Localization and Matching Using the Planar Trifocal Tensor With Bearing-Only Data

This paper addresses the robot and landmark localization problem from bearing-only data in three views, simultaneously to the robust association of this data. The localization algorithm is based on the 1-D trifocal tensor, which relates linearly the observed data and the robot localization parameters. The aim of this work is to bring this useful geometric construction from computer vision closer to robotic applications. One contribution is the evaluation of two linear approaches of estimating the 1-D tensor: the commonly used approach that needs seven bearing-only correspondences and another one that uses only five correspondences plus two calibration constraints. The results in this paper show that the inclusion of these constraints provides a simpler and faster solution and better estimation of robot and landmark locations in the presence of noise. Moreover, a new method that makes use of scene planes and requires only four correspondences is presented. This proposal improves the performance of the two previously mentioned methods in typical man-made scenarios with dominant planes, while it gives similar results in other cases. The three methods are evaluated with simulation tests as well as with experiments that perform automatic real data matching in conventional and omnidirectional images. The results show sufficient accuracy and stability to be used in robotic tasks such as navigation, global localization or initialization of simultaneous localization and mapping (SLAM) algorithms.