Look-Ahead NURBS-PH Interpolators for High Speed CNC Milling

Various methods for parametric interpolation of NURBS curves have been proposed in the past. However, the errors caused by the approximate nature of the NURBS interpolator were rarely taken into account. This paper proposes an integrated look-ahead algorithm for parametric interpolation along NURBS curves. The algorithm interpolates the sharp corners on the curve with the Pythagorean-hodograph (PH) interpolation. This will minimize the geometric and interpolator approximation errors simultaneously. The algorithm consists of four different modules: a sharp corner detection module, a PH construction module, a feedrate planning module, and a dynamics module. Simulations are performed to show correctness of the proposed algorithm. Experiments on an X-Y table confirm that the developed method improves contour accuracy significantly compared to previously proposed adaptive-feedrate and curvature-feedrate algorithms.