Based on the nonlinearity and time-variation of automatic parking path tracking control system, we use fuzzy control theories and methods to explore the control rules to improve fuzzy controllers and design an automobile steering controller. Then we build the simulation experiment platform of an automobile in Simulink to simulate the reversing settings of parallel parking. This paper adopts the Mamdani control rules; the membership function is the Gauss function. This paper verifies the fuzzy controller's kinematic model and the advantages of fuzzy control rules. Simulation results show that the design of the controller allows the automobile to stop into the parking space smaller than the space obtained by planning path, and automatic parking becomes possible in the parking plot. The control system is characterized by small tracking error, fast response and high reliability

Li, Yi

Liu, Guangya

Min, Jie

Sheng, Qiulin

Zhang, Xing

Zhang, Zhengwen

English

TELKOMNIKA (Telecommunication Computing Electronics and Control)

TELKOMNIKA, Vol.13, No.2, June 2015, pp. 539 ~ 546 
ISSN: 1693-6930, accredited A by DIKTI, Decree No: 58/DIKTI/Kep/2013 
DOI: 10.12928/TELKOMNIKA.v13i2.1258       539 
  
Received December 1, 2014; Revised March 22, 2015; Accepted April 12, 2015 
Design and Simulation of Small Space Parallel Parking 
Fuzzy Controller 
 
 
Qiulin Sheng*1, Jie Min2, Xing Zhang3, Zhengwen Zhang4, Yi Li5, Guangya Liu6 
College of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan, 
430068, Hubei Province, China 
*Corresponding author, email:  sql103@qq.com1, mj904820557@163.com2, 645371519@qq.com3, 
669037364@qq.com4, 1029519940@qq.com5, whltxz@aliyun.com6  
 
 
Abstract 
Based on the nonlinearity and time-variation of automatic parking path tracking control system, 
we use fuzzy control theories and methods to explore the control rules to improve fuzzy controllers and 
design an automobile steering controller. Then we build the simulation experiment platform of an 
automobile in Simulink to simulate the reversing settings of parallel parking. This paper adopts the 
Mamdani control rules; the membership function is the Gauss function. This paper verifies the fuzzy 
controller's kinematic model and the advantages of fuzzy control rules. Simulation results show that the 
design of the controller allows the automobile to stop into the parking space smaller than the space 
obtained by planning path, and automatic parking becomes possible in the parking plot. The control 
system is characterized by small tracking error, fast response and high reliability. 
 
Keywords: Parallel Parking, Fuzzy Control, Matlab Simulation 
 
 
1. Introduction 
The purpose of this study is to improve the control scheme of intelligent automobiles so 
that in reversing the smart automobile can be more close to the ideal reversing trajectory and it 
can stop into a small parking space. This technology can ease traffic pressure and enhance the 
safety performance of vehicles.Automatic parking technology is currently one of the most 
popular smart technology, which has attracted the attention of many researchers. There are two 
the most classic approaches [1]-[2]: (1) By path planning method, which previously was given a 
geometric path, combined with the car's dynamic model and parking restrictions generation 
control strategies,this is a research path tracking control of the vehicle based on the visual 
environment that has been more mature [3]-[4]. (2) Based on skill acquisition methods,which by 
fuzzy logic or neural networks [5], learning more skilled people parking technology transferred to 
the automatic parking controller. This method is not designed reference path, which control 
strategies was implemented to control the position and orientation angle according to the car in 
the parking. This paper studies fuzzy logic control method. On the basis of previous studies, we 
will design a fuzzy controller that was optimized its fuzzy control rules to control the car so that it 
can achieve a more ideal control performance,including the control precision and the minimum 
size of parking spaces and parking time. 
 
 
2. Kinematic Model of Car Parallel  Parking 
2.1. Detection of Car Parking Spaces 
Before the car automatically stopping into the parking spaces, it must be detected 
around the parking spaces. The image sensor or ultrasonic sensor is installed around car to 
detect the parking spaces. For example, the image sensor photographed scenery around, 
combined with  an algorithm, the car can identify parking spaces. The irregular spaces tuning as 
a rule rectangular spaces in Figure 1. If the parking space is large enough, the parking spaces 
will be the parking space of smart car.Tables and Figures are presented center, as shown below 
and cited in the manuscript. 
 
 
 
 
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2.2. The Establishing Reversing Model of Car Established 
2.2.1. The Ackerman angle of motor two wheels in actual movement 
In order to simplify the reverse model of the car, the car side-slip won't be considered 
and the parking speed is very low. Car wheels in the rotation follow the principle of Ackerman 
[13] angle as Figure 2. 
            Two corners of car two wheels computation equations are shown in the following: 
 
tan
tan
in
in
out
out
in out
L
R
L
R
R B R


    
                                              (1) 
 
According to equation (1), following equation will be came about in and out : 
 
tan +=
tan
in in
out in
R B
R

                                                                                                                   (2) 
 
There is a relationship of formula (2) of the two wheels rotational angle in the actual  
movement. 
But in order to simplify the model, a unified Ackerman angle will be defined as  , which 
is  midpoint rotational angle of car front axle following Fig.3. 
This   angle will be used for the mathematical model behind. The angle of the two 
wheels Ackerman angle has a certain relationship with the  . The equations are shown in the 
following: 
 
tan =
2in
L
R
BR R
  
                                                          (3) 
 
According to front equations (1), (2), (3); 
 
tan tan 2=
tan
tan 2
in
out
L B
L B
 




                                                                                                         (4) 
 
 
2.2.2. Car reversing model under the simplified model 
Two wheels of car were controlled with  two motors and two control chips respectively in 
the paper, and wheels rotational angle were determined by the Ackerman angle. In building 
model, Ackerman angle was represented with   in the paper. Automatic parallel parking 
algorithm is based on kinematic model of the car. In building kinematic model of the car, first of 
all model parameters need to be determined. For example, the coordinate of the center of the 
car is（ 、x y), the symbol of   represents speed of car, the symbol of l represents speed of left 
wheel of car and the symbol of r represents speed of right wheel of car. The   represents 
TELKOMNIKA  ISSN: 1693-6930  
 
Design and Simulation of Small Space Parallel Parking Fuzzy Controller (Qiulin Sheng) 
541
angle between X-axis and central axis of car. The   represents slip of car that is the rate of 
change of  . Every time the travel trajectory of rear has important relationship with distance of 
wheels and axle, and Ackerman angle of the center of front axle. The speed of car have no 
influence on the travel trajectory [2]-[3]. 
Kinematic equation of car are shown in the following: 
 
cos( )
sin( )
i i i dt
x i x i i i
y i y i i i
  
 
 

（ +1）=（）+（）
（ +1）=（）+（ +1） （ +1）
（ +1）=（）+（ +1） （ +1）
                                                                        (5) 
 
Speed equation of car left and right wheels are shown in the following: 
 
( ) ( )( )
2
( ) ( )
2
r l
r l
i ii
i ii
 
 
  
=
（）=
                                                                                                 (6) 
 
In each sample period, the car can obtain the rotational speed of the left and right 
wheels by the above equations. 
 
 
 
Figure 1. Detection an determination the car 
parking spaces 
 
 
Figure 2. The model of Ackerman angle 
 
 
 
 
Figure 3. Ackerman angle of car 
 
Figure 4. The reversing model of car 
 
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3. The Design of Controller of Car 
Fuzzy controller is the core of Fuzzy control system, and the design of Fuzzy controller 
directly affects the accuracy of final control outcome. The design of the controller should apply  
moderate principles that represent not only high accuracy, but also simplified fuzzy inference 
operation relatively. Because complex control system will lead to delayed response  of system 
that can have an influence on real-time control of car that will decrease accuracy of control in 
turn [8]. 
 
 
3.1. The Block Diagram of Fuzzy Controller 
The blur represents that the precise digital variable changes into fuzzy variable. The 
process of fuzzy inference presents that according to the fuzzy rule base, and the database has 
been established, the fuzzy inputsare processed to generate the corresponding control inputs 
and control strategy. Anti-blur process represents that the fuzzy outputs change into precise 
numeric variables, which were used to control output object. 
 
 
3.2. Block Diagram of the Fuzzy Controller 
The main differences between fuzzy control system and ordinary computer numerical 
control system is the use of a fuzzy controller. The performance of a fuzzy controller is decided 
these factors that are the structure of the fuzzy controller, synthetic reasoning algorithms and  
fuzzy control rules. The basic block diagram of the fuzzy control as Figure 6 shown, the fuzzy 
controller is the its core ,and fuzzy controller control rules is implemented by a computer 
program. Implementation process of fuzzy control algorithm is described as follows:firstly, 
computer obtain the precise value of controlled variables by the interrupt sampling, then this 
value compares with a given variable to obtain a difference of signal E, as an input; secondly, 
the  accurate difference of signal E change into blur, and using appropriate language represents 
the difference E, then based on the synthesis of rule-based reasoning, combined with he fuzzy 
relation R obtains fuzzy control volume. computation equations are shown in the 
following:u e R  . 
 
 
3.3. The fuzzy Controller Design 
Because the process of reversing is very complex,  we need to design a complex fuzzy 
controller so that the car can be controlled precisely. The length of the vehicle is defined in 4m, 
and the width is 1.6m; the center position coordinate of the vehicle is set (x, y), and the ordinate 
represents the distance from the car to the parking space. Fuzzy controller has three inputs  x, 
y, and   in the process of reversing; and a output   equal to the rotation angle of wheels 
approximately. This three-dimensional fuzzy controller to control have a total of 18 rules. The 
variables membership function are shown in the Figure 7, Figure 8, Figure 9, Figure 10. In this 
paper, Mamdani control rules were used, and membership functions use Gaussian function[9].  
The control rules of fuzzy controller were shown in Table 1: 
On the part of the fuzzy rules of parallel parking will be explained as follows: 
If x is S, and y is S, it means that the car has been reversed into the parking. When   
is N, it means that angle of direction of the vehicle at this time is a negative value, the direction 
of the vehicle need to be straightened rapidly. 
If x is S, and y is S, it means that the car has been reversed into the parking. When   is 
Z, it means that angle of direction of the vehicle at this time is zero, then reversing the process 
of the car ends. 
If x is B, y is B,and  is P, it means that the car has reached the outside of parking 
spaces, and ready to into the parking spaces; then the direction of the angle of the car is 
positive, and it began to turn the steering wheels to the right  making the car back to the parking 
space. 
 
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Design and Simulation of Small Space Parallel Parking Fuzzy Controller (Qiulin Sheng) 
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Figure 5. The block diagram of Fuzzy 
controller 
 
 
Figure 6. Block diagram of the fuzzy controller 
 
  
 
 
Figure 7. Membership function of x coordinate 
of the car 
 
 
Figure 8. Membership function of y coordinate 
of the car 
 
 
 
 
Figure 9. Membership function of the direction 
angle 
 
 
Figure 10. Membership function fuzzy 
controller output 
 
 
 
 
 
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544
Table 1. The control rules of fuzzy controller 
 x/y S B VB 
 
 =N 
S 
B 
VB 
PB 
PM 
PB 
PB 
 
PB 
PM 
 
 =Z 
S 
B 
VB 
Z 
Z 
Z 
PB 
 
 
PB 
Z 
 
 =P 
S 
B 
VB 
NB 
NM 
Z 
Z 
 
PM 
NB 
 
 
4. Simulink Simulation Module Structures 
The length of the vehicle is set to 4m, the width is set to 1.6m, and the vehicle speed is 
set to 5m/s [10] in simulation; there are three fuzzy controller input u (1), u (2), Controller, which 
are x coordinate, y coordinate, and the direction  of the vehicle respectively; a fuzzy controller 
input represents changed rate of the angle direction of the vehicle. S-function module of parking 
are used handling real-time image display and obstacle avoidance in parking process. truck 
kinematic modules is subroutine module for the mathematical model of the truck; other modules 
are some of the auxiliary module in simulation. Nesting of fuzzy logic controller : based on front 
the fuzzy control rules specify the format FIS files embedded into the fuzzy controller in three 
steps [9],[11]:  
(1). Using MATLAB command readfis in the MATLAB main window, type: new file name 
= readfis ('file-name') Enter. 
(2). Using the mouse in the FIS editor: Type "fuzzy file-name" in the MATLAB main 
window, then the file will be sent to the MATLAB work-space.  
(3). Double-click the fuzzy controller of being nested, and by modifying the parameter 
name, it was changed to "new file name". After nested Controller, we will inspect the fuzzy 
controller to verify available. Right key-fuzzy controller, and select "look under mask",  if the 
fuzzy controller shows FIS, it represents nesting success;  if the display is sffis,  it represents 
not nesting success when the fuzzy controller should be re-nested until Show FIS. 
 
 
 
Figure 11. Simulink simulation module structures 
 
 
 
 
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Design and Simulation of Small Space Parallel Parking Fuzzy Controller (Qiulin Sheng) 
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5. Simulink Simulation Results 
1. In the following three Figure 12, the dynamic processes of reversing parking were 
simulated in different starting points that are coordinates (10.5, 3.5), (10.5,4.0), and (10.5, 4.5) 
respectively. From the three coordinates We can find that they have difference y-coordinates.  
Based on Figure 13, when the pitch is the best distance, the longitudinal distance have no 
influence on automatic parking but making the minimum parking space larger [12]. 
2. On the basis of the best starting point, according to the reverse path geometry 
constraint between the car and the parking space obtains a method of steering control strategy, 
whose the simulation results are shown in Figure 14. 
3. On the basis of the best starting point, the simulation results of the fuzzy control 
algorithm was shown in Figure 15. 
 
 
          
 
 
Figure 12. The reversing process 
 
 
                     
 
Figure 13. The reversing process 
 
 
                  
 
   Figure 14. The reversing process on the        Figure 15. The reversing process on the basis  
              basis of path planning                                                           of fuzzy Control 
 
 
 
 
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6. Simulation Analysis 
According to the simulation results in Figure 12, it can be see that the samller distance 
between the car and the obstacle is more standard trajectory.so the best vertical distance is 
0.5m.On the basis of the best starting point of the reverse, the same 6m parking, Figure 14 
shows the path-based control method cannot make the car safe stop into parking spaces, but 
Figure 15 based on the fuzzy control simulation results show that cars can be safe stop into the 
parking space. 
 
 
7. Conclusion 
This paper studies the parking situation at low speeds, analyze of several steps in 
parallel parking,  simplify parking steps of the vehicle model, and abstract parking process 
parameters,and research the theory of fuzzy control. Fuzzy control is applied to the parallel 
automatic parking system. The input, output and the fuzzy control rules are designed in the 
process design of parking. we can draw that the controller designed in this paper can basically 
meet the parking demand. The parking space where the car can be parked has become 
smaller. The trace has higher control precision, which is better than that of path planning 
method. However, we can know from the simulation results that the controller design is an 
important aspect, but selecting a starting point is also essential to success parking, so that only 
two part must cooperate to make car into parking spaces safely. But in the actual process of 
reversing the situation would not be so idealistic, in order to make it control real vehicle, the 
controller needs further improvement. 
 
 
Acknowledgements 
The research is funded by Wuhan Fundamental Applied Research Project, 
No.2013012401010 845, BSQD Fund Research Project, No. BSQD12023, and science and 
technology support program of Hubei Province, No.2014BAA135 
 
 
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Design and Simulation of Small Space Parallel Parking Fuzzy Controller

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Design and Simulation of Small Space Parallel Parking Fuzzy Controller

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