[论文解读] Software Compensation of Undesirable Racking Motion of H-frame 3D Printers using Filtered B-Splines

Nosakhare Edoimioya, Keval S. Ramani+1 more|arXiv (Cornell University)|May 20, 2021

Iterative Learning Control Systems参考文献 34被引用 9

一句话总结

本文提出一种基于软件的前馈补偿方法，采用滤波B样条（FBS）以减轻H型框架3D打印机中的爬行误差，该误差源于高速运动时因力偶引起的寄生扭转运动。通过建立H型框架的耦合线性参数时变（LPV）动力学模型，并利用基于频响特性的FBS框架优化B样条控制点，该方法在无需机械改动的情况下实现了43%的零件形状精度提升。

ABSTRACT

The H-frame (also known as H-Bot) architecture is a simple and elegant two-axis parallel positioning system used to construct the XY stage of 3D printers. It holds potential for high speed and excellent dynamic performance due to the use of frame-mounted motors that reduce the moving mass of the printer while allowing for the use of (heavy) higher torque motors. However, the H-frame's dynamic accuracy is limited during high-acceleration and high-speed motion due to racking -- i.e., parasitic torsional motions of the printer's gantry due to a force couple. Mechanical solutions to the racking problem are either costly or detract from the simplicity of the H-frame. In this paper, we introduce a feedforward software compensation algorithm, based on the filtered B-splines (FBS) method, that rectifies errors due to racking. The FBS approach expresses the motion command to the machine as a linear combination of B-splines. The B-splines are filtered through an identified model of the machine dynamics and the control points of the B-spline based motion command are optimized such that the tracking error is minimized. To compensate racking using the FBS algorithm, an accurate frequency response function of the racking motion is obtained and coupled to the H-frame's x- and y-axis dynamics with a kinematic model. The result is a coupled linear parameter varying model of the H-frame that is utilized in the FBS framework to compensate racking. An approximation of the proposed racking compensation algorithm, that decouples the x- and y-axis compensation, is developed to significantly improve its computational efficiency with almost no loss of compensation accuracy. Experiments on an H-frame 3D printer demonstrate a 43 percent improvement in the shape accuracy of a printed part using the proposed algorithm compared to the standard FBS approach without racking compensation.

研究动机与目标

• 解决H型框架3D打印机在高速运动时因寄生扭转龙门架运动导致的爬行误差，此类误差会降低零件精度。
• 开发一种完全基于软件的解决方案，避免对机械结构进行修改或增加额外传感器。
• 将滤波B样条（FBS）前馈控制框架扩展至处理H型框架结构特有的耦合线性参数时变（LPV）动力学。
• 通过解耦近似方法实现高计算效率，同时在补偿精度上仅造成可忽略的损失。

提出的方法

• 通过整合x轴和y轴动力学与爬行运动的运动学模型，将H型框架建模为耦合线性参数时变（LPV）系统。
• 识别爬行模态的频率响应函数（FRF），以表征其在整个打印机工作空间内的动态行为。
• 通过将运动指令表示为B样条基函数的线性组合，并经由所识别的LPV系统模型进行滤波，来构建FBS控制器。
• 在有限预览窗口框架下，采用最小二乘法优化B样条控制点，以最小化跟踪误差。
• 开发FBS控制器的解耦近似方法，独立处理x轴和y轴的补偿，显著降低计算负载。
• 通过仿真和真实H型框架3D打印机上的实验验证该方法，与无爬行补偿的标准FBS方法进行性能对比。

实验结果

研究问题

• RQ1 基于软件的前馈控制方法是否能有效补偿H型框架3D打印机中的爬行误差，而无需机械改动？
• RQ2 如何将滤波B样条（FBS）框架扩展以处理H型框架系统中由爬行引起的耦合线性参数时变（LPV）动力学？
• RQ3 在FBS框架中，解耦x轴与y轴爬行补偿时，计算效率与补偿精度之间的权衡如何？
• RQ4 与无爬行补偿的标准FBS方法相比，所提出的基于FBS的爬行补偿在3D打印零件的形状精度方面提升了多少？

主要发现

• 所提出的基于FBS的爬行误差补偿方法在真实H型框架3D打印机上，相较于无爬行补偿的标准FBS方法，实现了43%的形状精度提升。
• FBS控制器的解耦近似在仿真中将计算复杂度降低了13倍，同时保持了近乎相同的补偿精度。
• 该方法成功补偿了整个打印体积内的爬行误差，误差幅值随末端执行器在x轴方向的位置变化而变化。
• 该方法与现有使用步进电机的开环3D打印机兼容，因其无需位置反馈或额外传感器。
• FBS框架成功扩展至建模和补偿LPV系统中的耦合动力学，证明其在传统解耦线性时不变系统之外的广泛适用性。
• 结果表明，基于软件的补偿可有效减轻平行轴运动系统中的寄生误差运动，为提升3D打印机性能提供了一种低成本、可改造的解决方案。