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

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 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. Front Matter ....Pages i-xxiv Front Matter ....Pages 1-1 Introductory examples and problems (Francesco Bullo, Andrew D. Lewis)....Pages 3-14 Linear and multilinear algebra (Francesco Bullo, Andrew D. Lewis)....Pages 15-48 Differential geometry (Francesco Bullo, Andrew D. Lewis)....Pages 49-140 Simple mechanical control systems (Francesco Bullo, Andrew D. Lewis)....Pages 141-245 Lie groups, systems on groups, and symmetries (Francesco Bullo, Andrew D. Lewis)....Pages 247-310 Front Matter ....Pages 311-311 Stability (Francesco Bullo, Andrew D. Lewis)....Pages 313-366 Controllability (Francesco Bullo, Andrew D. Lewis)....Pages 367-409 Low-order controllability and kinematic reduction (Francesco Bullo, Andrew D. Lewis)....Pages 411-440 Perturbation analysis (Francesco Bullo, Andrew D. Lewis)....Pages 441-477 Front Matter ....Pages 479-479 Linear and nonlinear potential shaping for stabilization (Francesco Bullo, Andrew D. Lewis)....Pages 481-527 Stabilization and tracking for fully actuated systems (Francesco Bullo, Andrew D. Lewis)....Pages 529-558 Stabilization and tracking using oscillatory controls (Francesco Bullo, Andrew D. Lewis)....Pages 559-581 Motion planning for underactuated systems (Francesco Bullo, Andrew D. Lewis)....Pages 583-617 Back Matter ....Pages 619-727