On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk

A parametric interpolator for the trajectory planning of non-uniform rational basis spline (NURBS) curves is proposed in this study. The input constraints include the chord error, speed limit, acceleration limit and jerk limit. Since there is no unique representation to relate these constraints, appropriate models are developed to determine several feedrates in terms of different kinematic conditions, the minimum one of which is selected as the desired feedrate. A look-ahead stage is developed to plan a series of segment points from the curves, where a segment point represents the change in the acceleration across zero. The segment points, which enable the appropriate design of kinematic profiles, are used in real-time sampling for determining the sampling points. Several examples are presented to demonstrate the feasibility of the proposed algorithm.