One-step Solving the Hand-Eye Calibration by Dual Kronecker Product

Abstract

Hand-eye calibration is a typical research direction in robotics applications. The current methods can be divided into two categories according to whether the rotational and translational equations are decoupled for computation: two-step methods and one-step methods. Both one-step and two-step methods generally convert such problems to linear null space computations, which is implemented by the corresponding computational operators. Owing to the booming development of the rotation operators, the two-step methods have been more fully researched. However, due to the limitations of the research on computational operators integrating rotation and translation, the one-step methods still have much scope for research. Dual algebra, as effective mathematical entities for screws and wrenches, provides the theoretical basis for the development of the one-step methods for hand-eye calibration. In this paper, a computational operator for the dual matrices computation was first proposed, i.e., dual Kronecker product. Subsequently, a hand-eye calibration framework was proposed based on the dual Kronecker product, which allowed the screw motion to be represented as multiple dual vectors. Furthermore, the equivalence of this framework with the orthogonal-dual-tensor-based approach was derived, providing a more intuitive computational representation. The feasibility and superiority of the proposed computational framework were experimentally verified.