An iterative feedrate optimization method for real-time NURBS interpolator

Non-uniform rational B-spline (NURBS) interpolator has been widely used in modern manufacturing systems to machine arbitrary geometries with great relief of the data flow bottleneck and feedrate fluctuation. However, in practice, real-time feedrate does not always meet the computer numerical control (CNC) command exactly subject to the system dynamics. To solve this problem, we present a real-time NURBS interpolator with feedrate optimization for CNC machining tools in this work. The parametric curve is first approximated with the Adams–Bashforth method which provides uniform feedrate in each sampling period in the interpolation process. And then, a feedback scheme is introduced to adjust the feedrate in real time so as to guarantee a specified deviation between the measured and the desired feedrate. The convergence condition for this closed-loop algorithm is presented and analyzed. Simulation and real experiments on an X–Y table are employed to verify its feasibility. And the comparisons with traditional interpolators based on Taylor's expansion are also provided to demonstrate its improvement in accuracy.