A Measurement-Driven Method for the Simultaneous Solution of AX = YB in the Implementation of Simulated Robotic Production Systems

This paper presents a novel, measurement-driven method for the simultaneous estimation of the User Coordinate System (UCS) and Tool Center Point (TCP) in industrial robot systems, formulated as a solution to the AX = YB calibration problem. The proposed algorithm minimizes the discrepancy between simulated and real-world robot poses by iteratively refining both coordinate transformations using external laser tracker measurements. A comparative evaluation was conducted using two ABB IRB-6640 robots and four calibration strategies, including internal three-point measurement, absolute orientation, geometrical referencing, and the proposed method. Experimental results show that the proposed approach outperforms standard industrial techniques, achieving an average translational error below 0.4 mm, compared to over 2 mm for conventional methods. The geometric method, while widely used for its simplicity, demonstrated the highest error and instability due to poor rotational alignment. The findings validate the proposed solution as an accurate, non-invasive alternative for implementing simulated programs in real production environments, particularly where direct access to robot controllers is limited.