A real-time configurable NURBS interpolator with bounded acceleration, jerk and chord error

Abstract

Advances in manufacturing technologies and in machine tools allow for unprecedented quality and efficiency in production lines, but also ask for new and increasing requirements on the motion planning and control systems. The increase of CPU processing power has permitted, in traditional CNC systems, the introduction of NURBS interpolation capabilities, thus determining a further increase in machining quality and efficiency. This has posed new and still unsolved issues, such as the need to satisfy multiple opposite constraints like limiting chord error, acceleration and jerk and offering real-time guarantees. In addition, the ability of privileging the production throughput by relaxing one or more of the previous constraints in a simple way, has emerged as another requirement of modern manufacturing plants. Nevertheless, none of the existing NURBS interpolators have these characteristics. In this work, we propose a NURBS interpolator that is able to satisfy all the manufacturing technology requirements and is able to respect, thanks to its bounded computational complexity, the position control real-time constraints. Such an interpolator is easily reconfigurable, i.e., it can relax some of the constraints while maintaining performances better than previously proposed solutions, and can be adapted in order to include constraints that were not originally considered. Performances of the proposed algorithm have been evaluated both by simulations and by real milling experiments.