Mechanical Control Systems Reading Group 

In this group, we are studying advances in nonlinear control
theory for mechanical systems. These advances combine results
from both classical and modern geometric approaches to mechanics
to pose controllability and steering results for mechanical control
systems, i.e. systems with second order dynamics. These results
can be thought of as dynamic extensions to the Lie bracket based
control results for kinematic systems. The primary tools used
here are affine connections and the symmetric product.
The aim of this group is to understand this body of work with an
eye towards extending and applying the results to the control of
robotic systems.

People 

Group Leader
 
    George Kantor
 
Group Members
 
    Ercan U. Acar
    Howie Choset
    David Conner
    Alfred Rizzi
    Elie Shammas
    Sarjoun Skaff
    Peter Staritz
    Ben Turk

List of Papers and Notes 
Title         : Visual servoing with dynamics: control of an unmanned blimp
Author(s) :  Hong Zhang, James P. Ostrowski
                IEEE International Conference on Robotics and Automation, 1999, Volume: 1, Page(s): 618 -623
 
Title         :  Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups
Author(s) :  Francesco Bullo, Naomi E. Leonard, and Andrew D. Lewis
                IEEE Transactions on Automatic Control 45(8), pages 1437-1454, 2000
 
  • Derivations of adjoint operators on Lie Algebras so(3) and se(3). pdf file, ps file

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    Title          : Simple mechanical control systems with constraints
    Author (s) :  Andrew D. Lewis
                     IEEE Transactions on Automatic Control 45(8), pages 1420-1436, 2000
     
  • Detailed derivations for example B (section. IV), the upright rolling disk, Mathematica file and its postscript version.

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    Related Reading Material 

    A nice treatment of Lagrangian, Hamiltonian formulations (how
    they are related to each other), the relation between Euler-Poincare
    equations and Euler equations for rigid body motion are given with
    historical background in Section 1 of the following paper.
     
     
     
    Title       :  The Euler-Poincare Equations and Semidirect Products with Applications to Continuum Theories
    Author (s) :  Darryl D. Holm, Jerrold E. Marsden and Tudor S. Ratiu
                         Advances in Math., 137, 1-81, 1998 
    Notes by Andrew D. Lewis, Francesco Bullo.
    This is a compilation of some of their papers and related mathematical tools.
     
    Title          :  Geometric Control of Lagrangian Systems (Link coming soon)
    Author (s) :  Andrew D. Lewis, Francesco Bullo

    Reference Books 

    Title          : Foundations of Mechanics
    Author (s) : Ralph Abraham, Jerrold E. Marsden
                        Addison-Wesley, 1978 
    Title        :  An Introduction to Differentiable Manifolds and Riemannian Geometry
    Author (s) : William M. Boothby
                        Academic Press, Incorporated, 1986 

    For suggestions and comments email Ercan U. Acar, eua@andrew.cmu.edu.