Globally Optimal Symbolic Hand-Eye Calibration

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 \boldsymbol {AX} = \boldsymbol {XB} and \boldsymbol {AX} = \boldsymbol {YB}. 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.