Free-form curves contour error estimation using the backward arc length approach

In high-precision contour machining applications, large contour error is an indication of poor machining accuracy. As such, many sophisticated control algorithms have been proposed to reduce contour error, with the overall goal of improving contouring accuracy. Many algorithms focus on developing the decoupling control laws for improving contouring accuracy, while others aim to improve tracking performance so as to reduce contour error. In particular, several previous studies emphasize on developing contour error estimation approaches which generate the accurate contour error estimation needed in contouring controllers. Generally, accurate contour error estimation facilitates the efficiency of the contouring controller. This paper proposes a modified parameter-based contour error estimation approach for obtaining accurate contour error estimation. In the proposed approach, the approximated arc length is used as a backward distance, assuring the estimated reference point will be close to the actual cutting point. Consequently, the contour error can be accurately estimated. Moreover, the Cross-Coupled Controller (CCC) scheme is employed to further improve the contouring accuracy of biaxial contour following tasks. To assess the performance of the proposed approach, several free-form contour following experiments have been conducted. Experimental results verify the effectiveness of the proposed approach.