Invitation to topological robotics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Zürich
European Math. Soc.
2008
|
| Series: | Zurich lectures in advanced mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 132 S. Ill., graph. Darst. |
| ISBN: | 9783037190548 303719054X |
Staff View
MARC
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| 100 | 1 | |a Farber, Michael |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Invitation to topological robotics |c Michael Farber |
| 264 | 1 | |a Zürich |b European Math. Soc. |c 2008 | |
| 300 | |a X, 132 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Zurich lectures in advanced mathematics | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Configuration space | |
| 650 | 4 | |a Robotics |x Mathematics | |
| 650 | 4 | |a Topology | |
| 650 | 0 | 7 | |a Robotik |0 (DE-588)4261462-4 |2 gnd |9 rswk-swf |
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| 776 | 0 | 8 | |i Erscheint auch als |a Farber, Michael |t Invitation to topological robotics |n Online-Ausgabe |z 978-3-03719-554-3 |w (DE-604)BV036758548 |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016759838&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
......................................
vii
Chapter
1.
Linkages and Polygon Spaces
............... 1
1.1.
Configuration space of a linkage
................ 2
1.2.
The robot arm workspace map
................. 5
1.3.
Varieties of quadrangles:
η
= 4 ................ 6
1.4.
Short, long and median subsets
................ 9
1.5.
The robot arm distance map
.................. 11
1.6.
Poincaré
polynomials of planar polygon spaces
...... 16
1.7.
Morse theory on manifolds with involutions
........ 19
1.8.
Proof of Theorem
1.7....................... 24
1.9.
Maximum of the total
Betti
number of
M¿
......... 30
1.10.
On the conjecture of Kevin Walker
.............. 31
1.11.
Topology of random linkages
.................. 36
Chapter
2.
Euler
Characteristics of Configuration Spaces
..... 41
2.1.
The
Euler
-
Gal power series
.................. 41
2.2.
Configuration spaces of manifolds
............... 45
2.3.
Configuration spaces of graphs
................. 46
2.4.
Recurrent formula for tux(t)
.................. 49
2.5.
Cut and paste surgery
...................... 54
2.6.
Cut and paste Grothendieck ring
............... 55
2.7.
Cones and cylinders
........................ 57
2.8.
Proof of Theorem
2.3....................... 59
Chapter
3.
Knot Theory of the Robot Arm
.............. 61
3.1.
Can a robot arm be knotted?
.................. 61
3.2.
Expansive motions
........................ 64
3.3.
Infinitesimal motions
....................... 67
3.4.
Struts and equilibrium stresses
................. 68
3.5.
Maxwell
-
Cremona Theorem
................. 72
3.6.
The main argument
........................ 75
3.7.
Global motion
........................... 77
x
CONTENTS
Chapter
4.
Navigational Complexity of Configuration Spaces
. . 87
4.1.
Alotion planning algorithms
................... 87
4.2.
The concept TC(X)
........................ 89
4.3.
The notion of relative complexity
............... 99
4.4.
Navigation functions
.......................102
4.5.
TC(X), cohomology, and cohomology operations
.....106
4.6.
Simultaneous control of multiple objects
..........114
4.7.
Collision-free motion planning
.................117
4.8.
Motion planning and the immersion problem
........121
Recommendations for further reading
..................125
Bibliography
..................................127
Index
.......................................133
|
| adam_txt |
Contents
Preface
.
vii
Chapter
1.
Linkages and Polygon Spaces
. 1
1.1.
Configuration space of a linkage
. 2
1.2.
The robot arm workspace map
. 5
1.3.
Varieties of quadrangles:
η
= 4 . 6
1.4.
Short, long and median subsets
. 9
1.5.
The robot arm distance map
. 11
1.6.
Poincaré
polynomials of planar polygon spaces
. 16
1.7.
Morse theory on manifolds with involutions
. 19
1.8.
Proof of Theorem
1.7. 24
1.9.
Maximum of the total
Betti
number of
M¿
. 30
1.10.
On the conjecture of Kevin Walker
. 31
1.11.
Topology of random linkages
. 36
Chapter
2.
Euler
Characteristics of Configuration Spaces
. 41
2.1.
The
Euler
-
Gal power series
. 41
2.2.
Configuration spaces of manifolds
. 45
2.3.
Configuration spaces of graphs
. 46
2.4.
Recurrent formula for tux(t)
. 49
2.5.
Cut and paste surgery
. 54
2.6.
Cut and paste Grothendieck ring
. 55
2.7.
Cones and cylinders
. 57
2.8.
Proof of Theorem
2.3. 59
Chapter
3.
Knot Theory of the Robot Arm
. 61
3.1.
Can a robot arm be knotted?
. 61
3.2.
Expansive motions
. 64
3.3.
Infinitesimal motions
. 67
3.4.
Struts and equilibrium stresses
. 68
3.5.
Maxwell
-
Cremona Theorem
. 72
3.6.
The main argument
. 75
3.7.
Global motion
. 77
x
CONTENTS
Chapter
4.
Navigational Complexity of Configuration Spaces
. . 87
4.1.
Alotion planning algorithms
. 87
4.2.
The concept TC(X)
. 89
4.3.
The notion of relative complexity
. 99
4.4.
Navigation functions
.102
4.5.
TC(X), cohomology, and cohomology operations
.106
4.6.
Simultaneous control of multiple objects
.114
4.7.
Collision-free motion planning
.117
4.8.
Motion planning and the immersion problem
.121
Recommendations for further reading
.125
Bibliography
.127
Index
.133 |
| any_adam_object | 1 |
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| ctrlnum | (OCoLC)261176490 (DE-599)BSZ285519212 |
| dewey-full | 514 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| dewey-search | 514 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T22:10:54Z |
| indexdate | 2024-07-09T21:22:00Z |
| institution | BVB |
| isbn | 9783037190548 303719054X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016759838 |
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| physical | X, 132 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | European Math. Soc. |
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| series2 | Zurich lectures in advanced mathematics |
| spelling | Farber, Michael Verfasser aut Invitation to topological robotics Michael Farber Zürich European Math. Soc. 2008 X, 132 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Zurich lectures in advanced mathematics Mathematik Configuration space Robotics Mathematics Topology Robotik (DE-588)4261462-4 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Robotik (DE-588)4261462-4 s Topologie (DE-588)4060425-1 s DE-604 Erscheint auch als Farber, Michael Invitation to topological robotics Online-Ausgabe 978-3-03719-554-3 (DE-604)BV036758548 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016759838&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Farber, Michael Invitation to topological robotics Mathematik Configuration space Robotics Mathematics Topology Robotik (DE-588)4261462-4 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4261462-4 (DE-588)4060425-1 |
| title | Invitation to topological robotics |
| title_auth | Invitation to topological robotics |
| title_exact_search | Invitation to topological robotics |
| title_exact_search_txtP | Invitation to topological robotics |
| title_full | Invitation to topological robotics Michael Farber |
| title_fullStr | Invitation to topological robotics Michael Farber |
| title_full_unstemmed | Invitation to topological robotics Michael Farber |
| title_short | Invitation to topological robotics |
| title_sort | invitation to topological robotics |
| topic | Mathematik Configuration space Robotics Mathematics Topology Robotik (DE-588)4261462-4 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Mathematik Configuration space Robotics Mathematics Topology Robotik Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016759838&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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