Active Estimation of 3D Lines in Spherical Coordinates
This addresses the need for accurate 3D line estimation in robotics, but it is incremental as it builds on existing observer methods with a specific coordinate representation.
The paper tackled the problem of estimating 3D line parameters for control applications like Visual Servoing by proposing a nonlinear observer with an algebraic constraint using spherical coordinates, and validated it in simulation and on a real robotic platform.
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.