Real-time contouring error estimation for multi-axis motion systems using the second-order approximation

To reduce contour error in contour-following tasks, a common approach is to design a controller based on the contour error information. Hence, real-time contouring error estimation plays an important role in contour-following control. However, the available second-order estimation formulas only apply to biaxial motion systems, and cannot be generalized to handle arbitrary contours tracked by multi-axis motion systems. In this paper, a point-to-curve distance function is defined, and its properties are investigated, especially, its second-order Taylor approximant is derived. On this basis, a novel second-order approach for calculating contour errors of arbitrary contours in real time is proposed. The inter-correlations between the present approach and four commonly used ones are classified. Simulation and experimental results demonstrate the effectiveness of the proposed contour error estimation algorithm.

► A point-to-curve distance function is defined, and its second-order Taylor approximant is derived.
► A novel second-order approach for calculating contouring errors in real time is proposed.
► In planar circumstances, its superiority over the existing second-order approaches is demonstrated.
► To the authors' knowledge, it is the first second-order approach applicable to spatial contours.