Modified Hand–Eye Calibration Using Dual Quaternions

Abstract

This paper presents a modified model for hand–eye calibration based on dual quaternion algebra. By using dual quaternions to represent the rotations and translations of a rigid body simultaneously in the task space, the formulation is elegant for the analysis of the hand–eye equation. The hand–eye transformation derived in this study is represented in a compact manner, which uses a combination of the dual part and the real part of the dual quaternion. Although the hand–eye equation can be solved by using six elements of a dual quaternion without using its scalar parts, the scaler numbers in both the real and dual parts of a dual quaternion contain part of the pose information. The originality is based on the derivation of the construct of the identification algorithm of external parameters of the camera by using all eight elements of a dual quaternion. Then, the data transformation between the cameras of the dual-arm hand–eye robot system is presented. The corresponding results demonstrate that the proposed hand–eye calibration algorithm can process measurement data with noise and can also improve the identification accuracy to verify its efficiency.

A Deep Learning-Based Hand-eye Calibration Approach using a Single Reference Point on a Robot Manipulator

“…Li et. al [10] propose a Kronecker product-based approach to simultaneously calculate both the translation and orientation components of X and Y . They also reveal that the Kronecker product has better performance than quaternion and dualquaternion approaches.…”

An Unified Iterative Hand-Eye Calibration Method for Eye-on-Base and Eye-in-Hand Setups

“…More recently Shah [20] formulated a closed-form solution for the hand-eye problem by using an SVD-based algorithm and the Kronecker product to solve for rotation and translation separately, while LI et al [21] instead used dual quaternions to solve them simultaneously to overcome the limitations of the Kronecker product.…”

“…Result of the simulated evaluation. The proposed approach, both in single-and multi-camera settings has been tested against Tsai [28], Park [16], Horaud [18], Andreff [19], Daniilidis [14], Shah [20] and Li [21]. Fig.…”

“…More in depth focus of the simulated evaluation regarding the proposed method only in single-and multi-camera settings. The proposed approach has been tested against the following methods (i.e., implementation from OpenCV ): [14], [16], [18]- [20], [28] and [21]. In the graphs and in the table we name them by reporting the first author of each one.…”

The optimal approximation solution of a constrained dual matrix equation

“…Condurache and Burlacu [6] applied orthogonal dual tensor methods to solve AX = XB sensor calibration problem. Li et al [7] solved the homogeneous transformation equation AX = Y B for the robot-to-world and hand-eye calibration problem by using dual-quaternions. Wang et al [8] transformed the multi-coordinate calibration problem of a dual-robot system into the matrix equation AXB = Y CZ.…”