基于Runge-Kutta的NURBS曲线实时前瞻插补算法

A Real-time Look-ahead Interpolation Algorithm for NURBS Curves Based on Runge-Kutta

针对传统的NURBS曲线加工过程中插补算法插补参数计算精度低、实时性不高以及加速度过大对机床造成的冲击大的问题,提出了基于Runge-Kutta的NURBS曲线实时前瞻插补算法.该算法采用经典Runge-Kutta方法计算插补参数,基于弓高误差和法向加速度约束条件自动调整进给速度,根据进给步长预期值与实际值的偏差进行参数校正.由粗插补得到的离线数据寻找进给速度极值点,并对曲线进行前瞻分段,找到各前瞻插补区间上的首末速度敏感点.根据敏感速度与插补距离之间的关系重新进行加减速控制,避免速度急剧变化,从而满足机床的加减速性能要求.最后,通过Matlab仿真验证了算法的有效性.

During the traditional NURBS machining,the calculation precision of the interpolation parameters of the interpolation algorithm is low,the real-time performance is poor,and too high acceleration causes a dramatic impact on machine tools. In order to solve these problems,a real-time look-ahead interpolation algorithm for NURBS curves based on Runge-Kutta is proposed. In the algorithm,first,the interpolation parameters are calculated by using the four-order Runge-Kutta method,and the feedrate is adjusted automatically according to the constraints of the chord error and the normal acceleration. Next,the parameters are revised according to the deviation between the theoretical feed step and the actual one. Then,based on the offline data from a rough interpolation,the extreme points of the feedrate are calculated and the parametric curves are divided into several look-ahead sections,thus finding the first and last sensitive feedrate points in each look-ahead section. Finally,the feedrate is re-planned according to the relationship between the sensitive feedrate and the interpolation distance,so as to avoid the dramatic variation of the feedrate. Thus,the demand of the machine tool in the acceleration and deceleration performance is satisfied. The proposed algorithm is proved to be effective by a Matlab simulation.