Control theory for mechanical systems is a topic that has received considerable interest in the past decade, motivated by applications such as robotics and automation, autonomous vehicles in marine, aerospace and other environments, flight control, problems in nuclear magnetic resonance, micro-electro mechanical systems (MEMS), and fluid mechanics. This book presents a unified approach for studying these systems using differential geometry. The emphasis is on understanding in a geometric way all components of a mechanical control system: configuration space, the Lagrangian, external forces, and nonholonomic constraints. This book is well-suited for use as a textbook, with numerous examples and exercises included to help consolidate the theory.
Author(s): Francesco Bullo, Andrew D. Lewis
Edition: 1
Publisher: Springer
Year: 2005
Language: English
Pages: 751
Series Preface......Page 7
Preface......Page 9
Contents......Page 17
Part I Modeling of mechanical systems......Page 25
ch5 Lie groups, systems on groups, and symmetries......Page 271
5.1 Rigid body kinematics......Page 272
5.1.1 Rigid body transformations......Page 273
5.1.2 Infinitesimal rigid transformations......Page 276
5.1.3 Rigid body transformations as exponentials of twists......Page 278
5.1.4 Coordinate systems on the group of rigid displacements......Page 280
5.2.1 Froups......Page 282
5.2.2 from one-parameter subgroups to matrix Lie algebras......Page 285
5.2.3 Lie algebras......Page 287
5.2.4 The Lie algebra of Lie group......Page 289
5.2.5 The Lie algebra of a matrix Lie group......Page 292
5.3.1 Invariant metrics and connections......Page 295
5.3.2 Simple mechanical control systems on Lie groups......Page 299
5.3.3 Planar and three-dimensional rigid bodies as systems on Lie groups......Page 301
5.4.1 Group actions and infinitesimal generaors......Page 307
5.4.2 Isometries......Page 312
5.4.3 Symmetres and conservation laws......Page 314
5.4.4 Examples of mechanical systems with symmetries......Page 317
5.5 Principlal bundles and reduction......Page 320
5.5.1 Principal fiber bundles......Page 321
5.5.2 Reduction by infinitesimal isometry......Page 322
temp......Page 326
Exercises......Page 329
Part II Analysis of mechanical control systems......Page 335
ch6 Stability......Page 337
6.1.1 Stability notions......Page 339
6.1.2 Linearization and linear stability analysis......Page 341
6.1.3 Lyapunov Stability Criteria and LaSalle Invariance Principle......Page 343
6.1.4 Elements of Morse theory......Page 349
6.1.5 Exponential convergence......Page 351
6.1.6 Quadratic functions......Page 353
6.2.1 Linearization of simple mechnical systems......Page 355
6.2.2 Linear sytsbility analysis for unforced systems......Page 358
6.2.3 Linear stability analysis for systems subject to Rayleigh dissipation......Page 360
6.2.4 Lyapunov stability analysis......Page 364
6.2.5 Global stability analysis......Page 368
6.2.6 Examples illustrating configration stability results......Page 369
6.3.1 Existence and stability definitions......Page 373
6.3.2 Lyapunov stability analysis......Page 375
6.3.3 Examples illustrating existence and stability of relative equilibria......Page 379
6.3.4 relative equilibria for simple mechanical systems on Lie groups......Page 381
Exercises......Page 384
ch7 Controllability......Page 391
7.1 An overview of controllability for contro-affine systems......Page 392
7.1.5 Some results on small-time local controllability......Page 401
当前位置......Page 406
7.2 Controllability definitions for mechanical control systems......Page 411
7.3 Controllability results for mechanical control systems......Page 413
ch8 Low-order controllability and kinematic reduction......Page 435
8.1 Vector-valued quadratic forms......Page 436
当前阅读......Page 437
