Contouring control based on equivalent errors and NURBS interpolation

The purpose of this study is to design an integrated interpolator and contouring controller for a multi-axis motion system. The desired path is described by the nonuniform rational B-spline (NURBS) interpolator. The method of equivalent errors is adopted for the contouring controller. To apply the method of equivalent errors, the desired path in the form of NURBS, which is a parametric form, has to be transformed into an algebraic representation. To achieve this, Sylvester´s implicitization method is introduced. The analysis is verified through a numerical example.