Real time parameter based contour error estimation algorithms for free form contour following

• The reference point used to estimate contour error is on the parametric curve.
• Linear/circular approximation is used to estimate contour error.
• Eight existing estimation methods are compared with six proposed methods.
• The proposed estimation algorithms outperform the existing ones.

The contour following task of a multi-axis servo system is one of the most important applications of modern Computer Numerical Control (CNC) machine tools, and is widely seen in many types of CNC machining. Hence, the reduction of contour error occurring in the contour following process is paramount and deserves more comprehensive investigation. In general, the calculation of precise contour error in real time is very challenging if not impossible, in free-form curve following tasks. To deal with such a problem, this paper proposes six real-time contour error estimation methods for free-form parametric curves. The feasibility of these methods is verified with several NURBS parametric curve contour following experiments. In addition, experimental results reveal that the proposed methods can provide more accurate contour error estimation for various free-form curves than the other estimation algorithms tested in the experiments. With the proposed contour error estimation approach, advanced motion control schemes can be designed to efficiently reduce contour errors of contour following tasks.