# Active Estimation of 3D Lines in Spherical Coordinates

## TL;DR

This paper introduces a nonlinear observer for estimating 3D line parameters in spherical coordinates, improving convergence and validation through simulations and real robotic experiments.

## Contribution

It presents a novel nonlinear observer using spherical coordinates and a change of basis to enforce algebraic constraints for 3D line estimation.

## Key findings

- Successful simulation validation of the observer.
- Real robot experiments demonstrating practical applicability.
- Enhanced convergence properties of the estimation method.

## Abstract

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.