Path smoothing and feed rate planning for robotic curved layer additive manufacturing

Robotic curved layer additive manufacturing (a.k.a. multi-axis 3D printing) has been gaining attention recently owing to its simplicity and unique ability of printing complex shapes without using a support structure. However, as the printing path now is no long planar and the nozzle orientation is no longer fixed but changes continuously during printing, even though it could be smooth when defined in the workpiece coordinate system in both position and orientation of the nozzle, due to the inevitable numerical errors, it typically is unsmooth with many sharp-changing undulations when transformed to the coordinate system of the robot arm. As a result, the feed rate of printing has to be set extremely conservatively lest the printer would chatter or vibrate and seriously jeopardize the printing quality. In this paper, first, we present a practical B-spline based smoothing algorithm for removing sharp corners on the printing path while upholding the required cusp-height threshold on the printed surface. Next, for the smoothed printing path, we propose a feed rate scheduling strategy that will try to maximize the variable feed rate while subject to the kinematic constraints of the six joints of the robot arm. Both computer simulations and physical printing experiments are carried out to assess the proposed methodologies and the results give a positive confirmation on their advantages.