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IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 00, NO. 00, 2020 1
Cooperative Comfortable-Driving at Signalized
Intersections for Connected and Automated Vehicles
1
2
Xun Shen , Xingguo Zhang , Tinghui Ouyang, Yuanchao Li, and Pongsathorn Raksincharoensak3
Abstract—This letter proposes a control framework for Con-4
nected and Automated Vehicles(CAVs) to approach the signalized5
intersections with good driving-comfortability. Both the velocity6
plan and longitudinal dynamics control are concerned in this study.7
Regarding the velocity plan problem, a two-layer framework is8
designed. First, a scenario identifier method is proposed to identify9
which scenario the target velocity profile should be according to10
the current vehicle speed, distance to the intersection, and traffic11
signal information. Then, an assigned-time velocity planning prob-12
lem with velocity and acceleration constraints is formulated and13
solved to obtain a smooth velocity profile with the minimal jerk.14
For the longitudinal dynamics control, a predictive controller with15
Online Sequential Extreme Learning Machine(OSELM) is applied16
to realize the smooth velocity profile tracking. CarMaker-Simulink17
co-simulation has been conducted to validate the proposed method.18
The validation results show that the proposed method can iden-19
tify the scenario in 100% of the time according to the validation20
results. On the other hand, the OSELM-based predictive control21
has improved MSE ev,e
a,e
jerk of 33.85%, 27.66%, and 38.03%22
respectively than PID control.23
Index Terms—Intelligent transportation systems, motion and24
path planning, model learning for control.25
I. INTRODUCTION26
RECENTLY, more and more research has been conducted27
to develop Connected and Automated Vehicles (CAVs)28
applications that involve controlling automated vehicles to travel29
through signalized intersections [1]. [2] proposed a Cooperative30
Adaptive Cruise Control for CAVs to realize eco-driving when31
traveling through the signalized intersections. In [3], upcoming32
traffic signal information is used in the predictive cruise control33
to achieve better fuel economy and less trip time. Besides, a34
reinforcement learning-based control method for autonomous35
driving is proposed in [4] which can ensure safety, efficiency,
Q1
36
and comfortability. Since the velocity profile with minimal jerk37
obtains both fuel economy and driving comfortability [5]–[8], it38
is important to achieve a velocity profile with the minimal jerk.39
Manuscript received April 23, 2020; accepted July 21, 2020. Date of pub-
lication; date of current version. This letter was recommended for publication
by Associate Editor S. Manzoor and Editor Youngjin Choi upon evaluation of
the Reviewers’ comments. This work was supported by JSPS KAKENHI under
Grant 18K13237. (Corresponding author: Xun Shen.)
Xun Shen, Xingguo Zhang, and Pongsathorn Raksincharoensak are with the
Department of Mechanical Systems Engineering, Tokyo University of Agricul-
ture and Technology, Tokyo 184-8588, Japan (e-mail: shenxun@go.tuat.ac.jp;
xgzhang@go.tuat.ac.jp; pong@go.tuat.ac.jp).
Tinghui Ouyang is with the Artificial Intelligence Research Center, National
Institute of Advanced Industrial Science and Technology Tokyo Bay Area
Center, Tokyo 135-0064, Japan (e-mail: ouyang.tinghui@aist.go.jp).
Yuanchao Li is with the Honda Innovation Lab. Tokyo, Honda R& D Co.,
Ltd, Tokyo 107-6238, Japan (e-mail: liyuanchao.24x@kyoto-u.jp).
Digital Object Identifier 10.1109/LRA.2020.3014010
A. Background and Related Works 40
Velocity profile generation or velocity planning in au- 41
tonomous vehicle applications often considers collision avoid- 42
ance [9]. For example, a human social norms-based collision 43
avoidance scheme is proposed in [10] in which a smooth velocity 44
profile with good comfortably is generated to avoid potential col- 45
lision. A merging trajectory generation method aiming for prac- 46
tical automatic driving was proposed to reduce drivers mental 47
load and traffic congestion caused by merging maneuvers [11]. 48
In [12], the interpolating cubic splines-based velocity planning 49
scheme is proposed for automated vehicles to realize minimal 50
jerk velocities. [13] applies Bezier curves to generate a smooth 51
speed profile with enhanced passenger comfort for intelligent 52
vehicles to avoid collision with the other traffic participants. 53
Besides, many types of researches on minimum-jerk velocity 54
planning from the robotics field can be applied in the velocity 55
planning problem for CAVs. For example, [14] solves an opti- 56
mization problem with constraints on initial and terminal points 57
to obtain a minimum-jerk profile for mobile robots. Smooth and 58
continuous accelerations with jerk limitation are obtained by 59
solving the time-optimal path tracking under limited joint range 60
and bounds on velocity, acceleration, and jerk in [15]. 61
B. Key Contributions of This Letter 62
This letter proposes a comfortably-driving control framework 63
for CAVs at intersections with the following contributions: 64
rThe minimal jerk velocity planning has a two-layer frame- 65
work. First, boundary point-based scenario identifier is 66
proposed to categorize the target velocity profile based 67
on the current vehicle speed, distance to the intersection, 68
and traffic signal information. Then, assigned-time velocity 69
planning problem with velocity, acceleration constraints is 70
formulated and solved to obtain a smooth velocity profile 71
with the minimal jerk; 72
rFor longitudinal vehicle dynamical control, OSELM-based 73
predictive control is applied to realize the obtained smooth 74
velocity profile with the minimal jerk; 75
rCarMaker-Simulink co-simulation was implemented to 76
validate the proposed method. The validation results show 77
that the proposed method can identify the scenario in 100% 78
of the time according to the validation results. On the other 79
hand, the OSELM-based predictive control has improved 80
MSE ev,e
a,e
jerk of 33.85%, 27.66%, and 38.03% respec- 81
tively than PID control. 82
2377-3766 © 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See https://www.ieee.org/publications/rights/index.html for more information.
IEEE Proof
2IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 00, NO. 00, 2020
Fig. 1. Target scene: an automated connected vehicle is approaching a signal-
ized intersection.
II. METHODOLOGY83
The problems of velocity planning and longitudinal velocity84
tracking must be addressed in order to achieve comfortably-85
driving for CAVs at intersections. This section gives the prob-86
lem formulations for velocity planning and velocity tracking.87
Then, the two-layer framework of the proposed methodology is88
introduced.89
A. Velocity Planning90
Consider the scene that an automated CV is approaching a91
intersection with a single traffic light as shown in Fig. 1. The92
available information is listed as:93
rThe current velocity of self-vehicle: v0;94
rThe current distance from self-vehicle to the intersection:95
s0;96
rThe traffic signal sequence: Z.97
The current velocity and distance are denoted as v0and s0
98
since they are the initial states in the velocity planning problem.99
The traffic signal sequence Zis a set written as100
Z={z(t)|t∈[t0,t
z]}(1)
where t0is the initial time or the current time and tzis larger101
enough for the velocity planning. Besides, z(t)is a binary102
variable denoted as103
z=0,if green
1,if red or yellow.(2)
Furthermore, the situation that there is traffic jam over the
104
intersection can also be taken into consideration by setting all105
z(t)as z(t)=1since self-vehicle cannot either go through the106
intersection.107
This application directly suggests some requirements on the108
states when the vehicle arrives at the intersection. The first one109
is the terminal velocity condition written as110
v(ta)=0,if z(ta)=1
v(ta)∈(0,v
max],if z(ta)=0 (3)
where tadenotes the time the vehicle arrives at the intersection111
and vmax is the velocity upper limitation of the road. The velocity112
v(t), acceleration a(t)and jerk J(t)are within proper bounds113
v(t)∈(0,v
max],∀t∈(t0,t
a),(4)
a(t)∈[−amax,a
max],∀t∈(t0,t
a),(5)
J(t)∈[−Jmax,J
max],∀t∈(t0,t
a),(6)
where amax and Jmax are absolute value limits of acceleration and114
jerk. Noticing that the lower bound of velocity is posed equal to115
zeros in order to avoid unwanted backward movements. Another 116
requirement is the terminal distance condition written as 117
s0=ta
t0
v(t)dt. (7)
Besides, the initial conditions are written as 118
s(t0)=0,(8)
v(t0)=v0,(9)
a(t0)=a0∈[−amax,a
max],(10)
J(t0)=J0∈[−Jmax,J
max],(11)
where v0,a
0, and J0are the initial values. This letter investi- 119
gates specifically the initial condition with J0=0and a0=0.120
Namely, the previous state of the vehicle is supposed to be 121
cruising. 122
Due to the above assignments, it is possible to define a feasible 123
profile v(t)as follows 124
Definition 1: A curve v(t)is feasible if it is l−1-continuity and 125
satisfies conditions (3)–(11). The set of feasible v(t)is written 126
as Fv.127
The letter addresses the following velocity planning problem 128
Problem 1: Given the distance s0, the initial velocity v0and 129
the traffic signal sequence Z, to approximate the optimal velocity 130
profile 131
v∗(t)=argmin
v(t)∈Fv
max{J(t)2|t∈(t0,t
a)}.(12)
B. Longitudinal Velocity Tracking Problem 132
The longitudinal velocity tracking problem is summarized as 133
Problem 2: Given the optimal velocity profile v∗(t),∀t∈134
[t0,t
f]and initial velocity v0at t0, to design the optimal profile of 135
ratio of the accelerating pedal or brake pedal r∗(t),∀t∈[t0,t
f]136
which satisfies 137
r∗(t)=argmin
r(t)∈Frtf
t0
(v(t)−v∗(t))2dt. (13)
Here, r(t)should be within [−100,100]. When r(t)<0,it 138
represents the ratio of brake pedal. When r(t)>0, it represents 139
the ratio of accelerating pedal. 140
C. Scheme of Proposed Methodology 141
This letter proposes a two-layer framework for CAVs 142
to approach the signalized intersections with good driving- 143
comfortability as shown in Fig. 2. The first layer is driver- 144
comfortably velocity planning with two blocks: scenario iden- 145
tifier and profile generator. The layer of driver-comfortably 146
velocity planning first identifies the scenario based on the traffic 147
signal sequence, the initial velocity, and distance to the inter- 148
section. Then, the profile with minimal jerk is generated for 149
the corresponding scenario. The details of driver-comfortably 150
velocity planning are introduced in Section III. The second layer 151
addresses velocity tracking control. The pedal ratio (accelerate 152
IEEE Proof
SHEN et al.: COOPERATIVE COMFORTABLE-DRIVING AT SIGNALIZED INTERSECTIONS FOR CONNECTED AND AUTOMATED VEHICLES 3
Fig. 2. The block diagram of the proposed methodology.
Fig. 3. Illustration of different scenarios for a vehicle approaching a signalized
intersection.
pedal or brake pedal) is determined to accomplish the minimal-153
jerk profile generated from the layer of velocity planning. The154
details of velocity tracking are presented in Section IV.155
III. DRIVER-COMFORTABLY VELOCITY PLANNING156
A. Traffic Signal-Based Scenario Identifier157
The idea of scenario identifier is from [5]. In Fig. 3, examples158
of four velocity profile scenarios are shown by the green, blue,159
red, and yellow lines. They have the same initial velocities and160
the same traveled distance. More specifically, the four scenarios161
are162
1) Scenario 1 (”cruise”): The vehicle cruises through the163
intersection with a constant speed that equals to the initial164
velocity (green line);165
2) Scenario 2 (”speed-up”): The vehicle speeds up to pass166
the intersection (blue line);167
3) Scenario 3 (”coast-down with a full stop”): The vehicle168
slows down and stops at the intersection (red line);169
4) Scenario 4 (”coast-down without a full stop”): The vehicle170
slows down to a mid-range speed and passes the intersec-171
tion (yellow line).172
As a preparation for giving optimal velocity profile, we firstly173
addresses scenario identifying problem174
Problem 3: Given the distance s0, the initial velocity v0and175
the traffic signal sequence Z, to categorize the scenario of the176
vehicle velocity profile177
S(s0,v
0,Z)=⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
1,if Scenario 1
2,if Scenario 2
3,if Scenario 3
4,if Scenario 4
(14)
Firstly, it is necessary to check whether scenario 1 is available 178
which has the smallest jerk as 0. Otherwise, whether scenario 179
2 or scenario 4 is available. If both scenario 2 and scenario 4 180
are not available, scenario 3 will be the last choice. To check 181
whether scenario 2 or scenario 4 is available, a time interval 182
[tmin,t
max]should be obtained for the scenario identification. 183
tmin and tmax are the boundary cases for scenario 2 and scenario 184
4, respectively. 185
To arrive at the intersection in the shortest time under scenario 186
2, the vehicle should accelerate as fast as possible. Thus, there 187
may be the following four steps: 188
1) Accelerating with J(t)=J1for a time period t1;189
2) Keep a constant acceleration a(t)=acfor a time period 190
t2;191
3) Accelerating with −J(t)=J2until a(t)=0for a time 192
period t3=J1·t1
J2;193
4) Keep a constant velocity vmax for a time period 194
t4=s0−s1−s2−s3
vmax
(15)
where 195
s1=v0t1+J1∗t3
1
6,(16)
s2=v0t2+1
2J1t2
1t2+1
2J1t1t2
2,(17)
and 196
s3=v0t3+1
2J1t2
1t3+J1t1t2t3+J2t3
3
6.(18)
Then, denote the umin =[J1,J
2,t
1,t
2], we want to minimize 197
t1+t2+J1t1
J2
+t4(t1,t
2,J
1,J
2)(19)
subject to 198
J1∗t1≤amax,(20)
J1∈(0,J
max],(21)
J2∈(0,J
max],(22)
1
2J1t2
1+t2J1t1+1
2∗J2
1t2
1
J2
=vmax −v0.(23)
The obtained u∗
min =[J∗
1,J∗
2,t
∗
1,t
∗
2]can be used to calculate tmin 199
as 200
tmin =t∗
1+t∗
2+J∗
1t∗
1
J∗
2
+t∗
4(24)
where t∗
4can be calculated using u∗
min according to (15)–(18). 201
For tmax, we should consider the boundary case of scenario 4 202
under which the vehicle must stop at the intersection. This is also 203
the boundary case of scenario 3, the shortest time in scenario 3. 204
Thus, there should have the following four steps: 205
1) Decelerating with J(t)=−J1for a time period t1;206
2) Decelerating with constant deceleration a(t)=ac<0for 207
a time period t2;208
3) Decelerating with J(t)=J2for a time period t3=J1·t1
J2.209
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4IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 00, NO. 00, 2020
Then, denote the umin =[J1,J
2,t
1,t
2], we want to minimize210
t1+t2+J1t1
J2
(25)
subject to
211
vt1+t2+J1t1
J2=0,(26)
s1+s2+s3=s(27)
where
212
s1=v0t1−J1t3
1
6,(28)
s2=v0t2−1
2J1t2
1t2−1
2J1t1t2
2,(29)
s3=v0t3−1
2J1t2
1t3−1
2J1t1t2t3−J2t3
3
6.(30)
and constraints for acceleration and jerk as in (20)–(22). The
213
obtained214
u∗
min =[J∗
1,J∗
2,t
∗
1,t
∗
2](31)
can be used to calculate tmax as215
tmax =t∗
1+t∗
2+J∗
1t∗
1
J2
.(32)
After obtaining the time interval [tmin,t
max], the available set216
of the time in [tmin,t
max]can be defined as217
Tf={tf∈[tmin,t
max]|z(tf)=0}.(33)
Due to the above discussion, the proposed algorithm for
218
solving problem 3 is summarized as:219
1) Calculate the time to intersection with constant velocity220
v0
221
tS=1 =s0
v0
.(34)
If z(t0+tS=1)=0,setS(s0,v
0,Z)=1and exit. Oth-222
erwise,gotostep2.223
2) If Tf=∅,setS(s0,v
0,Z)=3and exit. Otherwise, go to224
step 3.225
3) Set226
t∗
f=minTf.(35)
If t∗
f<t
S=1,setS(s0,v
0,Z)=2. Otherwise, set227
S(s0,v
0,Z)=4.228
As an example, Fig. 4 shows a example of arrival time-based229
scenario identifier result when s=50 m,v
0=30 km/h. Three230
red circles (from the left to the right) represent the points of231
the shortest time case, constant passing case, and maximal time232
case, respectively. For the shortest case, its jerk, acceleration,233
and velocity profiles are shown by the blue lines in Fig. 5. This234
is the extreme case of scenario 2. The maximal time case is the235
extreme case of scenario 4, and the profiles are shown by the red236
lines in Fig. 5.237
If the initial state of the vehicle s, v varies, the shortest time,238
longest time, and the corresponding required mean velocity239
values also change. The results are given in Fig. 6 and 7.240
Fig. 4. A example of arrival time-based scenario identifier: s=50 m,v
0=
30 km/h.
Fig. 5. Boundary cases of scenario 2 and scenario 4.
Fig. 6. Boundary times to intersection of scenario 2 and scenario 4 un-
der different initial velocity and distance: a) shortest time (scenario 2);
b) longest time (scenario 4).
B. Assigned-Time Velocity Planning 241
For scenario 1, the optimal profile is directly given as a 242
constant line v(t)=v0,∀t∈[t0,t
a].243
For scenario 2 or scenario 4, the assigned-time velocity plan- 244
ning problem should be addressed to give the optimal velocity 245
IEEE Proof
SHEN et al.: COOPERATIVE COMFORTABLE-DRIVING AT SIGNALIZED INTERSECTIONS FOR CONNECTED AND AUTOMATED VEHICLES 5
Fig. 7. Boundary mean velocity of scenario 2 and scenario 4 under different
initial velocity and distance: a) mean velocity at shortest time (scenario 2); b)
mean velocity at longest time (scenario 4).
Fig. 8. Typical acceleration profiles of scenario 2 and scenario 4.
profile. Fig. 8 shows the typical acceleration profiles of scenario
246
2 and scenario 4. The overall velocity file is parametrized by 4247
travelling times: t1,t
2,t
3,t
4and two jerk values: J1in t1and248
J2in t3.t3can be calculated as t3=J1·t1
J2. We choose249
h={J1,J
2,t
1,t
2,t
4}(36)
to minimize
250
J2
1+J2
2(37)
subject to
251
t1+t2+J1·t1
J2
+t4=t∗
f,(38)
s1+s2+s3+s4=s0,(39)
where
252
s1=v0t1+J1t3
1
6,if S=2,
v0t1−J1t3
1
6,if S=4,(40)
Fig. 9. Examples of solutions for scenario 2 (s=50 [m],v
0=30 [km/h]):
a) jerk; b) acceleration; c) velocity.
s2=v0t2+J1t2
1t2+J1t1t2
2
2,if S=2,
v0t2−J1t2
1t2+J1t1t2
2
2,if S=4,(41)
s3=⎧
⎨
⎩
v0t3+J1t2
1t3+2J1t1t2t3
2+J3
1t3
1
6J2
2
,if S=2,
v0t3−J1t2
1t3+2J1t1t2t3
2−J3
1t3
1
6J2
2
,if S=4,(42)
s4=⎧
⎨
⎩
v0t4+J1t2
1t4+2J1t1t2t4
2+J2
1t2
1t4
2J2,if S=2,
v0t4−J1t2
1t4+2J1t1t2t4
2−J2
1t2
1t4
2J2,if S=4,
(43)
and constraints for acceleration and jerk as in (20)–(22). Here, 253
Sis short for S(s0,v
0,Z). The optimal solution is 254
h∗={J∗
1,J∗
2,t
∗
1,t
∗
2,t
∗
4}.(44)
The obtained h∗or u∗
min corresponds to a jerk profile. The 255
acceleration and velocity profiles can be obtained by the inte- 256
gration of a jerk profile. 257
For scenario 3, the profile adopts the previously mentioned 258
boundary profile. 259
C. Proposed Algorithm 260
The proposed algorithm to approximate v∗(t)is as follows: 261
1) Do the scenario identification and obtain S(s0,v
0,Z);262
2) If S(s0,v
0,Z)=1, go across the intersection with con- 263
stant velocity v0and terminate the algorithm. Otherwise, 264
go to step 3 265
3) If S(s0,v
0,Z)=3, solve problem (25) and output ap- 266
proximation ˜v∗(t)by obtained u∗
min as in (32) and termi- 267
nate the algorithm. Otherwise, go to step 4; 268
4) Solve problem (37), and output approximation ˜v∗(t)by 269
obtained h∗.270
Fig. 9 and 10 shows the examples of solutions for sce- 271
nario 2 and scenario 4 under the initial state s=50 [m],v
0=272
30 [km/h], respectively 273
IEEE Proof
6IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 00, NO. 00, 2020
Fig. 10. Examples of solutions for scenario 4 (s=50 [m],v
0=30 [km/h]):
a) jerk; b) acceleration; c) velocity.
IV. OSELM-BASED PREDICTIVE CONTROL274
A. OSELM for Longitudinal Velocity Dynamics275
The OSELM modeling algorithm and update procedure for276
longitudinal velocity dynamics are presented as following [16]:277
Given an initial training dataset D0with N0input vectors278
xn=[vn,r
n]Tand scalar output yn=[vp,n]for n=1,...,N
0.279
Here, rn∈[−100,100] denotes the ratio of the accelerating280
pedal or decelerating pedal(rn<0for deceleration and rn>0281
for acceleration). vp,n is the prediction for velocity at nwhich is282
essentially vn+1. The OSELM for longitudinal velocity dynam-283
ics model with Hhidden nodes and Radial Basis Function(RBF)284
can be expressed by:285
ˆyn=f(xn)=
H
i=1
βiexp −ai−x
b2
i,(45)
where ˆyn=f(xn)is the prediction of the longitudinal velocity,286
ai=[a1,...,a
H],biare the centers and variances of the i−th287
RBF hidden node and βiis the weight connecting the i−th288
hidden node and the output node. In [17], it has been theoretically289
shown that aiand bican be randomly initialized and no further290
tuning is needed. βishould be optimized with291
β0=K−1
0GT
0y0,(46)
where β0=[β0
1,...,β0
H],y0=[y1,y
2,...,y
N0],G0denotes292
the hidden layer matrix that can be computed by293
G0=⎡
⎢
⎢
⎣
exp −a1−x1
b2
1... exp −aH−x1
b2
H
... ... ...
exp −a1−xN0
b2
1... exp −aH−xN0
b2
H
⎤
⎥
⎥
⎦
(47)
and K0is defined by K0=GT
0G0.294
When there is a new batch of dataset Dk+1,k ≥0of Nk+1 in- 295
put vectors xn,and scalar output ynfor n=Nk+1,...,N
k+296
Nk+1, the velocity dynamic model should be updated to adapt 297
the new scenario by updating βias 298
βk+1 =βk+K−1
k+1GT
k+1(yk+1 −Gk+1 βk),(48)
where βk+1 ∈RHis the updated weight vector, yk+1 =299
[yNk+1,...,y
Nk+Nk+1 ],Gk+1 is the hidden layer matrix at 300
k+1by replacing xwith the inputs of the new batch. Kk+1 =301
Kk+GT
k+1Gk+1 . Moreover, K−1
k+1 can be computed efficiently 302
by using the Woodbury formula [18] 303
K−1
k+1 =K−1
k−K−1
kGT
k+1(I+Gk+1 K−1
kGT
k+1)−1Gk+1 K−1
k.
(49)
The OSELM must be initialized with a training dataset of N0304
data such that N0>Lto make sure that the term GT
0G0is not 305
singular. In this study, the number of hidden nodes Lis chosen 306
as 15 based on model selection procedure introduced in [16]. 307
B. Predictive Control With OSELM 308
The controller consists of the OSELM velocity dynamic 309
model and the optimizaer based on Brent’s method [19]. The 310
OSELM velocity dynamic model predicts the velocity dynamic 311
over a specified time horizon, given the specified time series 312
of the pedal ratio. The predictions are used by the optimizer 313
to determine the pedal ratio decision, which minimizes the 314
following performance criterion 315
J(R)=
Np
i=1
(yref (t+idt)−ypred(t+idt))2
+
Np−1
i=1
(r(t+idt)−r(t+(i−1)dt))2(50)
where Npis the prediction horizon, dt represents the sample 316
time, yref denotes the reference value of output, ypred denotes 317
the predicted value of output and R=[r(t),...,r(t+(Np−318
1) ∗dt)] is the ratio decision sequence. Besides ρis a user- 319
defined weight that penalized excessive movement of the control 320
signal. We used ρ=0.3in this study. 321
The details of the Brent’s method is not introduced herein. 322
Only the intuitive concept of the Brent’s method is summarized 323
as 324
rInitialize two input sequences R0,R
1;325
rFrom iteration k, k > 1, repeat the following steps until ter- 326
minal condition (maximum iteration or (Rk+1 −Rk<327
γ) is satisfied: 328
1) If 329
|J(Rk+1)−J(Rk)|<0.5·min(Rk−a,b−Rk),
(51)
use parabolic interpolation, otherwise, use Golden- 330
section search(a, b are the minimum and maximum 331
limitation for ratio, respectively); 332
Output the solution. 333
In this study, γis setted as 0.1 and the maximum iteration is 334
as 100. 335
IEEE Proof
SHEN et al.: COOPERATIVE COMFORTABLE-DRIVING AT SIGNALIZED INTERSECTIONS FOR CONNECTED AND AUTOMATED VEHICLES 7
Fig. 11. Examples of simulated velocity profiles (s=50 [m],v
0=
30 [km/h]): a) scenario 2; b) scenario 3; c) scenario 4.
V. VALIDATION336
CarMaker-Simulink co-simulation was implemented to val-337
idate the proposed driver-comfortably cooperative adaptive338
cruise control. The sample time of the dynamic controller is 0.1339
seconds. For the predictive control with OSELM, the prediction340
horizon is chosen as 10.341
Fig. 11 gives examples of simulated velocity profiles. The342
initial state is s=50 [m],v
0=30 [km/h]. For the same initial343
state, if the traffic signal is different, the scenario identifier gives344
a different scenario choice, as shown in a), b) and c) of Fig. 11,345
respectively. The profiles in Fig. 11 are realized by Proportional346
Integral Derivative (PID) controller and predictive controller347
with OSELM (marked as OSELM-PC). The PID controller348
system outputs the decision of pedal ratio as349
rPID(t)=KPe(t)+KIt
0
e(t)dt+KD
de(t)
dt .(52)
Here, e(t)=vref (t)−v(t)is the error between reference ve-350
locity vref (t)and the real velocity v(t)at time t.KP,K
I,K
D>351
0are the coefficients for the proportional, integral, and derivative352
terms respectively. KP,K
I,K
Dare calibrated and determined353
as 2158,173,12 in this case. The integral and derivative terms354
are approximated numerically.355
Fig. 12 shows the comparison of profiles realized by different356
vehicle dynamical controllers. The corresponding tracking er-357
rors of velocity, acceleration, and jerk are plotted in Fig. 13.358
OSELM-PC gives a better tracking performance in velocity359
tracking. Besides, the tracking errors of acceleration and jerk360
are also better, even though they are not the objects which are361
directly tracked. With smaller glitches in the jerk, the maximal362
jerk was also smaller if OSELM-PC was applied. The control363
performances of two controllers are listed in Table 1 which364
supports the above discussion. The results adopt the mean perfor-365
mances in 100 different cases including all the four scenarios. ev
366
represents the mean of the Mean Square Error (MSE) of velocity367
Fig. 12. Comparison of profiles from different vehicle dynamical controllers
(s=50 [m],v
0=30 [km/h]): a) velocity; b) acceleration; c) jerk; d) Input.
Fig. 13. Comparison of tracking errors from different vehicle dynamical
controllers (s=50 [m],v
0=30 [km/h]): a) velocity; b) acceleration; c) jerk.
TAB L E I
THE SUMMARY OF TWO CONTROLLER’SPERFORMANCES
tracking. eais the mean of acceleration’s MSE. The 100 different 368
cases have following parameter settings: 369
rInitial distance to the intersection: s=50 m. Initial veloc- 370
ity: v0=16,20,24,28,32 [km/h]; 371
rPeriod of green: 25 seconds. Period of red (include yellow): 372
25 seconds; 373
rCase of time to transition from green to red: 374
tg→r=0,2,5,6,10,12.5,15,17.5,20,22.5.Case375
of time to transition from red to green: tr→g=376
0,2,5,6,10,12.5,15,17.5,20,22.5.377
IEEE Proof
8IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 00, NO. 00, 2020
Besides, the proposed method succeeded to identify the sce-378
nario and pass the intersection or stop at the intersection without379
violating the traffic signal in all cases.380
VI. CONCLUSION381
This letter proposes a control framework for connected and382
automated vehicles to approach the signalized intersections with383
good driving comfortability. The contributions of this letter is384
summarized as385
rThe minimal jerk velocity planning has a two-layer frame-386
work. First, boundary point-based scenario identifier is387
proposed to categorize the target velocity profile based388
on the current vehicle speed, distance to the intersection,389
and traffic signal information. Then, assigned-time velocity390
planning problem with velocity, acceleration constraints is391
formulated and solved to obtain a smooth velocity profile392
with the minimal jerk;393
rFor the longitudinal vehicle dynamical control, OSELM-394
based predictive control is applied to realize the obtained395
smooth velocity profile with the minimal jerk;396
rCarMaker-Simulink co-simulation was implemented to397
validate the proposed method. The validation results show398
that the proposed method can identify the scenario in 100%399
of the time according to the validation results. On the other400
hand, the OSELM-based predictive control has improved401
MSE ev,e
a,e
jerk of 33.85%, 27.66%, and 38.03% respec-402
tively than PID control.403
Since the proposed method has not been validated experimen-404
tally yet. The future work is to design the experimental tests to405
conduct experimental validations. Moreover, the case with the406
front car will be addressed by improving the current method by407
considering vehicle-to-vehicle interaction and communication.408
REFERENCES409
[1] S. I. Guler, M. Menendez, and L. Meier, “Using connected vehicle tech-410
nology to improve the efficiency of intersections,” Transp. Res. C, Emerg.411
Technol., vol. 46, pp. 121–131, Sep. 2014.412
[2] Z. Wang, G. Wu, and M. J. Barth, “Cooperative eco-driving at signalized413
intersections in a partially connected and automated vehicle environ-414
ment,” IEEE Trans. Intell. Transp. Syst., vol. 21, no. 5, pp. 2029–2038,415
May 2020.416
[3] B. Asadi and A. Vahidi, “Predictive cruise control: Utilizing upcoming 417
traffic signal information for improving fuel economy and reducing trip 418
time,” IEEE Trans. Control Syst. Technol., vol. 19, no. 3, pp. 707–714, 419
May 2011. 420
[4] M. Zhu, Y. Wang, Z. Pu, J. Hu, X. Wang, and R. Ke, “Safe, efficient, 421
and comfortable velocity control based on reinforcement learning for Q2422
autonomous driving,” 2019, arXiv:1902.00089.423
[5] O. D. Altan, G. Wu, M. J. Barth, K. Boriboonsomsin, and J. A. Stark, 424
“GlidePath: eco-friendly automated approach and departure at signal- 425
ized intersections,” IEEE Trans. Intell. Veh., vol. 2, no. 4, pp. 266–277, 426
Dec. 2017. 427
[6] J. Kim and C. Ahn, “Real-time speed trajectory planning for minimum 428
fuel consumption of a ground vehicle,” IEEE Trans. Intell. Transp. Syst.,429
vol. 21, no. 6, pp. 2324–2338, Jun. 2019. 430
[7] C. Yang, S. You, W. Wang, L. Li, and C. Xiang, “A Stochastic predictive 431
energy management strategy for plug-in hybrid electric vehicles based 432
on fast rolling optimization,” IEEE Trans. Ind. Electron., vol. 67, no. 11, 433
pp. 9659–9670, Nov. 2020. 434
[8] D. B. Licea, M. Bonilla, M. Ghogho, S. Lasaulce, and V. S. Varma, 435
“Communication-aware energy efficient trajectory planning with limited 436
channel knowledge,” IEEE Trans. Robot., vol. 36, no. 2, pp. 431–442, 437
Nov. 2019. 438
[9] G. Qi, H. Wang, M. Haner, C. Weng, S. Chen, and Z. Zhu, “Convolution 439
neural network based detection and judgement of environmental obstacle 440
in vehicle operation,”CAAI Trans. Intell. Technol.,vol. 4, no. 2, pp. 80–91, 441
Jun. 2019. 442
[10] F. Riaz, S. Jabbar, M. Sajid, M. Ahmad, K. Naseer, and N. Ali, “A collision 443
avoidance scheme for autonomous vehicles inspired by human social 444
norms,” Comput. Elect. Eng., vol. 69, pp. 690–704, Jul. 2019. 445
[11] W. Cao, M. Mukai, and T. Kawabe, “Merging trajectory generation method 446
using real-time optimization with enhanced robustness against sensor 447
noise,” Artif. Life Robot., vol. 24, pp. 527–533, 2019. 448
[12] C. G. Lo Bianco, A. Piazzi, and M. Romano, “Velocity planning for 449
autonomous vehicles,” in Proc. IEEE Intell. Veh. Symp., Jun. 2004, 450
pp. 413–418. 451
[13] C. You, J. Lu, D. Filev, and P. Tsiotras, “Autonomous planning and control 452
for intelligent vehicles in traffic,” IEEE Trans. Intell. Trasp. Syst., vol. 21, 453
no. 6, pp. 2339–2349, Jun. 2019. 454
[14] C. G. Lo Bianco, “Minimum-jerk velocity panning for mobile robot 455
applications,”IEEE Trans. Robot., vol. 29, no. 5, pp. 1317-1326, Oct. 2013. 456
[15] A. Palleschi, M. Garabini, D. Caporable, and L. Pallottino, “Time-optimal 457
path tracking for jerk controlled robots,” IEEE Robot. Autom. Lett.,vol.4, 458
no. 4, pp. 3932–3939, Oct. 2019. 459
[16] N. Liang, G. Huang, P. Saratchandran, and N. Sundararajan, “A fast and 460
accurate online sequential learning algorithm for feedforward networks,” 461
IEEE Trans. Neural Netw., vol. 17, no. 6, pp. 1411–1423, Nov. 2006. 462
[17] G. Huang, Q. Zhu, and C. Siew, “Extreme learning machine: Theory and 463
applications,” Neurocomputing, vol. 70, no. 1, pp. 489–501, Dec. 2006. 464
[18] G. Golub, and C. Loan, Matrix Computation, 3rd ed. Baltimore, MD, USA: 465
Johns Hopkins Univ. Press, 1996. 466
[19] T. Chandrupatla, “An efficient quadratic fit-sectioning algorithm for min- 467
imization without derivatives,” Comput. Methods Appl. Mech. Eng.,vol. 468
152, pp. 211–217, 1998. 469
