An adaptive parametric interpolator for trajectory planning

A real-time interpolation algorithm for trajectory planning is studied in this paper. The NURBS interpolation algorithm is proposed to confine contour errors and feedrate fluctuations. The feedrate is adjusted adaptively according to the specified acceleration/deceleration values and jerk value. A direct digital convolution method is also introduced into velocity planning for NURBS interpolator, and it is more efficient than the traditional method of polynomial functions. The feedrate at the sharp corner is smoothed by imposing limitations on the acceleration and jerk values generated in the machining process. Since the computation of the total length of NURBS curve is required for the digital convolution method, a numerical adaptive quadrature algorithm is used to approximate the integrand. Simulation results demonstrate the effectiveness of the proposed interpolator for machining curved paths.