A Bidirectional Adaptive Feedrate Scheduling Method of NURBS Interpolation Based on S-Shaped ACC/DEC Algorithm

To improve the interpolation accuracy for the non-uniform rational B-spline (NURBS) curves, this paper proposes a novel bidirectional adaptive feedrate scheduling (BAFS) method based on S-shaped acceleration/deceleration (ACC/DEC) algorithm. The NURBS interpolator with the proposed BAFS method is also presented. The BAFS method has two meanings. First, to consider the continuous constraints of feedrate especially in the areas near the endpoints of each NURBS curve segment, an adaptive feedrate scheduling method is designed, which can improve the interpolation accuracy compared with the conventional method only considering the constraints of endpoints. Second, a bidirectional adaptive interpolation strategy including an adaptive task scheduling method and a meeting processing method is proposed to conduct the acceleration and deceleration interpolation stages of each NURBS segment separately in two directions. The two directions interpolation can be realized orderly by the adaptive task scheduling and the smoothness of feedrate profile can be guaranteed by the meeting processing method whose solvability is also proved. Therefore, the feedrate constraints at both the start and end points areas can be considered, which can improve the interpolation accuracy. Meanwhile, the round-off errors caused by cycle sampling are also considered and compensated in the bidirectional feedrate scheduling process to maintain the motion smoothness. In addition, an optimized look-ahead strategy is designed to ensure the correctness of the endpoints feedrate. Finally, a series of simulations and experiments are conducted to validate the good performance and applicability of the proposed method.