Dual-quaternion-based kinematic calibration in robotic hand-eye systems: A new separable calibration framework and comparison

The kinematic calibration of the robotic hand-eye system is formulated as solving the AX = XB problem, with calibration accuracy serving as the sole evaluation criterion. Whether the rotational and translational parts of the kinematic equations are calculated decoupled or not, being regarded as an important factor affecting the calibration accuracy, serves as a categorization criterion to form the separable and simultaneous methods. While it is widely acknowledged that both separable and simultaneous methods have distinct advantages and disadvantages, no definitive conclusions have been reached. This is primarily due to the challenges of isolating various influencing factors and the inherent coupling among them. This study addresses the problem within the theoretical framework of dual quaternion, excluding accuracy variations attributable to computational tools. First, a kinematic calibration framework is established by introducing the generalized conjugate formula, which accommodates existing simultaneous methods. Subsequently, a separable framework is proposed, incorporating Chasles' decoupling of the generalized conjugate formula. In the experiments, a pose optimization scheme based on permutations and combinations is developed. This scheme decouples the primary influencing factors and clarifies the applicability conditions of both separable and simultaneous methods. The proposed calibration scheme can be directly applied to robot motion planning.