C2 continuous time-dependent feedrate scheduling with configurable kinematic constraints

Abstract

We present a configurable trajectory planning strategy on planar paths for offline definition of time-dependent C2 piecewise quintic feedrates. The scheduler can be applied to any path with a sufficiently smooth piecewise parametric representation and it can be used in different formulations subdivided in strict and relaxed. In the first case, control on chord tolerance, as well as on the Cartesian components of velocity, acceleration and jerk is ensured. Since the relaxed formulations can usually still ensure the desired bounds while simultaneously producing faster motions, the configurability feature is useful not only when reduced motion control is required but also when full kinematic control has to be guaranteed. When Pythagorean-hodograph spline curves are considered, the corresponding accurate and efficient CNC interpolator algorithms can be exploited, as shown in the numerical experiments.