Third-order contour-error estimation for arbitrary free-form paths in contour-following tasks

Abstract

The contour error in multi-axis free-form path-following tasks is inevitable due to the existence of factors such as servo lag and external disturbances. Therefore, the control of the contour error is of great significance for improving the precision of multi-axis motion systems. The estimation of the contour error is a premise for its control, and the estimation accuracy should be ensured as high as possible. Existing contour-error estimation methods can be mainly classified into four categories in terms of the first-order method, the second-order method, the iterative method, and their combination methods. Different from them, this paper proposes a third-order contour-error estimation algorithm, so as to improve the estimation accuracy without iterative computation. First, the desired contour is approximated as a third-order arc-length parameterized curve using the Taylor's expansion. Then, the shortest distance from the actual motion position to the approximated contour is solved analytically, thus obtaining the estimated contour error. The proposed estimation algorithm is suitable for arbitrary free-form paths because the analytical equation of the desired contour are not required, but merely kinematic parameters of multi-axis motion systems and the feedback position are utilized. Verification tests illustrate that the proposed method can distinctly improve the estimation accuracy of the three-dimensional contour error, when comparing with typical second-order methods.