Abstract:

To address the challenges of dynamic computation of NURBS curves in real-time systems， a real-time NURBS curve interpolation method was proposed based on acceleration-continuous ramp-up and ramp-down planning. The curves were interrupted at the curvature extrema， and reasonable connection speeds were assigned through preprocessing. S-curve velocity planning was employed throughout to ensure continuity of speed and acceleration， with controllable acceleration peaks. Experimental results demonstrate that the proposed methods achieve single-axis acceleration continuity. During the processing with NURBS curves， the losses of smoothness in single-axis speed caused by frequent curvature changes were effectively handled， and continuous variations in single-axis acceleration were maintained throughout the machining processes， significantly reducing peak values of single-axis acceleration. Under the same laser machining equipment， the proposed interpolation planning method exhibits higher efficiency and accuracy than that of traditional methods， resulting in improved workpiece quality.

Key words: non-uniform rational B-splines（NURBS） curve, acceleration smoothing, velocity planning, high-speed and high-precision laser processing

摘要：

为解决非均匀有理B样条（NURBS）曲线在实时系统中难以动态计算的问题，提出了一种基于加速度连续加减速规划的实时NURBS曲线插补方法。将曲线在曲率极值处打断，通过预处理赋以曲线合理的衔接速度，全程使用S形速度规划方法保证速度和加速度连续，加加速度峰值可控。实验结果表明，所提出的方法能够实现单轴加速度连续。在使用NURBS曲线加工时该方法可以有效处理频繁的曲率变化带来的单轴速度的平滑度损失，保持整个加工过程中单轴加速度的连续变化，有效减小单轴加加速度的峰值，同等激光加工机床设备下比传统的插补规划方法具备更高的效率和精度，工件加工质量更好。

关键词: 非均匀有理B样条曲线, 加速度平滑, 速度规划, 激光高速高精加工