Abstract: In the contour-following task, the contouring error estimation is not only used to estimate the errors, but also to yield the cross-coupled gains. Thus, it directly determines the accuracy of the contouring control. However, the traditional estimation methods may cause significant error when the curvature is large. For the planar arbitrary curves, the differential properties of the point-to-curve distance function are investigated, and a second-order estimation method based on its Taylor’s expansion for evaluating contouring errors is developed. The calculation problem for the traditional second-order estimation methods encountered in the case of quadrant converter is presented, and the corresponding computational formulas are corrected. Based on the developed quadratic contouring error estimation method, a contouring controller, which combines the position feedback and the cross-coupled controllers, is developed. A NURBS curve is applied for biaxial experimental validations. The results indicate that: The proposed estimation method has higher accuracy than the traditional ones; the designed cross-coupled controller based on the proposed estimation method improves the contouring accuracy significantly compared with those based on the traditional estimation methods.

Key words: contouring control;contouring error;cross-coupled control;distance function