Multi-Camera Robot-World Hand-Eye Calibration by Solving Multi-Unit Dual Quaternion Equations

In this paper, we study the solution to the multi-camera robot-world handeye calibration problem by employing dual quaternions to represent transformation matrices. This approach yields a system of multi-unit dual quaternion equations of the form adzˇd =(−1)σd⊙xˇb,d=1,. . ., p. We propose a novel formulation for the subspace constrained least squares solution to ad ˇzd= ˇ xb to avoid discussing the unknown signs (−1)σd and derive the closed-formexpression for the solution. We prove that when the transformation matrix equation associated with the multi-camera robot-world handeye calibration admits a solution, the corresponding unit dual quaternion obtained from this matrix equation constitutes a subspace constrained least squares solution for the system of multi-unit dual quaternion vector equations. We present an algorithm formulti-camera robot-world hand-eye calibration, using the derived closed-formsubspace constrained least squares solution to the multi-unit dual quaternion equations. We introduce a correction strategy to handle real-world data scenarios where the basic assumption may not hold. Experimental results demonstrate that the proposed subspace constrained least squares solutions exhibit competitive performance compared to state-of-the-artmethods in multi-camera robot-world hand-eye calibration.