Fast LS Image Matching and Vision-Based DIG Measurement for LSM's Positioning.

Linear servomotors (LSM) are widely used in industries. A LSM requires a mover positioning tool for precise control. A Vision-based digital image grating (DIG) measurement for LSM mover positioning is proposed in this study with advantages of simple system, low cost, and good robustness to environments. It estimates the LSM's rough position according to four mark-lines and obtains accurate LSM's positions by a fast least-square (FLS) image-matching algorithm. As a result, it can measure the LSM's position accurately in a wide range. The FLS proposed here represents the least-square cost function by the transformation parameters explicitly, and then calculates the parameters directly. Therefore, the image resampling process, which is inevitable for the existing least-square methods is not necessary. Simulations prove that the FLS is approximately 4.4 times faster than the classic inverse compositional Gauss–Newton (IC-GN) algorithm, and that the FLS is more accurate and robust than the IC-GN. Experiments show that the proposed DIG method can measure the LSM mover positions with an accuracy of 0.75  μ m mean absolute error.