臺灣博碩士論文加值系統

本論文的研究目的是針對一以三個無間隙全方位輪進行驅動之騎球型機器人，發展線性二次調整(LQR)和倒逆步順滑模式控制(backstepping sliding-mode control)等兩控制方法，用以達成原地平衡，位置控制以及軌跡追蹤。文中詳細地描述該騎球型機器人的新型夾球機構、感測電路與方位推算法、動態解耦數學模型以及控制系統架構。在運動控制器方面，首先利用線性化模型，提出一狀態迴授控制策略，並線性二次調整法設計其控制參數，用以達成原地平衡與位置控制。為達成時變軌跡追蹤控制的目標，該機器人的非線性模型被採用，結合倒逆步與順滑模式控制法，發展一新式的合計階層式順滑模式控制。許多電腦模擬被用來檢證所提出之兩運動控制法則的可行性與有效性。實驗數據可確認該騎球型機器人系統可達到預期控制性能之原地平衡與平台運動控制目標。

This thesis presents methodologies and techniques for linear quadratic regulation (LQR) and backstepping sliding-mode motion control of a ball-riding robot driven by three omnidirectional wheels, in order to accomplish station keeping, position control and trajectory tracking. In comparison with the previous ball-riding robot, this thesis pays significant efforts on constructing a new driving mechanism, sensing and driving circuits, and establishing a dead-reckoning method and decoupling dynamic models for control purposes. Based on the linearized models of the robot, two LQR controllers are synthesized to achieve station keeping and point stabilization. To achieve time-varying trajectory tracking, the nonlinear models of the robot are employed to synthesize two backstepping sliding-mode controllers so as to achieve station keeping, point stabilization and trajectory tracking. The performance and effectiveness of two types of proposed controllers are exemplified by conducting several computer simulations on station keeping, point stabilization and trajectory tracking. Through experimental results, both proposed controllers together with the built ball-riding robot are shown capable of achieving station keeping and point stabilization.

誌 謝 辭 i
中文摘要 ii
Abstract iii
Contents iv
List of Figures vii
List of Tables xi
List of Nomenclature xii
List of Acronyms xiv
Chapter 1 Introduction 1
1.1 Introduction 1
1.2 Literature Review 5
1.3 Motivation and Objectives 6
1.4 Main Contributions 6
1.5 Thesis Organization 7
Chapter 2 Mechatronic System Design and Control Structure 8
2.1 Introduction 8
2.2 System Structure 8
2.2.1 Mechatronic Design 9
2.2.1.1. Main Components 11
2.2.1.2. Supporting Rack 14
2.2.2 Sensors 15
2.2.2.1. Dual-Axis Tilt Sensor 15
2.2.2.2. Dual-Axis Gyroscope 16
2.2.2.3. Dual-Axis Accelerometer 17
2.2.2.4. Rotary Encoder 18
2.2.3 Digital Signal Processor 19
2.3 Decoupling Nonlinear Dynamic Models 24
2.3.1 Kinematic and Dynamic Models of the Inverse Atlas Spherical Motion Platform 25
2.3.2 Dynamic Modeling of the Two-Dimensional Mobile Inverted Pendulum 29
2.3.3 Vehicle Dynamics in the Median Sagittal plane 30
2.3.4 Vehicle Dynamics in the Median Coronal plane 31
2.4 Dead-Reckoning 33
2.5 Parameters Determination 34
2.6 Control System and Architecture 35
2.7 Concluding Remarks 36
Chapter 3 LQR Motion Control 38
3.1 Introduction 38
3.2 Linearized Model in the Median Sagittal Plane 38
3.3 Linearized Model in the Median Coronal Plane 39
3.4 Station Keeping and Point Stabilization Using LQR 39
3.5 Simulations and Discussion 42
3.5.1 Station Keeping 42
3.5.2 Point-To-Point Stabilization 45
3.5.3 Straight-Line Path-Following 48
3.6 Experimental Results and Discussion 50
3.7 Concluding Remarks 55
Chapter 4 Trajectory Tracking Using Backstepping Sliding-Mode Control 56
4.1 Introduction 56
4.2 Virtual Control Design 57
4.3 Backstepping Hierarchical Aggregated Sliding Surface and Control 60
4.4 Simulations and Discussion 62
4.4.1 Point-To-Point Stabilization 62
4.4.2 Straight-Line Trajectory Tracking 65
4.4.3 Circular Trajectory Tracking 68
4.5 Experimental Results and Discussion 70
4.6 Concluding Remarks 72
Chapter 5 Conclusions and Future Work 73
5.1 Conclusions 73
5.2 Future Work 74
References 75

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