利用分段G^2插值方法构造铺丝路径

Constructing Fiber Placement Paths With Piecewise G^2 Interpolation

提出了复合材料铺丝路径的规划方法,其中铺丝基准路线是通过对给定数据点的切方向及曲率向量或测地曲率值,G2连续地插值曲面上点列的方法得到。利用正则参数曲面上一点的切空间与其参数平面对应点的切空间同构原理。将曲面上曲线的插值问题转化为其参数平面上类似的曲线插值问题。该方法能够用显式方程来表示曲面上的G2连续插值曲线。由于引入了若干控制参数,可对曲线进行局部或整体的交互修改。利用该方法进行铺丝路径规划可以反映芯模面的曲率信息,改变纤维的局部走向,使其最终的结果更好地满足丝束铺放要求和构件几何性能的要求。实验证明该方法简单可行,还可用于计算机辅助设计、计算机图形学等领域。

This paper presents a method for path planning of robotic fiber placement,where the initial path is created with curvature continuous（G2） interpolation of data points on surface with specified tangent direction and curvature vector at every point.Making use of some conclusions deduced from the isomorphic relations between tangent spaces of both surface and its parametric domain at corresponding points,we convert the problem of curve interpolation on a parametric surface to a similar one on its parametric plane.The method enables us to express G2 interpolation curve of an arbitrary sequence of points on a parametric surface explicitly in parametric form.For introducing several free parameters into the method,we can modify the curve＇s shape locally or globally.Moreover,the resulted placement path can reflect the curvature of the mould surface and change the fiber＇s direction locally so as to satisfy better the demand of both fiber placement and surface geometry.Experiments demonstrate the method is simple,feasible and also applicable to computer aided design and computer graphics,etc.