Accurate and Effective Geometric Error Compensation for Ultrahigh-Precision Coordinate Measuring Machine Using Laser Tracking Interferometer

Geometric errors in coordinate measuring machines (CMMs) significantly degrade measurement accuracy. While laser tracking interferometer (LTI)-based compensation methods are widely used due to their high efficiency, the limited precision of existing positioning techniques restricts their application in ultra-high precision CMMs. To address these challenges, this study introduces an accurate and efficient geometric error compensation method that utilizes LTI positioning for ultra-high precision CMMs. The method begins with the development of a geometric error model that employs Homogeneous Transformation Matrices (HTMs) to map end-position deviations to error parameters. A highly accurate and robust positioning algorithm for LTI is then designed, incorporating a two-step process: initial positioning through semidefinite programming (SDP) and fine-tuning using enhanced Particle Swarm Optimization (EPSO). After parameter identification, geometric error compensation is applied based on the established model. The test experiments were conducted on a CMM with the nominal accuracy of 2 ± <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i>[<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mm</i>]/400 μ<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i>. The positioning results show that the proposed method achieves a distance mean absolute error of 0.10871, demonstrating superior precision over conventional methods. Additionally, the method exhibits excellent robustness and stability under noise interference. After compensation, precision validation results showed that the maximum detection error was reduced to 0.26 μ<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i>, with length measurement errors within 0.5 ± <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i>[<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mm</i>]/400 μ<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i>. These results highlight substantial improvements in both measurement precision and operational performance. This research presents an effective solution for geometric error compensation in CMMs, offering enhanced performance for industrial measurement applications.