Optimization and Systems Theory, Royal Institute of
Technology (KTH), Stockholm, Sweden
Johan Hamberg
Dept. of Autonomous Systems, Swedish Defence Research
Agency (FOI), Stockholm, Sweden
ABSTRACT:
In this paper, a geometrically intrinsic observer for Euler-Lagrange
systems is defined and analysed. This observer is an generalization of
the observer recently proposed by Aghannan and Rouchon. Their
contractivity result is reproduced and complemented by a proof
that the region of contractivity is infinitely thin. However, assuming
\emph{a priori} bounds on the velocities, convergence of the observer is
shown by means of Lyapunov's direct method in the case of configuration
manifolds with constant curvature. The convergence properties of the
observer are illustrated by an example where the configuration manifold
is the three-dimensional sphere, $S^3$.