World-Base Calibration by Global Polynomial Optimization

Abstract

This paper presents a novel solution to the world-base calibration problem. It is applicable in situations where a known calibration target is observed by a camera attached to the end effector of a robotic manipulator. The presented method works by minimizing geometrically meaningful error function based on image projections. Our formulation leads to a non-convex multivariate polynomial optimization problem of a constant size. However, we show how such a problem can be relaxed using linear matrix inequality (LMI) relaxations and effectively solved using Semi definite Programming. Although the technique of LMI relaxations guaranties only a lower bound on the global minimum of the original problem, it can provide a certificate of optimality in cases when the global minimum is reached. Indeed, we reached the global minimum for all calibration tasks in our experiments with both synthetic and real data. The experiments also show that the presented method is fast and noise resistant.