M13 – PARIS‐SACLAY 21/03/2016‐ ‐ 25/03/2016

Geometric mechanics and nonlinear control

Ravi N. Banavar
Systems and Control Engineering,
IIT Bombay


• Motivational examples: Satellite/quadrotor attitude stabilization, control of wheeled/spherical mobile robots.
• Smooth manifolds machinery: An introduction to differentiable manifolds, tangent vectors, vector fields, • 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.
• Riemannian manifolds: The metric tensor, covariant derivative, the connection and geodesic motion, the Euler-Lagrange equations on a Riemannian manifold
• Regulation problems on Riemannian manifolds: configuration error functions, stabilization, region of attraction.
• Tracking problems on Riemannian manifolds: the transport map and compatibility conditions.

Main references

• Geometric Control of Mechanical Systems - F. Bullo and A. D. Lewis, Springer, 2005.
• Geometric Mechanics and Symmetry - D .D. Holm, T. Schmah and C. Stoica, Oxford University Press, 2009.
• Nonholonomic Mechanics and Control - A. M. Bloch, Springer, 2003
• A Mathematical Introduction to Robot Manipulation and Control - R. Murray, Z. Li and S. Sastry, CRC Press, 1992
• Introduction to Mechanics and Symmetry - J. Marsden and T. Ratiu, Springer-Verlag, 1994.