Real-Time Contour-Error Estimation Methods for Three-Dimensional Free-Form Parametric Curves in Contour-Following Tasks

Abstract

It is crucial to control the contour error in curved contour-following tasks caused by reasons such as servo delay and external disturbance. Contour-error estimation plays as a precondition for its further control. Existing methods can hardly keep well estimation accuracy for high-speed following of free-form curves with sharp corners, especially for three-dimensional curves. Consequently, this paper presents three high-precision real-time contour-error estimation methods for spatial free-form parametric curved contour following. By generating and updating the backstepping point according to the tangential tracking error, a multiple tangential approximation method is presented first. Then, a spatial circular approximation method is given by means of approximating the actual-position nearby region of the desired contour with a spatial circle. Finally, via modification of the Newton method so as to improve its stability without sacrificing of its fast convergence property, an initial value regeneration-based Newton algorithm is proposed for contour-error estimation. All of the presented methods take both estimation precision and calculation burden into consideration, and possess their own advantages. Using these algorithms, the contour error can be rapidly estimated in vector form with a high accuracy. Simulation and experimental results demonstrate the feasibility and the superiority of the presented algorithms.