C2 continuous time dependent feedrate scheduling with configurable kinematic constraints

TL;DR

This paper introduces a configurable trajectory planning method for planar paths that ensures smooth, bounded, and efficient feedrate profiles, adaptable for different kinematic constraints and applicable to various path representations.

Contribution

It proposes a novel, configurable C2 continuous feedrate scheduling strategy that guarantees kinematic bounds and can be tailored for speed or control precision.

Findings

Ensures bounded velocity, acceleration, and jerk for smooth motion.

Provides a flexible framework adaptable to different path representations.

Achieves efficient CNC interpolation with Pythagorean-hodograph spline curves.

Abstract

We present a configurable trajectory planning strategy on planar paths for offline definition of time-dependent C2 piecewise quintic feedrates. The more conservative formulation ensures chord tolerance, as well as prescribed bounds on velocity, acceleration and jerk Cartesian components. Since the less restrictive formulations of our strategy can usually still ensure all the desired bounds while simultaneously producing faster motions, the configurability feature is useful not only when reduced motion control is desired but also when full kinematic control has to be guaranteed. Our approach can be applied to any planar path with a piecewise sufficiently smooth parametric representation. When Pythagoreanhodograph spline curves are considered, the corresponding accurate and efficient CNC interpolator algorithms can be exploited.