Contouring Control of Multi-Axis Motion Systems for NURBS Paths

A contouring control method that integrates the equivalent errors and non-uniform rational B-spline (NURBS) interpolator is proposed in this study. The method of equivalent errors has been shown to possess many advantages for the contouring control of multi-axis motion systems. A key requirement of the method is that the desired path should be represented by algebraic path equations in generalized coordinates. On the other hand, complicated curves are usually described by NURBS, which is in a parametric form. To be integrated with the method of equivalent errors, the parametric NURBS curve is transformed into a set of algebraic path equations by the Sylvester's implicitization method. As a result, the proposed method is useful for the contouring control of multi-axis motion systems following free form complicated paths. The effectiveness of the proposed method is verified experimentally through the application to a biaxial system following a star-like NURBS curve of degree 5.