or make lane changes to avoid any safety
risks or getting stuck behind a queue, and re-optimize its
speed trajectories based on the updated information. As
mentioned in Section 3.1, the lane-level RR construction
module developed in this study can also accommodate some
realistic trac interaction and can further integrate with
lateral control/maneuvers to enable more advanced eco-
driving strategies (e.g., queue balancing or overtaking) along
the signalized corridor.
FIGURE 12 Distance-time plot and speed trajectory of Run 2.
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14 Wu et al. / SAE Int. J. Sust. Trans., Energy, Env., & Policy / Volume 2, Issue 1, 2021
ConclusionsandFuture
Work
In this study, weproposed an innovative algorithm for
EADSC, featured with three major steps, that is, RR construc-
tion, target cycle determination, and vehicle trajectory planning.
Results from the numerical simulation on a real-world three-
intersection corridor showed great potential of the proposed
EADSC in terms of fuel savings without compromising the
mobility benets, compared to the baseline driving strategy
without knowing the SPaT information (by up to 28%) as well
as the trigonometric function like EAD strategy (by around
4.3%) that was previously developed by the authors. Using the
same vehicle trajectory planning algorithm, further energy
benets (ranging from 4% to 9%) could besqueezed out based
on the knowledge of corridor-wise signal timing plans rather
than using the SPaT information on an intersection basis. A
eld implementation with real passenger vehicle also validates
the eectiveness of the proposed EADSC system. In addition,
wediscuss some issues for real-world implementation of the
system, including the availability of only partial knowledge
about downstream signal information from current SPaT
messages, and the presence of more realistic trac interaction.
Potential work on the proposed EADSC system would
befocused on the validation in more complex environments.
ese may include handling intersections with actuated and
adaptive signals, as well as combination with platooning
operations. Other opportunities for additional research
include (a) the application of this algorithm in mixed trac
scenarios (i.e., with other legacy vehicles or connected but
manually driven vehicles); (b) the integration with queue
prediction technique and lateral control; (c) the consideration
of imperfect positional accuracy (e.g., under “urban canyon”
situations); and (d) the modications for case(s) of right-turn
on red (RTOR) or permissive le-turn. Testing and validation
of the proposed EADSC system in a microscopic trac envi-
ronment such as SUMO or Vissim would, to certain degree,
help better understand the aforementioned issues and prepare
for more sophisticated eld deployment.
Contact Information
Guoyuan Wu, PhD
Center for Environmental Research & Technology,
University of California at Riverside
gywu@cert.ucr.edu
Acknowledgments
This research is supported by the Federal Highway
Administration (FHWA). e contents of this article reect
the viewpoints of the authors, who are responsible for the facts
and the accuracy of the data presented, and do not necessarily
reect the viewpoints of the FHWA or the U.S. Department
of Transportation.
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