A NURBS interpolation method using circular arc mapping and improved S-shaped acc/dec algorithm based on filter processing

Currently, the primary challenges associated with Non-Uniform Rational B-Splines (NURBS) curve interpolation mainly are speed curve, interpolation error and machine efficiency. In order to achieve more efficient and stable speed interpolation, this study proposes a novel method of combining arc and NURBS curve mapping. And in speed planning， an improved S-shaped acceleration/deceleration (acc/dec) algorithm based on a novel filter processing of trapezoidal acc/dec model is proposed velocity planning. Firstly, the NURBS curve segmentation is determined by evaluating the arc length error between the mapping arc and NURBS curve fitting meeting accuracy requirements. Subsequently, instead of speed planning for the segmented NURBS curves, we apply the trapezoidal acc/dec speed planning based on the tangent vector to the mapping arc. Then each interpolation point data is gotten by using the relationship between the arc and NURBS curve to enhance interpolation accuracy and reduce speed fluctuation, this study divides the interpolation solution method into three cases based on the angle change of the mapping arc during each interpolation. Moreover, in order to avoid machine overshoot and the disadvantages of traditional S-shaped acc/dec algorithm with seven sections, in which the acceleration frequently changes between the maximum and 0, resulting in the overall running time prolongation. This study implements a filter processing method based on the trapezoidal acceleration and deceleration model, applied to the acquired trapezoidal acceleration and deceleration. This enables the achievement of the overall S-shaped acc/dec. Lastly, simulation and actual machining tests are conducted to verify the proposed method's efficiency and readability.