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Doctorat Paristech T H È S E L'école Nationale Supérieure D'arts Et Métiers N°: 2009 ENAM XXXX 2016-ENAM-0003 École doctorale n° 432 : Science des Métiers de l’Ingénieur Doctorat ParisTech T H È S E pour obtenir le grade de docteur délivré par l’École Nationale Supérieure d'Arts et Métiers Spécialité “ Automatique ” présentée et soutenue publiquement par Ke WANG le 28 janvier 2016 Robot manipulator modeling for robust force control used in Friction Stir Welding (FSW) ~~~ Modélisation d’un robot manipulateur en vue de la commande robuste en force utilisé en soudage FSW Directeur de thèse : Gabriel ABBA Co-encadrement de la thèse : François LEONARD Jury M. Guillaume MOREL, Professeur, Université de Pierre et Marie Curie, Paris VI Président T M. Wolfgang SEEMANN, Professeur, Karlsruher Institute of Technology Rapporteur M. Stéphane CARO, Chargé de recherche, IRCCyN, CNRS Rapporteur H M. Gabriel ABBA, Professeur, LCFC, Université de Lorraine Examinateur M. François LEONARD, Maître de conférences, LCFC, Université de Lorraine Examinateur È M. Aurélien ROBINEAU, Ingénieur, Institut de Soudure Invité S E Arts et Métiers ParisTech - Centre de Metz Laboratoire de Conception Fabrication Commande (LCFC EA CNRS 4495) N°: 2009 ENAM XXXX CONTENTS Contents Acknowledgements 4 List of Figures 7 List of Tables 10 List of Abbreviations 12 I English Version 15 1 General Introduction and Literature Review 17 1.1 Research Background and Motivations . 17 1.2 Literature Review on Industrial Robot Manipulators . 18 1.2.1 History of Industrial Robot Manipulators . 18 1.2.2 Current Developments of Industrial Robots . 21 1.3 Literature Review on Modeling of Flexible Joint Robot Manipulators 23 1.4 Literature Review on Control of Flexible Joint Robots . 24 1.4.1 Singular Perturbation and Integral Manifold . 24 1.4.2 Feedback Linearization . 25 1.4.3 Cascaded System and Integral Backstepping . 26 1.4.4 PD Control . 28 1.4.5 Other Control Methods . 28 1.5 Dissertation Outline . 29 2 Modeling of Flexible Joint Robot Manipulators 31 2.1 Introduction . 31 2.2 Spatial Descriptions and Coordinate Transformations . 31 2.2.1 Descriptions of Positions, Orientations and Frames . 31 2.2.2 Homogeneous Transformations . 33 2.2.3 X-Y-Z fixed angles . 34 2.3 Robot Kinematics . 35 2.3.1 Modified Denavit-Hartenberg Convention . 35 2.3.2 Forward Kinematics: Direct Geometric Model . 36 2.3.3 Inverse Kinematics: Inverse Geometric Model . 39 2.3.4 Forward Instantaneous Kinematics: Direct Kinematic Model . 43 2.3.5 Inverse Instantaneous Kinematics: Inverse Kinematic Model . 44 1 CONTENTS 2.4 Robot Dynamics . 44 2.4.1 Dynamic Modeling of the Robot . 44 2.4.2 Flexibility Model . 46 2.4.3 Friction Model . 47 2.4.4 Introduction of SYMORO+ . 48 2.5 Conclusion . 48 3 Simplification of Robot Dynamic Model Using Interval Method 49 3.1 Introduction . 49 3.2 Interval Analysis . 51 3.2.1 Basic Definitions and Operations of Intervals . 51 3.2.2 Inclusion Functions and Overestimation . 52 3.3 Symbolic Robot Dynamic Model . 54 3.4 Simplification Using Interval Method . 55 3.4.1 Simplification Algorithm . 56 3.4.2 Example of Simplification of Component M44 . 58 3.4.3 Results of Simplified Model for Whole Workspace . 62 3.4.4 Error Analysis of Simplified Model for Whole Workspace . 63 3.4.5 Further Simplification and Results . 64 3.5 Case Study: Simplification on Three Different Test Trajectories . 65 3.5.1 Evaluation Indexes of Simplification . 66 3.5.2 Case I: Simplification on an Identification Trajectory . 67 3.5.3 Case II: Simplification on a Linear FSW Trajectory . 72 3.5.4 Case III: Simplification on a Circular FSW Trajectory . 77 3.5.5 Case IV: Torques Analysis in Robot Dynamic Equation . 81 3.6 Discussion on Usage of the Simplified Model . 83 3.7 Conclusion . 84 4 Dynamic Modeling and Identification of Robotic FSW Process 85 4.1 Introduction . 85 4.2 Description of the FSW Process . 87 4.3 Static Modeling of Process Forces in FSW . 89 4.4 Experimental Setup . 91 4.5 Calculation of Plunge Depth and Data Filtering . 95 4.5.1 Definition of Plunge Depth . 95 4.5.2 Three Methods for Calculating Plunge Depth . 96 4.5.3 Derivative of Plunge Depth and Data Filtering . 99 4.6 Linear Dynamic Modeling and Identification of Axial Force . 102 4.6.1 Linear Dynamic Model of Axial Force . 102 4.6.2 Least Squares Method and Error Analysis Method . 103 4.6.3 Results and Error Analysis of Identified Linear Model . 105 4.7 Nonlinear Dynamic Modeling and Identification of Axial Force . 109 4.7.1 Nonlinear Dynamic Model and Identification Method . 109 4.7.2 Results and Error Analysis of Identified Nonlinear Model . 111 4.8 Conclusion . 112 2 CONTENTS 5 Design of Robust Force Controller in Robotic FSW Process 115 5.1 Introduction . 115 5.2 Force Control of Robot Manipulator . 116 5.2.1 Basic Force Control Approaches . 116 5.2.2 Advanced Force Control Approaches . 118 5.3 Force Control Strategy and System Modeling . 118 5.3.1 Force Control Strategy . 118 5.3.2 System Modeling in Cartesian Space . 119 5.4 Parameter Identification of Displacement Model of Rigid Robot . 123 5.4.1 Identification using Transfer Function Estimation . 124 5.4.2 Identification using Process Model Estimation . 126 5.5 Design of Robust Force Controller . 128 5.5.1 Description of Entire Control System . 128 5.5.2 Specifying Desired Performance of Controller . 129 5.5.3 Designing Structure of Controller . 130 5.5.4 Calculating Parameters of the Controller . 132 5.5.5 Results of Force Controller Design . 134 5.6 Simulation of Robotic FSW Process . 135 5.6.1 KUKA Robot Controller and Trajectory Generator . 135 5.6.2 Dynamic Control of KUKA Robot . 136 5.6.3 Joint Motion Controller of the Simulator . 138 5.6.4 Establishment of Simulator for Robotic FSW Process . 141 5.6.5 Simulations and Results Analysis . 144 5.7 Vibration Analysis of Axial Force . 147 5.7.1 Identification of Experimental Axial Force Model . 147 5.7.2 Disturbance Model for Force Vibration and Simulation . 149 5.8 Conclusion . 152 6 General Conclusions and Perspectives 155 6.1 General Conclusions . 155 6.2 Perspectives . 158 II Résumé Étendu en Français 159 7 Résumé en Français: Modélisation d’un robot manipulateur en vue de la commande robuste en force utilisé en soudage FSW 161 7.1 Introduction générale et revue de littérature . 161 7.2 Modélisation des robots manipulateurs à articulations flexibles . 176 7.3 Simplification des modèles dynamiques des robots en utilisant la méth- ode d’intervalle . 182 7.4 Modélisation dynamique et identification du procédé de soudage FSW robotisé . 194 7.5 Conception d’un contrôleur robuste en force pendant le procédé de soudage FSW robotisé . 203 7.6 Conclusions générales et perspectives . 212 3 CONTENTS Bibliography 217 Appendix 229 A Supplementary Materials for Modeling of Robot 231 0 A.1 Homogeneous Transformation Matrix Tt . 231 A.2 Jacobian Matrix . 232 B Supplementary Materials for Model Simplification of Robot 235 B.1 Expression of Original Component M21 and Simplified component Ms21 of Inertia Matrix . 235 B.2 Tables for choosing appropriate kt and kp for linear and circular FSW trajectories . 236 C Supplementary Materials for Design of Force Controller 239 C.1 Detailed Computation Procedures for Single-Stage Controller . 239 D Technical Documents of the Robot 243 D.1 Technical Documents of the Robot . 243 4 Acknowledgements I would like to acknowledge everyone who has helped me with my doctoral studies in any kind of way throughout the past three years. First and foremost, I would like to express my sincere gratitude to my thesis supervisor Dr. Gabriel Abba for providing me with the excellent opportunity to achieve this work. I am really grateful for his patient and continuous guidance, tremendous support and encouragement with my scientific research and professional development. His wisdom, enthusiasm and friendly attitude have inspired me to try my best to overcome any difficulty of my work. With the help of his extensive knowledge and countless suggestions, I have learned a great deal of things both for the research and life. I am also grateful for his invaluable help in proofreading the manuscript and assisting me in preparing my doctoral dissertation defense. I am also extremely grateful to my co-supervisor Dr. François Léonard for af- fording me technical guidance, generous support, flexible and valuable supervising time as well as his admirable patience and strong confidence on me. He has always been supportive and has provided me scientific knowledge and advice, insightful dis- cussions and helpful suggestions about my research. He has always encouraged me to think more independently and to get over the various obstacles. I have also ap- preciated the timely help that he has given to me, even in his vacation time, and the immense assistance in proofreading my manuscript and preparing my thesis defense. I would also like to thank all the members of my PhD thesis committee: Dr. Guillaume Morel, Dr. Wolfgang Seemann, Dr. Stéphane Caro and Mr. Aurélien Robineau for their support, encouragement, insightful questions and constructive suggestions. It is my great honor to have such a high level jury for my PhD defense. I want to give my special thanks to Dr. Wolfgang Seemann and Dr. Stéphane Caro for spending their precious time on reviewing my manuscript carefully and giving back their insightful comments and constructive advice to improve the quality of my thesis. Dr. Guillaume Morel has chaired the doctoral thesis defense and has given me some helpful comments on my research which inspired me a lot. I am also honored to be able to invite the FSW expert Mr.
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