Geometric Control of Mechanical Systems: Modeling, Analysis, and Design for Simple Mechanical Control Systems / Edition 1

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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.

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Editorial Reviews

From the Publisher
From the reviews:

"The book deals with the geometric theory of mathematical modeling, analysis, and control of ‘simple’ mechanical systems … . The text is written with great care and lucidity, includes many exercises, and has clearly benefited from being used in various undergraduate and graduate courses. The book will certainly become a main reference in this area … ." (A. J. van der Schaft, Mathematical Reviews, 2005h)

“Those who are interested in robotic mechanical systems will almost certainly enjoy reading this book. … intended to be used both as a textbook for graduate students, and at the same time as background material for researchers active in the field of geometric control theory or geometric mechanics. … authors provide an efficient geometric model for modeling mechanical control systems is brilliant. Precisely this fact makes this book very pleasant to read. In my opinion, it will become a standard reference work in the subject.” (Bavo Langerock, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008)

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Product Details

  • ISBN-13: 9780387221953
  • Publisher: Springer New York
  • Publication date: 11/1/2004
  • Series: Texts in Applied Mathematics Series, #49
  • Edition description: 2004
  • Edition number: 1
  • Pages: 727
  • Sales rank: 1,267,811
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.56 (d)

Table of Contents

Part I: 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.- Part II: Analysis of mechanical control systems; Stability; Controllability; Low-order controllability and kinematic reduction ; Perturbation analysis.- Part III: 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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