Due to the uniform sampling pattern and concise trajectory generation, the raster scan has become the mainstream scan mode for atomic force microscopes (AFMs). However, the high-frequency components of the triangular trajectory and the stair trajectory for generating the raster scan tend to motivate the lightly damped resonance of the nano-positioner insides AFMs and thus severely limit the imaging speed of AFMs. To handle this issue, a novel smoothed raster scan trajectory generation method is proposed in this article via replacing the non-imaging path of both fast axis and slow axis with an optimally designed smoothed transition trajectory. A universal mathematical expression of the smoothed raster scan trajectory is developed, following by the detailed frequency spectral analysis. The analysis results reveal that the inner model of the smoothed slow-axis trajectory is the sum of two cascaded integrators and a series of sinusoidal internal models distributed at the scanning frequency along with its harmonic frequencies. As a result, an embedded repetitive control (RC) scheme is adopted to achieve the high-bandwidth and high-accuracy tracking for both fast- and slow-axis trajectories so as to contribute to a high-speed raster scanning. Comprehensive trajectory tracking experiments and imaging experiments are performed on a commercial AFM. The experimental results show that, under the scanning frequency of 100 Hz, the root-mean-square tracking error of the proposed smoothed trajectory is reduced from 47.1 nm (fast axis) and 7.5 nm (slow axis) of the conventional trajectory to 6.9 nm (fast axis) and 3.8 nm (slow axis) with the same RC schemes, and maximum tracking error of the same smoothed slow-axis trajectory is reduced from 387.7 nm with PI scheme and 138.2 nm with PI+PDOB scheme to 13.0 nm with the RC scheme, which verify the effectiveness and advancement of the proposed trajectory smoothing method and the developed control scheme. Note to Practitioners—Raster trajectory implemented via fast- and slow-axis coordinated motion has been widely used within modern precision manufacturing and measuring systems such as the atomic force microscope, coordinate measuring machine, laser or ion-beam machine tool. The high-accuracy and high-speed tracking of the raster trajectory is the basic requirement for these sophisticated systems to achieve the intended function. However, the trajectory mutation of the raster trajectory induces large amounts of high-frequency trajectory components for each servo axis and thus brings a significant challenge for its high-performance motion control. In this article, a novel smoothed raster scan trajectory generation method is developed to reduce the high-frequency components of the conventional raster trajectory and thus facilitate its trackable performance on the basis of the frequency spectral analysis of the smoothed raster scan trajectory. The spectral analysis results reveal for the first time that the frequency spectral function of the smoothed slow-axis trajectory is the linear combination of those of two cascaded integrator and a periodic trajectory. This conclusion motivates the usage of a simple yet efficient embedded repetitive control (RC) scheme by integrating a proportional-integral (PI) controller with a repetitive controller for the high-performance tracking of both fast and slow axes whilst suppressing their cross-coupling errors without extra compensators. The effectiveness of the proposed smoothed raster scan trajectory as well as the developed embedded RC scheme have been preliminarily verified via high-speed AFM imaging. This development can also be applied on other systems involved in the high-speed tracking of the raster trajectory.

The dual-loop controller (DLC) with both inner damping and outer tracking controllers has demonstrated exceptional performance in high-speed control of piezo-actuated nano-positioners. However, the accurate low-order model of the plant is imperative for designing the damping controller, according to the conventional DLC design principle. This limits its application in controlling piezoelectric tube scanners (PTSs) with compound dynamics. To handle this problem, this study introduces a frequency domain method for designing the DLC based on the frequency response data of the PTS. This method mitigates issues related to modeling errors. Specifically, the Nyquist diagram is employed to provide the stability boundary for parameters determination. A constraint optimization problem is formulated to achieve a high bandwidth with a flat amplitude frequency response. And the differential evolution algorithm is then adopted to find an optimal solution. Experimental validation on a PTS comfirms the effectiveness of this frequency domain design method. The results indicate that the control bandwidth of the optimized DLC achieves 848 Hz for a PTS with the first resonant frequency of 702 Hz. The superiorities of the DLC designed by the proposed optimization method are also validated via comparative tracking experiments involving step and triangular trajectories.Note to Practitioners—Frequency response data (FRD)-based methods open a new perspective to the controller design and optimization. Unlike traditional methods relying on transfer function models, the FRD of the system is directly identified and employed for the controller design and optimization, eliminating the need for extensive modeling and system identification efforts, thereby reducing errors. This paper proposes an FRD-based method for the simultaneous optimization of the DLC to achieve a high control bandwidth with a flat amplitude frequency response. This method relieves the requisite of accurate low-order model of the plant in conventional DLC designs. A closed-loop control bandwidth that exceeds the first resonant frequency is obtained for a PTS with complex high-order dynamic models. The proposed method enriches the scope of the DLC for the high bandwidth control, extending its applications to the systems with compound dynamics, which is significant to the high-speed control tasks of nano-positioners, such as the atomic force microscope imaging.

The normal-stressed electromagnetic actuators (NSEAs) have emerged as a promising actuation technology for developing high-performance compliant nano-positioning stages. But less attention was devoted to the modeling of the multi degrees-of-freedom (DoF) NSEA-based stages. This paper aims to improve the modeling accuracy of the stages’ static and dynamic performances by introducing a novel electromagnetic-mechanical modeling method. Unlike the previous studies, the proposed modeling method considers the effects of the NSEAs’ negative stiffnesses along both its actuation direction and the vertical-to-actuation direction in the electromagnetic modeling step. Together with the model of the mechanisms, the coupled electromagnetic-mechanical model is analytically derived. As an application case, the working stroke and resonant frequency of a NSEA-based parallel-kinematic 2-DoF compliant nano-positioning stage are evaluated with the proposed model. It is demonstrated by numerical, simulation, and experimental studies, that the proposed modeling method is accurate for predicting the performances of the NSEA-based nano-positioning stages. This is significant for the future development and applications of NSEA-based mechatronic systems.Note to Practitioners—The multi-DoF NSEA-based nano-positioning stages are the promising choice to develop long stroke, high natural frequency nano-positioning stages. However, some inherent electromagnetic-mechanical coupling effects are ignored in previous study when modeling the multi-DoF NSEA-based stages, which leads to a significant prediction error. By considering the electromagnetic characteristics both along and vertical to actuation direction, this study proposed an electromagnetic-mechanical model for the 2-DoF NSEA-based stages. The proposed model shows a higher accuracy to evaluate the static and dynamic performances of the NSEA-based stages, which are beneficial to practical applications such as trajectories tracking.

Keypoint detection and tracking in traditional image frames are often compromised by image quality issues such as motion blur and extreme lighting conditions. Event cameras offer potential solutions to these challenges by virtue of their high temporal resolution and high dynamic range. However, they have limited performance in practical applications due to their inherent noise in event data. This paper advocates fusing the complementary information from image frames and event streams to achieve more robust keypoint detection and tracking. Specifically, we propose a novel keypoint detection network that fuses the textural and structural information from image frames with the high-temporal-resolution motion information from event streams, namely FE-DeTr. The network leverages a temporal response consistency for supervision, ensuring stable and efficient keypoint detection. Moreover, we use a spatio-temporal nearest-neighbor search strategy for robust keypoint tracking. Extensive experiments are conducted on a new dataset featuring both image frames and event data captured under extreme conditions. The experimental results confirm the superior performance of our method over both existing frame-based and event-based methods. Our code, pre-trained models, and dataset are available at https://github.com/yuyangpoi/FE-DeTr.

The achievable performance with repetitive control is limited due to its inherent sensitivity to the frequency shift away from the intended periodic frequencies and the undesired gain amplification of the aperiodic disturbances. To address these limitations, the paper proposed a general parametric repetitive control (GPRC) method based on the IIR filter with the features of low-order and excellent magnitude responses to result in better tracking performance in diverse applications. By analyzing its sensitivity function, it is found that the design of GPRC can be converted to the explicit parametric design of an IIR high pass filter. The controller design process and the stability analysis are presented in detail. To show the effectiveness of GPRC, comparative experiments are conducted via tracking sinusoids, triangular trajectories and other complex trajectories with multi-frequency components. The experimental results show that, in contrast with the conventional repetitive control (CRC) and a modified repetitive control (MRC), the GPRC exhibits excellent robustness against the frequency shift and advanced performance at the aperiodic frequencies. The tracking results of the sinusoids show that the maximum tracking error obtained with GPRC for a frequency shift of 3 Hz decreases from$0.0259~\mu m$(CRC) and$0.2207~\mu m$(MRC) to$0.0101~\mu m$at the nominal frequency of 1000 Hz, demonstrating the merits of the proposed GPRC. Note to Practitioners—To enable automation systems, one of the crucial requirements is to track repetitive references with high precision. Although the normal repetitive control (RC) based schemes are successfully applied to improve the tracking accuracy of periodic trajectories, the existing RC schemes suffer from the problems of lower robustness against frequency shift and the unwanted gain amplification at the aperiodic frequencies due to Bode’s sensitivity integral. To overcome this problem, this paper proposes a novel general parametric repetitive control (GPRC) method via characterizing the loop properties quantitatively based on the IIR high pass filter design. Focusing on specific issues, the detailed variations to handle the errors at only the odd- and even-harmonics are also demonstrated. This framework leads to a flexible solution in practical implementations. The experimental validation on a piezo-actuated nanopositioning stage is comparatively presented in terms of tracking accuracy and rejection ability of the gain amplification at the aperiodic frequencies. With its flexibility and effectiveness, the proposed GPRC can be easily implemented in diverse applications.

This article presents a novel high-gain loop-shaping (HGLS) method for precision motion devices by introducing high gains into the control loop. The high gains can be generated via the inclusion of a low pass filter in a feedback manner, which could significantly improve the tracking accuracy for general trajectories with a simple structure. This control law also endows the superiority of robustness against model variations and external disturbances. To evaluate the performance of the proposed HGLS method, tracking and disturbance rejection experiments are conducted on a custom-designed piezo-actuated nanopositioner. The experimental results demonstrate the advancement of HGLS in terms of precision motion control, where the root-mean-squared error is reduced from 7.8 nm to 1.8 nm as compared with the high-gain proportional-integral controller with the same phase margin when tracking a random Non-Uniform Rational B-splines curve with large external disturbances. With its remarkable advantages of high tracking accuracy and simple structure, this method offers a practical solution for industrial automation applications for enhancing the control performance.Note to Practitioners—Advanced control methods are of great importance in meeting the tremendous requirements of automation in mechanical and electronic systems. Nonetheless, it is still challenging for a controller to simultaneously realize high control accuracy and strong robustness for general trajectories while retaining a simple structure. In this paper, a novel HGLS method is proposed. For this method, high control accuracy and strong robustness can be achieved by introducing high gains into the control loop, which can be generated by the inclusion of a simple low pass inside the closed-loop plant. A trade-off between the control gain and stability margin can be balanced only by tuning the parameters of the employed low-pass filter, and thus the implementation of the HGLS is rather simple. This method has no constraints on the form or order of the plant models and holds robustness against model variations. As compared with the high-gain proportionalintegral controller with the same phase margin, the control gain of the HGLS is much higher within the effective control bandwidth. Therefore, outstanding control performance can be achieved for general trajectories within this bandwidth. Due to the strong universality and simple structure of the HGLS, it is promising to be implemented in various industrial automation equipment, such as machine tools, multi-axis systems, robotics, scanners, etc.

Batch is an important pattern in data streams, which refers to a group of identical items that arrive closely. We find that some special batches that arrive periodically are of great value. In this paper, we formally define a new pattern, namely periodic batches. A group of periodic batches refers to several batches of the same item, where these batches arrive periodically. Studying periodic batches is important in many applications, such as caches, financial markets, online advertisements, networks, etc. This paper proposes a unified framework, namely the HyperCalm sketch, to detect batch and periodic batch in data streams. HyperCalm sketch takes two phases to detect periodic batches. In phase 1, we propose a time-aware Bloom filter, called HyperBloomFilter (HyperBF), to detect batches. In phase 2, we propose an enhanced top-k algorithm, called Calm Space-Saving (CalmSS), to report top-itk periodic batches. Extensive experiments show HyperCalm outperforms the strawman solutions 4× in term of average relative error and 98.1× in term of speed. All related codes are open-sourced.

In this paper, we study steady flows in data streams, which refers to the flows whose arrival rate is always non-zero and around a fixed value for several consecutive time windows. To find steady flows in real time, we propose a novel sketch-based algorithm, SteadySketch, aiming to accurately report steady flows with limited memory. To the best of our knowledge, this is the first work to define and find steady flows in data streams. The key novelty of SteadySketch is our proposed reborn technique, which reduces the memory requirement by 75%. Our theoretical proofs show that the negative impact of the reborn technique is small. Experimental results show that, compared with the two comparison schemes, SteadySketch improves the Precision Rate (PR) by around 79.5% and 82.8%, and reduces the Average Relative Error (ARE) by around$905.9\times $and$657.9\times $, respectively. Finally, we provide three concrete cases: cache prefetch, Redis and P4 implementation. As we will demonstrate, SteadySketch can effectively improve the cache hit ratio while achieving satisfying performance on both Redis and Tofino switches. All related codes of SteadySketch are available at GitHub.

Repetitive disturbances exist widely within the automation systems, which is one of the major issues that hinder the achievement of precision operations. Dedicated to mitigating these disturbances, a generalized periodic-disturbance observer (PDOB) using spectrum-selection filtering scheme is proposed in this paper with an application to a non-minimum phase system. The design process of the spectrum-selection filter that derives from the comb-like notch filter for the proposed PDOB is presented in detail. The variants of the proposed PDOB are also presented for the disturbances distributed only in odd- and even-harmonics. To achieve tracking of the desired trajectories, the proposed PDOB is combined in parallel with a baseline Proportional-Integral (PI) controller. The stability condition of the closed-loop system is derived to provide criteria for parameters selection. The experimental validation of the generalized PI+PDOB is conducted via real-time cross-coupling suppression in raster scanning of atomic force microscope (AFM), where the coupling induced root-mean-square tracking errors are reduced from 141.8$nm$to 2.4$nm$by employing the proposed PDOB for the scanning rate of 100 Hz. The results of convergence testing, raster scanning and AFM imaging are compared to illustrate the significant improvements achieved with the proposed PDOB. In addition, experimental results show that the tracking performance using PI+PDOB in the case of existing periodic disturbances resembles with that using PI control without periodic disturbances, which implies that the employment of the proposed PDOB does not interfere with the tracking-based control schemes for staircase trajectories, showing the advantages of the proposed PDOB.Note to Practitioners—Repetitive motions facilitate diverse advanced functions within the automation systems, including the scanning electron microscope, atomic force microscope, manipulators, and robotic systems. These operations would unavoidably introduce repetitive disturbances, hindering its achievable precision. One particular issue is the widely existent cross-coupling effect that results in these repetitive disturbances. In this paper, a generalized periodic-disturbance observer (PDOB) based on the spectrum-selection filtering scheme is developed to address the repetitive disturbances for real-time coupling suppression in raster scanning of Atomic Force Microscopy. Consequently, the offline learning procedures required for other learning based schemes can be avoided. Without loss of generalization, the design of PDOB is demonstrated with an application to non-minimum phase systems. A scheme of the varying parameter is also developed to achieve both fast convergence and better performance at rejecting the periodic disturbances. The detailed variations to handle the disturbances distributed only in odd- and even-harmonics are also demonstrated. Different from other disturbance observers, the inclusion of the spectrum-selection filtering scheme provides more flexibility in rejecting specific repetitive disturbances. In terms of tracking accuracy and the simple structure, this development can also be easily implemented to other systems that suffer from repetitive disturbances.

In this article, an intelligent feedforward prediction and compensation scheme to combine with a dual-loop high-bandwidth controller is proposed for high-speed and high-precision tracking controls of a nanopositioning stage. First, the dual-loop controller consisting of an inner loop damping and an outer loop tracking controller is developed with all the parameters optimized simultaneously, which could provide a control bandwidth over the first resonant frequency of the stage. Next, the Gaussian process machine learning model is employed to capture the dynamic characteristics of the tracking error of the dual-loop controlled plant. Then, a feedforward compensator is constructed to add a compensation term to the initial reference trajectory. Experimental investigations on a self-made piezoelectric-actuated stage validate the effectiveness of the intelligent tracking error prediction method and the excellent performance of the control strategy for high-precision tracking of high-frequency reference trajectories.