A quaternion pose determination solution based on monocular vision model

Determination of relative three-dimensional position and orientation between two reference frames can be solved by the pose measuring methods based on monocular vision model. Owing to the special T-shaped configuration, the definition of object rotational matrix in the terms of quaternion elements helped in representing the problem by six nonlinear equations from which a closed-form solution can be obtained for all the unknown parameters. The calculating formulas of elements in the rotational matrix were deduced from the coordinates of feature points in camera frame as well as the converting vector which was also introduced into the process acting as corrected term. An approximate pose could be found by the assumption of zero difference in depth of all points in camera frame, then the converting vector should be initialized by the third row of current rotational matrix. The principle of computing priority of the max value in quaternion expression was proposed to ensure the convergence of the iteration loop through which the final pose was achieved in a few iterations. Simulation experiments show the validity of the solution and analysis of the calculating precision was made in detail. The measuring orientation error would constringe with the reduction of distance from camera focus to target object and performance of the algorithm went well in short distance, while the deformation went larger with the increasing of errors caused by imprecise correspondence.