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
Systems Reading Group
Ercan U. Acar
Derivations of adjoint operators on Lie Algebras so(3) and se(3).
Title : Simple
mechanical control systems with constraints
Author (s) : Andrew
IEEE Transactions on Automatic Control 45(8), pages 1420-1436, 2000
Detailed derivations for example B (section. IV), the upright rolling disk,
file and its postscript
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
Author (s) : Darryl D.
Holm, Jerrold E. Marsden
and Tudor S. Ratiu
Advances in Math., 137, 1-81, 1998
Related Reading Material
Notes by Andrew D.
Lewis, Francesco Bullo.
This is a compilation of some of their papers and related mathematical
Title : Geometric
Control of Lagrangian Systems (Link coming soon)
Author (s) : Andrew
D. Lewis, Francesco Bullo
Title : Foundations
Author (s) : Ralph Abraham,
Jerrold E. Marsden
Title : An Introduction
to Differentiable Manifolds and Riemannian Geometry
Author (s) : William
Academic Press, Incorporated, 1986
For suggestions and comments email Ercan U. Acar, firstname.lastname@example.org.