Double Taylor Expansion-Based Real-Time Contouring Error Estimation for Multiaxis Motion Systems

Abstract

In order to promote contouring performance in contour following tasks, many contouring control research works have been conducted based on real-time contouring error. Therefore, accurate contouring error estimation is always an important topic for multiaxis motion systems. In practice, accurate analytical expression of contouring error available to free-form spatial contours is hard to obtain. In this paper, a double Taylor expansion-based contouring error estimation method is proposed for spatial contours. Specifically, contouring error is first expressed by a third-order Taylor equation, which is related to the kinematics information of a datum point. Then, the datum point is determined by the Taylor approximation expanded at the desired point. Compared with the existing Taylor expansion based contouring error estimation strategies, the proposed one can not only achieve higher order accurate approximation, but also eliminate the inaccurate estimation caused by long distance between the datum point and the actual one. The effectiveness of the proposed estimation method is validated by a series of simulation and experiments conducted on a three-axis motion system.