本論文係針對軌跡追循議題各別探討兩種輪型機器人與其相對應的控制器之設計。首先，分別對於非完整約束與完整約束輪型機器人提出其相對應的運動模型；其中，前者的運動模型由反推控制法推導獲得，其控制器參數再由演化規劃程式加以訓練，而後者的運動模型則使用模糊邏輯控制器實現之。依據機器人運動上的限制，非完整約束輪型機器人的動態模組由拉格朗治公式加以求得。另一方面，由於完整約束輪型機器人全方位的運動特性，其動態模組則可由牛頓第二運動定律推導得之。同時，由於適應性模糊滑動控制器具備成功抑制滑動控制器之彈跳現象並有效抵抗雜訊與參數擾動之能力，因此採用它來確保兩種輪型機器人的軌跡追循能力。此外藉由李亞普諾夫穩定性理論，本論文進一步驗證了所提出方法的穩定性。在實際非完整約束輪型機器人的實驗中，證實了以所提方法控制該機器人進行軌跡追循的可行性。最後，相關的電腦模擬結果，均驗證所提出的適應性模糊滑動控制器，可有效地控制兩種輪型機器人完成軌跡追循之任務。

This dissertation presents two types of wheeled mobile robots (WMR) coupled with the controller design for trajectory tracking issue. First, we introduce both the kinematic models of the nonholonomic and holonomic WMRs; the kinematic controller for the former whose control gains are trained by evolutionary programming is derived by using the backstepping method, and the fuzzy logic controller is adopted as kinematic controller for the latter, the holonomic WMR. According to the motion constraint, the dynamic model for the nonholonomic WMR is developed by the Lagrange formula. The dynamic model of the holonomic WMR is then obtained from the Newton’s Second Law of Motion since the motion of this kind of robot is omni-directional. Next, the trajectory tracking abilities of both kinds of WMRs are ensured by utilizing the adaptive fuzzy sliding-mode controllers, which not only eliminate the chattering phenomenon in the sliding-mode control, but also cope with the system uncertainties and external disturbances. Additionally, the stabilities of the proposed methods are guaranteed by adopting the Lyapunov stability theory. The experimental results are done in the test field to demonstrate the feasibility of real nonholonomic WMR maneuvers. Finally, computer simulations on the tracking issues of these two WMRs successfully validate the effectiveness of the proposed adaptive fuzzy sliding-mode dynamic controllers.

Contents
Abstract (Chinese) I
Abstract (English) II
Acknowledgement (Chinese) III
Contents IV
List of Acronyms VII
Nomenclature VIII
List of Figures XIV
List of Tables XXII
Chapter 1 Introduction 1
1.1 Preliminary 1
1.2 Dissertation Contributions 6
1.3 Dissertation Organization 7

Chapter 2 Kinematic Controller Design for Nonholonomic and Holonomic WMRs 8
2.1 Introduction 8
2.2 Nonholonomic WMRs 9
2.2.1 Kinematic Model and Kinematic Controller Design 9
2.2.2 EP-based Kinematic Controller Design 13
2.2.3 Stability Verification 17
2.2.4 Simulation Results 18
2.3 Holonomic WMRs 20
2.3.1 Kinematic Model 20
2.3.2 Kinematic Controller Design 21
2.3.3 Simulation Results 24
2.4 Summary 26

Chapter 3 Dynamic Controller Design for Nonholonomic and
Holonomic WMRs 28
3.1 Introduction 28
3.2 Dynamic Model and Controller Design for Nonholonomic WMRs 29
3.2.1 Dynamic Model of Nonholonomic WMRs 29
3.2.2 Design of Sliding-Mode Dynamic Controller for Nonholonomic WMRs 30
3.3 Dynamic Model and Controller Design for Holonomic WMRs 33
3.3.1 Dynamic Model of Holonomic WMRs 33
3.3.2 Actuator Dynamic 36
3.3.3 Design of Sliding-Mode Dynamic Controller for Holonomic WMRs 39
3.4 Simulation Results 42
3.4.1 Round Rectangle Trajectory-Tracking for Nonholonomic WMRs 43
3.4.2 Round Rectangle Trajectory-Tracking for Holonomic WMRs 47
3.5 Summary 50
Chapter 4 Fuzzy Sliding-Mode Control Design 51
4.1 Introduction 51
4.2 The Fuzzy Sliding-Mode Control 52
4.2.1 Architecture of FLC 52
4.2.2 Fuzzy Sliding-Mode Control 54
4.3 Design of Fuzzy Sliding-Mode Controller for Nonholonomic WMRs 56
4.4 Design of Fuzzy Sliding-Mode Controller for Holonomic WMRs 59
4.5 Simulation Results 61
4.5.1 S-Typed Trajectory-Tracking for Nonholonomic WMRs 62
4.5.2 S-Typed Trajectory-Tracking for Holonomic WMRs 67
4.6 Summary 72
Chapter 5 Adaptive Control Design 73
5.1. Introduction 73
5.2 Adaptive Sliding-Mode Controller Design for Nonholonomic WMRs 74
5.2.1 The Adaptive Sliding-Mode Controller 74
5.2.2 Stability Verification of the Adaptive Sliding-Mode Controller 75
5.2.3 Experimental Results 78
5.3 Adaptive Fuzzy Sliding-Mode Controller Design for Nonholonomic WMRs 82
5.3.1 The Adaptive Fuzzy Sliding-Mode Controller 82
5.3.2 Stability Verification of the Adaptive Fuzzy Sliding-Mode Controller 83
5.3.3 Experimental Results 86
5.4 Adaptive Fuzzy Sliding-Mode Controller Design for Holonomic WMRs 88
5.4.1 The Adaptive Fuzzy Sliding-Mode Controller 88
5.4.2 EP-based Adaptive Fuzzy Sliding-Mode Controller Design 89
5.4.3 Stability Verification of the Adaptive Fuzzy Sliding-Mode Controller 91
5.5 Simulation Results 94
5.5.1 Circular Trajectory-Tracking (Constant Acceleration) 94
5.5.2 S-Typed Trajectory-Tracking (Variable Acceleration) 102
5.6 Summary 106
Chapter 6 Conclusions 107
6.1 Conclusions 107
6.2 Recommendations for Further Work 109
Bibliography 110

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