LAUSR

In this paper, a novel contouring error estimation based on the canonical approximation is proposed, which is applicable for three-dimensional contours. The approximation is derived from the Taylor expansion locally of the desired contour. It retains major geometric properties of a spatial curve, curvature and torsion. A systematic analysis and comparison is presented for the tangential approximation, the circular approximation, and the proposed canonical approximation. By transforming the identified dynamic model into local Frenet frame, contouring controllers are designed based on the estimated contouring errors using the three approximations. Experiments are conducted in a three-axis servo system for a cylindrical helix contour with different feed rates. The contouring error performance based on the proposed canonical approximation exhibits 70% and 36% improvement than those based on the tangential and the circular approximations, respectively.