Fast parametric curve interpolation with minimal feedrate fluctuation by cubic B-spline

Abstract

Due to the reliable feedrate fluctuation and computation load of the existing parametric curve interpolation, a fast interpolation method by cubic B-spline for parametric curve is presented which results in a minimum feedrate fluctuation and light computation load. As there are many geometry implementation tools and many good properties in the B-spline compared with the polynomial, the relation between the arc length s and curve parameter u can be fitted by the cubic B-spline accurately. Because the feedrate fluctuation of the generally used Taylor approximation method is sensitive to the curvature of the toolpath, its accuracy cannot be controlled. For a given feedrate fluctuation of 0.05%, the proposed interpolation method can guarantee the error requirements by increasing the number of the control points. After the de Boor method is applied in real time, the computation load of the cubic B-spline interpolation is decreased compared with the Taylor approximation method and higher order polynomial-fitting method. In order to save the memory consumption for storing the parameters of the fitted cubic B-spline, an iterative optimization process is applied to obtain the knot vector elements and optimize the control points. Simulations and experiments show that the interpolation method can attain high accuracy and computation efficiency. According to the simulations, for most of the complex curves, the feedrate fluctuation of the proposed interpolation method is decreased by about 50% when the feedrate is scheduled and the computation load of the proposed method is decreased by about 70% compared with the second-order interpolation method.