NURBS曲线S形加减速双向寻优插补算法研究

Research on the Algorithm of NURBS Curve Bidirectional Optimization Interpolation with S-type Acceleration and Deceleration Control

由于非均匀有理B样条(Non-uniform rational B-splines,NURBS)曲线的弧长与参数之间无精确解析关系,并且进给速度总是受到非线性变化的曲线曲率的约束,因此基于S形加减速进行NURBS曲线插补时,减速点难以准确预测。传统算法通常是沿曲线单方向插补,不仅未考虑曲率对进给速度的持续限制,而且加减速分类与计算公式复杂。为此,提出运动路程未知情况下不依赖于弧长精确计算的正向和反向同步加速的插补新算法,实时动态地求解曲线段内最大进给速度和正反向插补会合点,从而实现处处满足全部速度约束条件的最优插补。该算法无需求解高次方程与繁琐的加减速模式分类,并可保证以确定的速度通过曲率极值点和曲线终点。通过两个插补实例证明算法简明高效,适应性好,能够满足高速高精度数控要求。

There is no precise analytical relationship between the curve length and the parameter of non-uniform rational B-splines（NURBS）.Furthermore,the feedrate is always subject to the non-linearly varying curvature.Accordingly,it is hard to precisely determine the deceleration point when interpolating NURBS curves with S-type acceleration and deceleration（ACC/DEC）.The traditional algorithms usually flow only one direction along the curve,not only neglecting that feedrate is always constrained by curvature,but also having complex ACC/DEC classification and computing equations.Therefore,a new interpolation algorithm which is independent of precise calculating of curve length and based on synchronously positive and reverse acceleration is proposed on the condition of unknown moving distance.The proposed algorithm determines the maximum feedrate and the meet point of positive and reverse interpolation of each NURBS segment dynamically and in real time.Consequently,the optimal interpolation that satisfies all the feedrate conditions everywhere is realized.Solving high order equations and fussy classification of ACC/DEC modes is avoided and the velocities at the extreme curvature points and end points are guaranteed to map the determined values exactly by the proposed algorithm.Two interpolation examples are presented to verify its simplicity,efficiency,good adaptability and the ability to meet the requirements of both high speed and high accuracy of computer numerical control.