Interpolation of a Clothoid Curve Based on Iterative True-Value Prediction Considering the Discretization Error

Computerized numerical control (CNC) systems are widely used in the processing field. The key technology of these systems is the interpolation that connects the desired points. The interpolation using a clothoid curve is one of the effective methods for connecting the points because of its outstanding smoothness properties. A clothoid curve is a spatial function. Hence, synthesization with a time function is necessary to apply the curve for the actual CNC equipment. The clothoid curve can be easily synthesized with a time function by designing the tangential velocity as the time function. However, a numerical calculation is necessary because the clothoid curve has a limitation in that it does not have an analytical expression. Therefore, the discretization error of the numerical calculation must be considered because the calculating resolution of the clothoid curve is determined by the tangential velocity and the sampling time. This study proposes a clothoid interpolation based on an iterative true-value prediction. This method can immediately estimate the true value of a clothoid curve by pinching integration and Aitken acceleration even in the case where the calculation resolution is limited. Hence, the method can suppress the discretization error of the clothoid curve. A smooth interpolation for the CNC machines can be achieved using the proposed method.