Camera relative pose estimation for visual servoing using quaternions

We present a novel approach to estimate the rotation and translation between two camera views from a minimum of five matched points in the images. Our approach simultaneously recovers the 3D structure of the points up to a common scale factor, and is immune to a variety of problems that plague existing methods that are based on the Euclidean homography or Essential matrix. Methods based on homography only function when feature points are coplanar in 3D space. Methods based on the Essential matrix often lose accuracy as the translation between two camera views goes to zero or when points are coplanar. By recovering the rotation and translation independently using quaternions, our algorithm eschews the shortcomings of these methods. Moreover, we do not impose any constraints on the 3D configuration of the points (such as coplanar or non-coplanar constraints). Our method is particularly well-suited for Position-Based Visual Servoing (PBVS) applications. Investigations using both simulations and experiments validate the new method. Comparisons between the proposed algorithm and the existing algorithms establish that our algorithm is robust to noise. A Matlab implementation of our algorithm is available online and free.