This paper presents a design methodology of Adaptive Cruise Control ACC system for two smart car platform consist of the leading smart car and a host smart car move on a single lane on a
Trang 2Tracking Trajectory by Using The Polynomial Method for ACC System Based on Smart Car
Platform
Duc Lich Luu Faculty of Transportation Mechanical
Engineering University of Science and Technology
The University of Danang
Da Nang 550000, Vietnam
ldlich@dut.udn.vn
Nguyen Viet Hung Faculty of Information Technology East Asia University of Technology Bac Ninh, Viet Nam
hungnv@eaut.edu.vn
Ciprian Lupu Department of Automatic Control and Systems Engineering University Politehnica of Bucharest Bucharest, Romania
ciprian.lupu@upb.ro
Abstract—A well-known advanced driver assistance technology
that can be employed for that is the Adaptive Cruise Control
System (ACC) Cars equipped with ACC system are to control
the car speed to follow a driver’s set speed closely when there
is no leading car When a slower leading car is present based
on distance sensor, the ACC controlled car are able to keep
desired distance with respect to the position and velocity of
the car in front This paper presents a design methodology
of Adaptive Cruise Control (ACC) system for two smart car
platform consist of the leading smart car and a host smart car
move on a single lane on a laboratory installation RST algorithm
in the multi algorithms structure is proposed to design in
real-time architecture for ACC system RST algorithm is one of the
most effective solutions for the real-time control of nonlinear
systems or working regimes The results ofthe experiment have
been conducted to illustrate the effectiveness of the proposed
algorithm
Keywords—RST controller, Adaptive cruise control, Automotive
electronics, Tracking trajectory, Real-time systems
I INTRODUCTION
As travel demand has increased over the years, the
ex-pressway network has also been expanded to accommodate
the demand To overcome these problems, the concept of the
Advanced Driver Assistant System is one of the approaches
which are under considerable research in the autonomous
vehicle technology It ensure safety measures and comfort level
for drivers, passengers in urban areas [1] and improves the road
capacity [2] This claim is possible due to the development
of mechatronics technology [3] The car started to be driven
by hardware and software systems, creating the concept of
autonomous cars [4]
The ACC system is one of the subsystem of the Advanced
Driver Assistant System which is one application of keeping
small distance with the preceding vehicle The ACC system
have two modes of steady state operation: velocity control and
vehicle following i.e distance control based on the measured
signals of sensors [5], [6]
In autonomous robot area, the smart car platform has been
studied in recent years, some researchers of [7], [8] have
Fig 1 Two smart cars following each other on a single lane
been proposed many robot in the platooning to applied for the ACC system with different controllers including predictive controller, sliding mode controller, controller and review into account for the noise from hardware (devices and motors) Some other papers [6], [9], [10], they have been made and tested smart car platform to stay a formation same time avoiding collisions, spotting people, fire or a tracking lane system
However, one of the main problems of employing these algorithms is that the computation is large, complex and dif-ficult to implement in a real-time application or in a discrete-time system To the best of our knowledge, there are very few scientific works on multi algorithms structure consist of RST algorithms applied to autonomous cars, especially ACC systems Some researchers have introduced the RST control approach as in [9], [11], [12], [13]
In this paper, RST algorithm in the multi algorithms struc-ture is proposed to design for ACC system Digital Control De-sign by using the polynomial method such as RST algorithm with two outstanding advantages such as: simplicity and real-time applicability We focus on implementing digital control design by the polynomial method in the discrete time system for ACC system
The leading car is controlled by the ACC system with the reference of the closed-loop (CL) system is the desired velocity, based on a RST controller
Trang 3Fig 2 RST algorithm for ACC system
The host car is controlled by the ACC system with the
reference of the CL system is the desired distance, based on
a RST controller, it is to follow the leading car at the desired
distance based on the constant spacing policy and the testing
results is to verify the performances of two smart car platform
consist of the leading smart car and a host smart car as in Fig.1
This paper is structured as follows: In Section 2, we
first consider the mathematical modeling of cars Then ACC
Control Structure for host car is presented in Section 3 The
Real-Time Implementation and Results will be described in
Section 4 and in Section 5, conclusions will close this paper
II MATHEMATICAL MODELING OF CARS
For simplicity, the longitudinal dynamics of car assume be
described by the following differential equations [14], [15]:
˙ p(t) = v(t)
¨ p(t) = a(t)
ζ p (t) + ¨p(t) = u(t)
(1)
Where, the position, velocity, acceleration in longitudinal
axis of the car at time instant t are indicated by p(t), v(t),
a(t), respectively As a result, the longitudinal dynamics of
the car can be represented by:
H(s) = P (s)
U (s) =
1
III ACC CONTROLSTRUCTURE FOR LEADING CAR AND
HOST CAR
Two smart cars move on a single lane in as Fig.1 The
ACC system may also be consider as an autonomous control
system that is made to operate with good performances when
there is uncertainty in the system and in the environment
for a long time and must be able to compensate for system
failures without any outside interference This is employing
radar sensors, an electronic control unit and an appropriate
software which is processing the sensor data and providing
the necessary output to track the car ahead in safe conditions
The leading car is designed by the ACC system which is
to adjust the velocity of car, the desired for the CL system is
the velocity of car
Utilizing the ACC system of host car is to keep the same speed with the lead car while keeping the value of desired distance with respect to leading car
The transfer function (2) of the longitudinal dynamics used for digital controller design, expressed by the irreducible fraction:
H(z−1) = A(z
−1)
Where, A(z−1), B(z−1) polynomials are:
A(z−1) = 1 +
m a =3
P
j=1
aj.z−j
= 1 + a1z−1+ a2z−2+ a3z−3 B(z−1) =
mb=3
P
j=1
bj.z−j
= b0+ b1z−1+ b2z−2+ b3z−3
Various techniques, such as the RST controller have been applied in recent years The acronym RST stands for (R)-Regulation, (S)-Sensitivity , and (T)-Tracking control It is also linked to R(z−1), S(z−1), T (z−1) polynomials that are employed in the two-degree of freedom controller structure [11]
The RST control algorithm in multi algorithms structure with a closed-loop system was used with the ACC system structure (Fig.2):
u(k) ≡ −R(zS(z−1−1)) T (zS(z−1−1))
y(k)
yref(k)
≡ −R(z
−1) S(z−1)y(k) +
T (z−1) S(z−1)yref(k)
(4)
yref(k) - trajectory or filtered set point, in which: dref(k) is the desired distace defined by the constant spacing policy for host car or vref(k) is the desired velocity set by the human for leading car; u(k) - algorithm output, the desired acceleration for host car (control signal)
dref(k) = l0(k)(m) (5) y(k) - process output, in which: d(k) is actual distance for host car or v(k) is velocity for leading car, L is the car length, and it is defined as:
Trang 4Fig 3 The smart car platform in the laboratory [15]
TABLE I
C OMPONENTS OF A ELECTRIC CAR [15]
Component Qty Unit price Total price
(USD) (USD) Electric Car Module 1 20 20
MEGA 2560 microcontroller 1 9.0 9.0
L9110S driver module 2 2.0 4.0
WeMos D1 Mini ESP8266 1 7.0 7.0
Total 85.2
d(k) = plead(k) − phost(k) − L (6)
R(z−1), T (z−1) and S(z−1) polynomials of the proposed
RST digital feedback controller, the corresponding parameters
are defined as below:
R(z−1) =
m r =2
X
j=0
rj.z−j = r0+ r1z−1+ r2z−2
T (z−1) =
mt=0
X
j=0
tj.z−j = t0 1
S(z−1)=
1
ms=2
P
j=0
sj.z−j
s0+ s1z−1+ s2z−2
(7)
ms, mr, and mtillustrate the respective polynomial degrees
as well as the memory dimension for the algorithm’s software
implementation For example, if mr= 2, three memory places
should be saved for the process’s output: y(k), y(k −1), y(k −
2) The same method applies to u(k), respectively To apply
ms = mr = mt = 2, the control law computation is as the
following:
u(k) = 1
s0
[T (z−1)yref(k) − r0y(k) − r1y(k − 1)
− r2y(k − 2) − s1u(k − 1) − s2u(k − 2)]
(8)
and formula (8) gives the algorithm’s memory actualization
for the next iteration:
u(k − 1) = u(k), y(k − 1) = y(k),
yref(k − 1) = yref(k)
The constraint condition are considered as follows: umin≤
u(k) ≤ umax where umin < 0 and umax > 0 are bounds of
control input
IV REAL-TIMEIMPLEMENTATION ANDRESULTS
In the demonstrative section, a small laboratory installation that is used by a real-time software application for two smart car platform travelling single lane as in Fig.3 that allows practical verification of the proposed theoretical elements is presented The cost of components of each electric car can be seen in table.1
The smart car platform is described as in [15], consisting
of a leading car and a host car The cars is moved with the distance which is actually very small, so employing the infrared device is measured the distance between the leading car and the host car The longitudinal velocity is measured from encoder sensor mounted on the rear wheels
RST Controller Parameters Calculation: the choice of the RST controller parameters allows to solve as well the problem
of regulation as well as of tracking, and using a sampling period of Ts = 0.1 second, the system constraints as in [16] are −2.5(m/s2) ≤ u(k) ≤ 2.5(m/s2) and these polynomials are given by:
R(z−1) = 249.4258 − 387.5863z−1+ 148.0126z−2
T (z−1) = 9.8521 S(z−1) = 1 + 0.7841z−1+ 0.1404z−2 This sector only focus for the host car using ACC system based on the constant spacing policy which is a common type
of strategy that shows real-time applicability RST algorithm
is embedded in two smart cars (leading car and host car as in Fig.3), in which the leading car equipped with ACC system, maintains at reference velocity as in Fig.4 and the host car equipped with ACC system to keep the same speed with the leading car as in Fig.4 while keeping the value of desired distance with respect to leading car i.e,0.35m as in Fig.5 Adaptive Cruise control for the host car, i.e following the reference trajectory with the desired distance dref(k) at a discrete time k The constant spacing policy, the ACC system maintains at a fixed constant between leading smart car and host smart car in Fig.3), with the initial distance and the fixed desired distance is set to l0= 0.35m
The lead car stays the velocity at 0.5m/s in during time in-terval [0, 38.0s], and then decelerates from 0.5m/s to 0.4cm/s during interval [38.1s, 42.0s], and then stays the speed at 0.4m/s during interval [42.1s, 70.0s] Their velocities, the distances between leading smart car and host smart car are indicated in Figs.4, 5 respectively From these figures, the signals resulted after testing can be observed that velocity tracking operates well
Clearly, the distance of the host smart car converges to the desired value, i.e 0.35m
The host car exist a little large distance at time at 0s (start) and a little overshoot after that, mainly caused by a higher starting voltage than the minimum working voltage
From testing results, we observe that RST algorithm results for host cars satisfied with the request for real-time imple-mentation The time delay has existed as the micro-controler
Trang 5Fig 4 The velocities of two mart car platform based on the constant spacing
policy
Fig 5 Inter-car distance of the host smart car platform based on the constant
spacing policy
of cars calculate the control command for the motor driver;
the devices are affected by brightness, disturbance or noise
which leads to unstable measurement results However, the
result error is not large In general, an accurate sensor will
bring better performance to the smart car platform
V CONCLUSIONS
In this paper, RST algorithm in the multi algorithms
structure for the ACC system was studied The polynomial
method in the discrete time system for ACC system will
eliminate the need complex mathematical derivatives, model
uncertainties and linearization In real-time applications, two
smart car platform equipped with the ACC system is tested and
implemented on a laboratory control structure, each smart car
platform based on sensors Its purpose is to make the efficiency
of RST algorithm
Testing results show the leading car maintains at reference
speed and the host car to keep the same speed with the
leading car while keeping the desired distance with respect
to leading car However, there was the time delay and some
errors due to the influence of noise, disturbance, environment from hardware devices However, does not seriously affect the results In general, the accurate sensors will bring better performance
Next step in future, mathematical models of cars in the continuous time system convert to discrete time system ACC systems using RST algorithm will be implemented and simu-lated, thereby comparing simulation and testing
ACKNOWLEDGMENT
This paper was performed in the PRECIS Research Center, Laboratory 10 - Advanced Control Systems for Real - Time Applications The authors would like to thank the support of this institutions
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