Active Estimation of 3D Lines in Spherical Coordinates

Straight lines are common features in human made environments. They are a richer feature than points, since they yield more information about the environment (these are one degree features instead of the zero degrees of points). Besides, they are easier to detect and track in image sensors. Having a robust estimation of the 3D parameters of a line measured from an image is a must for several control applications, such as Visual Servoing. In this work, a classical dynamical system that models the apparent motion of lines in a moving camera's image is presented. In order to obtain the 3D structure of lines, a nonlinear observer is proposed. However, in order 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.