Vibration compensation of delta 3D printer with position-varying dynamics using filtered B-splines

Abstract

The delta robot can reach higher speeds than traditional serial-axis machines used in fused filament fabrication 3D printing. However, like serial machines, 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 computation of the model online, (2) computing 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 23× using the proposed method when compared to using the computationally expensive exact LPV model—all while maintaining high tracking accuracy. Accordingly, we demonstrate significant quality improvements on parts printed at various positions on a commercial delta 3D printer using our proposed controller compared to a baseline alternative, which uses an LTI model from one position. Acceleration measurements during printing show that the improvement in print quality of the proposed controller is due to vibration reductions of up to 39% when compared to the baseline controller.