Development of positioning and trajectory tracking controller for caterpillar vehicles with unknown environment

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Thesis for the Degree of Doctor of Philosophy

Development of Positioning and Trajectory Tracking Controller for Caterpillar Vehicles with Unknown Environment

by Van Lanh Nguyen

Department of Mechanical Design Engineering

The Graduate School

Pukyong National University

August 2020

Development of Positioning and Trajectory Tracking Controller for Caterpillar Vehicles with Unknown Environment

미지환경에서의 캐터필러차량용 위치결정과

궤도추적 제어기의 개발

by Van Lanh Nguyen

Advisor: Professor Sang Bong Kim

A thesis submitted in partial fulfillment of the requirements for

the degree of Doctor of Philosophy

In the Department of Mechanical Design Engineering,

The Graduate School, Pukyong National University

August 2020

Development of Positioning and Trajectory Tracking

Controller for Caterpillar Vehicles with Unknown Environment

A dissertation

by Van Lanh Nguyen

Approved as to styles and contents by:

(Chairman) Yeon Wook Choe

June 25th, 2020

Acknowledgments

It is a pleasure to express my gratefulness to all the helps and continuous supports from professors, colleagues, friends, and family First of all, I would like to express the most gratitude to Professor Sang Bong Kim for his valuable advice, guidance, and support since my first days studying and living in Korea His kindness, insight supports, the direction and skill of research, and strong motivation encouraged and helped me to accomplish my research and finish this dissertation scientifically I would like to wish my Professor and his family to have the long-lived health and happiness

I would like to thank the members of my thesis committee: Prof Yeon Wook Choe, Prof Gi Sik Byun, Prof Sea Jun Oh, and Prof Young Bok Kim who have provided wonderful feedback on my work and great suggestions for better contribution of my dissertation

I would like to thank Prof Hak Kyeong Kim for his great helps and advice to research and complete this dissertation I could not finish my dissertation on time without his great help and advice

I am grateful to Prof Tan Tien Nguyen, from Ho Chi Minh University of Technology for essential assistances I would like to thank all members of CIMEC Lab for giving me a comfortable and active environment to achieve my work: Dr Dae Hwan Kim, Dr Jotje Rantung, Minh Thien Tran, Sung Won Kim, Chang Kyu Kim, Sung Rak Kim, Dong Yong Kim, Chetan Chunilal Patel, and all other foreign friends

Thanks are due to all members of Vietnamese Students’ Association

in Korea, especially Dr Huy Hung Nguyen, Dr Van Tu Duong, Dr Manh Son Tran, Dr Phuc Thinh Doan, Dr Thanh Luan Bui, Thanh An

Do, Duc Quan Tran, Van Trong Nguyen for their vigorous support

Finally, I would like to thank to my mother, my wife, my brother,

my sister, and all my close relatives for their love, endless encouragements for me not only in the dissertation time but also in the whole of my life

Pukyong National University, Busan, Korea

June 25th, 2020

Nguyen Van Lanh

Contents

Acknowledgments i

Contents iii

Abstract vii

국문 요약서 x

List of Figures xiii

List of Tables xvii

Abbreviation xix

Nomenclatures xx

Chapter 1: Introduction 1

1.1 Background and Motivation 1

1.1.1 SLAM algorithm based on EKF 8

1.1.2 Model reference adaptive control 9

1.1.3 MIMO robust servo control 10

1.2 Problem statements 12

1.3 Objective and researching method 13

1.4 Outline of the dissertation and summary of contributions 16

Chapter 2: System Description and Modeling 21

2.1 Introduction 21

2.2 Mechanical design 21

2.2.1 Top cover 21

2.2.2 Body frame 22

2.2.3 Wheel system 23

2.2.4 Connector 26

2.3 Electrical design 26

2.3.1 Controller 29

2.3.2 Sensors 31

2.3.3 Actuator 38

2.3.4 Power supply and emergency button 44

2.4 System modeling 46

2.4.1 Kinematic modeling 46

2.4.2 Dynamic modeling 53

Chapter 3: Positioning System Based on SLAM Algorithm Using Lidar Sensor 57

3.1 Introduction 57

3.2 Concept of a SLAM 57

3.3 Landmark detection algorithm using Lidar sensor 59

3.4 Positioning algorithm using encoders 63

3.5 Extended Kalman Filter 66

3.5.1 EKF prediction Step 68

3.5.2 EKF update Step 72

3.6 Summary 78

Chapter 4: Trajectory Tracking Controller Design Using a Backstepping Control Method 80

4.1 Introduction 80

4.2 Tracking controller design 80

4.3 Simulation and experimental results 85

4.3.1 Parameters of the tracking controller 85

4.3.2 Estimation global trajectory tracking results 88

4.3.3 Estimation global tracking error results 92

4.3.4 Estimation local tracking error results 95

4.4 Summary 98

Chapter 5: Trajectory Tracking Controller Design Using a Backstepping-based Model Reference Adaptive Control 101

5.1 Introduction 101

5.2 A model reference adaptive controller design 102

5.2.1 Dynamic model 102

5.2.2 Tracking controller design 103

5.3 Simulation and experimental results 109

5.3.1 Parameters of the CV and controller 110

5.3.2 Global trajectory tracking results 111

5.3.3 Global posture tracking error results 114

5.3.4 Local posture tracking error results 116

5.4 Summary 123

Chapter 6: A MIMO Robust Servo Controller Design Using a Linear Shift-Invariant Differential Operator 126

6.1 Introduction 126

6.2 Linear shift-invariant differential operator 127

6.2.1 Linear shift-invariant differential operator concept 127

6.2.2 Internal model principle based on LSID operator 134

6.3 MIMO robust servo controller 138

6.4 Simulation and experimental results 147

6.4.1 Parameters of MIMO robust servo controller 148

6.4.2 Simulation results 152

6.4.3 Experimental results 158

6.5 Standard deviation of tracking errors 168

6.6 Summary 170

Chapter 7: Conclusions and Future Works 174

7.1 Conclusions 174

7.2 Future works 183

References 184

Publication and Conference 196

Appendix A The proof of Eqs (3.33), (3.49)  (3.50), and (3.58)  (3.59) 200

Appendix B The proof of Eq (4.7) and eˆv 0as t   208

Appendix C The proof of Eqs (5.13) and (5.18) (5.20) 212

Appendix D The proof of theorem 1 216

Development of Positioning and Trajectory Tracking Controller for Caterpillar

Vehicles with Unknown Environment

Nguyen Van Lanh

Department of Mechanical Design Engineering, The Graduate School, Pukyong National University

Secondly, to make the CV track desired trajectory, a positioning system design is needed In this dissertation, the positioning system for CV based on a simultaneous localization and mapping (SLAM) method using a Lidar sensor is suggested The encoders are used for detecting the motion state of CV In a slippery and unknown environment, the positioning method using encoder generates big errors Therefore,

an Extended Kalman Filter (EKF) is used to estimate the best position of the CV by combining the positioning result of the encoders and landmark positions obtained from the Lidar sensor The EKF consists of two steps such as prediction and update Thirdly, to track a desired sharp trajectory, a trajectory tracking controller using a backstepping control method is introduced This trajectory tracking controller based

on the kinematic modeling is designed such that the estimation global and local

tracking error vectors go to zero And then, by choosing a suitable Lyapunov function candidate and using a backstepping method, system stability is guaranteed and a control law is obtained To implement this tracking controller, the hardware consists

of a computer as the main controller, encoder sensors, compass sensor, and lidar sensor, etc Finally, to evaluate the trajectory tracking performance of the proposed controller, the simulation and experimental results are shown

Fourthly, a backstepping-based model reference adaptive controller (MRAC) for trajectory tracking of the CV by combining a kinematic controller using a backstepping method and a dynamic controller using an MRAC is proposed In this case, a dynamic modeling of the CV with some uncertain parameters is presented The trajectory tracking controller based on MRAC is utilized to estimate these uncertain parameters To design this controller, the followings are done Firstly, a kinematic controller is designed such that global and local tracking errors converge to zero Secondly, the dynamic controller based on the MRAC method is designed such that CV’s output velocities converge to velocity control inputs Thirdly, by choosing a suitable Lyapunov function candidate and using a backstepping method, system stability is proven, control laws and update laws are obtained Finally, to verify the effectiveness of the proposed MRAC method, the simulation and experimental results are shown

Finally, to guarantee the CV system to be strong robustness against external disturbances, a MIMO robust servo controller using a linear shift-invariant differential (LSID) operator is proposed To do this task, the followings are done Firstly, by using

an estimation posture vector obtained from EKF and a reference input signal, an estimation output tracking error vector is obtained Secondly, by operating the LSID operator to a system model and the estimation output tracking error vector, a new extended system and a new estimation control law are obtained The controllability of the new extended system is checked Thirdly, a MIMO robust servo controller is designed by using the pole assignment approach Fourthly, by applying the inverse LSID operator, a servo compensator and control law for the given MIMO system are obtained Finally, the simulation and experimental results are shown to verify the tracking performance of the proposed MIMO robust servo controller against the external disturbance These simulation and experimental results of the proposed MIMO robust servo controller are compared to those of the backstepping controller and the backstepping-based MRAC In addition, their standard deviations of global

tracking errors are presented for evaluating the tracking performance of the proposed MIMO robust servo controller, the backstepping controller, and the backstepping- based MRAC

Keywords: Caterpillar Vehicle, Extended Kalman filter, linear shift-invariant

differential operator, MIMO, model reference adaptive control, robust servo controller, simultaneous localization and mapping

미지환경에서의 캐터필러차량용 위치결정과

궤도추적제어기의 개발

뉴엔 반 란 부경대학교 대학원 기계설계학과

국문 요약서

캐터필러차량(CV)시스템들의 응용은 최근 수십년동안 다양한 분야에서 증가되어 오고 있다 이러한 캐터필러 차량시스템들은 작업자들이 들어갈 수 없는 불안전하고 위험한 장소에서 다양한 작업을 수행할 수 있다 그러므로, 실제 응용을

위한 캐터필러차량의 연구가 깊게 필요하게 된다 특히, 캐터필러 차량을 미지환경에서 자동적으로 움직이게 하는 것은 필요하고 중요한 업무들 중에 하나이다 이러한 문제를 해결하기 위해, 본 연구는 미지환경에서의 캐터필러차량시스템용 위치결정과 궤도추적 제어기의 개발결과들을 제시한다 이러한 일을 수행하기 위해, 다음과 같은 것들이 본 연구에서 수행된다

첫째, 캐터필러차량시스템에 대한 시스템 서술과 수학적 모델링이 제시된다 캐터필러차량시스템은 기계 설계와 전기 설계로 구성되어 있다 시스템 모델링은 운동학적 모델링과 동력학적 모델링으로 구성된다

둘째, 캐터필러차량이 원하는 궤도를 추적하게 하기 위해, 위치결정시스템 설계가 요구된다 본 연구에서는 라이더(Lider) 센서를 사용한 SLAM(동시위치결정 및 매핑)법에 기반을 둔 캐터필러차량용 위치결정시스템이 제안된다 엔코더들은 캐터필러차량의 운동상태를 탐지하기 위해 사용된다 미끄럽고 미지의 환경에서, 엔코더들을 사용한 위치결정은 큰 오차를 발생시킨다 따라서, 확장칼만필터(EFK)는 엔코드의 위치결정과 라이더센서로부터 얻어진 랜드마크 위치들을 결합함으로써 최선의 위치를 추정하기 위해 사용된다 EFK 는 예측(prediction)과 갱신(update)의 두 개의 스텝들로 구성된다

셋째, 캐터필러차량이 원하는 궤도를 추적하기 위해, 백스텝핑을 사용한 궤도추적제어기가 소개된다 운동학적 모델링에 기반을 둔 이러한 궤도추적제어기는 추정 전역 및 지역 추적오차벡터가 영으로 가게하기 위해

설계된다 그리고 나서, 적당한 리아푸노프 함수 후보를 선정 및 백스텝핑을 사용함으로써 시스템 안정성이 보증되며 제어칙이 얻어진다 이 추적제어기를 구현하기 위해, 하드웨어는 주제어기로서의 컴퓨터, 엔코더 센서, 라이더센서 등으로 구성된다 마지막으로, 제안된 제어기의 추적성능을 평가하기 위해, 시뮬레이션과 실험결과들이 제시된다

넷째, 캐터필러차량용 백스텝핑법을 사용한 운동학적 제어기와 모델기준 적응제어법((MRAC))을 사용한 동력학적 제어기를 결합함으로써 캐터필러차량이 원하는 궤도추적을 위하여 백스텝핑에 기반을 둔 모델기준 적응제어기가 제안된다 이러한 경우에 어떤 불확실한 매개변수들을 가진 캐터필러차량의 동력학적 모델링이 제시된다 그래서, 모델기준 적응제어법에 기반을 둔 궤도추적제어기가 이러한 불확실한 매개변수들을 추정하기 위해 사용된다 이러한 제어기를 설계하기 위해, 다음과 같은 작업들이 수행된다 첫째, 운동학적 제어기는 전역 및

지역 추적오차들이 영으로 수렴하도록 설계된다 둘째, 모델기준 적응제어법에 기반을 둔 동력학적 제어기는 캐터필러차량의 출력 속도들을 속도제어입력들로 수렴하도록 설계된다 셋째, 적절한 리아푸노프함수후보를 선정 및 백스텝핑을 사용함으로써 함으로써 시스템안정이 증명되고 제어칙과 갱신칙들이 얻어진다 마지막으로, 제안된 모델기준 적응제어법의 유효성을 검증하기 위해, 시뮬레이션과 실험결과들이 제시된다

마지막으로 캐터필러차량시스템이 외란과 목표입력에 강력한 강인성인 것을 보증하기 위해, 선형이동불변미분(LSID) 연산자를 사용한 다입력 다출력(MIMO) 강인서보제어기가 제안된다 이것을 위해 다음 것들이 수행된다 첫째, 확장칼만필터와 목표입력신호로부터 얻어진 추정위치 결과를 사용함으로써, 추정출력오차벡터가 얻어진다 둘째, LSID 연산자를 시스템모델과 추정출력오차에 적용함으로써 새로운 확장시스템과 새로운 추정제어칙이 얻어진다 새로운 확장시스템의 가제어성이 점검된다 셋째, 극배치법을 사용함으로써 MIMO 강인서보제어기가 설계된다 역 LSID 연산자를 적용함으로써, 주어진 MIMO 시스템용 서보보상기와 제어칙이 얻어진다 마지막으로 시뮬레이션과 실험결과들이 제안된 MIMO 강인서보제어기의 적절한 추적성능을 검증하기 위해 제시된다 넷째, 제안된 MIMO 강인서보제어기의 시뮬레이션과 실험결과들이 백스텝핑제어기의 시뮬레이션과 실험결과들, 백스텝핑에 기반을 둔

모델기준적응제어법의 시뮬레이션과 실험결과들과 비교된다 또한, 제안된 MIMO

강인 서보제어기, 백스텝핑제어기의 시뮬레이션과 실험결과들, 백스텝핑에 기반을 둔 모델기준적응제어법의 시뮬레이션과 실험결과들의 추적성능을 평가하기 위해, 이러한 제어기들에 대한 전역추적오차들의 표준편차들이 제시된다.

List of Figures

Fig 1.1 Mobile robot works in rough terrain environments 1

Fig 1.2 A mobile robot with a caterpillar type of wheels 2

Fig 2.1 Mechanical design of the Caterpillar Vehicle 22

Fig 2.2 Body frame of CV 23

Fig 2.3 Configuration of the wheel system 24

Fig 2.4 Configuration of a metal track (a), passive wheel (b), and driving wheel (c) 24

Fig 2.5 Structure of the bearing wheel and suspension 26

Fig 2.6 Electrical design of the CV 27

Fig 2.7 Structure of the CV 29

Fig 2.8 Mini PC CPCV5-070WR 30

Fig 2.9 Lidar sensor RPLIDAR-A2M8 32

Fig 2.10 Basic principle for distance measurement of Lidar sensor 33

Fig 2.11 Digital compass HMR300028 36

Fig 2.12 Motor driver MDC24D200D 38

Fig 2.13 Internal structure of the motor driver MDC24D200D 39

Fig 2.14 DC gearmotor with the encoder Pololu-4756 41

Fig 2.15 Hall effect encoder 42

Fig 2.16 Channel outputs A and B of Hall effect encoder 44

Fig 2.17 Structure of battery Protech AYP6800-3D 44

Fig 2.18 Emergency button 45

Fig 2.19 Coordinate frame for CV’s modeling 46

Fig 2.20 Relation of the velocity vectors  and C v  x 47

Fig 2.21 Schematic modeling of the CV 49

Fig 2.22 Relation of the velocity vectors  and  Φ 50

Fig 2 23 Kinematic modeling of the CV in discrete time 51

Fig 3.1 Concept of SLAM process 58

Fig 3.2 Concept of SLAM algorithm using EKF 59

Fig 3.3 Landmark detection 60

Fig 3.4 Position mesurement of the Lidar sensor 62

Fig 3.5 Block diagram of EKF 78

Fig 4.1 Schematic diagram of the CV 81

Fig 4.2 Configuration of the tracking controller 85

Fig 4.3 Desired sharp trajectory used in the experiment 87

Fig 4.4 Process of the experiment for the CV 88

Fig 4.5 Estimation global trajectory tracking result 89

Fig 4.6 Estimation global trajectory tracking result ˆX on X axis 90 A Fig 4.7 Estimation global trajectory tracking result ˆY on Y axis 90 A Fig 4.8 Estimation global orientation tracking result ˆ A 91

Fig 4.9 Estimation global tracking error eˆX on X axis 92

Fig 4.10 Estimation global tracking error eˆY on Y axis 93

Fig 4.11 Estimation global orientation error ˆe  94

Fig 4.12 Estimation local tracking error e on x axis 96 ˆv1 Fig 4.13 Estimation local tracking error e on y axis 96 ˆv2 Fig 4.14 Estimation local orientation tracking error e 97 ˆv3 Fig 4.15 Control input vector  98

Fig 5.1 Configuration of the MRAC tracking controller 109

Fig 5.2 Global trajectory tracking results of the CV 112

Fig 5.3 Global trajectory tracking results X A on X-axis 112

Fig 5.4 Global trajectory tracking results Y A on Y-axis 113

Fig 5.5 Global orientation tracking results  A 113

Fig 5.6 Global tracking error e of the CV on X axis 115 X Fig 5.7 Global tracking error e of the CV on Y axis 115 Y Fig 5.8 Global orientation tracking error e  of the CV 116

Fig 5.9 Loal tracking error e 1 of the CV on x axis 117

Fig 5.10 Local tracking error e 2 of the CV on y axis 118

Fig 5.11 Local orientation tracking error e 3 of the CV 118

Fig 5.12 Model error vector e m 119

Fig 5.13 Control input vector u 120

Fig 5.14 Adaptable parameters of the proposed controller ˆK 121 x Fig 5.15 Adaptable parameters of the proposed controller ˆK  122

Fig 5.16 Adaptable parameters of the proposed controller ˆK 122 h Fig 6.1 Commutative diagram 128

Fig 6.2 Block diagram of a closed-loop control system 137

Fig 6.3 Configuration of the proposed controller 147

Fig 6.4 Control law vector u 153

Fig 6.5 Estimation output ˆl at beginning 153 A Fig 6.6 Estimation output ˆ A at beginning 153

Fig 6.7 Estimation coordinate ˆX on the X-axis at beginning 154 A Fig 6.8 Estimation coordinate ˆ A Y on the Y-axis at beginning 154

Fig 6.9 Velocity vector at beginning 155

Fig 6.10 Angular velocity vector of the right and left wheels 155

Fig 6.11 Estimation output tracking error vector ˆe at beginning 156

Fig 6.12 Estimation global tracking error vector at beginning 157

Fig 6.13 Estimation servo compensator vector 157

Fig 6.14 Experimental environment of the CV 158

Fig 6.15 Experimental environment detection 159

Fig 6.16 Positions of the CV during the experiment 159

Fig 6.17 Estimation linear displacement output ˆl 160 A Fig 6.18 Estimation orientation output ˆ A 161

Fig 6.19 Estimation output tracking error eˆ1 162

Fig 6.20 Estimation output tracking error eˆ2 162

Fig 6.21 Desired trajectory tracking result of the CV 163

Fig 6.22 Estimation global coordinate ˆX on the X-axis 164 A Fig 6.23 Estimation global coordinate ˆY on the Y-axis 164 A Fig 6.24 Estimation global orientation ˆ A of the CV 165

Fig 6.25 Estimation global tracking error eˆX on the X-axis 166

Fig 6.26 Estimation global tracking error eˆY on the Y-axis 167

Fig 6.27 Estimation global orientation tracking error eˆ 167

List of Tables

Table 2.1 Specification of Mini PC CPCV5-070WR 30

Table 2.2 Specification of Lidar sensor RPLIDAR-A2M8 35

Table 2.3 Specification of the digital compass module HMR300028 37 Table 2.4 Pin configuration of the module HMR300028 37

Table 2.5 Specification of motor driver MDC24D200D 40

Table 2.6 Specification of DC gearmotor 41

Table 2.7 Wire functions of the Hall effect encoder sensor 43

Table 2.8 Parameters of Hall effect encoder sensor with 64 CPR 43

Table 2.9 Parameters of Battery Protech AYP6800-3D 45

Table 4.1 Parameters values of the CV 86

Table 4.2 Parameter values and initial values of the proposed controller 86

Table 4.3 Equations of the reference trajectory input 87

Table 5.1 Parameters values of the CV 110

Table 5.2 Parameter values of the proposed controller 110

Table 5.3 Initial values of the proposed controller 111

Table 6.1 Parameters of CV 148

Table 6.2 Matrices’ values of MIMO system 148

Table 6.3 Initial values of the CV 148

Table 6.4 Initial values of the proposed controller 149

Table 6.5 Parameter values of the proposed controller for the step reference input 149

Table 6.6 Parameter values of the proposed controller for the ramp reference input 150

Table 6 7 Parameter values of the proposed controller for the parabolic reference input 151Table 6.8 Estimation global tracking errors of the proposed method 168Table 6.9 Standard deviations of global tracking errors 169

Abbreviation

Nomenclatures

m

pulses into wheel rotation angle

motor and the driving wheel

-

L

v , v R Linear velocities of the left wheel and the

right wheel

m/s

X , Y r Reference position of CV in global

coordinate frame OXY

coordinate frame OXY

η Velocity vector of the CV -

Chapter 1: Introduction

1.1 Background and Motivation

For recent years, autonomous robots are commonly used in practice due to its potential wide applications in transportation and dangerous tasks Such mobile robots can be used in applications that include delivering components between stations in factories, delivering food and medication in hospitals, homecare mobile robots, or agricultural tasks F L Almeida et al [1] presented transportation with automatic guided vehicles in the factory A G Ozkil et al [2] presented service robots for hospitals T Chateau et al [3] presented automatic guidance for agricultural vehicles using a laser sensor Otherwise, some applications may take place in dirty, difficult, or dangerous environments as shown in Fig 1.1 And mobile robots could work in those unsafe environments

Fig 1.1 Mobile robot works in rough terrain environments

Furthermore, autonomous robots may take action instead of human beings The mobile robots are able to accomplish various tasks in dangerous places where workers cannot enter These tasks may take place in an unsafe environment, for example, nuclear waste facilities and such sites with harmful gases or high temperature of an inaccessible environment for humans Therefore, making a mobile robot move automatically in unknown environments is one of the requisite important applications To do these tasks, mobile robots with a caterpillar type of wheels are needed A mobile robot with a caterpillar type of wheels is called as a Caterpillar Vehicle (CV) system as shown

in Fig 1.2 It uses independently operated, self-propelled vehicles that are guided along the desired trajectory of users Especially, unlike the mobile robot with a conventional wheel, CV can work in rough terrain environments To make the CV move automatically, a trajectory tracking control and a positioning method are needed Besides, to guarantee safety and reliability, a robust servo control for trajectory tracking is required

Fig 1.2 A mobile robot with a caterpillar type of wheels

The CV was considered as the most important type of mobile robots for applications in all-terrain environments It has two tracked wheels

on the left and right sides of the CV’s body The tracked wheel is a special type of wheels for all-terrain conditions A large contact area of tracks with the ground provides superior advantages for the CV such as better mobility in unstructured environments The CV has good performance in moving over obstacles and adapting to rough terrain environments such as running on the grass, ditch, sands, and stairs quickly Therefore, the application of the CV systems has been increasing in different areas during recent years A lot of the work done

on the CVs has been summarized in [4] The CVs are used in a variety

of applications where terrain conditions are difficult or unpredictable: urban reconnaissance, forestry, mining, agriculture, rescue mission scenarios, fighting battles, and autonomous planetary explorations Therefore, researching for the CV in real applications is deeply needed The CVs resembles a conventional mobile robot with two driving wheels However, the kinematics on the traveling speed is very complex because the chain tracks make slippage unavoidable Besides, because the chain tracks bring a large torque loss, the dynamics on the traction force also is complicated So far, several types of researches for the CVs were reported in [5-9] Z Fan et al [5] presented the cross-coupling and adaptive control in the military robot Remotec Andros K Nagatani et

al [6] presented the slip-compensating and path-following control in the rescue robot CV-04 W Wang et al [7] presented an analysis of track-terrain interaction for a tracked mobile robot J Morales et al [8] presented a power consumption modeling of tracked mobile robots on rigid terrain B Sun et al [9] presented a design of a tracked robot with novel bio‑inspired passive legs However, their systems were simple

and not yet applied in real-world applications To improve the performance of these systems, there have been several researches [10-12] R Gonzalez et al [10] presented a localization and control of tracked mobile robots under slip conditions They used the feedback indirect Kalman Filter for the greenhouse robot Fitorobot J Jun et al [11] presented a path planning based on pose estimation for a tracked mobile robot traversing uneven terrains S Moriyama [12] presented a traction force estimator of a tracked mobile robot supported by an algorithm of “back to back text” T Hiramatsu et al [13] presented path tracking for a tracked mobile robot on rough terrain Unfortunately, the estimated slip of these researches is not accurate enough for motion control of the CV because of the slippage phenomenon and torque transmission loss occurring at the chain tracks

of the CV In addition, the effect of gravity on inclined fields of environments may generate slipping phenomena, thus making it quite difficult for the robot to achieve the required accuracy Moreover, slipping depends on soil conditions, geographical location, climate, and other environmental factors Therefore, the CV cannot be modeled in a simple and accurate way Recently, C Zong et al [14] presented an analysis of dynamic stability for a tracked mobile robot based on human-robot interaction M Asai et al [15] presented a neural network trajectory tracking of a tracked mobile robot However, their systems did not yet consider slip problems This means that it is needed to improve the robot controllers that solve complicated problems in unknown environments Therefore, in order to address these shortcomings, applying a new control method for the CV is deeply needed

To control the CVs, system modeling for the CVs is needed Several types of researches have been proposed for two-wheeled mobile robots

G Campion et al [16] presented structural properties and classification

of kinematic and dynamic models of wheeled mobile robots C C D Wit et al [17] presented robot control methods for two-wheeled mobile robots J Martinez et al [18] presented an approximating kinematics for tracked mobile robots A Moosavian et al [19] presented an exact kinematics modeling and control of a tracked mobile robot using experimental slip estimation In addition, backgrounds of kinematic and dynamic models for a nonholonomic mobile robot were presented in [22,30-32]

To track the desired trajectory, a trajectory tracking control for mobile robots is needed The trajectory tracking control problem is one

of the key techniques in mobile robot research Several types of researches for various control methods have been proposed for the trajectory tracking of mobile robots In conventional mobile robot systems, there are several types of methods that were used for controlling the mobile robot M V Gomes et al [20] proposed a PID controller for trajectory tracking of mobile robots S C Yuan et al [21] proposed another fuzzy control method for a mobile robot G Oriolo et al [22] proposed a dynamic feedback linearization control for

a wheeled mobile robot (WMR) N Hung et al [23] proposed the sliding mode controller design for mobile robots R Fierro et al [24] proposed a backstepping control method for a nonholonomic mobile robot In this control method, by choosing appropriate Lyapunov function, the system stability was guaranteed and the control law can be obtained S V Gusev et al [25] proposed an adaptive motion control for a nonholonomic vehicle T H Bui et al [26] proposed a nonlinear

controller for tracking of a wheeled welding mobile robot (WMR) However, most of the previous methods have been the slow response or were not robust due to the external disturbance as a friction and slip force Furthermore, these controllers used for a system with all known parameters In practical applications, some physical parameters that were difficult to measure or identify Therefore, it is necessary to develop a model-based controller to overcome this drawback

Recently, several neural network control algorithms have been proposed for robots W He et al [27] proposed an adaptive fuzzy neural network control for a constrained robot using impedance learning K Harikumar et al [28] proposed a neural network-based autonomous navigation for a homecare mobile robot H Gao et al [29] proposed a neural network control for a two-link flexible robotic manipulator using the assumed mode method However, it was rather complex for applying these control methods to the mobile robot as the CV system Therefore, it was not easy to find control laws

To solve the positioning and navigation problem, several types of researches have been proposed C Chen et al [33] proposed a navigation method based on inductive guidance by using electrical wire buried under the floor S Y Lee et al [34] proposed a semi-guided navigation methodology by using magnetic tapes Y S Chen et al [35] also proposed a navigation method based on a wall-following algorithm P.T Doan et al [36] proposed tracking control for robots using a camera sensor However, these navigation methods depended

on predetermined paths and these predetermined paths could not change easily

There are many different kinds of positioning technologies using wireless networks such as a global positioning system (GPS), cellular

phone tracking system, WiFi positioning system, and RFID positioning system Among these technologies, the most popular positioning system is GPS It is used in various positioning and navigation applications Y Zhang et al [37] proposed outdoor mobile robot navigation using the GPS system K Harikumar et al [38] proposed an autonomous unmanned ground vehicle (UGV) navigating based on GPS localization and known environment information from the unmanned aerial vehicle (UAV) However, the GPS does not implement well for indoor environments The signals of the GPS are easily blocked by most construction materials and hence useless for indoor positioning For indoor environments, positioning systems that rely on the existing network infrastructures such as the WiFi positioning system and Bluetooth can provide location accuracies for mobile robots [39] These networks must exist as a part of the experimental environment Otherwise, it requires expensive and time-consuming infrastructure deployment Thus, designing a cost-effective indoor positioning system has remained an open challenge so far Therefore, there have been many types of researches about positioning and navigation methods using laser sensors The navigation method based

on a laser sensor is very important for the detection of robot postures The laser sensor navigation methods were used in the indoor environment and outdoor environment H Golnabi [40] presented the role of laser sensor systems in automation and flexible manufacturing

E K Jung et al [41] presented a laser positioning method using a particle filter J M Kim et al [42] presented an improvement of the laser sensor positioning system using the unscented Kalman filter H

H Lin et al [43] presented a posture estimation method for an autonomous mobile robot using a laser scanner with at least three retro-

reflectors T L Bui et al [44] presented trajectory tracking control based on laser sensor navigation S Gatesichapakorn et al [45] presented an implementation of an autonomous mobile robot navigation using 2D Lidar and RGB-D camera P S Pratama et al [46] presented

a positioning for automated guided vehicles in a partially known environment However, these positioning methods depend on predetermined reflectors and landmarks Thus, mobile robots can work only in a known environment or partially known environment In an unknown environment, to design the positioning system, the landmarks must be extracted from the robot’s operating environment It cannot use predetermined reflectors and landmarks Therefore, positioning system design to make a mobile robot like the CV moving automatically in unknown environments is a challenging mission

From the above discussions, to make the CV moving automatically

in unknown environments, the following methods are considered

1.1.1 SLAM algorithm based on EKF

For operating mobile robots in unknown environments, the positioning system based on a simultaneous localization and mapping (SLAM) algorithm is needed SLAM is a process by which a mobile robot can build a map of an environment and at the same time use this map to deduce it's location To solve flexible positioning, the SLAM algorithm was proposed in [47-49] H Hu et al [47] proposed a navigation method based on landmarks for industrial mobile robots A Diosi et al [48] presented a laser scan matching in polar coordinates for application of the SLAM algorithm N M Kwok et al [49] proposed a data association using a cost function-based approach for bearing-only

SLAM In these papers, SLAM was applied for positioning a mobile robot within its operating environment and the robot was required to estimate its location as well as the landmark locations To solve SLAM problems, an extended Kalman filter (EKF) was the most popular candidate employed because of its efficiency and effectiveness The EKF is a variation of the standard Kalman filter to nonlinear systems

W H Durrant et al [50] presented solutions to the SLAM algorithm based on the extended Kalman filter T Bailey et al [51] presented an analysis of extended Kalman filter formulation for the SLAM algorithm C Suliman et al [52] presented position estimation for a mobile robot using the Kalman filter F Zhang et al [53] presented a SLAM algorithm for a mobile robot based on Kalman and particle filter

P S Paratama et al [46] presented a positioning method using SLAM for automated guided vehicle in a partially known environment However, the previous positioning methods were only applied to conventional mobile robots and did not yet apply to a special robot as the CV Thus, the design of the positioning system using the SLAM algorithm based on EKF for the CV’s operating in an unknown environment is deeply needed

1.1.2 Model reference adaptive control

In practical applications, in order to design a trajectory tracking controller for mobile robots, a model with all known parameters is needed However, some physical parameters are difficult to be computed or identified for constructing a system model Although some identification techniques can estimate unknown parameters of a system, but they require a high cost of typical hardware and software To solve

this problem, a control method called as model reference adaptive control (MRAC) was developed for various unknown systems E Canigur et al [56] presented model reference adaptive control for trajectory tracking of a wheeled mobile robot (WMR) with uncertain parameters in a dynamic model R Prakash et al [57] presented modeling and simulation for a fuzzy logic controller using model reference adaptive control However, they only presented simulation results Q Xu et al [58] presented model reference adaptive control with perturbation estimation for a micropositioning system U Montanaro et al [59] presented robust discrete-time MRAC with minimal controller synthesis for an electronic throttle body In these papers, the advantage of MRAC is used to control an unknown system model with its real output tracking the output of the reference model However, there are little researches applying MRAC for mobile robots

as the CVs Moreover, the above previous researches for the CV in 15] considered only the kinematic model which ignored the mechanical system dynamics and considered only the desired velocity vector as the system input, and so cannot provide good trajectory tracking performance Therefore, a control scheme that combines a kinematic controller and a dynamic controller based on MRAC proposed applying for controlling trajectory tracking of the CV is an interesting and promising approach

[5-1.1.3 MIMO robust servo control

The main advantages of the robust servo controller based on a linear shift-invariant differential (LSID) operator for a multi-input multi-output (MIMO) system are fast response and strong robustness against

external disturbances such as friction and slippage To solve the robust servo system design problem, S B Kim et al [60] introduced a new design concept for the robust servo control system by using the polynomial differential operator (PDO) P S Paratama [61] proposed

a robust servo controller design for an automated guided vehicle using

a PDO D H Kim [62] proposed a PDO application to for four-wheeled steering vehicle D H Kim et al [63-64] suggested a servo system design for speed control of AC induction motors using PDO This robust servo speed controller was able to track high order types of references but it was designed for a single input single output (SISO) system T H Nguyen [65] proposed a robust servo controller design for a mobible picking robot using a PDO T H Nguyen et al [66] proposed a servo controller design for speed control of a BLDC motors using a PDO method T H Nguyen et al [67] proposed a servo controller design for an induction conveyor system using a PDO S B Kim et al [68] developed perfectly this PDO design concept using a linear shift-invariant differential operator V L Nguyen et al [69] proposed a MIMO robust servo controller design for three-wheeled automated guided vehicles using a linear shift-invariant differential operator This controller is easy to be applied to a mobile robot system However, these methods were not applied to mobile robots with the caterpillar type of wheels Therefore, to guarantee the CV system to be strong robustness against external disturbances, a robust servo controller design for the CV under unknown environment is deeply needed

 For unknown indoor environments, the conventional navigation systems or the wireless networks such as WiFi system, GPS are not suitable due to their disadvantages To solve this problem, a flexible positioning system for the CV is designed based on EKF-SLAM algorithm using Lidar sensor

 To make the CV moving automatically, a trajectory tracking controller is required

• To design a trajectory tracking controller for CV using backstepping control method combines with a positioning system using EKF-SLAM algorithm

• Based on backstepping controller design, to design a trajectory tracking controller combining a kinematic controller using a backstepping method and a dynamic controller using an MRAC method In this case, MRAC is utilized to estimate uncertain parameters of the system modeling

• To design a MIMO robust servo controller for a desired trajectory tracking of the CV against external disturbances using linear shift -invariant differential operator

 To perform the simulation and experiment for verifying the desired trajectory tracking that the CV can move from a start point to a goal point in an unknown environment

1.3 Objective and researching method

The objective of this dissertation is to develop a positioning and trajectory tracking control for a Caterpillar Vehicle (CV) under an unknown environment The CV is a special mobile robot with caterpillar type of wheels and so it can easily move in unknown rough terrain To do this task, system modeling, positioning system design, trajectory tracking controller design, and simulation and experimental results to evaluate the proposed algorithm are performed

The objective of a positioning system for the CV is to estimate its location within an unknown environment To do this task, positioning system design using a SLAM algorithm based on EKF is developed for localizing the CV in its unknown environment The encoders are used for detecting the motion state of the CV In a slippery and unknown environment, an encoder positioning method generates big errors The EKF is used to get the best position estimation of the CV by combining the encoder positioning results and landmark positions obtained from a Lidar sensor These landmarks can be obtained from the unknown environment, for example, walls, obstacles, etc The main advantage of this method is that it does not need to use more landmarks The positioning of the CV is implemented as follows: Firstly, the position

of the landmarks is obtained using the Lidar sensor Secondly, the position of the CV is predicted using the EKF prediction step based on

encoders data Thirdly, the positions of the CV and landmarks are updated using the EKF update step based on landmarks position

To solve trajectory tracking control problem, this dissertation proposed three trajectory tracking controllers with three difference shape trajectories such as a trajectory tracking controller using backstepping control method, a trajectory tracking controller using a backstepping-based model reference adaptive control (MRAC), and a MIMO robust servo controller using a linear shift-invariant differential (LSID) operator

To design the trajectory tracking controller using a backstepping control method, the following are done Firstly, kinematic modeling of the CV is presented Secondly, estimation global and local tracking error vectors as the difference between the estimation posture vector of the CV obtained from EKF and a reference input vector with respect to the global coordinate frame and the local coordinate frame are defined Thirdly, a backstepping tracking controller based on the kinematic modeling and the estimation local tracking error vector of the CV is designed such that the estimation local tracking error vector can go to zero Fourthly, by choosing a suitable Lyapunov function candidate and using a backstepping method, system stability is guaranteed and a control law can be obtained Fifthly, this tracking controller is implemented by hardware which consists of a mini computer as the main controller, encoder sensors, compass sensor, and lidar sensor Finally, in order to evaluate the effectiveness of the proposed controller, the simulation and experimental results are shown

According to the backstepping controller design, a trajectory tracking controller combining a kinematic controller using a backstepping method and a dynamic controller using an MRAC is