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

Active Estimation of 3D Lines in Spherical Coordinates