Simple and Accurate Rotary Sensor Based on the Rotary Angle Gauss–Newton Image Matching Algorithm

Image-based rotary sensors have the advantages of being simple and low cost and exhibit good robustness to harsh conditions. Existing image-based sensors calculate angle positions by mark detection with low angle-positioning precision. Image matching methods offer high pixel-positioning accuracy and can be used for object-positioning in images, but no image matching method has yet been developed for rotary angle estimation. In this article, an image matching algorithm—namely, the rotary angle Gauss–Newton (RAGN) algorithm—was proposed to accurately calculate the rotation angle. In addition, a measurement technique—called rotary digital image grating (RDIG)—was also proposed. The RDIG method was used to estimate the approximate angles based on the positions of four circles in the image pattern and measure the angles accurately using the RAGN algorithm. The measuring system was simple and required no high-precision fabrication. Experiments showed that the accuracy of the RDIG method was approximately 1.20 arcsecs (RMSE) with a rotary diameter of 50 mm, which is 4.7 times better than the accuracy of existing monocular rotary sensors.