連豊力臺灣大學：電機工程學研究所林書賢Lin, Shu-HsienShu-HsienLin2007-11-262018-07-062007-11-262018-07-062004http://ntur.lib.ntu.edu.tw//handle/246246/53274本論文針對平面式載具提出一套連續軌跡產生法則。開始時提出了三種軌跡產生的方法。首先分析平面式載具在直線軌跡下的行為，然而在此情況下載具必須要在起始點和終點有原地自轉的動作，因此我們再規劃出單純由直線和弧形的段落組成的弧-直線軌跡。然而在此軌跡中，直線與弧形的接續處會產生曲率不連續點。最後我們以B-spline 曲線演算法提供平面式載具更具平滑性的軌跡產生法則。根據上述三種法則設計參考軌跡後，再參考文獻上前人提出的軌跡追蹤的控制器，使用一Lyapunov函數分析其穩定度。在討論直線及直線和弧形區段組成的軌跡當中，我們想找出具有連續曲率性質的軌跡。故我們使用B-spline曲線演算法取代由直線和弧型區段組成的弧-直線軌跡。首先根據環境提供的資訊做前端處理後得到控制點，組成B-spline 曲線軌跡。然後對B-spline曲線微分得到曲線上的速度和角速度資訊，根據此速度和角速度我們便可得到曲線上的曲率時間函數。接下來的問題便是據此軌跡做行進的動作。 本論文中，首先簡述自動載具的一些應用與我們要解決的問題針對軌跡，其次則介紹軌跡產生的方法和設計平面式載具的控制器。我們也做了演算法上的模擬結果以使用Pioneer 3做軌跡追蹤的實驗。比較這些演算法的性能後，提出結論和未來工作方向。This thesis presents continuous trajectory generation methods for a planar vehicle. Three trajectory generation methods are proposed. First, a line trajectory directly for the planar vehicle is studied. Second, because the vehicle must rotate at the start and target points for the line trajectory generation methods, a trajectory composed of line and arc segments for the vehicle is then planned. But such “arc-line” paths have discontinuities at the line-arc-line transition points. The curvature of the path is discontinuous at these points. Finally, a smoother trajectory generation method based on the B-spline algorithm for a planar vehicle is proposed. After designing the reference trajectory, a tracking control rule for vehicles is developed. Stability of the rule is proved through the use of a Lyapunov function. We use the B-spline algorithm to replace the arc-line trajectory. First, designing a continuous trajectory based on the environment information, we get some control points according to the pre-handling information. Then we differentiate the B-spline curve to get the translational and rotational velocity vectors. By the translational and rotational velocity information, we can get the curvatures of the curve. The problem is then to follow the designed path. In this thesis, we introduce the applications of the Autonomous vehicles and talk about our problems first. Second we introduce the trajectory generation methods and design the controller for the planar vehicle. We also do the simulation results of the algorithms and use Pioneer 3 to do the experiments. After comparing the performances, we summarize the conclusions and future work.Contents 摘要 I ABSTRACT II CONTENTS IV LIST OF FIGURE IX LIST OF TABLE XIX CHAPTER 1 1 INTRODUCTION 1 1.1 MOTIVATION 1 1.2 LITERATURE SURVEY OF RELATED RESEARCHES 1 1.3 ORGANIZATION OF THE THESIS. 4 CHAPTER 2 6 TRAJECTORY GENERATION 6 2.1 INTRODUCTION OF THE TRAJECTORY GENERATION 6 2.2. LINE TRAJECTORY 7 2.3 ARC-LINE TRAJECTORY 12 2.3.1 Algorithm & Flow chart 12 2.3.2 Example 15 2.3.3 Arc-line expansion algorithm 17 2.4. GENERATION OF THE B-SPLINE 20 2.4.1 The B-spline Curve 20 2.4.2 B-spline basis functions 20 2.5. DESIGN OF THE B-SPLINE 28 2.5.1 Knot vectors 28 2.5.2 Design of the trajectory 31 2.5.2.1 Derivatives of B-spline basis functions 31 2.5.2.2 Derivatives of B-spline Curves 34 CHAPTER 3 37 CONTROLLER DESIGN FOR TRAJECTORY TRACKING 37 3.1. CONTROL PROBLEM STATEMENTS 37 3.1.1 Path representation and vehicle kinematics 37 3.1.2 Error Posture 38 3.1.3 Problem Formulation 40 3.2 CONTROL SCHEME AND ITS STABILITY 41 3.2.1. Stability Analysis [17: Kanayama & Kimura 1991] 41 3.2.2 Input to the vehicle 44 3.2.3. Response Analysis and Simulation 44 3.3 THE CONTROLLER APPLYING TO B-SPLINE CURVE 47 3.3.1 The translational and rotational velocities on the B-spline curve. 47 3.3.2 Kinematics model simulation 49 3.4 IMPROVE THE VELOCITY SOLUTION 53 3.4.1 Position: 54 3.4.2 Velocity: 54 3.4.3 Velocity: 55 3.4.4 Change the control points and knot vector 56 CHAPTER 4 58 EXPERIMENTAL AUTONOMOUS VEHICLE: PIONEER 3 58 4.1 INTRODUCTION OF PIONEER [21: ACTIVMEDIA ROBOTICS 2003] 58 4.1.1 Client Software 58 4.1.2 Motors and Position Encoders 60 4.2 SIMULATOR AND DEVELOPMENT ENVIRONMENT 60 4.3 EXPERIMENT ENVIRONMENT 63 4.4 EXPERIMENTAL TESTING 65 4.4.1 Line Trajectory 65 4.4.2 Arc-line Trajectory 65 4.4.3. B-spline Trajectory 68 CHAPTER 5 71 PERFORMANCE COMPARISONS OF THE THREE TRAJECTORY GENERATION METHODS 71 5.1. ALGORITHM EFFECTIVENESS 71 5.2. COMPARISON CASE: CASE 7 76 5.2.1 B-spline 76 5.2.2. Arc-line 77 5.2.3. Line trajectory 79 5.2.4 Comparison Table and Figure 80 5.3. COMPARISON: CASE 1 82 5.3.1 B-spline 82 5.3.2. Arc-line 83 5.3.3. Line trajectory 84 5.3.4 Comparison Table and Figure 85 CHAPTER 6 88 CONCLUSIONS 88 APPENDIX A 90 DETAILED ANALYSIS OF THE ARC-LINE TRAJECTORY GENERATION 90 CASE 2: 91 CASE 3: 92 CASE 5: 93 Method 1: 93 Method 2: 94 CASE 6: 95 CASE 8: 96 Case 8_1_1: 96 Case 8_1_2: 97 Case 8_1_3: 98 Case 8_2_1: 99 Case 8_2_2: 100 Case 8_2_3: 101 APPENDIX B 102 EXPERIMENTAL RESULTS OF THE ARC-LINE TRAJECTORY GENERATION 102 B.1 COMPARISON CASE: CASE 2 102 B.1.1 B-spline 102 B.1.2. Arc-line 103 B.1.3. Line trajectory 105 B.1.4 Comparison Table 106 B.2 COMPARISON CASE: CASE 3 108 B.2.1 B-spline 108 B.2.2. Arc-line 109 B.2.3. Line trajectory 110 B.2.4 Comparison Table 111 B.3 COMPARISON CASE: CASE 4 113 B.3.1 B-spline 113 B.3.2. Arc-line 114 B.3.3. Line trajectory 115 B.3.4 Comparison Table 116 B.4 COMPARISON CASE: CASE 6 118 B.4.1 B-spline 118 B.4.2. Arc-line 119 B.4.3. Line trajectory 120 B.4.4 Comparison Table 121 B.5. COMPARISON CASE: CASE 8-1-2 123 B.1.1 B-spline 123 B.5.2. Arc-line 124 B.5.3. Line trajectory 125 B.5.4 Comparison Table 126 B.6. COMPARISON CASE: CASE 8-1-3 128 B.6.1 B-spline 128 B.6.2. Arc-line 129 B.6.3. Line trajectory 130 B.6.4 Comparison Table 131 B.7. COMPARISON CASE: CASE 8-2-2 133 B.7.1 B-spline 133 B.7.2. Arc-line 134 B.7.3. Line trajectory 135 B.7.4 Comparison Table 136 B.8. COMPARISON CASE: CASE 8-2-3 138 B.8.1 B-spline 138 B.8.2. Arc-line 139 B.8.3. Line trajectory 140 B.8.4 Comparison Table 141 APPENDIX C 143 MAIN COMPONENTS OF THE PIONEER 3 143 REFERENCES 145en-US弧-直線平面式載具Lyapunov分析B-spline曲線軌跡產生Planar vehicleLyapunov analysisTrajectory generationB-splineArc-linethesis