IEEE Systems, Man and Cybernetics Magazine - October 2023 - 29

of the center of gravity of the vehicle from the center line
of the lance, e2 is the orientation error of the vehicle with
respect to the road,
ei
o
are derived from their continuous counterparts
,,
AB00long
long
is the derivative of the corresponding
state, d is the expected steering angle of the front
wheel, and t is the curvature of the trajectory. The physical
implication of the system states could be shown as Figure
2. The discrete matrices Alat, Blat, and Pr are derived
from their continuous counterparts
AB and P ,r0
la00
tlat
which are defined as follows:
J
A
lat0 =
K
K
K
K
K
L
B
lat0 = a0
r0 =- mv -- Iv
cl -
ff
rr
v 0
cl +f f
z
1
-
-
22
cc
mv
fr
+
cl -
ff
rr
2 f
m
c
cl
ff
22
cc
m
fr
22cl 22cl
Ivz
+
-
Iz
2cl
Iz
ff k
22cl
T
(4)
P cm (5)
22clr r
22 T
where cf and cr are the front and rear cornering stiffness,
respectively; lf and lr are the distances from the center of
gravity to the front and rear axles; m is the total mass of
the vehicle; Iz is the vehicle yaw moment of inertia; and v is
the longitudinal driving speed.
The longitudinal control of the connected vehicle could
be interpreted as a special form of adaptive cruise control.
The roadside sensors acquire the location, speed, and
acceleration information of both the controlled and proceeding
vehicles. The roadside controller then comes up
with the expected acceleration for the controlled vehicle
to follow and sends it to the controlled vehicle. The
onboard low-level controller will determine the desired
throttle and braking pressure to track the desired acceleration.
By referencing previous studies on the adaptive
cruise control system [29], it becomes apparent that the
longitudinal control system can be depicted as follows,
after discretization with a zero-order holder:
xk Ax kB ak Ga k
f ^hdes
^^
() (),( ), ()@T
=
=
6TT
f
ak Kx k
xk dk vk ak
+= ++long fplong
long ()
1hh des () ()
(6)
(7)
where Along is the state matrix of the discrete cruise control
system, Blong is the input matrix of the discrete cruise
control system, G is the feedforward input matrix of the
discrete cruise control system, Klong is the feedback control
gain, and x represents the state vector of the cruise
control system and includes the following components:
T d and vT are the distance error and speed error
between the proceeding vehicle and the controlled vehicle,
respectively; af is the acceleration of the proceeding
vehicle; afdes is the expected acceleration of the controlled
vehicle; and ap is the acceleration of the proceeding vehicle.
The physical implication of the system states could be
shown as Figure 3. The discrete matrices Along, Blong, and G
C.G.
e1
Closest Road Point
rr 22clr r
Ivz
-+
-
cl
ff
mv
cl +f f
22
1
cl
rr
22
N
O
O
O
O
O
P
(3)
,,
A ,,
T
long00 0
L
=
where h
J
L
K
K
K
1
-
-
-
L
TL is the time constant.
Remark 1
It should be admitted that only the linearized vehicle
dynamic model is considered by the prediction-based
method in this study, which is not an unrealistic assumption.
In fact, although the real vehicle's dynamics are usually
with extra nonlinear uncertainty, the linearized
model is accurate enough to predict the future motion of
the vehicle to compensate for the delay effect under the
concerned scenarios. This is shown in the " Simulation
Experiments " section.
Remark 2
It also should be noted that there are various versions of
the linearized vehicle control dynamic, and the selection of
the model is not unique. This study adopts only one of the
well-applied and achievable control models to verify the
feasibility of the prediction-based control strategy, and any
other linearized control dynamic could also fit into the
control framework.
Formulation of Linear Output Feedback
System With Output Delay
Since the cloud control of the connected vehicle is able
to be linearized as the previously introduced model, the
e2
Reference Trajectory
xh
1
1
N
P
O
O
O
B == p
G
long
J
L
K
K
K
T
K
L
N
P
O
O
O
f
1
(8)
x is the headway time, KL is the system gain, and
and G0, which are defined as follows:
Figure 2. The physical implication of the lateral
control system states.
∆v = vp - vf
vf, af
ddes
Following Vehicle
d
∆d
Proceeding Vehicle
Figure 3. The physical implication of the longitudinal
control system states.
October 2023 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE 29
vp, ap
IEEE Systems, Man and Cybernetics Magazine - October 2023

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