Geometric Control of Mechanical Systems

Francesco Bullo and Andrew D. Lewis

Springer-Verlag, New York-Heidelberg-Berlin, 2004
Number 49 in Texts in Applied Mathematics
ISBN 0-387-22195-6

   author =	 {Francesco Bullo and Andrew D. Lewis},
   title =	 {Geometric Control of Mechanical Systems},
   publisher =	 {Springer Verlag},
   address =	 {New York-Heidelberg-Berlin},
   year =	 2004,
   volume =	 49,
   series =	 {Texts in Applied Mathematics},
   isbn =        {0-387-22195-6}

[Synopsis] [Reviews] [Free downloads] [For instructors] [Mathematica packages] [CDC workshop] [About the authors] [Contact] [How to buy the book]


From the back cover: 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.


  1. AMS Mathematical Reviews, MR2099139 (2005h:70030).
  2. IEEE Transactions on Automatic Control, 50(12), page 2111, 2005.
  3. International Journal of Robust and Nonlinear Control, 16, 547-548, 2006.
  4. Journal of Geometry and Symmetry in Physics, 4, 99-103, 2005.

Free downloads

The following are excerpts from the book:
  1. the cover page;
  2. the preface;
  3. the table of contents;
  4. Chapter 1.
We will keep, and periodically update, a list of errata and addenda.
  1. Errata
You can download a list of mechanical systems that appear in the text as examples and/or exercises. For each system, it is indicated where in the text it appears.
  1. Guide to examples and exercises
  2. Supplementary chapters
Also available for download are
  1. Mathematica packages.

Information for instructors

A few words are said in the preface about using the book as a text, and we shall expand on these here with the following material:
  1. possible course outlines for courses taught from the book;
  2. slides for a course taught at the advanced undergraduate level at Queen's University;
  3. slides from our workshop on the material in the book.

CDC workshop

There was a
workshop, run by the authors, on material related to the book that was held at the 43rd IEEE Conference on Decision and Control. The slides for the workshop are available for download in the information for instructors section.

About the authors

Francesco Bullo received the Laurea degree ``summa cum laude'' in Electrical Engineering from the University of Padova, Italy, in 1994, and the Ph.D. degree in Control and Dynamical Systems from the California Institute of Technology in 1999. From 1998-2004 he was an Assistant Professor with the Coordinated Science Laboratory at the University of Illinois at Urbana-Champaign. He is currently an Associate Professor with the Mechanical & Environmental Engineering Department at the University of California, Santa Barbara. His research interests include motion planning and coordination for autonomous vehicles, and geometric control of mechanical systems.

Andrew Lewis received his undergraduate degree in Mechanical Engineering from the University of New Brunswick in 1987, and his MSc and PhD in 1988 and 1995, respectively, both in Applied Mechanics from the California Institute of Technology. From 1995-1996 he was a Postdoctoral Fellow in Control and Dynamical Systems at the California Institute of Technology, and from 1996-1998 he was a Postdoctoral Fellow in the Mathematics Department at the University of Warwick. He is now an Associate Professor in the Mathematics and Statistics Department at Queen's University in Kingston, Ontario in Canada. His research interests include geometric mechanics and differential geometric control theory.


Let us know if you have comments on the book, or if you have found an error. To make an error report, please send us email. It is easiest for us if error reports include page and line numbers, e.g., ``Page 246, d7'' if the error is on the 7th line from the top on page 246, or ``Page 410, u10'' if the error is on the 10th line from the bottom on page 410. Thanks.

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