五维空间样条插补算法及其应用  

Five Dimensional Spline Interpolation Algorithm and Its Application

作　　者：金岳泉 朱孔峰 鄢继红 王兴波[1] Jin Yuequan;Zhu Kongfeng;Yan Jihong;Wang Xingbo(Department of Mechatronic Engineering,Foshan University,Foshan,Guangdong 528000,China;GSK CNC Equipment Co.,Ltd.,Guangzhou 510530,China)

机构地区：[1]佛山科学技术学院机电工程系,广东佛山528000 [2]广州数控设备有限公司,广州510530

出　　处：《机电工程技术》2023年第3期177-181,共5页Mechanical & Electrical Engineering Technology

摘　　要：对多自由度运动轨迹进行仿真时存在轨迹不平滑,曲面重合度低等问题。因此提出了一种以五维空间样条曲线为理论基础的插补算法。算法以五自由度运动为研究基础,可以将离散的五坐标数据统一到五维空间样条曲线上,建立对应的数学模型,直观地对其进行分析处理,输出平滑的轨迹曲线曲面,最终在计算机上实现运动轨迹仿真。还提出一种基于Hausdorff距离求解法的拟合曲线和原始曲线进行重合度比较的算法,可以直观地输出曲线间距变化折线图并算出两条曲线的重合度,并以这种比较算法对本文插补算法与常用的双样条插补算法进行比较。综合实验得出的重合度比较结果和运动角度变化曲线,结果本文算法输出的运动轨迹更为平滑,与原始设计运动轨迹重合度更高。There are some problems in the simulation of multi-degree-of-freedom(multi-DOF)motion trajectory,such as unsmooth trajectory and low surface coincidence.Therefore,an interpolation algorithm based on five-dimensional spatial spline curve is proposed.The algorithm is based on five-DOF motion,it can unify the discrete five coordinate data onto the five dimensional space spline curve,establish the corresponding mathematical model,intuitively analyze and process it,output the smooth track curve and surface,and finally realize the motion track simulation on the computer.An algorithm based on Hausdorff distance solution method is also proposed to compare the coincidence degree between the fitting curve and the original curve,which can intuitively output the broken line chart of curve spacing change and calculate the coincidence degree of the two curves.This comparison algorithm is used to compare the interpolation algorithm in this paper with the commonly used double spline interpolation algorithm.According to the comparison results of coincidence degree and the curve of motion angle change obtained from the comprehensive experiment,the motion trajectory output by the algorithm in this paper is smoother,and the coincidence degree with the original design motion trajectory is higher.

关 键 词：运动轨迹仿真 五维样条 双样条 插补算法 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]