Precision manufacturing equipment suffer from unwanted vibrations triggered in rapid motion. Unless mitigated, these vibrations limit achievable accuracy and productivity of motion systems. This article presents a novel technique to generate reference motion trajectories that can robustly avoid triggering unwanted inertial vibrations. The reference trajectory is defined in B-spline form, and its frequency spectrum is optimized to attenuate spectral energy in a desired frequency band to avoid excitation of unwanted vibrations. A novel time-domain smoothing objective is also proposed to improve tracebility of generated trajectories. The trajectory optimization problem is put in a convex form, and a novel windowing scheme is designed to solve it efficiently for real-time implementation. Robustness and effectiveness of the proposed method is validated experimentally on an industrial three-axis Cartesian machine tool. Experiments show that the proposed method can robustly avoid unwanted structural vibrations without introducing delay to the motion and outperform state-of-the-art prefiltering methods.

中文翻译：

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避免多轴振动的稳健轨迹生成

精密制造设备会遭受快速运动触发的有害振动。除非加以缓解，否则这些振动会限制运动系统可实现的精度和生产率。本文提出了一种新颖的技术来生成参考运动轨迹，该参考轨迹可以稳健地避免触发不必要的惯性振动。参考轨迹以B样条曲线形式定义，并且其频谱经过优化以衰减所需频带中的频谱能量，以避免激发不想要的振动。还提出了一种新颖的时域平滑目标，以提高生成轨迹的可跟踪性。轨迹优化问题采用凸形形式，设计了一种新颖的加窗方案以有效地解决该问题，以实现实时实现。该方法的鲁棒性和有效性在工业三轴笛卡尔机床上进行了实验验证。实验表明，所提出的方法可以稳健地避免有害的结构振动，而不会给运动造成延迟，并且性能优于最新的预过滤方法。