Geometric Control of Mechanical Systems Modeling, Analysis, and Design for Simple Mechanical Control Systems

ISBN-10: 0387221956
ISBN-13: 9780387221953
Edition: 2005
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Description: The primary emphasis of this book is the modeling, analysis, and control of mechanical systems. The methods and results presented can be applied to a large class of mechanical control systems, including applications in robotics, autonomous vehicle  More...

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Book details

Copyright year: 2005
Publisher: Springer
Publication date: 11/4/2004
Binding: Hardcover
Pages: 727
Size: 6.50" wide x 9.50" long x 1.50" tall
Weight: 2.596
Language: English

The primary emphasis of this book is the modeling, analysis, and control of mechanical systems. The methods and results presented can be applied to a large class of mechanical control systems, including applications in robotics, autonomous vehicle control, and multi-body systems. The book is unique in that it presents a unified, rather than an inclusive, treatment of control theory for mechanical systems. A distinctive feature of the presentation is its reliance on techniques from differential and Riemannian geometry. The book contains extensive examples and exercises, and will be suitable for a growing number of courses in this area. It begins with the detailed mathematical background, proceeding through innovative approaches to physical modeling, analysis, and design techniques. Numerous examples illustrate the proposed methods and results, while the many exercises test basic knowledge and introduce topics not covered in the main body of the text. The audience of this book consists of two groups. The first group is comprised of graduate students in engineering or mathematical sciences who wish to learn the basics of geometric mechanics, nonlinear control theory, and control theory for mechanical systems. Readers will be able to immediately begin exploring the research literature on these subjects. The second group consists of researchers in mechanics and control theory. Nonlinear control theoreticians will find explicit links between concepts in geometric mechanics and nonlinear control theory. Researchers in mechanics will find an overview of topics in control theory that have relevance to mechanics.

Modeling of mechanical systems
Introductory examples and problems
Linear and multilinear algebra
Differential geometry
Simple mechanical control systems
Lie groups, systems on groups, and symmetries
Analysis of mechanical control systems
Stability
Controllability
Low-order controllability and kinematic reduction
Perturbation analysis
A sampling of design methodologies
Linear and nonlinear potential shaping for stabilization
Stabilization and tracking for fully actuated systems
Stabilization and tracking using oscillatory controls
Motion planning for underactuated systems
Appendices
Time-dependent vector fields
Some proofs

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