Globally Optimal Symbolic Hand-Eye Calibration

Abstract

Hand-eye calibration (HEC) is a kernel technique guaranteeing precision industrial visual servoing and robotic grasping. Extensive studies have been conducted to various closed-form and iterative solutions to HEC problems using different pose parameterizations. However, these approaches are either sensitive to input noise or time-consuming for implementation. This article provides a new perspective on a deterministic solution to two major branches of HEC problems of forms <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AX</b> = <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">XB</b> and <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AX</b> = <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">YB</b> . We use symbolic methods to derive a globally optimal solution. Different from representatives based on optimization, this method is not only the most accurate against others but also with repeatability of 100%. Experiments via industrial robotic manipulator verify the superiority of the proposed algorithm.