Feed-rate and trajectory optimization for CNC machine tools

The key task performed by CNCs is the generation of the time-sequence of set-points for driving each physical axis of the machine tool during program execution. This interpolation of axes movement must satisfy a number of constraints on axes dynamics (velocity, acceleration, and jerk), and on process outcome (smooth tool movement and precise tracking of the nominal tool-path at the desired feed-rate). This paper presents an algorithm for CNC kernels that aims at solving the axes interpolation problem by exploiting an Optimal Control Problem formulation. With respect to other solutions proposed in the literature, the approach presented here takes an original approach by assuming a predefined path tracking tolerance-to be added to the constraints listed above-and calculating the whole trajectory (path and feed-rate profile) that satisfies the given constraints. The effectiveness of the proposed solution is benchmarked against the trajectory generated by an industrial, state-of-the-art CNC, proving a significant advantage in efficiency and smoothness of axes velocity profiles.