A Real-Time Contour Error Estimation Method Based on Triple Taylor Expansion for Multiaxis Motion Systems

As an important indicator directly related to processing quality, contour error has been widely used in multi-axis contouring following tasks. And because conventional sensors cannot directly and accurately measure contour errors in real-time motion control tasks, many approximation methods are proposed to estimate real-time contour errors. In this paper, the contour error is estimated through a third-order Taylor expansion of a point-to-curve distance function at datum point. Furthermore, the datum point can be obtained by the Taylor expansion of the reference contour curve at the desired point and the contour error vector obtained based on the Taylor expansion. In other words, this paper uses triple Taylor expansion to estimate the contour error, which can achieve higher precision. Compared with other approximation methods based on Taylor expansion, the proposed triple Taylor expansion method can further decrease the estimation error and improve the estimation performance of contour error, which is validated by numerical simulation comparison and experimental results.