Speed planning and interpolation algorithm of high-speed NURBS curve based on an elliptical arc fitting

Taking advantage of the gradual change characteristic of the curvature of the conventional conic ellipse, this paper proposes a method of fitting a non-uniform rational B-spline (NURBS) curve with an elliptical arc and, thereafter, performing speed planning and interpolation of the elliptical arc itself. First, the method of elliptical arc fitting is introduced and then proven by simulation with comparative previous linear and arc fittings to obtain better fitting accuracy with fewer segments. Subsequently, the tangent vector of any point of an ellipse is used to complete the speed planning and interpolation of that ellipse. In terms of speed planning, the maximum acceleration of any point in the elliptical arc can be obtained by using a tangent vector, and the time speed curve in this work is completed based on this phenomenon. In the interpolation stage, the longest axis of the current point is determined by using the tangent vector of any point of the elliptical arc, according to which the pulse is sent, thereby completing the interpolation operation via this iterative cycle. This method unifies the processing model of the interpolation algorithm, the simplicity and efficiency of which is verified by subsequent simulation data. This method can also be universally applied to processing most other types of curve.