Cubic spline trajectory generation with axis jerk and tracking error constraints

Abstract

This paper presents a cubic spline trajectory generation algorithm that produces continuous position, velocity, and acceleration profiles for CNC machines with confined axis jerk and tracking error. A series of reference knots are connected using cubic spline functions in time t for constructing axis trajectories. They are generated in such a way that continuity up to the second derivative is preserved along the overall composite curve. For CNC machines governed by a typical PID controller, the tracking error is also constrained as well as the velocity, acceleration, and jerk for each axis. The time intervals between each pair of adjacent knots are scheduled such that the machining time is minimized subject to all the constraints. Experiment results are presented to illustrate the application of the algorithm.