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Jie Li, Xiaodong Wu, Member, IEEE, Min Xu, and Yonggang Liu, Senior Member, IEEE
Abstract—To improve the driving experience of connected and
automated electric vehicles in urban scenarios, this paper
proposes a novel hierarchical multi-objective eco-driving
strategy. This strategy aims to co-optimize energy economy, ride
comfort, and travel efficiency while prioritizing driving safety. In
the upper level controller, we present a driving safety model and
a driving speed advisor model that transform complex, multi-
scale, and multi-dimensional traffic influence factors into speed
constraints. This transformation facilitates the formulation of the
multi-objective eco-driving problem as an optimal control
problem, characterized by stringent safety constraints and a
multi-objective cost function. Subsequently, we design a model
predictive control based controller to solve this eco-driving
problem in real time. The upper level controller generates an
optimal reference target speed, which is transmitted to the lower
level vehicle controller. In the lower level controller, we derive an
analytical optimal motor torque control law based on linearized
system state equations, enabling real-time tracking of the
reference speed. Finally, to validate our proposed strategy, we
conducted simulations within a dynamic virtual traffic simulation
scenario. This scenario is modeled using real road and traffic
data from Shanghai, China, effectively simulating a real-world
traffic environment. The simulation results affirm the
effectiveness of the proposed strategy, demonstrating its capacity
to safely and robustly control ego vehicles in complex traffic
scenarios. Additionally, our strategy optimizes energy efficiency
and ride comfort while maintaining travel times comparable to
the contrast eco-driving strategies.
Index Terms—Connected and automated vehicle; Multi-objective
eco-driving; Model predictive control; Safety constraints;
Complex urban scenarios
I. INTRODUCTION
attery electric vehicles (BEVs) have received
significant attention in the research community due to
their high efficiency, zero emissions, and low noise. To
This work was supported by the National Key Research and Development
Program of China under Grant 2018YFB0106000 in part and the National
Natural Science Foundation of China (No. 52172400) in part. (Corresponding
authors: Xiaodong Wu and Yonggang Liu)
J. Li is with Institute of Intelligent Vehicle, School of Mechanical
Engineering, Shanghai Jiao Tong University, Shanghai 200240, China. (email:
jelly_961@sjtu.edu.cn)
X. Wu and M. Xu are with Institute of Intelligent Vehicle, School of
Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240,
China. (email: xiaodongwu@sjtu.edu.cn, mxu@sjtu.edu.cn)
Y. Liu is with the State Key Laboratory of Mechanical Transmission &
College of Mechanical and Vehicle Engineering, Chongqing University,
Chongqing 400044, China (email: andyliuyg@cqu.edu.cn).
further improve their energy economy, eco-driving
technology, which optimizes vehicle driving behavior to
reduce energy consumption, has gained prominence [1].
Traditionally, eco-driving strategies for manual BEVs have
focused on manual driving skills that regulate
accelerator/brake pedals to improve energy efficiency [2]. The
emergence of connected and automated vehicle (CAV)
technologies has led to the evolution of eco-driving strategies
that optimize vehicle speed based on real-time data received
from the surrounding traffic and road terrain, facilitated by
vehicle-to-everything (V2X) communication [3]. In practical
applications, it is important that the eco-driving strategy is
widely accepted by passengers. While the optimization of
energy consumption remains a fundamental goal for CAVs in
urban scenarios, it is equally vital to consider other crucial
factors such as driving safety, ride comfort, and travel
efficiency to enhance the overall driving experience.
Consequently, eco-driving strategy for CAV has evolved into
a multi-objective optimal control problem that must consider
complex driving safety factors.
Theoretically, the most economically eco-driving strategy
for free-driving scenarios is "pulse-and-glide" strategy [4],
which involves periodic control of the vehicle acceleration,
alternating between reaching a specific speed and coasting at a
slower speed [5]. However, executing the desired "pulse-and-
glide" cycle in urban scenarios poses significant challenges
due to factors such as the presence of preceding vehicles,
interruptions at signalized intersections, road speed limits, etc.
It is essential for a practical eco-driving strategy to avoid
hazardous situations, including running red lights, collisions,
and sideslip incidents. In [6], they transform the traffic light
constraints into linear state constraints and compute the
optimal vehicle speed trajectory that minimizes hydrogen
consumption while satisfying the traffic light constraints. But
the constraints imposed by preceding vehicles and road bends
are ignored in this research. In [7], they introduce a solution to
minimize energy consumption and ensure car-following safety
constraints. However, the constraints posed by traffic lights
and road bends were disregarded. Similarly, in [8], two eco-
driving strategies are designed for car-following and traffic
light scenarios, with a switch logic algorithm used to select the
appropriate eco-driving strategy based on the current driving
scenario. Nevertheless, this approach disregards the road bend
constraints and is impractical for real-world scenarios
characterized by intricate and interconnected traffic dynamics.
Multi-objective eco-driving strategy for connected
and automated electric vehicles considering complex
urban traffic influence factors
B
At present, there are few studies that comprehensively satisfy
multiple driving safety constraints arising from diverse
influence factors such as traffic lights, preceding vehicles, and
road bends. These factors span multiple state dimensions,
including time, distance, speed, and acceleration, and involve
both discrete and continuous variables. Designing an eco-
driving strategy that satisfies these complex, multi-scale, and
multi-dimensional safety constraints presents a challenge.
In addition to satisfying safety constraints, eco-driving
strategies must comprehensively consider multiple objectives,
such as energy economy, ride comfort, and travel efficiency.
Prior research has indicated that passengers are more
susceptible to motion sickness with greater longitudinal and
lateral vehicle motion [9]. In [10], a deep reinforcement
learning based multi-objectives eco-driving strategy is
proposed to optimize fuel consumption, distance headway, and
total travel time. However, this approach may lead to
passenger discomfort due to the acceleration associated with
speed changes. Besides, it is imperative to prioritize driving
safety as the foremost factor, with its constraints rigorously
enforced, taking precedence over economy and efficiency. In
[11], a safe, efficient, and comfortable eco-driving strategy is
developed by co-optimizing time to collision, short time
headway, and longitudinal acceleration. However, this study
does not consider fuel consumption for energy economy and
lateral acceleration for ride comfort. In [12], a model
predictive control (MPC) based vehicle speed optimizer is
proposed to optimize fuel consumption and total travel time
for Plug-in hybrid electric buses. Nonetheless, the lack of
optimization for acceleration may lead to passenger
discomfort. To comprehensively consider the energy
economy, ride comfort, and travel efficiency of connected and
automated electric vehicles (CAEVs), the eco-driving strategy
should co-optimize energy consumption, longitudinal
acceleration, lateral acceleration, and total travel time.
Additionally, in the context of the eco-driving strategy for
CAVs, an efficient real-time controller is required to control
the motor torque for propelling the ego vehicle and accurately
following the reference target vehicle speed [13, 14]. Previous
works have employed proportional–integral (PI)-based
controllers [15, 16], which are renowned for their robustness
and computational efficiency. However, accumulated errors in
the integration term may reduce the controllers' response
speed. In [17], a pseudospectral method based hybrid
powertrain controller is proposed for tracking the optimized
reference speed while minimizing energy consumption.
However, the heavy computation burden associated with this
numerical solution makes it challenging for deployment in an
on-board control unit. In [18], an MPC problem is formulated
to distribute the power from the battery and two traction
motors to track the reference speed. They compute the optimal
solution offline and represent it as a discrete lookup table for
online applications. However, this discretization process may
result in suboptimal fuel economy and tracking accuracy.
Therefore, there is a compelling need to develop a responsive
and computationally efficient closed-loop controller for
CAEVs. This controller should be capable of accurately
tracking the optimal reference speed and correcting tracking
errors in real-time.
To address the limitations of prior research, this paper
proposes a hierarchical multi-objective eco-driving strategy
for CAEVs. In this strategy, the upper level controller plans a
reference target speed that co-optimizes the electric
consumption, ride comfort, and travel efficiency while
satisfying multiple safety constraints from the preceding
vehicle, traffic light, road limit, etc. Then, the lower level
vehicle controller computes motor torque command and wheel
steering angle command to propel the vehicle while tracking
the target speed and waypoint accurately. The contributions of
this study in methodological and experimental verification are
summarized as follows.
1) We propose a novel method to transform the complex
traffic influence factors into speed constraints. Compared to
prior studies, this method addresses the challenge of
integrating complex driving safety constraints into the eco-
driving strategy and simplifies the eco-driving problem in
complex scenarios. Furthermore, our proposed strategy
considers comfort optimization, especially concerning lateral
acceleration, which extends the applicability of the eco-
driving strategy to routes with bends.
2) We design a highly responsive and computationally
efficient longitudinal speed tracking controller. This
innovative controller is developed by employing a Taylor
series expansion to linearize the nonlinear differential system
state equations and leveraging linear quadratic regulator
theory to derive an analytical optimal motor torque control law.
To the best of the author's knowledge, it has not been reported
in the prior research.
3) We conducted simulation experiments on the proposed
strategy within a dynamic traffic simulation scenario. Unlike
the static simulation scenarios utilized in previous research,
this dynamic scenario effectively simulates the dynamic
interactions among diverse traffic participants on real-world
roadways. Our dynamic simulation provides a more
comprehensive assessment of the eco-driving strategy's
expected performance in real-world scenarios.
The structure of this paper is structured as follows: the eco-
driving problem and ego vehicle model are stated in Section
II. Section III introduces the proposed hierarchical multi-
objective eco-driving strategy. Section IV provides detailed
simulations and discussions of the proposed strategy. Finally,
in Section V, we summarize the main conclusions and outline
potential directions for future research in this field.
II. ECO-DRIVING PROBLEM AND VEHICLE MODELING
DESCRIPTION
A. Eco-driving Problem and Urban Traffic Model
In complex urban traffic scenarios (as illustrated in Fig. 1.),
CAVs are influenced by various factors, including
surrounding vehicles, signal intersections, road speed limits,
road bends, etc. This study is dedicated to improving the
driving experience of CAVs in complex urban traffic
environments by developing a multi-objective eco-driving
strategy. This strategy is designed to co-optimize energy
consumption, acceleration, and total travel time while
adhering to safety constraints within the traffic environment.
Specifically, energy consumption represents the aspect of
energy efficiency, acceleration is indicative of ride comfort,
and total travel time reflects traffic efficiency. The safety
constraints encompass compliance with traffic signals,
avoiding speeding, preventing collisions, and avoiding sideslip
incidents.
GPS
60
Speed limit
Surrou nding vehicl es
(Yellow)
Ego vehicle (Red )
Ego vehicle route
Traffic light
Fig. 1. Schematic diagram of urban traffic scenario.
(a) (b)
ego
ego
Fig. 2. The road network of the virtual Shanghai traffic
simulation model. (a) Google Map; (b) SUMO road network.
Considering the current low penetration rate of CAVs, we
assume that the other vehicles on the road are conventional
manually driven vehicles. CAVs, in this context, rely on
onboard radar and cameras to obtain information about the
preceding vehicles' speed, acceleration, and distance headway.
In addition, CAVs can access information about the traffic
light timing and phase at the next signalized intersection via
V2X communication, and they can obtain information about
the distance to the next signalized intersection, road speed
limits, and road slopes through navigation services. It is
important to note that this study does not delve into driving
route planning, which has been extensively investigated in
prior research [20-22]. In this work, the ego vehicle follows
predetermined routes and waypoints.
To simulate a realistic urban traffic scenario, we use the
Simulation of Urban Mobility (SUMO) software to build a
virtual Shanghai traffic simulation model. The road network in
this model is edited based on real-world road data sourced
from Shanghai, China. As depicted in Fig. 2. (a), the origin of
the ego vehicle is the Minhang campus of Shanghai Jiao Tong
University. And the destination of the ego vehicle is the Xuhui
campus of Shanghai Jiao Tong University. The route spans
approximately 21 km and includes 25 signalized intersections.
Within the virtual Shanghai traffic simulation model, the ego
vehicle (depicted in a red vehicle in Fig. 1 and 2.) is controlled
by our proposed eco-driving strategy. Meanwhile, each of the
other vehicles (illustrated in the yellow vehicles in Fig. 1 and
2.) is autonomously controlled by independent driver models
integrated into the SUMO software [23]. These driver models
enable other vehicles to dynamically adjust their behaviors
(e.g. lane change, overtaking, acceleration, etc.) in response to
their immediate surroundings during simulation. For instance,
if the ego vehicle's speed decreases, resulting in a reduced
inter-vehicle distance, the surrounding vehicles may
proactively initiate lane change or overtaking maneuvers. The
virtual Shanghai traffic simulation model effectively simulates
the dynamic interactions that occur among diverse traffic
participants on real-world roadways. Thus, our simulation
environment inherently embodies dynamism which
distinguishes it from static simulation setups frequently used
in prior studies [6-8, 10-12, 17-19]. These static setups often
involve fixed vehicle trajectories and speeds, whereas our
dynamic simulation offers a more comprehensive evaluation
of the expected performance of eco-driving strategies. The
detailed procedure of simulation is provided in Section IV.
B. Longitudinal and Lateral Vehicle Dynamics Model
Based on Newton's second law, the ego vehicle longitudinal
dynamics is derived as [24]
()
x
ego equi tra air slope roll
am I F F F F (1)
where
x
a is longitudinal acceleration. ego
m is ego vehicle
mass. equi
I is equivalent rotational inertia at wheel. tra
F
is
traction force at wheel. 2
0.5
air D ego
F
CAv
is air drag. ego
v is
ego vehicle longitudinal speed. sin
slope ego
Fmg
is slope
resistance. cos
roll ego r
Fmgf
is rolling resistance.
D
C,
A
,
,
g
, r
f
, and
are air drag coefficient, windward area, air
density, acceleration of gravity, rolling resistance coefficient,
and road slop, respectively. Based on the "bicycle" vehicle
model with two degrees of freedom [25], the ego vehicle
lateral dynamics is characterized as:
11 12
21 22
22 T
yy
go
ff
e
f
z
ClC
AAv
Am
AI
a
(2)
where 11
22
r
ego
f
ego
CC
m
Av
, 12
22
o
ff r
ego
ego eg
r
Cl Cl
Av mv
,
21
22
ego
ff rr
z
lC lC
AIv
, and
22
22
22
ego
ff rr
z
lC lC
AIv
. y
a is
lateral acceleration. y
v and
are ego vehicle lateral speed
and yaw angular speed. f
C
and r
C
are cornering stiffness
of the front and rear wheels. f
l and r
l are the distances from
the center of gravity to the front and rear axles, respectively.
z
I
is yaw moment of inertia.
is the front wheel steering
angle.
C. Vehicle Powertrain Model
In this study, the BEV's powertrain structure is shown in Fig.
3. The motor, final drive, and differential are sequentially
assembled in the driveline.
+
-
Wheel
Batte ry
Motor
Inverter
Differ ential
Final dr ive
Plug
Fig. 3. Powertrain structure diagram of the BEV.
A control-oriented powertrain model is developed for the
MPC based eco-driving strategy to reduce the computational
burden. The motor output torque m
and speed m
n can be
calculated as
sgn( )
()
m
mtrawheelfd fddif
Fr i
(3)
mfdegowheel
nivr (4)
where wheel
r is the tire radius. fd
i is the final drive ratio.
0.98
fd
and 0.99
dif
are the efficiency of the final drive
and differential. The motor efficiency map (Fig. 4. (a)) is
extracted from Autonomie software [26]. Typically, it is
modeled as a two-dimensional numerical table. But looking up
a table is time-consuming, especially when solving optimal
control problem. Thus, we select a fractional polynomial to fit
its approximate analytical function.
5
2
122
34 67
(,)
1( ) 1( )
mmm
mm
p
p
np
npp pp
(5)
where m
is the motor efficiency. ,1,,7
i
p i are the
fitting coefficients. 10.953p, 2-0.2941p, 3181p,
4-1044 p ,5-0.3893 p , -7
61.282 10p, and
7-7.071p. The correlation coefficient is ²0.9424R,
which proves that the fractional polynomial can effectively
substitute the lookup table. The battery output power can be
expressed as
sgn( ) sgn( )
mm
inv eleacc
out
bat m m m
Pn P
(6)
where 0.98
inv
is the efficiency of power inverter.
220
eleacc
PW is the power of electrical accessories. The
battery is modeled as a typical equivalent internal resistance
model, including a voltage source and a resistance [27]. In
consequence, the battery current can be calculated as
24
2
OCV OCV bat
bat
bat
out
bat
EERP
IR
(7)
where OCV
E and bat
R are the open circuit voltage (OCV) and
battery internal resistance, respectively. As shown in (Fig. 4.
(b)), the OCV and internal resistance are nonlinear functions
of state of charge (SOC). The SOC can be calculated by the
Coulomb counting method.
0
0
0
1
() ()
t
bat
t
bat
SOC SOC t I t dt
C
(8)
where 0
() 0.8SOC t is the initial SOC. bat
C is the battery
rated capacity. Since the SOC change does not change
significantly in a short period, the OCV
E and bat
R can be
approximated as constants within the receding horizon of
MPC. The battery power bat
P can be derived as
bat OCV bat
PEI (9)
Effic iency To rque Max Torq ue Min
0 2000 4000 6000 8000 10000
Speed (rpm)
-400
-300
-200
-100
0
100
200
300
400
Torque (Nm)
(a)
0.6
0.7
0.8
0.840.87 0.94 0.96
0.95
0.93
(b)
SOC
0 0.2 0.4 0.6 0.8 1
280
300
320
340
360
380
400
0.3
0.4
0.5
0.6
Open cir cuit volta ge (Nm)
Internal resi stance (ohm)
0.55
0.45
0.35
Open circuit voltage
Internal resistance
Fig. 4. The powertrain component data. (a) Motor efficiency
map; (b) Open circuit voltage and internal resistance curves.
III. HIERARCHICAL MULTI-OBJECTIVE ECO-DRIVING STRATEGY
The proposed hierarchical multi-objective eco-driving control
strategy is depicted in Fig. 5. In the upper level, we designed a
driving safety model and a driving speed advisor model. These
models are responsible for calculating the safety limit speed
and green light speed boundary, respectively. They transform
the complex, multi-scale, and multi-dimensional traffic
influencing factors into speed constraints. Then, to satisfy
multiple safety constraints in urban scenarios and co-optimize
the electric consumption, ride comfort, and travel efficiency,
we designed an MPC based speed planning strategy. This
strategy integrates stringent safety constraints and a multi-
objective cost function within the receding horizon
framework. The outcome of this upper-level process is the
computation of an optimal reference speed ref
v through the
MPC-based speed planning strategy. This optimal reference
speed is then sent to the lower level vehicle controller. In the
lower level, to accurately track the ref
v, an optimal torque
control law is derived to compute the motor torque command
m
online. Additionally, we employ a typical Stanley method
to determine the wheel steering angle command
. In the
subsequent subsections, the proposed multi-objective eco-
driving control strategy will be elaborated.
Ego vehicle model
Dyna mic s model
Co ntro l comm and
Ego vehicle speed/position
Upper level speed planning
Safety speed limit Preceding vehicle
predicted speed
Traffic light
adviso r speed
Ego v ehi cl e stat e
Traff ic infor mat ion
m
,
v
ego
, x, y
t
rem
, v
his
, v
limit
, etc.
Optimal
reference speed
sequence
v
adv
(k)v
max
(k)
v
ref
Powertrain model
Eco-driving
Lower level vehicle control
MPC based speed planning strategy
kk+p
v
ego
Output
[(1),,( )]
pre pre
vk vkp
Dynamic traffic
environment
1
22
23
12
4
Cost function: ( )
()
() ()
(() ())
pbat
kpT
x
yp
ik
ego adv
Jk
Pi
ai ai T
vivk
Optimal speed tracking controller
*
sgn( )
()
(cos()
)sin (
() ()) (
)
() ()
m
ego ref
wheel
m
fd fd d
r
if r
u
mg f k
F
vkvk k
kk
r
i
Lateral tracking controller
()
( ) ( ) arctan ()
Stan cs
ego
k
k
kek v
ek
() ( 1)
ref ego
vk vk
Fig. 5. Framework of the proposed hierarchical multi-objective
eco-driving control strategy.
A. Upper Level Speed Planning Design
1) Driving Safety Model
Throughout the driving process, a safe distance headway
should satisfy (10) to prevent collision.
min
() ( () () ) ()
saf
cegeo
e ego pre
head d c b head de
vdtstT td st (10)
where ()
safe
head
dt is safe distance headway between the
preceding vehicle and the ego vehicle. 0.1
b
T s is maximum
brake system response time. min 1
head md is minimum physical
distance headway.
p
re
dec
s
and ego
dec
s
represent the expected
distances at which the preceding vehicle and ego vehicle
decelerate to stop.
2
_min
2
_min
2
2
pre
dec pre pre
ego
dec xego
sv a
sv a
(11)
where
p
re
v is preceding vehicle speed. _minpre
a and _minx
a are
the maximum deceleration of preceding vehicle and ego vehicle.
In this study, _ min _ minpre x
aa. Assuming that the current
distance headway ()
head
dt is equal to the ()
safe
head
dt, we can
derive the safe speed limit ()
col_limit
vt that avoids collision based
on (10) and (11).
min
2
_min _min
() () ( () () ) ()
()
0
()
()
,
0
safe ego pre
head head dec b head deego
col_limi
c
x
t
xb b
v
, if
vt
d
Othe
td t stT td st
aT aT t
rwise
(12)
where
2min
_min _min
2()()2()
x
head pre pre head
adtvt dta .
In addition, to avoid the sideslip of the ego vehicle, the
maximum feasible lateral acceleration of the ego vehicle can be
defined as:
_max oyaodcdc a
ag
(13)
where 0.8
adco
is adhesion coefficient of the tire. 0.9
adco
is scaling factors. The ego vehicle speed should satisfy (14).
_max
2
ego y
va
(14)
where
is the road curvature. Thus, to avoid sideslip of the ego
vehicle, the maximum speed along the driving route can be
calculated based on (14).
_ max _ max
s
id y p
va
(15)
where
p
is the road curvature at the discrete reference waypoint
p. Before reaching the discretized reference waypoint p, the
ego vehicle must proactively decelerate to a safe speed below its
maximum speed _max ()
s
id p
v
. Due to the limit of longitudinal
deceleration, the safe speed limit profile to avoid sideslip is an
envelope of the maximum feasible deceleration speed trajectory
of each waypoint (as depicted in Fig. 6.). According to the
reference driving route, the safe speed limit profile can be
calculated in advance and modeled as lookup table function.
Thus, the safe speed limit that avoids sideslip can be expressed as:
(())() gsi _ sitdmedli i eo
fdvtt (16)
where ()
side
f
means the lookup table of the safe speed limit
profile to prevent sideslip. ()
ego
dt is the ego vehicle position.
Position
0
4
3
2
n
Speed
1
Saf ety s peed limi t prof ile
Deceleration speed trajectory
Fig. 6. Schematic of the speed limit profile to avoid sideslip.
Based on the safe speed limits ()
col_limit
vt (12) and ()
sid_limit
vt
(16), the maximum feasible speed for the ego vehicle can be
defined as:
max () min (), (),
col_limit sid_limit limit
vt v tv tv
(17)
where limit
v is the road speed limit based on the China traffic rules.
2) Driving Speed Advisor Model
The ego vehicle can traverse a signalized intersection during
the green light phase. Referring to Fig. 7. (a) and (b), we define
two important speed limits. The upper limit _maxlight
v represents
the constant speed at which the ego vehicle can move through the
signalized intersection at the beginning of the green light phase.
Similarly, the lower limit _minlight
v is defined as a constant speed
at which the ego vehicle can safely move through the intersection
as the green light phase approaches its end. Fig. 7. (c) shows the
flowchart to determine the suggested green light speed boundary
_min _max
[, ]
light light
vv , where 2VS
D is the distance between the ego
vehicle and the next signalized intersection. rem
t is the remaining
time within the current traffic light phase. _
g
cycle
t is the green
light duration time. cycle
t is the length of the traffic light cycle. n
is the number of delay cycles that would transpire if the ego
vehicle fails to move through the signalized intersection during
the next green light phase.
Based on the green light speed boundary _min _max
[, ]
light light
vv ,
we define a suggested green light speed for the ego vehicle.
__max _min
(1 )
gl adv light light
vmv mv (18)
where (0,1)m is the weighting factor. Thus, _
g
ladv
v can be
adjusted to accommodate the passenger preference for different
driving styles. Furthermore, in situations where the ego vehicle
is unable to traverse the signalized intersection within the
current traffic light phase, if _4
gl adv limit
vv, the ego vehicle
should follow the preceding vehicle. This ensures that the ego
vehicle does not obstruct other vehicles due to its slower
speed. In this scenario, the suggested speed for the ego vehicle
is defined as:
_min , ,
fo adv col_limit limit vir_limit
vvvv
(19)
where vir_limit
v is a speed limit determined based on a stationary
virtual preceding vehicle positioned at the stop line of the next
signalized intersections, as illustrated in Fig. 7 (d). vir_limit
v
ensures that the ego vehicle stops prior to reaching the stop
line.
2
_min
_min min
2_min
()
2()
vir_limit
VS
xb
xb
x
head
aT
vD
aT adt
(20)
Consequently, based (18) and (19), the suggested driving speed
of the ego vehicle can be summarized as:
2
__
_
_
,( )( )
4
,
V S limit
fo adv rem gl adv
gl adv
adv
gl adv
Dv
v if t v
v
v
v Otherwise
(21)
(d)
Tra ffic l ight
Virtu al p rec eding veh icle
v
pre
=0
d
head
=D
V2S
Stop line
(b)
Ego vehicle
v
light_max
v
light_m in
D
v2s
t
rem
n=0
n=1
n=2
(a)
Ego vehicle
v
light_max
v
light_min
D
v2s
t
rem
n=0 n=1
Ego vehicle trajectoryEgo vehicle trajectory
(c)
Start
End
Init ialing: n=0 ; Receiv ing traffi c
information: D
V2S
, t
rem
, v
limit
, t
g_cy cle
, t
cycl e
Is the traf fic
ligh t gree n ?
Is
Is
2
?
limit V S rem
vDt
Is
Control step k start
1nn
1nn
Yes No
Yes
No
No
Yes Yes
No
Output speed boundary
_min 2
_max 2 _
()
()
light V S rem cycle
light V S rem cycle g cycle
vDtnt
vDtntt
_min 2 _
_max 2
()
()
light V S rem g cycle cycle
light V S rem cycle
vDttnt
vDtnt
_max
?
light limit
vv
_min 2
_max
light V S rem
light limit
vDt
vv
_max
?
light limit
vv
_min _max
[, ]
light light
vv
Fig. 7. Illustration of the driving speed advisor model. (a)
Diagram of red traffic light scenario; (b) Diagram of green traffic
light scenario; (c) Flowchart of calculating the suggested green
light speed boundary; (d) Diagram of the stationary virtual
preceding vehicle.
3) Preceding Vehicle Speed Prediction Model
The primary source of uncertainty that affects the ego vehicle's
operations is the behavior of the preceding vehicle. Substantial
research has been dedicated to the development of vehicle
behavior prediction models [28]. In our approach, we use a
typical genetic algorithm (GA)-back propagation neural network
(BPNN) to create a speed predictor. This predictor optimizes the
initial weights and biases of the neural network (NN) using the
GA, thereby improving the training effectiveness of the NN. Its
performance has been widely investigated and verified in our
previous work [29, 30]. The speed predictor's input is the
preceding vehicle's historical speed vector. The output is the
preceding vehicle speed profile over the receding horizon of
MPC.
(|,)
GA BPNpre hiNs
f
wb
VV (22)
where 12
[, ,, ]
pre k k k p
vv v
V is the predicted vehicle speed
sequence at the control time step k, and 10p is the output
sequence length. 1
[, ,,]
his k h k h k
vv v
V is the historical speed
sequence, and 5h is the input sequence length. w and b are
the weight and bias of the BPNN. The BPNN speed predictor
consists of one hidden layer with 20 nodes.
The vehicle speed data used for model training and testing is
extracted from the virtual Shanghai traffic simulation model. This
dataset comprises the speed trajectory of 26,825 vehicles, with a
total recorded length is 5,706,869 s. 75% of the dataset was used
for training, and the remaining 25% was used for testing. This
dataset encompasses various vehicle speed trajectories under
various traffic conditions and road types encountered in the
simulation scenario. In our evaluation, the average root-mean-
square error (RMSE) for the test data set equals 1.5932. This
RMSE value is lower than that of similar NN predictors used in
previous studies [31, 32]. This result demonstrates that the GA-
BPNN based predictor can predict the vehicle speed satisfactorily.
4) MPC Based Speed Planning Strategy Design
As mentioned in Section II.A, to improve the overall driving
experience by co-optimizing the electric economy, ride comfort,
and travel efficiency, the eco-driving strategy needs to find a
balance among energy consumption, acceleration, and total travel
time. Thus, at the control step k, the cost function ()
J
k of the
proposed MPC strategy can be formulated as
22
123
2
14
() () ()
() (() ())
p
kp T
bat x y
p
ik ego adv
P i ai ai
J
kT
vivk
(23)
where 1()
bat
Pi
represents electric economy. 22
23
() ()
xy
ai ai
signifies ride comfort. 2
4(() ())
ego adv
vivk
determines the
total travel time of the ego vehicle, which directly impacts
travel efficiency. 10p s is the length of the receding horizon
of MPC. 1
p
T s is the length of discrete time step of the
receding horizon.
In this work, the distance headway head
d and ego vehicle speed
ego
v are selected as the state and control variable. The preceding
vehicle speed pre
v is regarded as external disturbance. The
acceleration of the preceding vehicle and ego vehicle is assumed
to be constant in each discrete time step of the receding horizon.
Thus, the discrete state equation can be modeled as
1
(1) () (1) ()
2
1(1) ()
2
head head p ego ego
ppre pre
dk dk Tvk vk
Tv k v k
(24)
At the control step k, to obtain the reasonable external
disturbance information of the preceding vehicle within the
receding horizon of MPC, we utilize the trained GA-BPNN
predictor (22) to predict the preceding vehicle's future speed
sequence [(1), (2),, ( )]
pre pre pre
vk vk vkp based on its
historical speed sequence [ ( ), ( 1), , ( )]
pre pre pre
vkhvkh vk
.
Meanwhile, the following inequality constraints need to be
satisfied to ensure ego vehicle safety.
i
min ma
mn
x()
e
h
go
headead
v
d
vk
v
d (25)
where ma x ()vk is determined by the proposed driving safety
model (17). It transforms the safe distance headway, safe
lateral acceleration, and road speed limit into a variable
maximum speed limit, simplifying the eco-driving problem
that involves complex traffic influence factors. The other two
constraints, minimum vehicle speed and minimum physical
distance headway, are constant values. min 0v and
min 1
head md.
Besides, due to the limits of the maximum acceleration and
deceleration, the control variable ego
v should be constrained as:
_min _max
((1) ())
xego egopx
avkvkTa (26)
where _maxx
a and _minx
a are the maximum acceleration and
deceleration of the ego vehicle. 2
_max _min 3/
xx
aa ms .
From the above, the eco-driving problem of the ego vehicle is
formulated as
min ( )
..
(24); (25); (26).
Jk
st
(27)
In this study, the eco-driving problem is solved by direct
multiple shooting method and sequential quadratic programming
(SQP) algorithm [33]. The direct multiple shooting method
transforms the optimal control problem (27) into a nonlinear
programming problem (NLP) (28). Then the SQP solver is used
to solve the NLP. At present, the direct method is preferred for
solving nonlinear MPC due to its lower computational intensity
than the typical dynamic programming algorithm [34].
2
12
22
134
0
1
im
_min
1_ma
n
x
min
(, ) (, )
(, ) ( )
..
() 0;
() 0;
() 0;
0, 1, 2, , ;
0; 1, 2, , ;
0; 1, 2, ,
p
hea
pT
bat i i x i i
p
iyii i adv
head
ego p x
ego p x
ii
i
i
d
Pux aux
OT
aux u v
st
xd k
vku Ta
uvk Ta
ip
ip
vu i p
sx
dx
max
1_min
1_max
;
0; 1, 2, , ;
0, 1, 2, , ;
0, 1, 2, , ;
i
ii px
ii px
uv i p
uu Ta i p
uuTa i p
(28)
where ()
iego
uvki
is the control variable. 1][, ,
p
s
s are
discrete auxiliary variables. i
x
is the state variable. The
relationship between the i
s
and i
x
can be expressed as:
11
1
2
1(1) (), 1,2,,
2
ii pi i
ppre pre
Tu u
Tv i v i i p
sx
(29)
The detailed application of the direct method in the vehicle
optimal control problem can refer to the previous studies [30].
Our SQP solver is implemented by MATLAB code with the
underlying QP problem being solved by a high speed C code
based QP solver, CVXGEN [35]. For real-time vehicle motion
control, at each control step, the first value from the solved
optimal speed sequence 1(1)
ego
uvk is sent to the lower level
vehicle controller as the target vehicle speed )(1)(
ref ego
vkkv.
B. Lower Level Vehicle Control Design
1) Optimal Longitudinal Speed Tracking Control
To control the motor torque for propelling the ego vehicle and
accurately tracking the target vehicle speed, an optimal
longitudinal speed tracking controller is developed. The state
variable is ego vehicle speed ego
v. The control variable is the
motor output torque m
. Based (1) and (3), the system state
equation can be formulated as:
s
2
gn( ) co
)2(
() s
(
si
)
n
m
ego ego
ego equi
mfd fd dif ego
ego equi wheel ego e
D
r
qui
mI
im
mm
CA
vv
g
I
f
Ir
(30)
It can be simplified as:
2
(1
2( )
,)
ego equi ego equ
D
i
mI mI
CA
x
fxu x u
(31)
where ego
x
v,
sgn( )
(cos sin)
()
m
mfd fd di
r
f
wheel
umgf
i
r
.
Besides, we assume reference value of
x
and u are f
x
and
f
u. Similarly, they are related by:
2
(,) 2(
1
)
D
rrr r r
ego equi ego equi
mI mI
CA
x
fxu x u
(32)
Eq. (31) and (32) are nonlinear differential equations. (31) can
be expanded as a Taylor series around the reference point
(,)
rr
x
u. Then the expanded equation ignores higher-order terms.
Hence, (31) is derived as:
() ()
(, ) (, )
(, )
rr
rr
rr r r
xx xx
uu uu
fxu fxu
x
fxu x x u u
xu
(33)
Based (33) (32), the linearized equation can be derived as
(,) (, )
rr
rr
rr r
xx xx
uu uu
tt
fxu fxu
x
xxx uu
xu
XAXBU
(34)
where r
X
x
x means the error between the actual speed ego
v
and target speed ref
v. It reflects the tracking performance of the
controller. r
Uuu is related to the control variable m
.
1
()
ego eq fitDreu
Am AICv
. 1
)( otegequi
mIB
. Thus, the
discrete-time linear state equation can be described as:
(1) () ()
X
kAXkBUk
(35)
where ()
t
A
IAT
, t
BBT
. 0.1T s is each control
step length. The cost function and algebraic Riccati equation
(ARE) are expressed as:
0
TT
i
J
QURUXX
(36)
1
()
TT T T
P A PA A PB R B PB B PA Q
(37)
where Q and R are constant weighting factors. According to
linear quadratic regulator theory, the optimal *
U that minimizes
the cost function (36) can be derived as:
*() ()Uk FXk (38)
where 1
()
TT
A
F
RBPB BP
, P can be calculated by
solving ARE (37). Based on r
X
x
x , and r
Uuu , and
(38), the optimal ()uk is:
)(())))(((
rr
ukkxkxFku (39)
where ()
r
xk equates to target speed ()
ref
vk
. ()
r
uk can be
calculated based on (32).
2
() ( 1)
() ) ()(2
ref
regoequi
ref D
ref
kk
um vA
kI k
T
vCv
(40)
Thus, based on (39), (40), and
sgn( )
(cos sin)
()
m
mfd fd di
r
f
wheel
umgf
i
r
, the discrete
optimal control law of the motor torque ()
mk
can be derived as:
*
sgn( )
()
(cos()
)sin (
() ()) (
)
() ()
m
ego ref
wheel
m
fd fd d
r
if r
u
mg f k
F
vkvk k
kk
r
i
(41)
In addition, the motor output torque is constrained by the
maximum battery charging and discharging power [,]
cha dis
bat bat
PP,
as well as the motor maximum torque mi n max
,
mm
. Thus, the
actual motor torque command can be expressed as:
*max*
1
*min*
min , , ,
(
max ,
() () 0
)
() () 0,,
eleacc
mmm
inv
ele
i
dis
ba
c
acc
m
t
mm
on
mcha
bat
m
m
m
m
nv
P if
n
P if
P
kk
P
n
kk
(42)
At each control step, the motor torque command con
m
is
transmitted to the vehicle model, thereby propelling the vehicle to
track the planned target speed ()
ref
vk.
2) Lateral Waypoint Tracking Control
The lateral control task of the ego vehicle is to minimize the
position and angle error between the reference waypoint and the
current vehicle's position and orientation. In this study, we
implemented a simple and effective lateral waypoint tracking
controller based on the Stanley method [36] (Fig. 8). The steering
angle ()k
command of the front wheel given by
()
( ) ( ) arctan ()
Stan cs
ego k
k
kek v
ek
(43)
where ( )ek
and ()
cs
ek are yaw angle error and crosstrack error
of the ego vehicle. Stan
k is gain parameter.
e
e
cs
Fig. 8. Illustration of the lateral waypoint tracking controller.
IV. SIMULATION AND DISCUSSION
A. Introduction of Simulation Experiment Environment
To evaluate and analyze the performance of the proposed eco-
driving strategy, we have developed a SUMO/Simulink based co-
simulation platform. This platform combines the SUMO based
virtual Shanghai traffic simulation model with the Simulink based
high-fidelity ego vehicle model. The framework of the designed
simulation platform is illustrated in Fig. 9. (a). The SUMO is
responsible for simulating urban traffic scenarios, whereas
Simulink encompasses critical components such as the eco-
driving strategy, vehicle powertrain model, and vehicle dynamics
model.
(a)
(b)
m
MATLAB/Simuliunk
SUMO traffic model
Powertrain
mode l
Dynamics
mode l
Ego vehicle model
Eco-driving
control strategy
Traffic info.
Vehicle
info .
a
x
v
x
Vehicle
state
SUMO control
module
Control strategy/
vehicle model
Display
SUMO
traffic model
Fig. 9. SUMO/Simulink based co-simulation platform (a)
Framework of the simulation platform; (b) Graphical User
Interface (GUI) of the simulation platform.
To realize data interaction between Simulink and SUMO, we
developed a Python script and integrated it into Simulink via an s-
function block (i.e. SUMO control module in Fig.9 (b)). The
implementation procedure of the co-simulation is detailed as
follows.
1) At the beginning of each control step, the SUMO control
module leverages the SUMO's Traffic Control Interface (TraCI)
[37] to retrieve essential data such as the ego vehicle state,
preceding vehicles state, and traffic light information within the
traffic simulation model, and send this traffic data to eco-driving
strategy module.
2) Then, by utilizing traffic information from the SUMO and the
vehicle state information from the vehicle model, the eco-driving
strategy computes the motor torque command and front-wheel
steering angle command.
3) Third, based on the torque command, the ego vehicle's
longitudinal acceleration and speed are calculated online by the
powertrain model and longitudinal dynamics model. Then, the
lateral dynamics model (i.e., bicycle model) computes the lateral
speed, lateral acceleration, and yaw angular speed of the ego
vehicle online based on the longitudinal velocity and front wheel
steering angle.
4) Finally, the SUMO control module feeds back the computed
actual ego vehicle state, encompassing the speed, acceleration,
position, and orientation, into the SUMO simulation environment.
This feedback loop ensures that the ego vehicle state within the
traffic simulation model is continually updated.
20 40 60 80 100 12 0
Sample time (min)
5
10
15
20
2
4
6
8
10
12
14
16
18
20
0
Position (km)
(10:00 a.m.) (12:00 p.m.)
Average
speed (m/s)
Fig. 10. Real-world average vehicle speed data along the ego
vehicle's driving route. (Note: We collect the average speed
data during the same time period (10 a.m. to 12 p.m.) from
March 1st to 5th, 2022, with a spatial resolution of 100 m and a
sampling interval of 1 min.)
TABLE I
PARAMETERS OF THE BATTERY ELECTRIC VEHICLE
Parameters Value Uni
t
Vehicle mass 1835
k
g
Motor peak torque 386 Nm
Motor peak powe
r
202
k
W
Battery voltage 345.6 V
Battery capacity 173.5 Ah
Final drive ratio 9.1 [-]
Tire radius 0.344 m
Yaw moment of inertia 3885 kg
m
2
Cornering stiffness of front wheel 99423 N/rad
Cornering stiffness of rear wheel 100423 N/rad
Distances from CG to front axis 1.232 m
Distances from CG to rear axis 1.468 m
For the ego vehicle, the powertrain model and longitudinal
dynamics model are developed using Autonomie software to
reflect the accurate performance of the BEV. Additionally, the
lateral dynamics model is built according to the bicycle model.
The driver models for other vehicles in the simulation utilize
the Krauss car-following model [38] to represent conventional
manually driven vehicles. Lane change behavior, both the ego
vehicle and other vehicles, is implemented using SUMO's
default LC2013 model [39]. The traffic flows in the virtual
Shanghai traffic simulation model are designed according to the
real-world average speed dataset (Fig. 10) along the ego vehicle's
driving route. It is detailed in our previous research [40]. The
parameters of the ego vehicle model are summarized in Table I.
All the simulations were performed on a laptop with AMD
Ryzen7 4800U CPU.
B. Functional verification of longitudinal speed tracking
controller
In this subsection, to verify the performance of the derived
optimal speed tracking controller, we conducted a comparative
analysis against a commonly used proportional-integral-
derivative (PID) based speed tracking controller [17, 41, 42].
Similar to the proposed optimal speed tracking controller, the
PID based contrast controller calculates the output torque of
the traction motor based on the error between the reference
target speed and the actual speed, thereby propelling the
vehicle to follow the target speed.
_0
()
() ()
tspd
m pid p spd i spd d
de t
Ke t K e tdt K dt
(44)
where
_mpid
is the motor torque generated by the PID
controller. () () ()
spd ref ego
et vtvt is the error between the
reference target speed and the actual speed. 9000
p
K,
10
i
K, and 1
d
K are the parameters of the PID controller.
They were determined through several careful try-and-error
iterations. The simulation test framework of the speed tracking
controller is shown in Fig. 11. To ensure the test's focus
remains on the lower-level speed tracking controller, we
eliminated the influence of the upper-level reference speed
planning strategy. For the comparative simulation test, we
employed a standard driving cycle, China Light-Duty Vehicle
Test Cycle (CLTC), as the reference target vehicle speed. In
this setup, the proposed optimal speed tracking controller or
the PID based controller sends the motor torque commands to
the vehicle model and receives real-time speed feedback from
the model, facilitating closed-loop control. The mileage and
total travel time of the CLTC are 14480 m and 1800 s,
respectively. The simulation road slope data (as displayed in
Fig. 12.) is real urban road data obtained through automotive
road tests. The actual speed trajectories are shown in Fig. 13.
The RMSE of the actual speed trajectories of the two methods
is calculated and listed in Table II.
CLTC
cycle
Speed tracking
controller
Ego vehicle
mode l
v
ref
v
ego
m
Z
-1
Closed-loop control
Fig. 11. The schematic diagram of the simulation test of speed
tracking controller.
Slope (rad)
0 3 6 9 12 15
Distance (km)
-0.12
-0.08
-0.04
0
0.04
0.08
0.12
Fig. 12. Road slope data along the test cycle.
0 200 400 600 800 1000 1200 1400 1600 1800
Time (s)
0
20
40
60
80
100
120
Speed ( km/h)
Ref
PID
Pro p
Ref
PID
Prop
Refere nce PI D Propo sed
Fig. 13. Actual speed trajectories of the contrast PID
controller and the proposed controller.
TABLE II
SIMULATION RESULTS OF TRAVEL DISTANCE AND RMSE
Method Travel distance RMSE
PID based controller 14481 m 0.1050
Proposed controller 14478 m 0.0207
Note: Length is the total travel distance.
As shown in Fig. 13, both the PID controller and the
proposed controller can control the ego vehicle to track the
reference speed. However, the response speed of the proposed
controller is faster than that of the PID controller. The actual
vehicle speed trajectory of the proposed strategy is more
closely with the reference vehicle speed trajectory in contrast
to the PID based strategy. Table II shows that the total travel
distance of both methods only slightly deviates from that of
the reference cycle. And the speed's RMSE of the proposed
controller is lower than the RMSE of the PID controller.
Therefore, we can conclude that both methods are viable for
longitudinal speed tracking control. But the proposed optimal
longitudinal speed tracking controller surpasses the typical
PID based controller in terms of performance and response
speed.
C. Influence Analysis of Weighting Factors
The weighting factors represent the tradeoffs among energy
economy, ride comfort, and travel efficiency in the eco-
driving strategy. As introduced in Section III.A.3), in the cost
function (23), the battery power term 1()
bat
Pi
, acceleration
squared terms 22
23
() ()
xy
ai ai
, and speed difference squared
term 2
(() )
ego adv
vivare related to the energy economy, the
ride comfort, and the travel efficiency, respectively. To make
different terms in (23) have similar magnitudes, the baseline
values of the weighting factors are as follows:
12 3 4
1; 2000; 2500; 540
(45)
Furthermore, (23) can be influenced by the suggested
driving speed adv
v. In this subsection, the baseline value of the
weighting factor m in (18) equals 0.5. It represents that an
intermediate speed within the green light speed boundary
_min _max
[, ]
light light
vv is selected as the suggested green light
speed. To evaluate the impact of different weighting factors on
the proposed strategy, we design five contrast strategies, each
of which changes only one weighting factor compared to the
baseline strategy. The weighting factors values of the baseline
strategy and the five contrast strategies are presented in Table
III. We conducted simulations of these six strategies under
identical lower level vehicle controllers, vehicle models, and
virtual Shanghai traffic simulation model. The traffic flows
were not loaded into the traffic model to avoid disturbance
from other vehicles. The simulation results of all six methods
are depicted in Fig. 14, 15, and Table IV.
TABLE III
WEIGHTING FACTORS VALUES OF BASELINE STRATEGY AND
FIVE CONTRAST STRATEGIES
Method Weighting facto
r
s value
1
2
3
4 m
Baseline 1 2000 2500 540 0.5
Strategy I 4 ↑ 2000 2500 540 0.5
Strategy II 1 2000 2500 2160 ↑ 0.5
Strategy III 1 8000 ↑ 10000 ↑ 540 0.5
Strategy IV 1 2000 2500 540 0.1 ↓
Strategy V 1 2000 2500 540 0.9 ↑
Note: ↓ or ↑ denotes the reduction or increase in the five Contrast
s
trategies when compared to the Baseline strategy.
Position (km)
Time (s)
0 50 0 10 00 1500 20 00 2500 3000
0
2
4
6
8
10
12
14
16
18
20
22
Baseline
Strate gy I
Strategy II
Strategy III
Strategy IV
Strate gy V
Fig. 14. Spatial-temporal diagrams of the six strategies.
0
6
12
18
24
6
12
18
24
0
6
12
18
24
0
6
12
18
24
0
6
12
18
24
0
6
12
18
24
vego (m/s)vego (m/s)vego (m/s)vego (m/s)vego (m/s)
Baseli ne
Strategy I
Strategy II
Strategy III
Strategy IV
Strategy V
0 500 10 00 1500 20 00 2500 3000
Time (s )
vego (m/s)
Fig. 15. Speed profiles of the six strategies.
TABLE IV
SIMULATION RESULTS COMPARISON OF THE SIX STRATEGIES
Method
SOC
Change
(%)
Travel
time
(s)
Average
absolute ay
(m/s2)
Average
absolute ax
(m/s2)
Baseline 0.0374 2116 0.0652 0.1996
Strategy I 0.0318 ↓ 2839 ↑ 0.0413 ↓ 0.1715 ↓
Strategy II 0.0378 ↑ 1991 ↓ 0.0753 ↑ 0.1999 ↑
Strategy III 0.0364 ↓ 2221 ↑ 0.0622 ↓ 0.1780 ↓
Strategy IV 0.0348 ↓ 2848 ↑ 0.0369 ↓ 0.1620 ↓
Strategy V 0.0403 ↑ 1846 ↓ 0.0901 ↑ 0.2535 ↑
Note: ↓ or ↑ denotes the reduction or increase in the five contrast
s
trategies when compared to the Baseline strategy.
As shown in Tables III and IV, the strategy I, with its
substantial emphasis on battery power weight factor, exhibits
the lowest electric consumption. However, it does so at the
cost of reduced speed, resulting in a significant increase in
travel time compared to the baseline strategy, as demonstrated
in Fig. 14 and 15. Additionally, Table IV highlights that the
strategy I also achieves lower average absolute lateral and
longitudinal accelerations compared to the baseline strategy.
While it improves ride comfort, it also diminishes travel
efficiency.
In Tables III and IV, the strategies II and V, with increased
weight factors for the reference speed term or an aggressive
green light speed, respectively, resulted in decreased travel
time but increased energy consumption and acceleration. In
particular, the strategy V, driven by an aggressive green light
speed results in the shortest travel time (as evident in Fig. 14
and 15). However, it's important to note that the acceleration
of the strategy V is significantly increased compared to the
other strategies. It could potentially lead to discomfort for the
passengers.
As indicated in Table III, the strategy III aims to improve
ride comfort by increasing the weight assigned to the vehicle
acceleration term. As a result, the acceleration of the strategy
III is lower than that of the baseline strategy. This reduction in
acceleration not only improves ride comfort but also leads to a
decrease in the average speed, particularly evident in Fig. 15.
Conversely, the strategy IV adopts an extremely conservative
driving style, selecting a green light speed that is close to the
lower limit of the speed boundary as the reference speed. As
illustrated in Fig. 15, this conservative approach results in the
vehicle traveling at a notably slower speed, leading to the
lowest acceleration and the longest total travel time, as
observed in Table IV. However, driving too slowly in real-
world scenarios can cause severe traffic congestion or even
accidents.
As highlighted by the above analyses, the three objectives
of energy economy, ride comfort, and travel efficiency are
interplay and challenging to improve simultaneously.
Achieving eco-driving control requires finding a delicate
balance among these objectives, which is more complex
because of passengers' varying preferences. In practice,
different passengers may have different preferences for these
objectives. In our proposed strategy, we can adjust the
weighting factors and the suggested green light speed to align
with the preferences of different passengers.
D. Performance Evaluation of Proposed Eco-driving Control
Strategy
To evaluate the performance of the proposed MPC based
multi-objective eco-driving control strategy, a widely used rule-
based intelligent driver model (IDM) [43] is employed as the
baseline strategy. In addition, our proposed strategy is compared
with a typical MPC based car-following strategy (MPC-CF) and
a state-of-the-art MPC based energy-efficient control strategy
considering preceding vehicle and traffic lights (MPC-CFTL).
1) The original IDM was developed only for the car-following
task. To avoid incidents such as running red lights or sideslips,
we have designed a rule-based monitor model to modify the
unreasonable speed of the original IDM. The modified IDM
(M-IDM) can be defined as
42
_
0
min ,
..
()
()
1()
() () () (2 )
() ( 1),
(1) () 1
(1)
I
DM tl tl_limit
IDM IDM
ego
I
ref IDM sid sid_limi
DM
limit head
ego ego
t
ego
vvvv
st
vaT
vk s
aa
vdk
ssTvk vk
kk
kv k
v
k
kab
k
(46)
where _()
ref IDM
vk is the output reference speed of the M-IDM.
s
id_limit
v is the safe speed limit that computed by the driving safety
model in Section III.A. tl_limit
v is the traffic light safety speed
limit that avoids running a red light; the details of computed
the traffic light safety speed limit can be found in [40]. ()vt
is the speed difference between the ego vehicle and the
preceding vehicle. 2
1.4a ms and 2
2.0b ms are
maximum acceleration and desired deceleration (From [6]).
02
s
m is jam distance. 1.6T s is safe time headway.
2) The MPC-CF is designed based on the previous research [44].
It achieves optimal fuel economy while satisfying a safe
following distance.
3) The MPC-CFTL is formulated based on the previous research
[19] with the goal to reduce fuel consumption and travel time.
This strategy achieves this goal by generating an optimal speed
trajectory to move smoothly through signalized intersections and
satisfy a safe following distance.
It is important to highlight that, as explained in Section IV.C,
there exists a delicate balance among energy economy, ride
comfort, and travel efficiency. For instance, adopting an
aggressive driving approach may reduce travel time but lead to
higher energy consumption and cause motion sickness. To
make a fair comparison, the weighting factors for the MPC-CF,
the MPC-CFTL, and the proposed strategy were carefully fine-
tuned through a series of try-and-error iterations. This process
persisted until the travel times of the three strategies
approximated that of the baseline M-IDM strategy.
The simulations of these strategies are conducted in the
SUMO/Simulink based co-simulation platform with the virtual
Shanghai traffic simulation scenario. The simulation results of
the three contrast strategies and the proposed strategy are
shown in Fig. 16 to Fig. 20, and summarized in Table V.
Additionally, for a comprehensive understanding of the
experiment, we have included four supplementary videos in
Appendix A. These videos record the entire simulation testing
procedures of these four strategies.
Position (km)
0 500 1000 1500 2000 2500 3000
Time (s )
0
2
4
6
8
10
12
14
16
18
20
22
M-IDM
MPC-CF
MPC-CFTL
Propo sed
(a)
(b)
(c)
Fig. 16. Spatial-temporal diagrams of the four strategies.
0
100
200
0
8
16
24
(a)
(b)
D
head
(m)v
pre
(m/s)
0
100
200
0
8
16
24
(c)
(d)
0
100
200
0
8
16
24
0
100
200
0
8
16
24
0 500 1000 1500 2000 2500 3000
Time (s )
D
head
(m)v
pre
(m/s)D
head
(m)v
pre
(m/s)D
head
(m)v
pre
(m/s)
Distance headway
Speed
Distance headway
Speed
Distance headway
Speed
Distance headway
Speed
Fig. 17. The distance headway trajectories between ego
vehicle and preceding vehicle and the preceding vehicle speed
trajectories. (a) M-IDM; (b) MPC-CF; (c) MPC-CFTL; (d)
Proposed strategy. (Note: We assume the maximum physical
perception distance of the ego vehicle is 200 m.)
First of all, we evaluate the driving safety of the four eco-
driving strategies. As depicted in Fig. 16, the M-IDM, MPC-
CFTL, and proposed strategies adhere to the traffic light rules.
In contrast, the MPC-CF, which primarily focuses on
satisfying a safe following distance and optimizing fuel
economy without considering traffic light information, ran a
red light at approximately 1873rd seconds (as demonstrated in
Fig. 16 (b)). The behaviors of preceding vehicles are random
and dynamic, as depicted in Fig. 17, where various line colors
represent different preceding vehicles detected by the ego
vehicle. These dynamic behaviors, including lane changes and
overtaking, meticulously emulate real-world traffic dynamics.
Thus, the virtual Shanghai traffic simulation model can
faithfully represent real-world traffic scenarios. Even in these
challenging dynamic traffic scenarios, the distance headway
between the ego and the preceding vehicle remains greater
than zero. It demonstrates that all four eco-driving strategies
can effectively control the ego vehicle to avoid collisions
throughout the trip.
Additionally, in Fig. 19, both the M-IDM and the proposed
strategy effectively limit the absolute lateral acceleration to
values below the maximum feasible lateral acceleration _maxy
a.
Conversely, the MPC-CF and MPC-CFTL, not considering the
lateral acceleration constraint, exhibit absolute lateral
acceleration values that exceed the maximum limit. This
uncontrolled lateral acceleration can lead to dangerous sideslip
conditions for vehicles employing these two strategies. As
shown in Table V, the maximum absolute lateral accelerations
of the MPC-CF and MPC-CFTL exceed 22 and 29 m/s2,
respectively. It highlights the significance of considering
lateral acceleration constraints in urban traffic scenarios, as
they play a crucial role in ensuring driving safety. Our
proposed strategy designs the driving safety model and the
driving speed advisor model to consider complex car-
following, lateral, and traffic light constraints. As a result, it
can effectively and robustly ensure driving safely within the
complex urban traffic scenario.
TABLE V
SIMULATION RESULTS OF ELECTRIC CONSUMPTION,
ACCELERATION, AND TRAVEL TIME
Electric
Consumption
(%)
Maximum
absolute ay
(m/s2)
Average
absolute ay
(m/s2)
Average
absolute ax
(m/s2)
Travel
time
(s)
M-IDM 4.05 6.99 0.0607 0.3143 2581
MPC-CF 3.90 22.5 0.0670 0.3698 2587
MPC-CFTL 3.59 29.4 0.0620 0.2800 2599
Propose
d
3.67 6.5 0.0541 0.2720 2598
N
ote: Electric consumption is represented by int 100
end
SOC SOC %（）.
v
ego
(m/s)v
ego
(m/s)v
ego
(m/s)v
ego
(m/s)
0
8
16
24
0
8
16
24
0
8
16
24
0
8
16
24
0 500 1000 1500 2000 2500 30 00
Time (s)
Fig. 18. Speed profiles of the four strategies.
2543.31
22.99 17.07 4.15 4.44 3.95 3.1
0
20
40
2600
MPC-CFTL
2553.49
21.88 12.82 3.35 3.89 2.88 0
0
20
40
2600 Pr oposed
2532.35
24.17 14.92 6.27 4.05 3.51 2.54
0
20
40
2550 MPC-CF
2518.9
34.88 15.61 4.36 4.6 3.46 0
0
20
40
2550 M-IDM
Duration time (s)
[0, 0.5) [0 .5, 1) [1, 2) [2, 3) [3, 5) [5 , 7.1) [7.1, ∞)
Absolute la teral acceleration (m/s
2
)
Fig. 19. Distributions of absolute lateral acceleration.
Duration time (s)
1758.81
319.6 276.2 166.3 26.9 9.8 24.2
0
200
400
1800
1771.21
341.21 249.8 131 51 18.2 25.39
0
200
400
1800
1899.61
349.21 220.2 69.8 29.2 12.2 18.79
0
200
400
1900
2)
1939.02
326.6 215 64.8 24.7 10.4 17.79
0
200
400
2000
M-IDM
MPC-CF
MPC-CFTL
Propo sed
Absolute longitudinal acceleration (m/s
2
)
[0, 0.25 )[0.2 5, 0.5) [0.5, 1) [1, 1.5) [1 .5 , 2) [2, 2.5) [2, 3]
Fig. 20. Distributions of absolute longitudinal acceleration.
Second, in terms of economy, the MPC-CF, MPC-CFTL,
and proposed strategy can optimize vehicle speed to improve
the economy. As shown in Table V, the electric consumption
of the MPC-CF, MPC-CFTL, and proposed strategy is
reduced by 3.7 %, 11.4 %, and 9.4 %, respectively, compared
to the baseline M-IDM strategy. The MPC-CF effectively
reduces electric consumption while maintaining a safe
following distance. However, its lack of integration with
traffic light information during speed optimization leads to
unnecessary braking and acceleration at signalized
intersections. This has adverse effects on energy efficiency.
On the other hand, both the MPC-CFTL and our proposed
strategy can optimize vehicle speed based on the preceding
vehicles and traffic light information. As depicted in Fig. 16
(a), (b), and (c), they effectively avoid unnecessary stop-and-
go behavior at signalized intersections, in contrast to the
MPC-CF. The electric consumption of the MPC-CFTL and
our proposed strategy is significantly lower than that of the
MPC-CF. Additionally, our proposed strategy not only
considers safety constraints related to preceding vehicles and
traffic lights but also considers sideslip safety constraints and
ride comfort optimization. Its economy is slightly lower than
that of the MPC-CFTL.
Third, with regard to ride comfort, Table V shows that the
average absolute lateral and average absolute longitudinal
accelerations of the proposed strategy are lower than those of
the contrast M-IDM, MPC-CF, and MPC-CFTL strategies.
This is attributed to the incorporation of acceleration squared
terms in the cost function (23), which imposes a sub-objective
to minimize lateral and longitudinal acceleration by
optimizing driving speed. The acceleration distributions are
visualized in Fig. 19 and 20. Under the control of our
proposed strategy, the duration time of lateral acceleration
within the low acceleration range of 0 to 0.5 m/s2 is the longest.
Furthermore, in other acceleration ranges, the lateral
acceleration duration time is shorter than that of the M-IDM,
MPC-CF, and MPC-CFTL strategies. Therefore, the proposed
strategy can effectively reduce average absolute lateral
acceleration. Similar to the lateral absolute acceleration
distributions, the proposed strategy exhibits the longest
duration of longitudinal acceleration within the low
acceleration range of 0 to 0.25 m/s2. In other acceleration
ranges, the duration time is shorter than that of the contrast
strategies. The proposed strategy results in a smaller average
absolute longitudinal acceleration compared to the contrast
strategies. As a result, our proposed strategy provides a more
comfortable ride compared to the contrast M-IDM, MPC-CF,
and MPC-CFTL strategies.
Finally, with respect to travel efficiency, we adjusted the
weighting factors of the MPC-CF, MPC-CFTL, and proposed
strategy to ensure that the total travel times of these three
strategies approximate that of the baseline M-IDM strategy.
As shown in Table V, the total travel times of all four
strategies are around 2600 s. However, as shown in the speed
profiles in Fig. 18, both the MPC-CFTL and proposed strategy,
which considers traffic light information for speed
optimization, significantly reduce the time spent halted at
traffic lights compared to the contrast M-IDM and MPC-CF
strategies. This improvement is further exemplified by the
segments (a), (b), and (c) displayed in Fig. 16, and can also be
observed in detail in our supplementary materials provided in
Appendix A. The driving speed advisor model of our proposed
strategy calculates the suggested green light speed based on
traffic signal information. This enables the ego vehicle,
controlled by our proposed strategy, to move through the
traffic light during the green light phase, thereby reducing the
frequency of unnecessary stops at signalized intersections.
Thus, the proposed strategy effectively reduces waiting time at
signalized intersections and improves the overall travel
experience.
Simulation duration (ms)
0 500 1000 1500 20 00 2500 3000
Time (s )
0
20
40
60
80
100
Fig. 21. Simulation duration for each control step involving
the proposed strategy.
Furthermore, concerning real-time performance, the
simulation duration for each step involving the proposed
strategy is illustrated in Fig. 21. As shown in Fig. 21, the
proposed strategy demonstrates an average computation
duration of approximately 46.8 ms per control step, which is
feasible for online applications with a control step 0.1T s .
To summarize, the proposed strategy can co-optimize energy
economy, ride comfort, and travel efficiency, resulting in a
superior passenger experience while ensuring driving safety.
V. CONCLUSION
This paper proposes a novel MPC based multi-objective eco-
driving strategy for CAVs in urban scenarios while
considering complex driving safety influence factors. In the
upper level, the proposed strategy includes a driving safety
model and a driving speed advisor model to transform the
multiple safety constraints arising from diverse influence
factors such as traffic lights, preceding vehicles, and road
bends into speed constraints. Then, we propose a speed
planning strategy with stringent safety constraints and a multi-
objective cost function. It can calculate the optimal reference
speed that balances the energy economy, ride comfort, and
travel efficiency while prioritizing driving safety. In the lower
level, a highly responsive and computationally efficient
longitudinal speed tracking controller is designed to compute
the demand torque of the traction motor. It can fast and
robustly track the optimal reference speed. The simulation
results in the dynamic virtual Shanghai traffic simulation
scenario demonstrate the effectiveness and reliability of our
proposed strategy. Specifically, the electric consumption of
the proposed strategy is reduced by 9.4 % and 5.9 % compared
to the M-IDM and MPC-CF strategies, respectively. The
average acceleration of the proposed strategy is reduced by
12.2 %, 22.9 %, and 7.8 % compared to the M-IDM, MPC-CF,
and MPC-CFTL strategies, respectively. In addition, the
proposed strategy significantly reduces waiting time at
signalized intersections in comparison to the M-IDM and
MPC-CF strategies.
As for future work, we plan to improve the lateral waypoint
tracking controller and extend the proposed strategy to
different types of CAV (e.g., internal combustion engine
vehicles or hybrid electric vehicles). Besides, to improve the
performance of the upper-level MPC based speed planning
strategy, we will explore additional methods to further
enhance the accuracy of the prediction model.
APPENDIX A. SUPPLEMENTARY MATERIALS
The following videos record the simulation test procedures
of the contrast strategies and the proposed strategy.
Simulation record video of the baseline M-IDM strategy.
Video link: https://youtu.be/Jhe38kJZtb8
Simulation record video of the MPC-CF strategy.
Video link: https://youtu.be/UxUeGRW234Y
Simulation record video of the MPC-CFTL strategy.
Video link: https://youtu.be/EltbL-ZWk2A
Simulation record video of the proposed strategy.
Video link: https://youtu.be/h_AxGZFNifw
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