  Straight lines are common features in human made environments, which makes
them a frequently explored feature for control applications. Many control
schemes, like Visual Servoing, require the 3D parameters of the features to be
estimated. In order to obtain the 3D structure of lines, a nonlinear observer
is proposed. However, to guarantee convergence, the dynamical system must be
coupled with an algebraic equation. This is achieved by using spherical
coordinates to represent the line's moment vector, and a change of basis, which
allows to introduce the algebraic constraint directly on the system's dynamics.
Finally, a control law that attempts to optimize the convergence behavior of
the observer is presented. The approach is validated in simulation, and with a
real robotic platform with a camera onboard.
