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1

Abstract

Path Generation Using 3rd

Polynomial

Curve and Control Algorithm for

Autonomous Parking

Jiwhan Yoon

Mechanical and Aerospace Engineering

The Graduate School

Seoul National University

This paper presents a vehicle control algorithm for autonomous parking system. The

position and heading angle of subject vehicle or parking spot are acquired from the GPS

information. Those determine the middle point. Paths which connect the subject vehicle

and middle point are generated as a 3rd

polynomial curve. It is successfully done by

constraints including subject vehicle states, position and heading angle of middle point.

The path links the middle point and the goal point follows the same generation process.

The steering angle should not exceed the threshold value which is possible to be kept up

2

by vehicles. The vehicle moves to a position near the parking lot. Then using a camera

attached to the tail end vehicle, not only parking lanes are recognized in the backward

situation but also the accurate middle point and goal point are determined. Automatic

Transmission Shifting Control(ATSC) is applied for a gear shift. To generate the paths at

various positions around the parking spot, it is verified by a simulation. Also the real

size vehicle test is implemented and had a success rate higher than 97 percent.

Keywords : 3rd

polynomial curve, GPS goal point, vision goal point, middle point,

parking lot detection, steering lock up

Student Number : 2012-20684

3

Contents

Abstract .............................................................................................................................. I

List of Figures .................................................................................................................... V

Nomenclature .................................................................................................................... VI

Chapter 1. Introduction ....................................................................................................... 1

Chapter 2. Vehicle Model .................................................................................................... 2

Chapter 3. Control Algorithm for Automated Parking ........................................................ 3

3.1 Assumption of Parking Environment ................................................................ 3

3.2 Path Generation ................................................................................................. 3

3.2.1 Middle Point Decision .......................................................................... 4

3.2.2 Constraints ............................................................................................ 6

3.2.3 Coordinate Transformation ................................................................... 7

3.2.4 3rd

Polynomial Path Generation ............................................................ 8

3.3 Steering Wheel Angle Decision ......................................................................... 9

3.4 Velocity Control .............................................................................................. 10

3.5 Parking Sequence ............................................................................................ 10

4

3.6 Vision Information Analysis ............................................................................ 11

Chapter 4. Simulation Results ......................................................................................... 13

Chapter 5. Vehicle Test .................................................................................................... 14

5.1 Vehicle Composition ....................................................................................... 14

5.2 Test Results ..................................................................................................... 16

Chapter 6. Summary / Conclusions ................................................................................... 19

Bibliography...................................................................................................................... 20

초 록 ................................................................................................................................. 22

5

List of Figures

Figure 1 Vehicle Geometry .................................................................................... 3

Figure 2 Control Block Diagram ............................................................................. 5

Figure 3 Process of Middle Point Decision ............................................................. 7

Figure 4 Coordinate Transformation ........................................................................ 8

Figure 5 Auto Parking Sequence ............................................................................. 8

Figure 6 Results of Vision Analysis ......................................................................... 9

Figure 7 Images of Parking Line Detection ........................................................... 10

Figure 8 Simulation Result .................................................................................... 11

Figure 9 Vehicle Component ................................................................................. 12

Figure 10 Actuator Systems ..................................................................................... 13

Figure 11 Brake System ........................................................................................... 14

Figure 12 Vehicle Test Result .................................................................................. 15

Figure 13 Result Plots .............................................................................................. 18

6

Nomenclatures

steering angle

k , veh vehicle yaw angle

x global x position

y global y position

v velocity

L wheel base

k k-th sequence

veh Vehicle

des Desired

1 subject position

2 object position

1

Chapter 1. Introduction

Control techniques for automated parking system are actively conducted

ecumenically.[9] Including a backward parking, algorithms of forward parking, parallel

parking and diagonal parking are developed. Particularly the backward and parallel

parking algorithms that many drivers feel difficulty are developed. Recently, the

automated parking systems that support Parking Assistant(PA) and Steering Parking

Assist System(SPAS) are commercialized partially. Many papers introduces control

methods such as the fuzzy logic control.[8] But the functions commercialized for now

are limited to the steering control assistance. In this paper, dealing with not only the

steering control but also the control algorithm including velocity and transmission

switch, it is expected to contribute to the commercialization of automated parking

system. The validation for the control algorithms are fulfilled by simulations using mass

particle model method and real size vehicle tests.

Figure 1. Vehicle Geometry

xv

kx

ky

k

2

Chapter 2. Vehicle Model

The mass particle model is used to analysis the behavior of the vehicle.[4],[5] The

model is adequate for the vehicle moving slowly. Figure 1 shows the vehicle model

schematically. By observing the central point of rear axle, The motion of the vehicle is

presented as follows.

1

1

1

sin /

cos cos

cos sin

k k x

k k x k

k k x k

v t L

x x v t

y y v t

(1)

VisionCAM

Process module Control algorithm

Lab View Micro Autobox

Actuators

Vision Computer

(Vision analysis)

Parking Section Decision

Decision

desdesv

Goal point Decision

Steering control

Velocity control

ATSC

WireEPB

EMSthrottle

MDPS

desv

des

Control input

x,y,yaw,v

Figure 2. Control Block Diagram

3

Chapter 3. Control Algorithm for Automated Parking

The vehicle control algorithm suggested in this paper calibrates the goal point using

the vision information near the parking spot. It is also based on the information from the

GPS device. The 3rd

polynomial paths are generated on constraints which contain

positions and heading angles of subject vehicle and object point. The objet point might

be the middle point as well as the goal point so that the 3rd

path is applied to both cases.

The control algorithm generates the 3rd

path and determines the steering angle using a

curvature in real time.

3.1 Assumption of Parking Environment

Some of general assumptions exist regarding environments for the automated parking

system. The parking spot lies on a pave road and there are parking spots rectangle-

shaped more than two in white. And the GPS information containing each parking spot’s

state is known. But the information is given randomly in the parking spot. Also there are

no obstacles which can make trouble with the parking process.

3.2 Path Generation

The key point for the automated parking system is a path generation. The path

generation methods using circles and straights and 5th polynomial curve are conducted

today. In case of using the 5th polynomial curve, the method is introduced for the

parallel parking system.[6] The methods above are based on the nonholonomic

constraints and the desired optimal path is generated[1]. The method that combines

circles and straights draws an unique solution considering of conditions of vehicle and

parking spot.[3] But it has benefits that align the yaw angles of vehicle and parking spot

before enter the goal or middle point.

4

The 3rd

polynomial curve, this paper presents, also give an unique solution with the

constraints including states of vehicle and parking spot. It is applied to the ways to

middle point and goal point both. To correct the errors occurred when tracks the paths,

the automated parking system searches the 3rd curve in real time. The vehicle follows

the path in both case of moving backward and forward.

3.2.1 Middle Point Decision

As mentioned above, the 3rd

path gives an unique solution for constraints. Therefore it is

needed to be possible that the connection between a start point and an end point. A

present point of vehicle could be the start point with the end point as the middle point.

And the middle point can be the start point with the end point as the goal point.

Naturally the system re-searches a path in real time to decrease control errors. However

cases that the vehicle isn’t able to follow are generated sometimes. So the process

confirms whether the path is usable for following is essential.

The first step for confirming process is to consider the road’s width affordable or not for

vehicle following. Especially in case of a parking lot, recognition for the following is

required by ultrasonic sensors or laser scanners. In this paper, it is assumed that the

region can usable is known and selects the middle point which the path can be generated

adequately. For the second step, selects the candidates for the middle point in the region

around the goal point. If the numbers of N points are selected, the points could be

represented as follows.

1 1 1 1 1 2 1 1 5, , , , , , , ,{ , , , ,x y yaw x y yaw x y yaw x y yawp p p p

1 2 1 1 2 2, , , ,, , ,x y yaw x y yawp p (2)

1 2 5 5, , , ,, , }n mx y yaw x y yawp p

5

N nm (3)

It is recommended not to space between the candidate points out. Besides, the possible

case of multiple heading angles at the same candidate point should be kept in mind and

five angles for each point is set-up in this paper. Finally, select a path which can be

followed by a vehicle in position the system starts. And repeat the same process to link

the middle point and the goal point.

Figure 3 shows the process’s image explore the paths that links from the vehicle to

middle point and from the middle point to the goal point. The left point spreading lines

out is the vehicle’s position and points on the central area are the candidates of middle

points. The point on the bottom of the figure is the goal point. The paths which can be

followed by vehicle are plotted in red and the others are plotted in black lines. Let the

points which make usable paths from the vehicle to the middle point be named in

2veh midp and other points which make usable path from the middle point to the goal

point being named 2mid goalp. Then, the middle points possess usable paths are

represented as follows.

2 2( , )mid veh mid mid goalp x y p p (4)

If there are more than a path that makes vehicle can follow, the system selects the

nearest point.

6

3.2.2 Constraints

There are four constraints needed to generate the 3rd

polynomial curve. Each constraint

includes position, heading angle of the vehicle, a position and heading angle of the

object point. The object point can be the middle point and the goal point. Using the

constraints, the unique 3rd

polynomial curve solution is generated and the constraints are

expressed as follows.

3 2

1 2 3 4y a x a x a x a (5)

3 2

1 1 1 2 1 3 1 4y a x a x a x a (6)

3 2

2 1 2 2 2 3 2 4y a x a x a x a (7)

2

1 2 3' 3 2y a x a x a (8)

2

1 1 1 2 1 3' tan( ) 3y a x a x a (9)

2

2 1 2 2 2 3' tan( ) 3goaly a x a x a (10)

Variables with subscript 1 can be a start point. In case of going to the middle point, the present

position of the vehicle always would be the start point. In the same manner, in case of going to

the goal point from middle point, the middle point will be the start point. After leaving the

middle point, the present position of the vehicle would be the start point. In the other hand, the

middle point would be a destination with subscript 2 when the vehicle is going to the middle

point. And when the vehicle is going to the goal point, the goal point would be a destination with

subscript 2.

7

Figure 3. Process of Middle Point Decision

3.2.3 Coordinate Transformation

The general formula for the 3rd

polynomial is expressed as (5) and the derivative

formula is shown in the expression (8). The expressions (7),(8), (9), and (10) are made

using the position and heading angle of vehicle, the position and heading angle of the

object point. The generation of 3rd

polynomial curve is progressed in a rotated

coordinate, because there are some improper cases for the vehicle to follow. It comes

from the excessive curvature exceeding the vehicle’s maximum steering angle. Whereas

the proper 3rd

polynomial curve is obtained by generating the curve in the coordinate

rotated as much as the angle theta in the expression (11).

Figure 4 shows the results of the 3rd

polynomial curves generated in two of different

coordinates. The upper one is generated in the global coordinate which is not rotated

and the lower one is generated in the local coordinate which is rotated. The origin is set

8

to the vehicle’s position and x axis is aligned

1 2 1 22 ( , )cart pol x x y y (11)

veh (12)

with the line connecting the vehicle and the object point. The latter one is make good

performance to follow the path because it doesn’t ask for the large steering wheel angle

and stiff rate of change.

3.2.4 3rd

Polynomial Path Generation

The 3rd

polynomial path is generated using the constraints and coordinate transformation

mentioned.

The equations (7), (7), (9) and (10) are expressed in relations of matrices X, Y and A.

Then using the equation (13), coefficients of the curve are substituted to the equation (5).

And it generates the 3rd

polynomial curve linking the vehicle and object point as shown

in the figure 3.

3 2

1 1 1

3 2

2 2 2

2

1 1

2

2 2

1

1

3 2 1 0

3 2 1 0

x x x

x x xX

x x

x x

1

2

tan( )

tan( )goal

y

yY

9

1

21

3

4

a

aA X Y

a

a

(13)

Figure 4. Coordinate Transformation

3.3 Steering Wheel Angle Decision

With generated 3rd

polynomial curve, curvatures on the vehicle’s position can be

calculated and using reciprocals of the curvatures, a desired steering angle is defined.

The desired steering angle is calculated with Ackerman angle.[7]

1 26 2y a x a (14)

2 3/2(1+y )radius =

y (15)

( / )des atan L radius (16)

10

3.4 Velocity Control

To control low speed control, the Model Free Control Algorithm is applied. The

algorithm operates regardless of kinds of vehicles.[2]

3.5 Parking Sequence

Mid point dec

3rd path gen

V > 0

Gear status “D”

3rd backward path generation

Gear status “R”

Closer than 0.5m to middle pointYaw Err < 5deg

Stop sig =1

Closer than 1.2m to goal

Yaw Err < 5deg

Stop sig = 1

Vision

Mode 1 Mode 3Mode 2

Mode 4

Parking lot num decision

Gear status “D”Steer. Angle = 0

Mode 5

ReasonableVision count>10Distance > 6m

Stop sig =1Gear status “N”

Goal.p 0.35m 내Yaw Err < 3deg

Stop sig = 1Gear status “N”Steer. Angle = 0

Vision count>20

Gear status “R”Backward path

generation

Mode 6 Mode 7 Mode 8

Figure 5. Auto Parking Sequence

The sequence for the automated parking consists of four phases. Figure 5 shows the

whole process of the automated parking system. The system gives numbers to each

parking spot and generates paths from the vehicles to the middle point. At this phase,

the vehicle’s position is on the road in having been progressed. When the vehicle

approaches the middle point closer than 0.5m with satisfying the heading angle error

within 5deg, it stops with maximum deceleration. The vehicle at the middle point shifts

11

a transmission gear into reverse. In the next phase that the vehicle moves to the goal

point, the system searches another middle point and let the vehicle move forward to the

point if the 3rd

polynomial path isn’t proper for behavior of vehicles. The desired

steering angle should be smaller than maximum steering angle through the all point on

the path. Have following the path satisfying the terms, the vehicle stops at the goal point

similar to the stop conditions at the middle point. However there is the assumption that

the known GPS information of the goal point is not exact. Thus the vehicle moves

forward until the rear camera can secure a clear view of the parking lines. When the

vision system acquires enough visional data to estimate the goal point, the vehicle turns

to a backward state and follows the regenerated path for the goal point which is newly

updated with vision information.

3.6 Vision Information Analysis

10 15 20 25 30

-50

-48

-46

-44

-42

-40

-38

-36

-34

-32

-30

Vision Goal Process

y

x

Figure 6. Results of Vision Analysis

12

Figure 7. Images of Parking Line Detection

The vision analysis system gives each edge’s point information in local coordinate.

Using the information from the visional system, the goal point is calibrated more exactly.

In the figure 6, the red line shows a detection of left parking spot and a green line shows

right one. A trajectory of the vehicle is plotted in blue. Figure 7 shows images captured

by the rear camera. The camera should be calibrated to measure distance and angle

between the vehicle and parking lines. Using the acquired information of parking lines

in a local coordinate and GPS information of vehicle’s position in a global coordinate,

an exact goal point is calculated.

13

Chapter 4. Simulation Results

Matlab & Simulink is used for the simulation tool and the mass particle model method

is applied for the vehicle plant model. The red lines in the figure 8 indicate vehicle’s

trajectory. The forward movement for acquiring vision information is skipped in the

simulation. As shown in the figure 8, the vehicle follows the 3rd

polynomial path.

-90 -85 -80 -75 -70 -65

-130

-128

-126

-124

-122

-120

-118

-116

-114

-112

-110

Trajectory

So

uth

-

----

---

N

ort

h [

m]

West -------- East [m]

Figure 8. Simulation Result

14

Chapter 5. Vehicle Test

5.1 Vehicle Composition

Actuators for the test vehicle consist of four equipments, MDPS for controlling the

steering angle, EMS, MBS for acceleration or deceleration and ATSC for the automatic

transmission shift control. The command for the EMS throttle and MDPS is delivered

by Control Area Network(CAN). The EMS throttle board sends a signal after receiving

a control input and the throttle operates. The MDPS board generates PWM signals to

actuate a motor to follow the desired steering wheel angle. Figure 9 shows the overall

compositions of sensors, actuators and process devices.

Camera X 4

LIDAR X4

GPS Computer X3 Autobox

ATSC

MDPS

Smart Motor

EMS

Figure 9. Vehicle Component

15

DAQ

CAN

PC

EMSSwitchingBoard

APS

Selection

Controller

Driver

Throttle System

DAQ

CAN

PC

Controller

Wire

Brake System

Brake Pedal

DSPControlBoard

SmartMotor

Serial

Steering System

Figure 10. Actuator Systems

Throttle system is controlled through the control board. It operates by driver and control

logic regarding the throttle ON/FF switch. The switch enables drivers control the

autonomous and manual mode.

Brake system pulls brake pedal using motor and wire. The control board calculates

motor’s torque and the motor pulls the wire which is fixed to the brake pedal.

For the steering system, a new MDPS is attached to the vehicle. Because it is much easy

to modify the steering control logic.

16

Figure 11. Brake System

As explained above, the brake system operates using wire. Specification of the motor

has to be powerful because the commands from control logic require the high speed

pulling and acceleration.

5.2 Test Results

The suggested control algorithm is verified through the vehicle test. The whole process

is automatically carried out including parking spot decision, parking line recognition, 3rd

polynomial curve generation, steering, velocity, gear shift control. On the step from

mode 3 to mode 8, vehicles moves with low speed, 5km/h and maximum steering angle

is set up within 34deg. As shown in the figure 13, an inflection point exist on the path

and the vehicle successfully followed the path. Also the visional calibration sequence

17

-10 -5 0 5 10

20

22

24

26

28

30

32

34

36

38

40

Vision Goal Processy

x

Figure 12. Vehicle Test Result

385 390 395 400 405 410 415 420 425 430

-5

0

5

10

15

20

time [sec]

ve

locity[k

m/h

]

velocity

380 385 390 395 400 405 410 415 420 425 430

-30

-20

-10

0

10

20

time [sec]

Ste

eri

ng

an

gle

[de

g]

Steering angle

Figure 13. Result Plots

18

for the exact goal point is shown in the plots. Green lines indicate the calibrated goal

point and the vehicle finally has brought the automated parking to a successful issue.

19

Chapter 6. Summary/Conclusion

This paper presented the whole process for the automated parking system. The 3rd

polynomial path is suggested that makes an unique solution linking the vehicle and

object point and the path is re-searched in real time. Inaccurate GPS information of the

goal point is calibrated by vision analysis. The performance of the algorithm is validated

through vehicle tests.

20

Bibliography

[1] Douglas Lyon, “Parallel Parking with Curvature and Nonholonomic Constraints,”

Intelligent Vehicles 1992-01-252283, 1992, doi:10.1109/IVS.1992.252283

[2] Hakgu Kim, Kwangsuk Oh, Kyongsu Yi, “Development of Speed Control Algorithm

for Autonomous Vehicle “, KSAE, 2011

[3] Hanseung Lee, Dongwook Kim, Kyongsu Yi, “DGPS and Ultrasonic Sensor

fusion for Perpendicular Parking of Autonomous Parking System”, KSAE, 2011B.

Song, “Cooperative Lateral Vehicle Control for Autonomous Valet Parking,” IJAT,

2013

[4] Tzuu-Hseng S. Li, “Autonomous Fuzzy Parking Control of a Car-Like Mobile

Robot,” Man and Cybernetics Society, 2003-07-811766,

doi:10.1109/TSMCA.2003.811766

[5] Ming Feng Hsieh, Umit Ozguner, “A Parking Algorithm for an Autonomous

Vehicle”, Intelligent Vehicles Symposium, 2008-06-4621317,

doi:10.1109/IVS.2008.4621317

[6] Shuwen Zhang, “Automatic Vehicle Parallel Parking Design Using Fifth Degree

Polynomial Path Planning”, VTC,2011-09-6093275,

doi:10.1109/VETECF.2011.6093275

21

[7] Gupta A, “Autonomous Parallel Parking System for Ackerman Steering Four

Wheelers,” ICCIC, 2010-12-5705869, doi:10.1109/ICCIC.2010.5705869

[8] Zhi-Long Wang, “The design of an autonomous parallel parking neuro-fuzzy

controller for a car-like mobile robot”, SICE Annual Conference, 2010-08

[9] Jae-Hwan Kim, “The research of parking mission planning algorithm for unmanned

ground vehicle,” ICCCAS, 2010-10

22

초 록

본 논문에서는 자동 주차를 위한 차량 제어 알고리즘을 다루고 있다. Global

Positioning System(GPS) 정보로부터 차량의 위치와 heading angle, 주차 구역의

위치와 각도를 알 수 있다. 이를 기반으로 후진 시작 지점인 Middle Point를

결정하고, 현재 차량의 위치에서부터 Middle Point까지의 경로와 Middle

Point에서부터 Goal Point까지의 경로를 현재 차량의 위치와 heading angle, 목적

지점의 위치와 각도를 구속조건으로 하여 3차 곡선으로 생성한다. 경로를

따르기 위한 조향각은 임계값을 넘지 않아야 한다. GPS 정보를 이용하여 주차

구역 근처의 지점으로 이동한다. 그리고 차량 후미에 Camera를 장착하여 후진

상황에서 주차구역을 인지하고 정확한 Goal Point와 Middle Point를 결정한다.

기어 변속을 위한 장치로서 Automatic Transmission Shifting Control (ATSC)을

사용하였다. 다양한 지점에서 주차가 가능한 경로를 생성하기 위해

시뮬레이션을 통해 검증하였고, 시험 차량을 통해 실제 차량에서의 안정적인

주차가 가능함을 검증하였다.

주요어 : 3rd polynomial curve(3차 곡선), GPS Goal Point(GPS기반

주차지점), Vision Goal Point(카메라 기반 주차지점), Middle Point(후진

지점), Steering Lock Up(조향각 고정), Parking Lot Detection(주차구역

인지)

학 번 : 2012 – 20684

저 시-비 리- 경 지 2.0 한민

는 아래 조건 르는 경 에 한하여 게

l 저 물 복제, 포, 전송, 전시, 공연 송할 수 습니다.

다 과 같 조건 라야 합니다:

l 하는, 저 물 나 포 경 , 저 물에 적 된 허락조건 명확하게 나타내어야 합니다.

l 저 터 허가를 면 러한 조건들 적 되지 않습니다.

저 에 른 리는 내 에 하여 향 지 않습니다.

것 허락규약(Legal Code) 해하 쉽게 약한 것 니다.

Disclaimer

저 시. 하는 원저 를 시하여야 합니다.

비 리. 하는 저 물 리 목적 할 수 없습니다.

경 지. 하는 저 물 개 , 형 또는 가공할 수 없습니다.

1

Abstract

Path Generation Using 3rd

Polynomial

Curve and Control Algorithm for

Autonomous Parking

Jiwhan Yoon

Mechanical and Aerospace Engineering

The Graduate School

Seoul National University

This paper presents a vehicle control algorithm for autonomous parking system. The

position and heading angle of subject vehicle or parking spot are acquired from the GPS

information. Those determine the middle point. Paths which connect the subject vehicle

and middle point are generated as a 3rd

polynomial curve. It is successfully done by

constraints including subject vehicle states, position and heading angle of middle point.

The path links the middle point and the goal point follows the same generation process.

The steering angle should not exceed the threshold value which is possible to be kept up

2

by vehicles. The vehicle moves to a position near the parking lot. Then using a camera

attached to the tail end vehicle, not only parking lanes are recognized in the backward

situation but also the accurate middle point and goal point are determined. Automatic

Transmission Shifting Control(ATSC) is applied for a gear shift. To generate the paths at

various positions around the parking spot, it is verified by a simulation. Also the real

size vehicle test is implemented and had a success rate higher than 97 percent.

Keywords : 3rd

polynomial curve, GPS goal point, vision goal point, middle point,

parking lot detection, steering lock up

Student Number : 2012-20684

3

Contents

Abstract .............................................................................................................................. I

List of Figures .................................................................................................................... V

Nomenclature .................................................................................................................... VI

Chapter 1. Introduction ....................................................................................................... 1

Chapter 2. Vehicle Model .................................................................................................... 2

Chapter 3. Control Algorithm for Automated Parking ........................................................ 3

3.1 Assumption of Parking Environment ................................................................ 3

3.2 Path Generation ................................................................................................. 3

3.2.1 Middle Point Decision .......................................................................... 4

3.2.2 Constraints ............................................................................................ 6

3.2.3 Coordinate Transformation ................................................................... 7

3.2.4 3rd

Polynomial Path Generation ............................................................ 8

3.3 Steering Wheel Angle Decision ......................................................................... 9

3.4 Velocity Control .............................................................................................. 10

3.5 Parking Sequence ............................................................................................ 10

4

3.6 Vision Information Analysis ............................................................................ 11

Chapter 4. Simulation Results ......................................................................................... 13

Chapter 5. Vehicle Test .................................................................................................... 14

5.1 Vehicle Composition ....................................................................................... 14

5.2 Test Results ..................................................................................................... 16

Chapter 6. Summary / Conclusions ................................................................................... 19

Bibliography...................................................................................................................... 20

초 록 ................................................................................................................................. 22

5

List of Figures

Figure 1 Vehicle Geometry .................................................................................... 3

Figure 2 Control Block Diagram ............................................................................. 5

Figure 3 Process of Middle Point Decision ............................................................. 7

Figure 4 Coordinate Transformation ........................................................................ 8

Figure 5 Auto Parking Sequence ............................................................................. 8

Figure 6 Results of Vision Analysis ......................................................................... 9

Figure 7 Images of Parking Line Detection ........................................................... 10

Figure 8 Simulation Result .................................................................................... 11

Figure 9 Vehicle Component ................................................................................. 12

Figure 10 Actuator Systems ..................................................................................... 13

Figure 11 Brake System ........................................................................................... 14

Figure 12 Vehicle Test Result .................................................................................. 15

Figure 13 Result Plots .............................................................................................. 18

6

Nomenclatures

steering angle

k , veh vehicle yaw angle

x global x position

y global y position

v velocity

L wheel base

k k-th sequence

veh Vehicle

des Desired

1 subject position

2 object position

1

Chapter 1. Introduction

Control techniques for automated parking system are actively conducted

ecumenically.[9] Including a backward parking, algorithms of forward parking, parallel

parking and diagonal parking are developed. Particularly the backward and parallel

parking algorithms that many drivers feel difficulty are developed. Recently, the

automated parking systems that support Parking Assistant(PA) and Steering Parking

Assist System(SPAS) are commercialized partially. Many papers introduces control

methods such as the fuzzy logic control.[8] But the functions commercialized for now

are limited to the steering control assistance. In this paper, dealing with not only the

steering control but also the control algorithm including velocity and transmission

switch, it is expected to contribute to the commercialization of automated parking

system. The validation for the control algorithms are fulfilled by simulations using mass

particle model method and real size vehicle tests.

Figure 1. Vehicle Geometry

xv

kx

ky

k

2

Chapter 2. Vehicle Model

The mass particle model is used to analysis the behavior of the vehicle.[4],[5] The

model is adequate for the vehicle moving slowly. Figure 1 shows the vehicle model

schematically. By observing the central point of rear axle, The motion of the vehicle is

presented as follows.

1

1

1

sin /

cos cos

cos sin

k k x

k k x k

k k x k

v t L

x x v t

y y v t

(1)

VisionCAM

Process module Control algorithm

Lab View Micro Autobox

Actuators

Vision Computer

(Vision analysis)

Parking Section Decision

Decision

desdesv

Goal point Decision

Steering control

Velocity control

ATSC

WireEPB

EMSthrottle

MDPS

desv

des

Control input

x,y,yaw,v

Figure 2. Control Block Diagram

3

Chapter 3. Control Algorithm for Automated Parking

The vehicle control algorithm suggested in this paper calibrates the goal point using

the vision information near the parking spot. It is also based on the information from the

GPS device. The 3rd

polynomial paths are generated on constraints which contain

positions and heading angles of subject vehicle and object point. The objet point might

be the middle point as well as the goal point so that the 3rd

path is applied to both cases.

The control algorithm generates the 3rd

path and determines the steering angle using a

curvature in real time.

3.1 Assumption of Parking Environment

Some of general assumptions exist regarding environments for the automated parking

system. The parking spot lies on a pave road and there are parking spots rectangle-

shaped more than two in white. And the GPS information containing each parking spot’s

state is known. But the information is given randomly in the parking spot. Also there are

no obstacles which can make trouble with the parking process.

3.2 Path Generation

The key point for the automated parking system is a path generation. The path

generation methods using circles and straights and 5th polynomial curve are conducted

today. In case of using the 5th polynomial curve, the method is introduced for the

parallel parking system.[6] The methods above are based on the nonholonomic

constraints and the desired optimal path is generated[1]. The method that combines

circles and straights draws an unique solution considering of conditions of vehicle and

parking spot.[3] But it has benefits that align the yaw angles of vehicle and parking spot

before enter the goal or middle point.

4

The 3rd

polynomial curve, this paper presents, also give an unique solution with the

constraints including states of vehicle and parking spot. It is applied to the ways to

middle point and goal point both. To correct the errors occurred when tracks the paths,

the automated parking system searches the 3rd curve in real time. The vehicle follows

the path in both case of moving backward and forward.

3.2.1 Middle Point Decision

As mentioned above, the 3rd

path gives an unique solution for constraints. Therefore it is

needed to be possible that the connection between a start point and an end point. A

present point of vehicle could be the start point with the end point as the middle point.

And the middle point can be the start point with the end point as the goal point.

Naturally the system re-searches a path in real time to decrease control errors. However

cases that the vehicle isn’t able to follow are generated sometimes. So the process

confirms whether the path is usable for following is essential.

The first step for confirming process is to consider the road’s width affordable or not for

vehicle following. Especially in case of a parking lot, recognition for the following is

required by ultrasonic sensors or laser scanners. In this paper, it is assumed that the

region can usable is known and selects the middle point which the path can be generated

adequately. For the second step, selects the candidates for the middle point in the region

around the goal point. If the numbers of N points are selected, the points could be

represented as follows.

1 1 1 1 1 2 1 1 5, , , , , , , ,{ , , , ,x y yaw x y yaw x y yaw x y yawp p p p

1 2 1 1 2 2, , , ,, , ,x y yaw x y yawp p (2)

1 2 5 5, , , ,, , }n mx y yaw x y yawp p

5

N nm (3)

It is recommended not to space between the candidate points out. Besides, the possible

case of multiple heading angles at the same candidate point should be kept in mind and

five angles for each point is set-up in this paper. Finally, select a path which can be

followed by a vehicle in position the system starts. And repeat the same process to link

the middle point and the goal point.

Figure 3 shows the process’s image explore the paths that links from the vehicle to

middle point and from the middle point to the goal point. The left point spreading lines

out is the vehicle’s position and points on the central area are the candidates of middle

points. The point on the bottom of the figure is the goal point. The paths which can be

followed by vehicle are plotted in red and the others are plotted in black lines. Let the

points which make usable paths from the vehicle to the middle point be named in

2veh midp and other points which make usable path from the middle point to the goal

point being named 2mid goalp. Then, the middle points possess usable paths are

represented as follows.

2 2( , )mid veh mid mid goalp x y p p (4)

If there are more than a path that makes vehicle can follow, the system selects the

nearest point.

6

3.2.2 Constraints

There are four constraints needed to generate the 3rd

polynomial curve. Each constraint

includes position, heading angle of the vehicle, a position and heading angle of the

object point. The object point can be the middle point and the goal point. Using the

constraints, the unique 3rd

polynomial curve solution is generated and the constraints are

expressed as follows.

3 2

1 2 3 4y a x a x a x a (5)

3 2

1 1 1 2 1 3 1 4y a x a x a x a (6)

3 2

2 1 2 2 2 3 2 4y a x a x a x a (7)

2

1 2 3' 3 2y a x a x a (8)

2

1 1 1 2 1 3' tan( ) 3y a x a x a (9)

2

2 1 2 2 2 3' tan( ) 3goaly a x a x a (10)

Variables with subscript 1 can be a start point. In case of going to the middle point, the present

position of the vehicle always would be the start point. In the same manner, in case of going to

the goal point from middle point, the middle point will be the start point. After leaving the

middle point, the present position of the vehicle would be the start point. In the other hand, the

middle point would be a destination with subscript 2 when the vehicle is going to the middle

point. And when the vehicle is going to the goal point, the goal point would be a destination with

subscript 2.

7

Figure 3. Process of Middle Point Decision

3.2.3 Coordinate Transformation

The general formula for the 3rd

polynomial is expressed as (5) and the derivative

formula is shown in the expression (8). The expressions (7),(8), (9), and (10) are made

using the position and heading angle of vehicle, the position and heading angle of the

object point. The generation of 3rd

polynomial curve is progressed in a rotated

coordinate, because there are some improper cases for the vehicle to follow. It comes

from the excessive curvature exceeding the vehicle’s maximum steering angle. Whereas

the proper 3rd

polynomial curve is obtained by generating the curve in the coordinate

rotated as much as the angle theta in the expression (11).

Figure 4 shows the results of the 3rd

polynomial curves generated in two of different

coordinates. The upper one is generated in the global coordinate which is not rotated

and the lower one is generated in the local coordinate which is rotated. The origin is set

8

to the vehicle’s position and x axis is aligned

1 2 1 22 ( , )cart pol x x y y (11)

veh (12)

with the line connecting the vehicle and the object point. The latter one is make good

performance to follow the path because it doesn’t ask for the large steering wheel angle

and stiff rate of change.

3.2.4 3rd

Polynomial Path Generation

The 3rd

polynomial path is generated using the constraints and coordinate transformation

mentioned.

The equations (7), (7), (9) and (10) are expressed in relations of matrices X, Y and A.

Then using the equation (13), coefficients of the curve are substituted to the equation (5).

And it generates the 3rd

polynomial curve linking the vehicle and object point as shown

in the figure 3.

3 2

1 1 1

3 2

2 2 2

2

1 1

2

2 2

1

1

3 2 1 0

3 2 1 0

x x x

x x xX

x x

x x

1

2

tan( )

tan( )goal

y

yY

9

1

21

3

4

a

aA X Y

a

a

(13)

Figure 4. Coordinate Transformation

3.3 Steering Wheel Angle Decision

With generated 3rd

polynomial curve, curvatures on the vehicle’s position can be

calculated and using reciprocals of the curvatures, a desired steering angle is defined.

The desired steering angle is calculated with Ackerman angle.[7]

1 26 2y a x a (14)

2 3/2(1+y )radius =

y (15)

( / )des atan L radius (16)

10

3.4 Velocity Control

To control low speed control, the Model Free Control Algorithm is applied. The

algorithm operates regardless of kinds of vehicles.[2]

3.5 Parking Sequence

Mid point dec

3rd path gen

V > 0

Gear status “D”

3rd backward path generation

Gear status “R”

Closer than 0.5m to middle pointYaw Err < 5deg

Stop sig =1

Closer than 1.2m to goal

Yaw Err < 5deg

Stop sig = 1

Vision

Mode 1 Mode 3Mode 2

Mode 4

Parking lot num decision

Gear status “D”Steer. Angle = 0

Mode 5

ReasonableVision count>10Distance > 6m

Stop sig =1Gear status “N”

Goal.p 0.35m 내Yaw Err < 3deg

Stop sig = 1Gear status “N”Steer. Angle = 0

Vision count>20

Gear status “R”Backward path

generation

Mode 6 Mode 7 Mode 8

Figure 5. Auto Parking Sequence

The sequence for the automated parking consists of four phases. Figure 5 shows the

whole process of the automated parking system. The system gives numbers to each

parking spot and generates paths from the vehicles to the middle point. At this phase,

the vehicle’s position is on the road in having been progressed. When the vehicle

approaches the middle point closer than 0.5m with satisfying the heading angle error

within 5deg, it stops with maximum deceleration. The vehicle at the middle point shifts

11

a transmission gear into reverse. In the next phase that the vehicle moves to the goal

point, the system searches another middle point and let the vehicle move forward to the

point if the 3rd

polynomial path isn’t proper for behavior of vehicles. The desired

steering angle should be smaller than maximum steering angle through the all point on

the path. Have following the path satisfying the terms, the vehicle stops at the goal point

similar to the stop conditions at the middle point. However there is the assumption that

the known GPS information of the goal point is not exact. Thus the vehicle moves

forward until the rear camera can secure a clear view of the parking lines. When the

vision system acquires enough visional data to estimate the goal point, the vehicle turns

to a backward state and follows the regenerated path for the goal point which is newly

updated with vision information.

3.6 Vision Information Analysis

10 15 20 25 30

-50

-48

-46

-44

-42

-40

-38

-36

-34

-32

-30

Vision Goal Process

y

x

Figure 6. Results of Vision Analysis

12

Figure 7. Images of Parking Line Detection

The vision analysis system gives each edge’s point information in local coordinate.

Using the information from the visional system, the goal point is calibrated more exactly.

In the figure 6, the red line shows a detection of left parking spot and a green line shows

right one. A trajectory of the vehicle is plotted in blue. Figure 7 shows images captured

by the rear camera. The camera should be calibrated to measure distance and angle

between the vehicle and parking lines. Using the acquired information of parking lines

in a local coordinate and GPS information of vehicle’s position in a global coordinate,

an exact goal point is calculated.

13

Chapter 4. Simulation Results

Matlab & Simulink is used for the simulation tool and the mass particle model method

is applied for the vehicle plant model. The red lines in the figure 8 indicate vehicle’s

trajectory. The forward movement for acquiring vision information is skipped in the

simulation. As shown in the figure 8, the vehicle follows the 3rd

polynomial path.

-90 -85 -80 -75 -70 -65

-130

-128

-126

-124

-122

-120

-118

-116

-114

-112

-110

Trajectory

So

uth

-

----

---

N

ort

h [

m]

West -------- East [m]

Figure 8. Simulation Result

14

Chapter 5. Vehicle Test

5.1 Vehicle Composition

Actuators for the test vehicle consist of four equipments, MDPS for controlling the

steering angle, EMS, MBS for acceleration or deceleration and ATSC for the automatic

transmission shift control. The command for the EMS throttle and MDPS is delivered

by Control Area Network(CAN). The EMS throttle board sends a signal after receiving

a control input and the throttle operates. The MDPS board generates PWM signals to

actuate a motor to follow the desired steering wheel angle. Figure 9 shows the overall

compositions of sensors, actuators and process devices.

Camera X 4

LIDAR X4

GPS Computer X3 Autobox

ATSC

MDPS

Smart Motor

EMS

Figure 9. Vehicle Component

15

DAQ

CAN

PC

EMSSwitchingBoard

APS

Selection

Controller

Driver

Throttle System

DAQ

CAN

PC

Controller

Wire

Brake System

Brake Pedal

DSPControlBoard

SmartMotor

Serial

Steering System

Figure 10. Actuator Systems

Throttle system is controlled through the control board. It operates by driver and control

logic regarding the throttle ON/FF switch. The switch enables drivers control the

autonomous and manual mode.

Brake system pulls brake pedal using motor and wire. The control board calculates

motor’s torque and the motor pulls the wire which is fixed to the brake pedal.

For the steering system, a new MDPS is attached to the vehicle. Because it is much easy

to modify the steering control logic.

16

Figure 11. Brake System

As explained above, the brake system operates using wire. Specification of the motor

has to be powerful because the commands from control logic require the high speed

pulling and acceleration.

5.2 Test Results

The suggested control algorithm is verified through the vehicle test. The whole process

is automatically carried out including parking spot decision, parking line recognition, 3rd

polynomial curve generation, steering, velocity, gear shift control. On the step from

mode 3 to mode 8, vehicles moves with low speed, 5km/h and maximum steering angle

is set up within 34deg. As shown in the figure 13, an inflection point exist on the path

and the vehicle successfully followed the path. Also the visional calibration sequence

17

-10 -5 0 5 10

20

22

24

26

28

30

32

34

36

38

40

Vision Goal Processy

x

Figure 12. Vehicle Test Result

385 390 395 400 405 410 415 420 425 430

-5

0

5

10

15

20

time [sec]

ve

locity[k

m/h

]

velocity

380 385 390 395 400 405 410 415 420 425 430

-30

-20

-10

0

10

20

time [sec]

Ste

eri

ng

an

gle

[de

g]

Steering angle

Figure 13. Result Plots

18

for the exact goal point is shown in the plots. Green lines indicate the calibrated goal

point and the vehicle finally has brought the automated parking to a successful issue.

19

Chapter 6. Summary/Conclusion

This paper presented the whole process for the automated parking system. The 3rd

polynomial path is suggested that makes an unique solution linking the vehicle and

object point and the path is re-searched in real time. Inaccurate GPS information of the

goal point is calibrated by vision analysis. The performance of the algorithm is validated

through vehicle tests.

20

Bibliography

[1] Douglas Lyon, “Parallel Parking with Curvature and Nonholonomic Constraints,”

Intelligent Vehicles 1992-01-252283, 1992, doi:10.1109/IVS.1992.252283

[2] Hakgu Kim, Kwangsuk Oh, Kyongsu Yi, “Development of Speed Control Algorithm

for Autonomous Vehicle “, KSAE, 2011

[3] Hanseung Lee, Dongwook Kim, Kyongsu Yi, “DGPS and Ultrasonic Sensor

fusion for Perpendicular Parking of Autonomous Parking System”, KSAE, 2011B.

Song, “Cooperative Lateral Vehicle Control for Autonomous Valet Parking,” IJAT,

2013

[4] Tzuu-Hseng S. Li, “Autonomous Fuzzy Parking Control of a Car-Like Mobile

Robot,” Man and Cybernetics Society, 2003-07-811766,

doi:10.1109/TSMCA.2003.811766

[5] Ming Feng Hsieh, Umit Ozguner, “A Parking Algorithm for an Autonomous

Vehicle”, Intelligent Vehicles Symposium, 2008-06-4621317,

doi:10.1109/IVS.2008.4621317

[6] Shuwen Zhang, “Automatic Vehicle Parallel Parking Design Using Fifth Degree

Polynomial Path Planning”, VTC,2011-09-6093275,

doi:10.1109/VETECF.2011.6093275

21

[7] Gupta A, “Autonomous Parallel Parking System for Ackerman Steering Four

Wheelers,” ICCIC, 2010-12-5705869, doi:10.1109/ICCIC.2010.5705869

[8] Zhi-Long Wang, “The design of an autonomous parallel parking neuro-fuzzy

controller for a car-like mobile robot”, SICE Annual Conference, 2010-08

[9] Jae-Hwan Kim, “The research of parking mission planning algorithm for unmanned

ground vehicle,” ICCCAS, 2010-10

22

초 록

본 논문에서는 자동 주차를 위한 차량 제어 알고리즘을 다루고 있다. Global

Positioning System(GPS) 정보로부터 차량의 위치와 heading angle, 주차 구역의

위치와 각도를 알 수 있다. 이를 기반으로 후진 시작 지점인 Middle Point를

결정하고, 현재 차량의 위치에서부터 Middle Point까지의 경로와 Middle

Point에서부터 Goal Point까지의 경로를 현재 차량의 위치와 heading angle, 목적

지점의 위치와 각도를 구속조건으로 하여 3차 곡선으로 생성한다. 경로를

따르기 위한 조향각은 임계값을 넘지 않아야 한다. GPS 정보를 이용하여 주차

구역 근처의 지점으로 이동한다. 그리고 차량 후미에 Camera를 장착하여 후진

상황에서 주차구역을 인지하고 정확한 Goal Point와 Middle Point를 결정한다.

기어 변속을 위한 장치로서 Automatic Transmission Shifting Control (ATSC)을

사용하였다. 다양한 지점에서 주차가 가능한 경로를 생성하기 위해

시뮬레이션을 통해 검증하였고, 시험 차량을 통해 실제 차량에서의 안정적인

주차가 가능함을 검증하였다.

주요어 : 3rd polynomial curve(3차 곡선), GPS Goal Point(GPS기반

주차지점), Vision Goal Point(카메라 기반 주차지점), Middle Point(후진

지점), Steering Lock Up(조향각 고정), Parking Lot Detection(주차구역

인지)

학 번 : 2012 – 20684