Riemannian Observers for Euler-Lagrange Systems
Abstract
In this paper, a geometrically intrinsic observer forEuler-Lagrange systems is defined and analysed. This observer is angeneralization of the observer recently proposed by Aghannan andRouchon. Their contractivity result is reproduced and complemented by a proof that the region of contractivity is infinitelythin. However, assuming a priori bounds on the velocities,convergence of the observer is shown by means ofLyapunov's direct method in the case of configuration manifolds withconstant curvature. The convergence properties of the observer are illustrated by an example where the configuration manifold is the three-dimensional sphere.
