An Interpolator for a Non-Uniform Rational B-Spline Curve with a High Efficiency and Accuracy Using Polynomial Representations

Abstract

This paper introduces an efficient and accurate interpolator for NURBS (non-uniform rational B-spline) curves, addressing the challenge of regulating feedrate under machining accuracy and dynamic constraints, particularly at sensitive corners. A recursive matrix representation and polynomial conversion are utilized to enhance the computation of NURBS curve intermediate points and derivatives. An improved adaptive planning method is presented to adjust the feedrate at sensitive corners, ensuring that chord error and dynamic constraints are met. The method integrates linear acceleration and deceleration stages to mitigate abrupt changes in acceleration and jerk. Additionally, a prediction–correction scheme-based interpolator is developed, employing an asynchronous mechanism to improve computational efficiency. The proposed method’s effectiveness and correctness are validated through simulation tests and machining experiments.

Keywords

• NURBS curve
• interpolation
• sensitive corner
• feedrate planning
• prediction–correction scheme