Geometric control of mechanical systems: modeling, analysis, and design for simple mechanical control systems
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New York, NY [u.a.]
Springer
2010
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| Edition: | [1.ed., softcover version of original hardcover ed. 2004] |
| Series: | Texts in Applied Mathematics
49 |
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| Physical Description: | XXIV, 726 S. Ill., graph. Darst. |
| ISBN: | 9781441919687 1441919686 |
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| 015 | |a 10,N47 |2 dnb | ||
| 016 | 7 | |a 1008418498 |2 DE-101 | |
| 020 | |a 9781441919687 |c Pb. : EUR 67.36 (DE) (freier Pr.), sfr 98.00 (freier Pr.) |9 978-1-441-91968-7 | ||
| 020 | |a 1441919686 |c Pb. : EUR 67.36 (DE) (freier Pr.), sfr 98.00 (freier Pr.) |9 1-441-91968-6 | ||
| 024 | 3 | |a 9781441919687 | |
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| 100 | 1 | |a Bullo, Francesco |e Verfasser |0 (DE-588)133913414 |4 aut | |
| 245 | 1 | 0 | |a Geometric control of mechanical systems |b modeling, analysis, and design for simple mechanical control systems |c Francesco Bullo ; Andrew D. Lewis |
| 250 | |a [1.ed., softcover version of original hardcover ed. 2004] | ||
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2010 | |
| 300 | |a XXIV, 726 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Texts in Applied Mathematics |v 49 | |
| 650 | 0 | 7 | |a Mechanisches System |0 (DE-588)4132811-5 |2 gnd |9 rswk-swf |
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| 689 | 0 | 0 | |a Kontrolltheorie |0 (DE-588)4032317-1 |D s |
| 689 | 0 | 1 | |a Mechanisches System |0 (DE-588)4132811-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Lewis, Andrew D. |e Verfasser |0 (DE-588)1229535365 |4 aut | |
| 830 | 0 | |a Texts in Applied Mathematics |v 49 |w (DE-604)BV002476038 |9 49 | |
| 856 | 4 | 2 | |m X:MVB |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=3598347&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
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Contents
Series
preface
.
vii
Preface
.
,
.
bc
Part
í.
Modeling of
ходзсііашсаі
systoms
Introductory examples and problems
.,. 3
1.1
Rigid body systems
. 4
1.2
Manipulators and multi-body systems
. 6
1.3
Constrained mechanical systems
. 8
1.4
Bibliographical notes
. 10
Linear and multilinear algebra
. 15
2.1
Basic concepts and notation
. 15
2.1.1
Sets and set notation
. 16
2.1.2
Number systems and their properties
. 16
2.1.3
Maps
. 17
2.1.4
Relations
. 19
2.1.5
Sequences and permutations
. 19
2.1.6
Zom's Lemma
. 20
2.2
Vector spaces
. 21
2.2.1
Basic dermitkms and concepts
. 9
J
2.2.2
Linear
mapü
. 24
2.2.3
linear maps and matrices
. 26
2.2.4
Invariant subspaces, eigenvalues, and eigenvectors
. 29
2.2.5
Dual spaces
. 30
2.3
Inner products and bilinear maps
. . 33
2.3.1
Inner products and norms
. 33
2.3.2
Linear maps on inner product spaces
. 35
2.3.3
Bilinear maps
.,. 36
xviii Contents
2.3.4 Linear
maps associated with bilinear maps
. 39
2.4
Tensors
. 40
2.4
Л
Basic definitions
. 41
2.4.2
Representations of tensors in bases
. 42
2.4.3
Behavior of tensors under linear maps
. 43
2.5
Convexity
. 44
3
Differential geometry
. 49
3.1
The prelude to differential geometry
. 50
3.1.1
Topology
. 51
3.1.2
Calculus in
Г
. 56
3.1.3
Convergence of sequences of maps
. 59
3.2
Manifolds, maps, and submanifolds
. 60
3.2.1
Charts, atlases, and differentiable structures
. 60
3.2.2
Maps between manifolds
. 66
3.2.3
Submanifolds
. 68
3.3
Tangent bundles and more about maps
. . 70
3.3.1
The tangent bundle
. ,. . 70
3.3.2
More about maps
.,. 73
3.4
Vector bundles
. 77
3.4.1
Vector bundles
. 78
3.4.2
Tensor bundles
. 83
3.5
Vector fields
. 84
3.5.1
Vector fields as differential operators
. 85
3.5.2
Vector fields and ordinary differential equations
. 89
3.5.3
Lifts of vector fields to the tangent bundle
. 94
3.6
Tensor fields
. 95
3.6.1
Covector fields
. 96
3.6.2
General tensor fields
. 98
3.7
Distributions and codistributions
.104
3.7.1
Definitions and basic properties
.104
3.7.2
Integrable
distributions
.105
3.7.3
The Orbit Theorem for distributions
.108
3.7.4
Codistributions
.110
3.8 Affine
differential geometry
. .
Ill
3.8.1
Definitions and general concepts
. 112
3.8.2
The
Levi·
Ci vit a affine
connection
.
,
. 114
3.8.3
Coordinate formulae
. . . 116
3.8.4
The symmetric product
.,.,,., 118
3.9
Advanced topics in differential geometry
,,.,,,.,,.,.,,. 1.1.9
3.9.1
The
diffère
ntiable structure of an immersed submamfckl
120
3.9.2
Comments on smoothness, in particular analyticity
. 121
3.9.3
Properties of generalized subbundles
.123
3.9.4
An alternative notion of distribution
., . 125
3.9.5
Fiber bundles
.130
Contents xix
3.9.6
Additional topics in
affine
differential geometry
.131
Simple mechanical control systems
.141
4.1
The configuration manifold
.143
4.1.1
Interconnected mechanical systems
.143
4.1.2
Finding the configuration manifold
.146
4.1.3
Choosing coordinates
.152
4.1.4
The forward kinematic map
.155
4.1.5
The tangent bundle of the configuration manifold
.157
4.2
The kinetic energy metric
.162
4.2.1
Rigid bodies
.162
4.2.2
The kinetic energy of a single rigid body
.166
4.2.3
From kinetic energy to a Riemannian metric
.168
4.3
The Euler-Lagrange equations
.172
4.3.1
A problem in the calculus of variations
.173
4.3.2
Necessary conditions for minimization
—
the
Euler-Lagrange equations
.174
4.3.3
The Euler-Lagrange equations and changes of coordinate
176
4.3.4
The
Euler—Lagrange
equations on a Riemannian
manifold
. . . .
Г78
4.3.5
Physical interpretations
. 182
4.4
Forces
. 187
4.4.1
From rigid body forces and torques to Lagrangian forces
188
4.4.2
Definitions and examples of forces in Lagrangian
mechanics
.189
4.4.3
The Lagrange-d'Alembert Principle
.193
4.4.4
Potential forces
.195
4.4.5
Dissipative forces
.198
4.5
Nonhoionomic constraints
. 198
4.5.1
Prom rigid body constraints to a distribution on
Q
. 199
4.5.2
Definitions and basic properties
.200
4.5.3
The Euler-Lagrange equations in the presence of
constraints
.,.204
4.5.4
Simple mechanical systems with constraints
. 207
4.5.5
The constrained connection
, . . . ,. 209
4.5.6
The
Poincaré
representation of the equations of motion
Я13
4.5.7
Special features of hoionomic constraints
. 215
4.6
Simple mechanical control systems and their reprecentationc
, . 218
4.6.1
Control-
-affine système
.218
4.6.2
Classée
of cimple mechanical control
sysÎexny
,,.,., 9,9,1
4.6.3
Global representations of equations of motion
. 224
4.6.4
Local representations of equations of motion
. 225
4.6.5
Linear mechanical control systems
. 227
4.6.6
Alternative formulations
.229
xx Contents
5
Lie groups, systems on groups, and symmetries
.247
5.1
Rigid body kinematics
.248
5.1.1
Rigid body transformations
.249
5.1.2
Infinitesimal rigid body transformations
.252
5.1.3
Rigid body transformations as exponentials of twists
. . . 254
5.1.4
Coordinate systems on the group of rigid displacements
255
5.2
Lie groups and Lie algebras
.258
5.2.1
Groups
.258
5.2.2
From one-parameter subgroups to matrix Lie algebras
. 261
5.2.3
Lie algebras
.263
5.2.4
The Lie algebra of a Lie group
.265
5.2.5
The Lie algebra of a matrix Lie group
.268
5.3
Metrics, connections, and systems on Lie groups
. . 271
5.3.1
Invariant metrics and connections
.271
5.3.2
Simple mechanical control systems on Lie groups
.275
5.3.3
Planar and three-dimensional rigid bodies as systems
on Lie groups
.277
5.4
Group actions,
isometri
es,
and symmetries
.283
5.4.1
Group actions and infinitesimal generators
.283
5.4.2
Isometries
. 288
5.4.3
Symmetries and conservation laws
.290
5.4.4
Examples of mechanical systems with symmetries
.293
5.5
Principal bundles and reduction
.296
5.5.1
Principal fiber bundles
.297
5.5.2
Reduction by an. infinitesimal isometry
. 298
Part II Analysis of mechanical control systems
6
Stability
.313
6.1
An overview of stability theory for dynamical systems
.315
6.1.1
Stability notions
.315
6.1.2
Linearization and linear stability analysis
.317
6.1.3
Lyapunov Stability Criteria and LaSalle
Invariance
Principle
. 319
6.1.4
Elements of Morse theory
.,. . . . 325
6.
Lő
Exponential convergence
.,. 327
6.1.6
Quadratic functions
. 329
6.2
Stability analysis for equilibrium configurations of mechanical
systems
. 331
6.2.1
Linearization of simple mechanical systems
.,331
6.2.2
Linear stability analysis for unforced systems
. 334
6.2.3
Linear stability analysis for systems subject to
Rayleigh dissipation
.336
6.2.4
Lyapunov stability analysis
.340
Contents xxi
6.2.5 Global
stability analysis
.344
6.2.6
Examples illustrating configuration stability results
. 345
6.3
Relative equilibria and their stability
. . .349
6.3.1
Existence and stability definitions
.349
6.3.2
Lyapunov stability analysis
.351
6.3.3
Examples illustrating existence and stability of
relative equilibria
.355
6.3.4
Relative equilibria for simple mechanical systems on
Lie groups
.357
7
Controllability
.367
7.1
An overview of controllability for control-afrme systems
.368
7.1.1
Reachable sets
.369
7.1.2
Notions of controllability
.,.371
7.1.3
The Sussmann and Jurdjevic theory of attainability.
. . . 372
7.1.4
From attainability to accessibility
.374
7.1.5
Some results on small-time local controllability
. 377
7.2
Controllability definitions for mechanical control systems
. 387
7.3
Controllability results for mechanical control
système
., . 389
7.3.1
Linearization results
. 390
7.3.2
Accessibility of
affine
connection control systems
. 392
7.3.3
Controllability of
affine
connection control syutemo
. 394
7.4
Examples illustrating controllability results
. 398
7.4.1
Robotic leg
.398
7.4.2
Planar body with variable-direction thruster
. 400
7.4.3
Rolling disk
.402
8
Low-order controllability and kinematic reduction
.411
8.1
Vector-valued quadratic forms
.412
8.1.1
Basic definitions and properties
.412
8.1.2
Vector-valued quadratic forms and
affine
connection
control systems
.414
8.2
Low-order controllability results
.415
8.2.1
Constructions concerning vanishing input vector fields
. 416
8.2.2
First-order controllability results
.417
8.2.3
Examples and discussion
. 4.20
8.3
Reductions of
affine
connection control systems.
. 422
8.3.1
inputs for dynamic and kinematic
cysterno
. 422
8.3.2
Kinematic reductions
. 424
8.3.3
Maximally reducible systems
.,,.,.,.,,,,.,,., 429
8.4
The relationship between controllability and kinematic
controllability
. 432
8.4.1
Implications
. 433
8.4.2
Counterexamples
.,. . 434
xxii Contents
9
Perturbation
analysis
.441
9.1
An overview of averaging theory for oscillatory control systems
442
9.1.1
Iterated integrals and their averages
.443
9.1.2
Norms for objects defined on complex neighborhoods
. . 446
9.1.3
The variation of constants formula
.447
9.1.4
First-order averaging
.451
9.1.5
Averaging of systems subject to oscillatory inputs
.454
9.1.6
Series expansion results for averaging
. 459
9.2
Averaging of
affine
connection systems subject to oscillatory
controls
.463
9.2.1
The homogeneity properties of
affine
connection
control systems
.463
9.2.2
Flows for homogeneous vector fields
.466
9.2.3
Averaging analysis
.466
9.2.4
Simple mechanical
control
systems with potential
control forces
.471
9.3
A series expansion for a controlled trajectory from rest
. 473
Part III A sampling of design methodologies
10
Linear and nonlinear potential shaping for stabilization
. 481
10.1
An overview of stabilization
.482
10.1.1
Defining the problem
.483
10.1.2
Stabilization using linearization
.485
10.1.3
The gaps in linear stabilization theory
.487
10.1.4
Control-Lyapunov functions
.489
10.1.5
Lyapunov-based dissipative control
.490
10.2
Stabilization problems for mechanical systems
.493
10.3
Stabilization using linear potential shaping
.495
10.3.1
Linear PD control
.495
10.3.2
Stabilization using linear PD control
.497
10.3.3
Implementing linear control laws on nonlinear systems
. 501
10.3.4
Application to the two-link manipulator
.505
10.4
Stabilization using nonlinear potential shaping
.507
10.4.1
Nonlinear PD control and potential energy shaping
. . . . 507
10.4.2
Stabilization using nonlinear PD control
. 509
10.4.3
A mathematical example
., . . . . 515
10.5
Notes on stabilization of mechanical systems
. 515
10.5.1
General linear techniques
. . ,. 516
10.5.2
Feedback linearization and partial feedback linearization
öl 7
10.5.3
Backstepping
.,.517
10.5.4
Passivity-based methods
.518
10.5.5
Sliding mode control
.518
10.5.6
Total energy shaping methods
.,,.,. 519
Contents xxiii
10.5.7
When stabilization by smooth feedback is not possible
. 520
11
Stabilization and tracking for fully actuated systems
.529
11.1
Configuration stabilization for fully actuated systems
.530
11.1.1
Stabilization via configuration error functions
.530
11.1.2
PD control for a point mass in three-dimensional
Euclidean space
.532
11.1.3
PD control for the spherical pendulum
.533
11.2
Trajectory tracking for fully actuated systems
.534
11.2.1
Time-dependent feedback control and the tracking
problem
. 534
11.2.2
Tracking error functions
.535
11.2.3
Transport maps
. . 536
11.2.4
Velocity error curves
.538
11.2.5
Proportional-derivative and feedforward control
.540
11.3
Examples illustrating trajectory tracking results
.542
11.3.1
PD and feedforward control for a point mass in
three-dimensional Euclidean space
.,.,,.
54Я
11.3.2
P D
and feedforward control for the spherical pendulum
543
11.4
Stabilization, and tracking on Lie
groupe
.,.,,.,. 546
11.4.1
PD control on Lie groups
. 547
11.4.2
PD and feedforward control on Lie groups
.548
11.4.3
The attitude tracking problem for a fully actuated
rigid body fixed at a point
.,.552
12
Stabilization and tracking using oscillatory controls
.559
12.1
The design of oscillatory controls
.560
12.1.1
The averaging operator
.560
12.1.2
Inverting the averaging operator
.563
12.2
Stabilization via oscillatory controls
.567
12.2.1
Stabilization with the controllability assumption
.568
12.2.2
Stabilization without the controllability assumption.
. . . 571
12.3
Tracking via oscillatory controls
.574
13
Motion planning for underactuated systems
. 683
13.1
Motion
planning
for driftless systems
.,.,,.,.,., 584
13.1.1
Definitions
. 584
13.1.2
A brief literature survey of synthesis methods
,,.
58V'
13.2
Motion, planning for mechanical systems
. 589
13.Я.1
Definitionc
._._. . 589
13.2.2
Kmematically controllable systems
. 590
13.2.3
Maximally reducible systems
. 591
13.3
Motion planning for two simple systems
.593
13.3.1
Motion planning for the planar rigid body
. , 593
13.3.2
Motion planning for the robotic leg
. 596
xxiv
Contents
13.4
Motion planning for the snakeboard
.598
13.4.1
Modeling
.598
13.4.2
Motion planning on SE(2) for the snakeboard
.605
13.4.3
Simulations
.612
A Time-dependent vector fields
.619
A.I Measure and integration
.619
A.
1.1
General measure theory
.619
A.
1.2
Lebesgue measure
.621
A.
1.3
Lebesgue integration
. 622
A.
2
Vector fields with measurable time-dependence
.624
A.
2.1
Carathéodory
sections of vector bundles and bundle
maps
.624
A.
2,2
The time-dependent Flow Box Theorem
.625
В
Some proofs
.,. 627
B.I Proof of Theorem
4.38.,.627
B.2 Proof of Theorem
7.36.629
B.3 Proof of Lemma
8.4.,._635
B.4 Proof of Theorem
9.38._.638
B.5 Proof of Theorem
11.19.648
B.6 Proof of Theorem
11.29 .652
B.7 Proof of Proposition
12.9.654
References
.657
Symbol index
.689
Subject index
.705 |
| any_adam_object | 1 |
| author | Bullo, Francesco Lewis, Andrew D. |
| author_GND | (DE-588)133913414 (DE-588)1229535365 |
| author_facet | Bullo, Francesco Lewis, Andrew D. |
| author_role | aut aut |
| author_sort | Bullo, Francesco |
| author_variant | f b fb a d l ad adl |
| building | Verbundindex |
| bvnumber | BV042319871 |
| classification_rvk | SK 950 SK 880 |
| ctrlnum | (OCoLC)903780235 (DE-599)DNB1008418498 |
| discipline | Mathematik |
| edition | [1.ed., softcover version of original hardcover ed. 2004] |
| format | Book |
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| id | DE-604.BV042319871 |
| illustrated | Illustrated |
| indexdate | 2024-08-03T02:07:27Z |
| institution | BVB |
| isbn | 9781441919687 1441919686 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027756822 |
| oclc_num | 903780235 |
| open_access_boolean | |
| owner | DE-739 DE-898 DE-BY-UBR |
| owner_facet | DE-739 DE-898 DE-BY-UBR |
| physical | XXIV, 726 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Texts in Applied Mathematics |
| series2 | Texts in Applied Mathematics |
| spelling | Bullo, Francesco Verfasser (DE-588)133913414 aut Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems Francesco Bullo ; Andrew D. Lewis [1.ed., softcover version of original hardcover ed. 2004] New York, NY [u.a.] Springer 2010 XXIV, 726 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in Applied Mathematics 49 Mechanisches System (DE-588)4132811-5 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s Mechanisches System (DE-588)4132811-5 s DE-604 Lewis, Andrew D. Verfasser (DE-588)1229535365 aut Texts in Applied Mathematics 49 (DE-604)BV002476038 49 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3598347&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027756822&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bullo, Francesco Lewis, Andrew D. Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems Texts in Applied Mathematics Mechanisches System (DE-588)4132811-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| subject_GND | (DE-588)4132811-5 (DE-588)4032317-1 |
| title | Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems |
| title_auth | Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems |
| title_exact_search | Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems |
| title_full | Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems Francesco Bullo ; Andrew D. Lewis |
| title_fullStr | Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems Francesco Bullo ; Andrew D. Lewis |
| title_full_unstemmed | Geometric control of mechanical systems modeling, analysis, and design for simple mechanical control systems Francesco Bullo ; Andrew D. Lewis |
| title_short | Geometric control of mechanical systems |
| title_sort | geometric control of mechanical systems modeling analysis and design for simple mechanical control systems |
| title_sub | modeling, analysis, and design for simple mechanical control systems |
| topic | Mechanisches System (DE-588)4132811-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| topic_facet | Mechanisches System Kontrolltheorie |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3598347&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027756822&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
| work_keys_str_mv | AT bullofrancesco geometriccontrolofmechanicalsystemsmodelinganalysisanddesignforsimplemechanicalcontrolsystems AT lewisandrewd geometriccontrolofmechanicalsystemsmodelinganalysisanddesignforsimplemechanicalcontrolsystems |