Modeling and IPC control of interactive mechanical systems: a co-ordinate free approach
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2001
|
| Series: | Lecture notes in control and information sciences
266 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Delft, Univ., Diss., 1998 |
| Physical Description: | XIII, 278 S. graph. Darst. |
| ISBN: | 1852333952 |
Staff View
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Record in the Search Index
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| adam_text | Contents
1. Rigid Bodies and Motions 1
1.1 Projective geometry and Euclidean spaces 3
1.2 Rigid bodies and Observers 8
1.2.1 Numerical representation of configurations 14
1.3 Twists 15
1.3.1 Transports to the identity of the domain Lie group ... 16
1.3.2 Transports to the identity of the range Lie group 18
1.3.3 Relations between twists 20
1.3.4 Numerical representation of twists 22
1.3.5 The link with standard Lie groups 28
1.4 Wrenches 29
1.4.1 Power and Power conjugate variables 29
1.4.2 Numerical representation of Wrenches 30
1.5 The relation between Lie groups and Screw theory 30
1.5.1 Bi invariant forms on se(3) and reciprocity of twists .. 31
1.5.2 Identification of twists and wrenches 31
1.5.3 Decomposition of se(3) 32
1.5.4 Decomposition of se * (3) 36
1.5.5 The space of screw vectors 37
1.5.6 Operations on screw vectors 38
1.6 Conclusions 39
2. Kinematics of Rigid Mechanisms 41
2.1 Kinematic pairs 41
2.1.1 Kinematic pairs actuation 44
2.1.2 Position independent Kinematic pairs: lower pairs 46
2.2 Mechanisms Topology 50
2.2.1 Kinematic pairs and bond graphs 51
2.2.2 Serial linkages 54
2.2.3 Forking linkages 59
2.2.4 Closed kinematic chains 64
2.3 Conclusions 66
3. Dynamics of Rigid Mechanisms 69
3.1 Study of Dynamical systems 69
3.1.1 The behavioral approach 69
3.1.2 A step further: physics and bond graphs 71
3.2 Physical Interaction and Interconnection 72
3.2.1 Power Ports 72
3.2.2 Vector spaces and interconnections 73
3.2.3 Causality 73
3.2.4 Interconnection 74
3.3 Lagrangian Formulation 76
3.3.1 The simplest case: no potential energy and no ports .. 76
3.3.2 Adding energetic ports 78
3.3.3 Adding potential energy 80
3.4 Hamiltonian Formulation 81
3.4.1 Port Controlled Hamiltonian Systems using Poisson
structures 81
3.4.2 Port controlled Hamiltonian Systems using Dirac Struc¬
tures 84
3.5 Nodic elements 86
3.5.1 Inertial references 87
3.6 Springs 88
3.6.1 Geometrical Springs 89
3.6.2 Winding Springs 94
3.7 Inertias 95
3.7.1 Kinetic co energy and energy 95
3.7.2 The second law of dynamics 98
3.7.3 A Hamiltonian formulation of a rigid body motion: the
Lie Poisson bracket 99
3.8 Dissipation elements 102
3.8.1 Irreversibility 102
3.8.2 Algebra representation 103
3.9 Actuators and Interaction ports 103
3.10 Elements Interconnection 104
3.10.1 Kirchhoff s laws and power continuous interconnection. 106
3.11 Hamiltonian interconnection in the Poisson framework 110
3.11.1 Inertias equations 110
3.11.2 Springs equations Ill
3.11.3 Dissipative elements equations Ill
3.11.4 The interconnected system equations 112
3.12 Hamiltonian interconnection in the Dirac framework 114
3.13 Direct Lagrangian equations 118
3.13.1 Total kinetic co energy 119
3.13.2 The potential energy and the Lagrangian 120
3.13.3 The Constraints 121
1 Contents xi
3.13.4 Damping elements 122
3.13.5 The work space and the interaction with the environ¬
ment 122
3.13.6 Elimination of the constraints 123
3.14 Conclusions 123
4. Intrinsically Passive Control 125
4.1 Force versus Interactive control 126
4.2 Physical Passivity 128
4.2.1 Collocated control 129
4.2.2 Robustness and Performance 129
4.2.3 Supervision 129
4.3 Interconnection of port controlled Hamiltonian systems 130
4.4 Intrinsically Passive Feedback 134
4.4.1 Energy Shaping 135
4.4.2 Damping Injection 136
4.4.3 The resulting controller 137
4.5 A simple example 137
4.5.1 Actuator s Saturations 140
4.5.2 The multidimensional case 140
4.5.3 The Bosch Turbo SCARA 141
4.6 Considerations on Power Continuous Compensations 142
4.6.1 Transformer like compensations 143
4.6.2 Antisymmetric compensations 143
4.7 Conclusions 145
5. A Novel Impedance Grasping Strategy 147
5.1 Controllable Springs 148
5.2 Physical Controller Structure 149
5.2.1 The Virtual Object Dynamics 151
5.2.2 The Springs 151
5.2.3 Interconnection object springs 154
5.2.4 Creating Damping 154
5.3 The Controlled Hand 155
5.4 Implementation of the Control Scheme 158
5.4.1 Suitable Springs energy functions 159
5.4.2 Storing Positions 168
5.4.3 The Wrenches of the system 169
5.4.4 Simulation of the Virtual Object dynamics 171
5.4.5 Varying the length of springs 172
5.5 Taking the Robot Kinematics into account 173
5.5.1 Internal Passive Compensation 174
5.6 Grasping strategies 176
5.7 Conclusions 177
xii Contents
6. IPC in Telemanipulation 179
6.1 Geometric scattering 179
6.1.1 Dimension of the space of scattering decompositions .. 183
6.1.2 Plus product invariance 183
6.1.3 Scattering decomposition 183
6.2 Causality and sign issues 184
6.3 Line Impedance adaptation 185
6.4 Impedance Matching 186
6.4.1 An interconnection approach 189
6.5 Spatial telemanipulation 190
6.5.1 A three dimensional simulation 191
6.6 Damping injection in telemanipulation 192
6.7 Experiments 194
6.7.1 Laboratory Set Up 194
6.7.2 Case studies 195
6.8 Conclusions 199
A. Mathematical Background 203
A.I Basic concepts 203
A.2 Graph theory 205
A.3 Concepts from topology 207
A.4 Groups 207
A.5 Vector spaces 209
A.5.1 Tensors 211
A.6 Lie algebras 213
A.7 Differential geometry 214
A.7.1 Manifolds 214
A.7.2 Tangent spaces 216
A.7.3 Distributions 219
A.7.4 Mappings between manifolds 221
A.7.5 Orientation 221
A.7.6 Riemannian manifolds 222
A.7.7 Connections 222
A.7.8 Euclidean manifolds 227
A.8 Lie groups 228
A.8.1 Left and right translations 228
A.8.2 Relations Lie group and algebra 229
A.8.3 The Killing Form 230
A.8.4 Matrix Lie groups 231
B. Basics of Bond Graphs 237
B.I Physical domains 238
B.2 Power conjugate variables 238
B.3 The physical model structure and Bond Graphs 239
B.4 Energy Storage and Physical States 241
Contents xiii
B.4.1 Bond graphs representations 242
B.4.2 Mechanical domain 244
B.4.3 Electrical domain 246
B.4.4 Duality 248
B.4.5 Extra supporting states 249
B.5 Free Energy Dissipation 249
B.5.1 Electrical domain 250
B.5.2 Mechanical domain 250
B.6 Ideal Transformations and Gyrations 251
B.6.1 Ideal Transformers 251
B.6.2 Ideal Gyrators 253
B.6.3 Multi bonds 254
B.7 Ideal Sources 256
B.8 Kirchhoff s laws, junctions and the network structure 256
B.8.1 1 junctions 257
B.8.2 O junctions 259
B.8.3 Effort difference 259
B.8.4 Flow difference 260
B.9 Bond graph modeling of electrical networks 260
B.10 Bond graph modeling of mechanical systems 261
B.ll Examples 261
B.ll.l DC motor example 261
B.ll.2 Multidimensional example 265
Bibliography 267
Index 273
|
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| author | Stramigioli, Stefano |
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| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
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| indexdate | 2024-07-09T18:48:28Z |
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| isbn | 1852333952 |
| language | English |
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| physical | XIII, 278 S. graph. Darst. |
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| series | Lecture notes in control and information sciences |
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| spelling | Stramigioli, Stefano Verfasser aut Modeling and IPC control of interactive mechanical systems a co-ordinate free approach Stefano Stramigiolo London [u.a.] Springer 2001 XIII, 278 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in control and information sciences 266 Zugl.: Delft, Univ., Diss., 1998 Commande automatique - Modèles mathématiques ram Robots ram Mathematisches Modell Automatic control Mathematical models Robots Control systems Industrieroboter (DE-588)4026861-5 gnd rswk-swf Regelung (DE-588)4048971-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Industrieroboter (DE-588)4026861-5 s Hamiltonsches System (DE-588)4139943-2 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Regelung (DE-588)4048971-1 s Lecture notes in control and information sciences 266 (DE-604)BV005848579 266 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009279434&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stramigioli, Stefano Modeling and IPC control of interactive mechanical systems a co-ordinate free approach Lecture notes in control and information sciences Commande automatique - Modèles mathématiques ram Robots ram Mathematisches Modell Automatic control Mathematical models Robots Control systems Industrieroboter (DE-588)4026861-5 gnd Regelung (DE-588)4048971-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4026861-5 (DE-588)4048971-1 (DE-588)4114528-8 (DE-588)4139943-2 (DE-588)4113937-9 |
| title | Modeling and IPC control of interactive mechanical systems a co-ordinate free approach |
| title_auth | Modeling and IPC control of interactive mechanical systems a co-ordinate free approach |
| title_exact_search | Modeling and IPC control of interactive mechanical systems a co-ordinate free approach |
| title_full | Modeling and IPC control of interactive mechanical systems a co-ordinate free approach Stefano Stramigiolo |
| title_fullStr | Modeling and IPC control of interactive mechanical systems a co-ordinate free approach Stefano Stramigiolo |
| title_full_unstemmed | Modeling and IPC control of interactive mechanical systems a co-ordinate free approach Stefano Stramigiolo |
| title_short | Modeling and IPC control of interactive mechanical systems |
| title_sort | modeling and ipc control of interactive mechanical systems a co ordinate free approach |
| title_sub | a co-ordinate free approach |
| topic | Commande automatique - Modèles mathématiques ram Robots ram Mathematisches Modell Automatic control Mathematical models Robots Control systems Industrieroboter (DE-588)4026861-5 gnd Regelung (DE-588)4048971-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Commande automatique - Modèles mathématiques Robots Mathematisches Modell Automatic control Mathematical models Robots Control systems Industrieroboter Regelung Hamiltonsches System Hochschulschrift |
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