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研究生：	林愉珍 Lin, Yu-Chen
論文名稱：	基於六自由度移動平台之高自由度機械手臂之最佳化命令生成 Optimal Command Generation of High Degree of Freedom Manipulator Based on a 6 DOF Floating Platform
指導教授：	彭兆仲 Peng, Chao-Chung
學位類別：	碩士 Master
系所名稱：	工學院 - 航空太空工程學系 Department of Aeronautics & Astronautics
論文出版年：	2019
畢業學年度：	107
語文別：	英文
論文頁數：	91
中文關鍵詞：	機械手臂、機械手臂運動學、逆向運動學、命令生成、最佳化
外文關鍵詞：	Robotics, robot kinematics, robot inverse kinematics, command generation, optimization
相關次數：	點閱：163 下載：4
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在機械手臂的控制應用中，手臂的基底通常置於固定平台上，若機械手臂於海上或空中載具上欲執行吊掛、焊接以及組裝等工作，則受到干擾的基底易造成手臂之末端執行器(End-effector)的定位不佳，此外，近年來因應智慧自動化工廠的增加，對於高機動性機械手臂制的需求也因此增加。在實踐高自由度機械手臂的運動過程中總是會牽涉到複雜的逆向運動學(Inverse kinematics)計算，故總是無法有效率地求得關節角度解，為了解決這個問題，本研究提出一個新穎的數值疊代方式來改善機械手臂於逆向運動學的求解效率，並將末端執行器位置控制的問題闡述為最佳化問題。對於已知的目標位置點和基座姿態，可藉由數次疊代找到局部最佳解，在疊代收斂後因而產生相對應的最佳關節角度解，故藉由此方法可以獲得不同類型的機械手臂逆解(Inverse kinematics solutions)，並且不會因為不同的手臂組態而須重新討論其逆解，再者，此演算法亦可處理機械手臂因高自由度所產生的複雜幾何之求解問題。總而言之，相較於一般傳統方式，如逆向運動學，本研究所提出的演算法對於基於移動平台上的機械手臂應用提供一個更高效率、高度彈性的求解方法。

For general robot arm control applications, the base of the manipulator is equipped on a fixed platform and the difficulty of end effector (EE) position control usually results from the moving base under the complex working environment causing low mobility to manipulators. For instance, performing marine engineering, such as assembling, lifting, and welding operations need the high mobility of manipulators in order to achieve the tasks accurately. Furthermore, the demand for high mobility robot control is increasing dramatically especially for intelligent factory automation. However, realizing the high mobility moving robot arm control involves complicated kinematics computations. To deal with this issue, an innovative method is proposed to improve the efficiency of calculating the solutions to robot manipulators. The EE position control is formulated as an optimization problem and a numerical method is proposed. For a given target point and a base orientation, the sub-optimal solution can be found by each iteration and the optimal joint angle positions can be generated eventually. Therefore, it is unnecessary to take various physical configurations into consideration that users try to obtain joint angle solutions. Also, this method allows users to tackle with solutions to any number of degree of freedom (DOF). To sum up, comparing with the traditional method, such as inverse kinematics, the proposed algorithm is more efficient and is with high flexibility for a moving platform robot control applications.

CONTENTS

ABSTRACT	I
中文摘要	II
ACKNOWLEDGMENT	III
CONTENTS	IV
LIST OF TABLES	VI
LIST OF FIGURES	VII
CHAPTER 1 INTRODUCTION	1
1.1 Motivation and Objective	1
1.2 Literature Survey	2
1.3 Structure of this Dissertation and Contribution	4
CHAPTER 2 KINEMATICS MODEL AND SIMULATION SYSTEM OF MANIPULATOR	5
2.1 Description of DH Convention	5
2.2 Coordinate System of Manipulator	8
2.3 Forward Kinematics	12
2.3.1 Planar Two Links Manipulator	12
2.3.2 Planar Multiple Links Manipulator	13
2.3.3 Multiple Links Manipulator in Three Dimensions	15
2.4 Inverse Kinematics of Manipulator	16
2.4.1 Planar Two Links Manipulator	16
2.4.2 Multiple Links Manipulator	19
CHAPTER 3 OPTIMAL SOLUTION ALGORITHM	21
3.1 Optimal solution algorithm	21
3.1.1 Planar Two Links Manipulator	21
3.1.2 Multiple Links Manipulator	25
3.2 Switching error function	28
CHAPTER 4 SIMULATION RESULTS	31
4.1 Two Links Manipulator	31
4.2 Planar Multiple Links Manipulator	35
4.3 Multiple Links Manipulator in Three Dimensions	38
CHAPTER 5 APPLICATION FOR INDUSTRIAL ROBOT ARM: UR5	46
5.1 Introduction of UR5	46
5.2 Introduction of Floating Scenarios	50
5.3 Identification of Singularity	51
5.4 Introduction of Graphical User Interface (GUI)	53
5.5 Simulation of UR5	56
5.5.1 Simulation results based on the proposed algorithm	56
5.5.2 Results with Joint Angular limitation	61
5.5.3 Results with End-Effector’s Constraint	65
5.5.4 Other Results	73
CHAPTER 6 CONCLUSION AND FUTURE PROGRESS	82
APPENDIX	85
A.1	QR code of video demonstration	85
A.2	Levenberg-Marquardt Algorithm (LM)	86
A.3	Modified Jacobian matrix	88
REFERENCES	90

LIST OF TABLES
Table 1. Definition of DH parameters	6
Table 2. The process of defining DH coordinate.	8
Table 3. DH parameters of planar redundant manipulator.	11
Table 4. DH parameters of three-dimensional redundant manipulator.	12
Table 5. DH parameters of planar three links redundant manipulator.	20
Table 6. Table of parameters for 2 links manipulator.	32
Table 7. ICs for the dynamics of moving platform.	32
Table 8. ICs of joint angles for two sets of 2 links manipulator.	32
Table 9. ICs for planar manipulator in LM.	33
Table 10. The relation between number of DOF and unknowns.	36
Table 11. Sets of desired target points OE for multiple links manipulator.	36
Table 12. ICs of joint angles for planar redundant manipulator.	36
Table 13. The values of perturbation coefficient as different number of DOF is adopted.	39
Table 14. Symbol of Coordinate for multiple links manipulator in three dimensions.	39
Table 15. ICs of joint angles for redundant manipulator in three dimensions.	40
Table 16. DH parameters of UR5.	48
Table 17. Joint angle working range of UR5.	48
Table 18. ICs of joint angle for UR5 with a fixed target point under ellipse-type perturbation.	57
Table 19. ICs for UR5 in LM.	57
Table 20. ICs for UR5 with wavelike perturbation and fixed target point.	73
Table 21. ICs for UR5 with ellipse-type perturbation and moving target path.	77
Table 22. ICs for UR5 with wavelike perturbation and moving target path.	80
Table 23. List of videos regarding planar links manipulator.	85
Table 24. List of videos regarding multiple links manipulator in three dimensions.	85
Table 25. List of videos regarding UR5.	86

LIST OF FIGURES
Figure 1. Definition of DH parameters [28].	7
Figure 2.  2-DOF manipulator with a moving platform.	9
Figure 3.  Schematic diagram of moving platform.	9
Figure 4.  Schematic diagram of redundant planar manipulator.	10
Figure 5.  Schematic diagram of three-dimensional redundant manipulator.	11
Figure 6. (a) Half of the system - robot 01 (b) The schematic of geometry structure.	17
Figure 7. Partial enlarged detail of Figure 6 (a).	17
Figure 8. The attitude of manipulator in situation 2.	19
Figure 9. Flowchart of the proposed algorithm.	24
Figure 10. Flowchart of the proposed algorithm for multiple links manipulator with function switching.	30
Figure 11. Time response of joint angle resulting from IK.	34
Figure 12. Time response of joint angle resulting from LM.	34
Figure 13. Attitude of manipulator generated by the IK versus time.	35
Figure 14. Planar multiple links manipulator generated by LM algorithm versus time.	37
Figure 15. Error responses of multiple links manipulator generated by LM algorithm versus time. The error responses for 3, 6, 8, 12 links manipulator are shown in (a), (b), (c), and (d), respectively.	38
Figure 16. Screenshots of video regarding motion of five links manipulator in three dimension in Case 1-1.	41
Figure 17. Screenshots of video regarding motion of multiple links manipulator in three dimension in Case 1-1.	42
Figure 18. Screenshots of video regarding motion of five links manipulator in three dimensions in Case 1-2.	43
Figure 19. Angle and error responses of multiple links manipulator in three dimensions in Case 1-2.	43
Figure 20. Screenshots of video regarding motion of multiple links manipulator in three dimensions in Case 2.	44
Figure 21. Error responses of multiple links manipulator in three dimensions in Case 2.	45
Figure 22. Configuration and frame position of UR5.	47
Figure 23. Workspace of UR5 without EE [30].	48
Figure 24. The detail workspace of UR5 in MATLAB.	49
Figure 25. Scenarios (a) ellipse (b) wavelike motion curve.	50
Figure 26. UR5 on a boat.	53
Figure 27. Complete GUI of UR5 simulation.	54
Figure 28. Part of GUI Figure 27 (a). Main interface of simulation.	55
Figure 29. Part of GUI Figure 27 (b).	55
Figure 30. Part of GUI Figure 27 (c). The result of singularity identification and operation buttons.	56
Figure 31. Joint angle response of UR5 based on LM in Case 3-1.	58
Figure 32. Error response of UR5 based on LM in Case 3-1.	59
Figure 33. Singularity identification of UR5 based on LM in Case 3-1.	59
Figure 34. Screenshots of video regarding UR5’s motion at different moments in Case 3-1.	60
Figure 35. Flowchart of LM for UR5 with angular limitation in Case 3-2.	62
Figure 36. Joint angle response of UR5 based on LM with angular limitation in Case 3-2.	63
Figure 37. Error response of UR5 based on LM with angular limitation in Case 3-2.	64
Figure 38. Singularity identification of UR5 based on LM with angular limitation in Case 3-2.	64
Figure 39. Screenshot of video regarding UR5’s motion at different moment with orientation constraint in Case 3-3.	67
Figure 40. Joint angle and error response of UR5 based on LM with orientation constraint in Case 3-3.	68
Figure 41. Singularity identification of UR5 based on LM with orientation constraint in Case 3-3.	68
Figure 42. Joint angle response of UR5 with both constraints in Case 3-4.	70
Figure 43. Error response of UR5 with both constraints in Case 3-4.	70
Figure 44.Angular orientation error of UR5 with both constraints in Case 3-4.	71
Figure 45. Singularity identification of UR5 with both constraints in Case 3-4.	71
Figure 46. Screenshots of video regarding UR5’s motion at different moments with both constraints in Case 3-4.	72
Figure 47. Joint angle and error response of UR5 with OC in Case 4.	74
Figure 48. Angular orientation error of UR5 with OC in Case 4.	74
Figure 49. Singularity identification of UR5 with OC in Case 4.	75
Figure 50. Screenshots of video regarding UR5’s motion at different moment in Case 4.	76
Figure 51. Angle and orientation error response of UR5 in Case 5 with OC.	77
Figure 52. Error response of UR5 with OC in Case 5.	78
Figure 53. Singularity identification of UR5 with OC in Case 5.	78
Figure 54. Screenshot of video regarding UR5’s motion at a moment in Case 5.	79
Figure 55. Angle and error response of UR5 with OC in Case 6.	80
Figure 56. Angular orientation error of UR5 with OC in Case 6.	80
Figure 57. Singularity identification of UR5 with OC in Case 6.	81
Figure 58. Screenshot of video regarding UR5’s motion at a moment in Case 6.	82
Figure 59. Schematic of redundant manipulator.	83
Figure 60. Schematic of application on quadrotor.	83
Figure 61. Schematic of UR5 with the welding operation.	84
Figure 62. Simulation of Figure 13.	85
Figure 63. Complete simulation of LM.	85
Figure 64. Simulation of Figure 14(a).	85
Figure 65. Simulation of Figure 14(b).	85
Figure 66. Simulation of Figure 14(c).	85
Figure 67. Simulation of Figure 14(d).	85
Figure 68. Simulation of Case 1-1 shown in Figure 16.	85
Figure 69. Simulation of Case 1-2 shown in Figure 18.	85
Figure 70. Simulation of Case 2 shown in Figure 20 (a).	85
Figure 71. Simulation of Case 2 shown in Figure 20 (b).	85
Figure 72. Simulation of Figure 34 shown in Case 3-1.	86
Figure 73. Simulation of Case 3-2.	86
Figure 74. Simulation of Figure 39 shown in Case 3-3.	86
Figure 75. Simulation of Figure 46 shown in in Case 3-4.	86
Figure 76. Simulation of Figure 50 shown in Case 4.	86
Figure 77. Simulation of Figure 54 shown in Case 5.	86
Figure 78. Simulation of Figure 58 shown in Case 6.	86



                                    

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