Determine turntable coordinate system considering its non-orthogonality

In industrial measurement and laboratory research, many measured objects are placed on the three-axis turntable. In this paper, we propose a fast and practical method to determine the turntable coordinate system with the aid of spatial coordinate of point cloud data. By sphere fitting, plane fitting, and point projection, the scattered point cloud data are combined together to obtain initial direction vectors. Considering the non-orthogonality of turntable, the least two pairs of skew lines are used to compute the approximate turntable center. And the intersection angles and distances between each axis are given to judge the degree of non-orthogonality. Then, based on the approximate sphere center and the initial rotation vectors, the direction vectors are, respectively, optimized in a predefined order. An experimental system is set up to validate the proposed method. Attitude parameters computed by spatial point coordinates before and after turntable calibration are employed to give the quantitative evaluation results. And the total attitude errors in three axes motion forms all reduce, which demonstrates the effectiveness and practicality of the proposed method.