Geometric fundamentals of robotics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer
2005
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Monographs in computer science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Rev. ed. of: Geometrical methods in robotics. c1996. Includes bibliographical references and index |
| Beschreibung: | xv, 398 p. ill. 24 cm |
| ISBN: | 0387208747 |
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| 650 | 4 | |a Geometry | |
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Datensatz im Suchindex
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| adam_text | Titel: Geometric fundamentals of robotics
Autor: Selig, J. M.
Jahr: 2005
Contents
Preface
vu
Introduction 1
1.1 Theoretical Robotics?........................ 1
1.2 Robots and Mechanisms....................... 2
1.3 Algebraic Geometry......................... 4
1.4 Differential Geometry........................ 7
Lie Groups 11
2.1 Definitions and Examples...................... 12
2.2 More Examples — Matrix Groups................. 15
2.2.1 The Orthogonal Group O(n)................ 15
2.2.2 The Special Orthogonal Group SO(n)........... 16
2.2.3 The Symplectic Group Sp(2n, R).............. 17
2.2.4 The Unitary Group U(n) .................. 18
2.2.5 The Special Unitary Group SU(n)............. 18
2.3 Homomorphisms........................... 18
2.4 Actions and Products........................ 21
2.5 The Proper Euclidean Group.................... 23
2.5.1 Isometries........................... 23
2.5.2 Chasles s Theorem...................... 25
2.5.3 Coordinate Frames...................... 27
i Contents
Subgroups 31
3.1 The Homomorphism Theorems................... 31
3.2 Quotients and Normal Subgroups.................. 34
3.3 Group Actions Again......................... 36
3.4 Matrix Normal Forms........................ 37
3.5 Subgroups of S E (3) ......................... 41
3.6 Reuleaux s Lower Pairs....................... 44
3.7 Robot Kinematics .......................... 46
Lie Algebra 51
4.1 Tangent Vectors ........................... 51
4.2 The Adjoint Representation..................... 54
4.3 Commutators............................. 57
4.4 The Exponential Mapping...................... 61
4.4.1 The Exponential of Rotation Matrices........... 63
4.4.2 The Exponential in the Standard Representation of SE(3) 66
4.4.3 The Exponential in the Adjoint Representation of S E (3) 68
4.5 Robot Jacobians and Derivatives.................. 71
4.5.1 The Jacobian of a Robot .................. 71
4.5.2 Derivatives in Lie Groups.................. 73
4.5.3 Angular Velocity....................... 75
4.5.4 The Velocity Screw...................... 76
4.6 Subalgebras, Homomorphisms and Ideals.............. 77
4.7 The Killing Form........................... 80
4.8 The Campbell-Baker-Hausdorff Formula.............. 81
A Little Kinematics 85
5.1 Inverse Kinematics for 3-R Wrists..................85
5.2 Inverse Kinematics for 3-R Robots.................89
5.2.1 Solution Procedure......................89
5.2.2 An Example .........................92
5.2.3 Singularities..........................94
5.3 Kinematics of Planar Motion....................98
5.3.1 The Euler-Savaray Equation................101
5.3.2 The Inflection Circle.....................103
5.3.3 Ball s Point..........................104
5.3.4 The Cubic of Stationary Curvature.............105
5.3.5 The Burmester Points....................106
5.4 The Planar 4-Bar...........................108
Line Geometry 113
6.1 Lines in Three Dimensions......................113
6.2 Pliicker Coordinates.........................115
6.3 The Klein Quadric..........................117
6.4 The Action of the Euclidean Group.................119
Contents xiii
6.5 Ruled Surfaces............................123
6.5.1 The Regulus .........................124
6.5.2 The Cylindroid........................126
6.5.3 Curvature Axes........................128
6.6 Line Complexes............................130
6.7 Inverse Robot Jacobians.......................133
6.8 Grassmannians............................135
Representation Theory 139
7.1 Definitions............................... 139
7.2 Combining Representations..................... 142
7.3 Representations of 50(3)...................... 148
7.4 SO(3) Plethyism........................... 151
7.5 Representations of SE(3)...................... 153
7.6 The Principle of Transference.................... 158
Screw Systems 163
8.1 Generalities..............................163
8.2 2-systems...............................167
8.2.1 The Case M2.........................169
8.2.2 The Case 50(2) x K.....................169
8.2.3 The Case 50(3).......................170
8.2.4 The Case Hp « R2......................170
8.2.5 The Case S E (2).......................171
8.2.6 The Case SE{2) xl.....................171
8.2.7 The Case SE(3).......................172
8.3 3-systems...............................175
8.3.1 The Case E3.........................176
8.3.2 The Case 50(3).......................176
8.3.3 The Case S E (2).......................176
8.3.4 The Case Hp k K2......................177
8.3.5 The Case SE{2) xl.....................177
8.3.6 The Case S E (3).......................177
8.4 Identification of Screw Systems...................183
8.4.1 1-systems and 5-systems...................183
8.4.2 2-systems...........................184
8.4.3 4-systems...........................188
8.4.4 3-systems...........................189
8.5 Operations on Screw Systems....................193
Clifford Algebra 197
9.1 Geometric Algebra..........................199
9.2 Clifford Algebra for the Euclidean Group .............206
9.3 Dual Quaternions...........................210
9.4 Geometry of Ruled Surfaces.....................214
xiv Contents
10 A Little More Kinematics 221
10.1 Clifford Algebra of Points, Lines and Planes............221
10.1.1 Planes.............................221
10.1.2 Points.............................222
10.1.3 Lines..............................223
10.2 Euclidean Geometry.........................224
10.2.1 Incidence...........................224
10.2.2 Meets.............................225
10.2.3 Joins—The Shuffle product.................226
10.2.4 Perpendicularity—The Contraction.............228
10.3 Pieper s Theorem...........................231
10.3.1 Robot Kinematics......................231
10.3.2 The T3 Robot ........................234
10.3.3 The PUMA..........................238
11 The Study Quadric 241
11.1 Study s Soma.............................241
11.2 Linear Subspaces...........................245
11.2.1 Lines..............................245
11.2.2 3-planes............................246
11.2.3 Intersections of 3-planes...................248
11.2.4 Quadric Grassmannians...................250
11.3 Partial Flags and Projections....................252
11.4 Some Quadric Subspaces.......................255
11.5 Intersection Theory..........................256
11.5.1 Postures for General 6-R Robots..............262
11.5.2 Conformations of the 6-3 Stewart Platform........264
11.5.3 The Tripod Wrist.......................266
11.5.4 The 6-6 Stewart Platform..................267
12 Statics 271
12.1 Co-Screws...............................271
12.2 Forces, Torques and Wrenches....................272
12.3 Wrist Force Sensor..........................274
12.4 Wrench at the End-Effector.....................276
12.5 Gripping................................278
12.6 Friction................................283
13 Dynamics 287
13.1 Momentum and Inertia........................287
13.2 Robot Equations of Motion.....................292
13.2.1 Equations for a Single Body.................292
13.2.2 Serial Robots.........................293
13.2.3 Change in Payload......................296
13.3 Recursive Formulation........................296
Contents xv
13.4 Lagrangian Dynamics of Robots ..................300
13.4.1 Euler-Lagrange Equations.................. 301
13.4.2 Derivatives of the Generalised Inertia Matrix....... 303
13.4.3 Small Oscillations ...................... 304
13.5 Hamiltonian Dynamics of Robots.................. 306
13.6 Simplification of the Equations of Motion............. 309
13.6.1 Decoupling by Design....................309
13.6.2 Ignorable Coordinates....................312
13.6.3 Decoupling by Coordinate Transformation.........316
14 Constrained Dynamics 321
14.1 Trees and Stars............................321
14.1.1 Dynamics of Tree and Star Structures...........323
14.1.2 Link Velocities and Accelerations..............324
14.1.3 Recursive Dynamics for Trees and Stars..........325
14.2 Serial Robots with End-Effector Constraints............327
14.2.1 Holonomic Constraints....................327
14.2.2 Constrained Dynamics of a Rigid Body..........330
14.2.3 Constrained Serial Robots..................331
14.3 Constrained Trees and Stars.....................333
14.3.1 Systems of Freedom.....................333
14.3.2 Parallel Mechanisms.....................334
14.4 Dynamics of Planar 4-Bars .....................336
14.5 Biped Walking............................340
14.6 The Stewart Platform........................343
15 Differential Geometry 349
15.1 Metrics, Connections and Geodesies ................ 349
15.2 Mobility of Overconstrained Mechanisms.............. 355
15.3 Controlling Robots Along Helical Trajectories........... 360
15.4 Hybrid Control............................ 363
15.4.1 What is Hybrid Control? .................. 363
15.4.2 Constraints.......................... 364
15.4.3 Projection Operators..................... 365
15.4.4 The Second Fundamental Form............... 369
References 373
Index 383
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T20:06:54Z |
| institution | BVB |
| isbn | 0387208747 |
| language | English |
| lccn | 2004059103 |
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| spelling | Selig, J. M. Verfasser aut Geometric fundamentals of robotics J.M. Selig 2. ed. New York Springer 2005 xv, 398 p. ill. 24 cm txt rdacontent n rdamedia nc rdacarrier Monographs in computer science Rev. ed. of: Geometrical methods in robotics. c1996. Includes bibliographical references and index Géométrie Lie, Groupes de Robotique Robotics Geometry Lie groups Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Robotik (DE-588)4261462-4 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Robotik (DE-588)4261462-4 s Geometrie (DE-588)4020236-7 s DE-604 Algebraische Geometrie (DE-588)4001161-6 s Differentialgeometrie (DE-588)4012248-7 s Lie-Gruppe (DE-588)4035695-4 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013146254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Selig, J. M. Geometric fundamentals of robotics Géométrie Lie, Groupes de Robotique Robotics Geometry Lie groups Lie-Gruppe (DE-588)4035695-4 gnd Geometrie (DE-588)4020236-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd Robotik (DE-588)4261462-4 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4020236-7 (DE-588)4012248-7 (DE-588)4261462-4 (DE-588)4001161-6 |
| title | Geometric fundamentals of robotics |
| title_auth | Geometric fundamentals of robotics |
| title_exact_search | Geometric fundamentals of robotics |
| title_full | Geometric fundamentals of robotics J.M. Selig |
| title_fullStr | Geometric fundamentals of robotics J.M. Selig |
| title_full_unstemmed | Geometric fundamentals of robotics J.M. Selig |
| title_short | Geometric fundamentals of robotics |
| title_sort | geometric fundamentals of robotics |
| topic | Géométrie Lie, Groupes de Robotique Robotics Geometry Lie groups Lie-Gruppe (DE-588)4035695-4 gnd Geometrie (DE-588)4020236-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd Robotik (DE-588)4261462-4 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Géométrie Lie, Groupes de Robotique Robotics Geometry Lie groups Lie-Gruppe Geometrie Differentialgeometrie Robotik Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013146254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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