A NURBS curve interpolator with small feedrate fluctuation based on arc length prediction and correction

Non-uniform rational B-spline (NURBS) curve has been widely used in manufacturing systems. A good interpolator can help the system to improve the contour accuracy and get smooth dynamics performance, but it is hard to get a balance between the interpolation performance and computational load. As the derivative and curvature of NURBS curves used in manufacturing systems are high-order continuous, it is possible to predict a desired interpolation arc length based on the relationship of historical feed chord length and its corresponding arc length in one interpolation cycle. Therefore, this paper proposes a novel interpolation method, which consists three stages. Firstly, a NURBS curve is split into several high-order continuous segments based on its degrees and control points. Secondly, a prediction model based on Newton's divided differences interpolation equation is derived from the relationship of interpolated chord length and its corresponding arc length, so that the target arc length of the next interpolation cycle can be predicted. Finally, target parameter u of every interpolation cycle is calculated with Taylor's expansion, whose values are corrected by iteration, and then the position of the target interpolation point can be achieved. Performance of the proposed algorithm is tested and compared with other methods, and the simulation results show the proposed method can achieve smaller velocity fluctuation with low computational load.