Smooth tracking controller for AGV through junction using CMU camera

Nghiên cứu thiết kế bộ điều khiển bám line cho AGV qua giao lộ Smooth tracking controller for AGV through junction using CMU camera Huu Danh Lam, Tran Duc Hieu Le, Tan Tung Phan and Tan

Hội Cơ điện tử Việt Nam Trường Đại học Lạc Hồng (Đơn vị đăng cai tổ chức) Viện Cơ học và Tin học ứng dụng, Viện Công nghệ Thông tin, Viện Hàn lâm

Khoa học và Công nghệ Việt Nam Khu Công nghệ cao Thành phố Hồ Chí Minh Chương trình Nghiên cứu Ứng dụng và Phát triển Công

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Toàn quốc lần thứ 7 (VCM-2014)

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Huu Danh Lam, Tran Duc Hieu Le, Tan Tung Phan, Tan Tien Nguyen and Hoai Quoc Le

Smooth Tracking Controller for AGV through Junction using CMU Camera 597

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Nghiên cứu thiết kế bộ điều khiển bám line cho AGV qua giao lộ

Smooth tracking controller for AGV through junction using CMU camera

Huu Danh Lam, Tran Duc Hieu Le, Tan Tung Phan and Tan Tien Nguyen

Hochiminh City University of Technology, Hochiminh City, Vietnam

Hoai Quoc Le Saigon Hi-Tech Park, Vietnam

Email : nttien@hcmut.edu.vn

Tóm tắt

Bài báo đề xuất một dạng đường qua giao lộ cho

AGV sử dụng CMU camera Sơ đồ tính toán sai số

cho AGV được trình bày Mô hình hóa động học của

AGV được thiết lập, từ đó xây dựng bộ điều khiển

bền vững cho bài toán bám đường của AGV Kết quả

mô phỏng chứng minh hiệu quả và tính khả thi của

phương pháp đề nghị

Abstract

This paper suggests a new path pattern for junction

for AGV line tracking using CMU camera The

scheme for calculation the tracking error with CMU

camera is introduced The system modelling bases on

kinematic configuration is given to drive a robust

nonlinear controller for AGV line tracking The

simulation is done to verify the effectiveness of the

proposed method

1 Introduction

An automatic guided vehicle (AGV) is a mobile robot

that follows markers or wires in the floor, or uses

vision, magnets, or lasers for navigation AGVs are

most often used in industrial applications to move

materials around a manufacturing facility or a

warehouse The first AGV was invented by Barrett

Electronics in 1953 The AGV can tow objects behind

them (or store objects on a bed) in trailers to which

they can autonomously attach AGVs are employed in

nearly every industry, including, pulp, paper, metals,

newspaper, and general manufacturing Transporting

materials such as food, linen or medicine in hospitals

is also done

There are several problems need to concern for design

an AGV, such as: navigation, path decision, traffic

control, system management, vehicle types,

applications, battery management, … There are

numbers of research relating to the design, control and

implementation of AGV The whole picture of AGV

system can be seen in the work of Le Anh Tuan [4]

This paper studies on design or robust tracking

controller for AGV through junction using CMU

camera First, a new path pattern for junction using

for AGV line tracking with CMU camera is

introduced Then, the scheme for calculation the

tracking error with CMU camera is presented The

system modelling bases on kinematic configuration is given to drive a robust nonlinear controller for AGV line tracking The simulation is done to verify the effectiveness of the proposed method

2 Problem Setting

2.1 AVG structure

The AGV using in this study is a conventional type of mobile robot platform, which is driven by two driving

wheels as shown in the Fig.1

Fig.1 AVG structure using in this paper

The tracking point is the center of AGV, it is also the camera position The center of AGV is the middle of two driving wheels Note that, the tracking point and

the AGV center is not coincide

2.2 Path pattern

The conventional junction path patterns used for AGV can be seen in the Fig.2 For the square-shaped junction, the AGV will stop at the intersection, then rotate in the desired direction That means the AGV speed is not continuous To avoid this problem, the arc-shaped junction is introduced To follow these path patterns, there are numerous of solutions One of the simplest way is using well known CMU camera It provides a vision capabilities to small embedded systems in the form of an intelligent sensor The CMUcam open source programmable embedded color vision sensors are low-cost, low-power sensors for mobile robots It can be used to do many different kinds of on-board, real-time vision processing tasks However, for a complex junction such as crossroads (Fig.2, a and b), the application of CMU is difficult

To overcome this, this paper proposes a new junctions for using with CMU camera as shown in the Fig.2.c The curve sections is added to provide the ability of smooth tracking for mobile robot when the turn left or right The algorithm for tracking with CMU camera

will be stated in the section 4 of this paper

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DOI: 10.15625/VCM.2014-306

a Square-shaped junctions

b Arc-shaped junctions

c Proposed junctions

Fig.2 Path patterns using for AGV tracking

3 Controller design

3.1 System modeling

To drive the tracking controller for the proposed

junction, the system coordinate is introduce as in the

following Fig.3 For both directional moving ability,

two structures with different position of driving

wheels are examined

a 𝑑 > 0 b 𝑑 < 0

Fig.3 System coordinate for driving motion of equation with

different position of driving wheels

The dynamic equation of AGV

�𝑥̇𝑦̇

𝜑̇� = �

𝑐𝑜𝑠𝜑 0

𝑠𝑖𝑛𝜑 0

where 𝑣, 𝜔 are the linear and angular velocities of

AGV

The dynamic equation of tracking point 𝐶

�𝑦̇𝑥̇𝐶𝐶= 𝑦̇ + 𝑑𝑐𝑜𝑠𝜑𝜑̇= 𝑥̇ − 𝑑𝑠𝑖𝑛𝜑𝜑̇

where 𝑑 is the distance from center of AGV to the

tracking point 𝐶 (also camera position)

The dynamic equation of reference point 𝑅

�𝑥̇𝑦̇𝑅𝑅= 𝑣= 𝑣𝑅𝑅𝑐𝑜𝑠𝜑𝑠𝑖𝑛𝜑𝑅𝑅

where 𝑣𝑅 is the desired velocity of AGV

The controller is designed for the tracking point 𝐶 to

track the target point 𝑅 in the reference path with the

desired velocity 𝑣𝑅 To do this, let’s define the

tracking error as the following

�𝑒𝑒12

𝑒3

� = �−𝑠𝑖𝑛𝜑 𝑐𝑜𝑠𝜑 0𝑐𝑜𝑠𝜑 𝑠𝑖𝑛𝜑 0

𝑥𝑅− 𝑥𝐶

𝑦𝑅− 𝑦𝐶

𝜑𝑅− 𝜑𝐶

After some calculations, the error dynamics can be

derived as follows

�𝑒̇𝑒̇12

𝑒̇3

� = �𝑣𝑣𝑅𝑅𝑐𝑜𝑠𝑒𝑠𝑖𝑛𝑒33

𝜔𝑅

� + �−10 −𝑑 − 𝑒𝑒2 1

0 −1 � �𝑣𝜔� (5)

In the case the AGV moves to the reverse direction, the equation is still available with replace 𝑑 by −𝑑, that means 𝑑 is positive or negative depending on the moving direction of AGV

3.2 Controller Design

Theorem: The system (5) is stabilized by the

following tracking controller

� 𝑣 = 𝑣𝑅𝑐𝑜𝑠𝑒3+ 𝑘1𝑒1

𝜔 = 𝑘2𝑣𝑅𝑒2+ 𝜔𝑅+ 𝑘3𝑠𝑖𝑛𝑒3 (6)

Proof Choose the Lyapunov’s function

𝑉 =12 𝑒1 +12 𝑒2 +1 − 𝑐𝑜𝑠𝑒𝑘 3

where 𝑘1, 𝑘2, 𝑘3 are positive values

Its derivative yields

𝑉̇ = 𝑒1(𝑣𝑅𝑐𝑜𝑠𝑒3− 𝑣)

+𝑠𝑖𝑛𝑒𝑘 3

2 (𝑘2𝑣𝑅𝑒2+ 𝜔𝑅− 𝜔) The controller (6) leads to achieve the negative of 𝑉̇ That means the system (5) is stable with the tracking controller (6) in the sense of Lyapunov’s stability, and all tracking errors 𝑒1, 𝑒2, 𝑒3 will be converged to zero

as 𝑡 → ∞

In the tracking controller (6), when starting with

𝑣0≈ 𝑣𝑅, the error 𝑒1 can be set to be zero (or small enough to be ignored) resulting on the measuring errors 𝑒2, 𝑒3 as shown in the next section

4 Measure tracking error with CMU

camera

In this section, together with the proposed path patterns, the CMU camera is used for measuring the tracking errors 𝑒2, 𝑒3

Fig.4 Errors measuring scheme form CMU camera frame

The CMU camera sensor outputs are the path captured frame and the center of captured path, from which we can calculate (𝑥1, 𝑦1), (𝑥2, 𝑦2) and (𝑥3, 𝑦3) Then the errors can derived as follows

�𝑒2= 𝑘(160 − 𝑥3)

𝑒3≈ 𝑘(𝑥2− 𝑥1− 𝑏/𝑘)/200 (7) where 𝑘 is the conversion factor between the real

length and camera pixel

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In case of multi-path (at the proposed crossroads), the

signal will be shifted with the designed color Because

each line has the same width of 𝑏, the measured errors

can be modified as follows

�𝑒2= 𝑘(160 − 𝑥3) ∓ 𝑏

𝑒3≈ 𝑘(𝑥2− 𝑥1− 𝑏/𝑘)/200 (8)

5 Simulation Results and Discussion

The proposed method is verified by the mean of

simulation The AGV will be controlled using the

controller (6) with the tracking error calculated from

(8) for both tracking line as shown in the Fig.6

a The proposed tracking line b Normal tracking line

Fig.6 Two cases of tracking line for simulation study

The parameters of AGV using in the simulation are

given in the Table.1

Table 1 The parameters using for simulation study

Width of the tracking line, 𝑏 5 𝑚𝑚

Curve radius of the tracking line 412 𝑚𝑚

Distance from tracking point to

The simulation results are shown in the Fig.7 for the

proposed tracking method and Fig.8 for conventional

tracking

a Tracking error 𝑒𝑖

b Path following of AGV

c Wheels velocity as input AGV

Fig.7 Simulation results for proposed tracking method

a Tracking error 𝑒𝑖

b Path following of AGV

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c Wheels velocity as input AGV

Fig.7 Simulation results for normal tracking

From the results as shown in the Fig.6.a and Fig 7.a,

the tracking errors 𝑒𝑖 are almost the same for both

case of tracking lines, except at the shifting tracking

point between straight and curve line (near 1𝑠 and

1.8𝑠) At this point, the control inputs (driving motor

speed) was required higher for keeping AGV to

follow the reference line as shown in the Fig.6.b and

Fig.7.b In both cases, the AGV can track the

reference line robustly as shown in the Fig.6.c and

Fig.7.c

6 Conclusion

This paper presents the studies on design or robust

tracking controller for AGV through junction using

CMU camera This is a part of the Restaurant Service

Robot Project, which is studying at HiTech

Mechatronics Lab at Hochiminh City University of

Technology A new path pattern for junction using for

AGV line tracking with CMU camera is introduced

The scheme for calculation the tracking error with

CMU camera is presented The system modelling

bases on kinematic configuration is given to drive a

robust nonlinear controller for AGV line tracking

The simulation results prove that the proposed method

can be used for control the AGV through complex

junction with CMU camera The experiment is

studying and we do hope it will be further proof for

the proposed method

Tài liệu tham khảo

[1] Wu Xing et al., Intersection Recognition and

Guide-path Selection for a Vision-based AGV in a

Bidirectional Flow Network, Int’l Journal of

Advanced Robotic Systems, DOI: 10.5772/58218,

pp 1-17, 2014

[2] M Sharma, Control Classification of Automated

Guided Vehicle Systems, Int’l Journal of

Engineering and Advanced Technology (IJEAT),

Vol.2, Issue.1, pp.2249–8958, 2012

[3] P.T Doan, et al., Path Tracking Control of

Automated Guided Vehicle Using Camera Sensor,

Proc of The 2011 Int’l Symposium on

Automotive and Convergence Engineering, pp

89-94, Vietnam, January 19-21, 2011

[4] T.L Anh et al., A Review of Design and Control

of Automated Guided Vehicle Systems European

Journal of Operational Research, Vol 171, Issue

1, pp.1-23, 2006

[5] T.T Nguyen et al., Tracking Control of a Spot

Bead Welding Mobile Robot Using Camera Sensor, Proc of The 2003 International Symposium on Advanced Engineering (ISAE’03), Pusan, Korea, pp 408-414, November 2003

[6] T.L Chung et al., A Chattering-Free Sliding

Mode Control of Two-Wheeled Welding Mobile Robot for Tracking Smooth Curved Welding Path, Proc of The Int’l Symposium on Mechatronics’03 (ISM’03), Hochiminh City, Vietnam, pp 1-8, September 2003

[7] T.L Chung et al., Backstepping-Based Nonlinear

Controller of a Two-Wheeled Mobile Robot Tracking Smooth Curved using USB Camera, Proc of The Int’l Symposium on Mechatronics’03

(ISM’03), Hochiminh City, Vietnam, pp 39-45,

September 2003

[8] T.H Bui et al., Nonlinear Adaptive Control for

Tracking Trajectory of a Two-Wheeled Welding Mobile Robot, Proc of The Int’l Symposium on Mechatronics’03 (ISM’03), Hochiminh City, Vietnam, pp 120-125, September 2003

[9] T.L Chung et al., Control of Two-Wheeled

Mobile Robot Tracking Complicated Curvature Wall, Proc of the Korean Society for Power System Engineering 2002 Spring Annual Meeting (KSPSE’2002), Cheju, Korea, pp 196-202, May 10-11, 2002

Lam Huu Danh was born in Viet Nam on October 30, 1979 He received the B.S degrees from Faculty of Mechanical Engineering,

Ho Chi Minh City University of Technology (HCMUT), Viet Nam

in 2001 He received the M.S degrees from Faculty of Information, Media and Electrical Engineering, Cologne University of Applied Sciences, Germany on October, 2008 He works at Saigon Port, Ho Chi Minh City, Viet Nam His research Interests are Automation and Optimization method including industrial applications

Tran Duc Hieu Le was born in Viet Nam on May 25th, 1986 She is M.S student at the Department of Mechatronics at HCMUT Her interests is mobile robot control and application

Tan Tung Phan was born in Viet nam on May 3th, 1959 He received the B.S and M.S degrees from the Faculty of Mechanical Engineering, HCMUT, Vietnam in 1982 and

1995 He received Ph.D degree from Dept of Mechanical Engineering, Pukyong Nat’l

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University, Pusan, Korea in February, 2005 He is a

senior lecturer of the Faculty of Mechanical

Engineering, HCMUT His fields of interest are Robot

Control and Welding Automation Process Control

Tan Tien Nguyen received the B.S degree in Mechanical Engineering from HCMUT, Vietnam, in 1990 and the M.S

degree and Ph.D degree in Mechanical Eng., Pukyong Nat’l University, Pusan, Korea, in August, 1998, and August, 2001, respectively Now

he is an Ass Professor at the Faculty of Mechanical

Engineering, HCMUT His interests are robust

control theory and industry automation control

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