M13 â PARISâSACLAY 21/03/2016â â 25/03/2016
Geometric mechanics and nonlinear control
Ravi N. Banavar
Systems and Control Engineering,
Outline:â¢ Motivational examples: Satellite/quadrotor attitude stabilization, control of wheeled/spherical mobile robots.
â¢ Smooth manifolds machinery: An introduction to differentiable manifolds, tangent vectors, vector fields, â¢ co-vector fields, immersions and submersions, vector fields, integral curves, push-forward and pull-back of vector fields. Lie groups, actions of groups, Lie algebras, adjoint co-adjoint maps, symmetries.
â¢ Riemannian manifolds: The metric tensor, covariant derivative, the connection and geodesic motion, the Euler-Lagrange equations on a Riemannian manifold
â¢ Regulation problems on Riemannian manifolds: configuration error functions, stabilization, region of attraction.
â¢ Tracking problems on Riemannian manifolds: the transport map and compatibility conditions.
Main referencesâ¢Â Geometric Control of Mechanical Systems - F. Bullo and A. D. Lewis, Springer, 2005.
â¢Â Geometric Mechanics and Symmetry - D .D. Holm, T. Schmah and C. Stoica, Oxford University Press, 2009.
â¢Â Nonholonomic Mechanics and Control - A. M. Bloch, Springer, 2003
â¢Â A Mathematical Introduction to Robot Manipulation and Control - R. Murray, Z. Li and S. Sastry, CRC Press, 1992
â¢ Introduction to Mechanics and Symmetry - J. Marsden and T. Ratiu, Springer-Verlag, 1994.