  The delta robot is becoming a popular choice for the mechanical design of
fused filament fabrication 3D printers because it can reach higher speeds than
traditional serial-axis designs. Like serial 3D printers, delta printers suffer
from undesirable vibration at high speeds which degrades the quality of
fabricated parts. This undesirable vibration has been suppressed in serial
printers using linear model-inversion feedforward control methods like the
filtered B-splines (FBS) approach. However, techniques like the FBS approach
are computationally challenging to implement on delta 3D printers because of
their coupled, position-dependent dynamics. In this paper, we propose a
methodology to address the computational bottlenecks by (1) parameterizing the
position-dependent portions of the dynamics offline to enable efficient online
model generation, (2) computing real-time models at sampled points (instead of
every point) along the given trajectory, and (3) employing QR factorization to
reduce the number of floating-point arithmetic operations associated with
matrix inversion. In simulations, we report a computation time reduction of up
to 23x using the proposed method, while maintaining high accuracy, when
compared to a controller using the computationally expensive exact LPV model.
In experiments, we demonstrate significant quality improvements on parts
printed at various positions on the delta 3D printer using our proposed
controller compared to a baseline alternative, which uses an LTI model from one
position. Through acceleration measurements during printing, we also show that
the print quality boost of the proposed controller is due to vibration
reductions of more than 20\% when compared to the baseline controller.
