Spatial Trajectories Research Articles

Direct Manufacturing Technology for High‐Precision Follow‐the‐Shape Circuits on Complex, Hard, Curved Surfaces

Abstract3D curved electronics are a trend in the microelectronics industry, but conformal printing of circuits on complex curved surfaces remains challenging, especially for electronics comprising concave surfaces with large curvature. In this study, a new manufacturing method is proposed for follow‐the‐shape circuits, using high‐precision direct printing technology to print circuits on hard, arbitrarily curved surfaces. A circuit with any complex curved surface can be directly digitized and programmed for fully autonomous and controlled printing without indirect transfer or pad printing processing. The proposed direct printing method begins with using unique 3D projection technology to map a 2D planar functional circuit onto a 3D digital curved surface. The next step is directly printing the integrated circuit on a complex surface by controlled planning of the spatial motion trajectory, high‐frequency drive control of the precision nozzle, and precise switching control of the heterogeneous functional material. Optimal printing parameters are obtained by exploring the main factors affecting molding quality and electrical conductivity of curved surface circuits. Simple examples, such as an acoustic‐optic touch time‐delay three‐control multifunction system, demonstrate the feasibility and broad potential of the proposed technology.

Spatial-MGCN: a novel multi-view graph convolutional network for identifying spatial domains with attention mechanism.

Recent advances in spatial transcriptomics technologies have enabled gene expression profiles while preserving spatial context. Accurately identifying spatial domains is crucial for downstream analysis and it requires the effective integration of gene expression profiles and spatial information. While increasingly computational methods have been developed for spatial domain detection, most of them cannot adaptively learn the complex relationship between gene expression and spatial information, leading to sub-optimal performance. To overcome these challenges, we propose a novel deep learning method named Spatial-MGCN for identifying spatial domains, which is a Multi-view Graph Convolutional Network (GCN) with attention mechanism. We first construct two neighbor graphs using gene expression profiles and spatial information, respectively. Then, a multi-view GCN encoder is designed to extract unique embeddings from both the feature and spatial graphs, as well as their shared embeddings by combining both graphs. Finally, a zero-inflated negative binomial decoder is used to reconstruct the original expression matrix by capturing the global probability distribution of gene expression profiles. Moreover, Spatial-MGCN incorporates a spatial regularization constraint into the features learning to preserve spatial neighbor information in an end-to-end manner. The experimental results show that Spatial-MGCN outperforms state-of-the-art methods consistently in several tasks, including spatial clustering and trajectory inference.

Spatial Variability of the Frontal Zones and its Eddies Generated in the Norwegian Sea

The Norwegian Sea is the meeting place of warm and salty Atlantic waters with cold and fresh Arctic waters. The thermal and haline frontal zones (FZs) formed as a result of this interaction are areas of increased horizontal gradients of physical, chemical, and biological parameters, and have a significant impact on regional circulation. Many mesoscale eddies are generated in the FZs which are actively involved in the eddy dynamics of the Norwegian Sea. The aim of this work is to analyze the spatio-temporal variability of the vertical structure of FZs in the Norwegian Sea, as well as the eddies that form within their boundaries. The work uses data from the oceanic reanalysis GLORYS12V1, as well as the Atlas of Mesoscale Eddies "Mesoscale Eddy Trajectory Atlas product META 3.2 DT" for the period 1993--2021. We analyze the average depth and thickness of FZs, the vertical distribution of their thermohaline gradients and areas. The work examines the seasonal and interannual variability of the volumes of thermal and haline FZs, the seasonal and interannual variability of mesoscale eddies, their spatial distribution, trajectories, and main parameters. In some areas, deepening of FZs has been established, and their thickness can reach 900 m. The presence of significant haline gradients in the layer of 250--750 m has been found, while thermal FZs can be traced vertically up to 1000 m compared with haline FZs. In some FZs, the interannual variability may exceed the seasonal one. The greatest variability of haline FZs can be traced in the autumn period, and the smallest -- in the winter--spring. It is noticeable in the summer period that thermal FZs weaken. Eddies can leave the boundaries of the FZs and move away from the place of origin for hundreds of kilometers. The number and lifetime of cyclones exceed similar estimates for anticyclones, while anticyclones travel long distances compared to cyclones.

Вертикальная изменчивость интенсивности фронтальных зон Норвежского моря

The Norwegian Sea is the meeting place of warm and salty Atlantic waters with cold and fresh Arctic waters. The thermal and haline frontal zones (FZs) formed as a result of this interaction are areas of increased horizontal gradients of physical, chemical, and biological parameters, and have a significant impact on regional circulation. Many mesoscale eddies are generated in the FZs which are actively involved in the eddy dynamics of the Norwegian Sea. The aim of this work is to analyze the spatio-temporal variability of the vertical structure of FZs in the Norwegian Sea, as well as the eddies that form within their boundaries. The work uses data from the oceanic reanalysis GLORYS12V1, as well as the Atlas of Mesoscale Eddies "Mesoscale Eddy Trajectory Atlas product META 3.2 DT" for the period 1993--2021. We analyze the average depth and thickness of FZs, the vertical distribution of their thermohaline gradients and areas. The work examines the seasonal and interannual variability of the volumes of thermal and haline FZs, the seasonal and interannual variability of mesoscale eddies, their spatial distribution, trajectories, and main parameters. In some areas, deepening of FZs has been established, and their thickness can reach 900 m. The presence of significant haline gradients in the layer of 250--750 m has been found, while thermal FZs can be traced vertically up to 1000 m compared with haline FZs. In some FZs, the interannual variability may exceed the seasonal one. The greatest variability of haline FZs can be traced in the autumn period, and the smallest -- in the winter--spring. It is noticeable in the summer period that thermal FZs weaken. Eddies can leave the boundaries of the FZs and move away from the place of origin for hundreds of kilometers. The number and lifetime of cyclones exceed similar estimates for anticyclones, while anticyclones travel long distances compared to cyclones.

Dynamic Optical Vortex Trajectory Guided by the Symmetric Pearcey Gaussian Vortex Beam in the Uniformly Moving Parabolic Potential

AbstractThis paper analytically and numerically proposes the propagation dynamics of the symmetric Pearcey Gaussian vortex beam (SPGVB) in the uniformly moving parabolic potential. The optical vortex located in the initial plane produces a vortex channel in the presence of the uniformly moving parabolic potential, called the vortex trajectory. The vortex trajectory can be manipulated dynamically by configuring different combinations of the parameters, and the optical intensity and the focal position can also be affected. Moreover, the spatial dynamic vortex trajectory is derived analytically, and the 2D on‐axis and off‐axis vortex scenarios are also presented. Our work expands the methods of the vortex trajectory manipulation and may broaden more practical potential applications in the particle manipulation.

Normal-Stressed Electromagnetic Triaxial Fast Tool Servo for Microcutting

Short strokes and complicated structures commonly degrade the operating performance of current piezo-actuated triaxial fast tool servos (FTSs). To overcome those deficiencies, we present a novel normal-stressed electromagnetic triaxial FTS for micro-cutting, which achieves a compact structure and a high resonant frequency with triaxial motions in hundreds of micrometers. The magnetic FTS has a single armature to provide the triaxial decoupled and non-contact driving forces, as well as a symmetric 3-DOF corrugated compliant bearing to support and guide the decoupled outputs. With the parameters jointly optimized by an analytical and finite element model, the prototype showed a high degree of agreement with the design target for both static and dynamic performances. A linear active disturbance rejection control is implemented for the triaxial FTS, and an iterative learning scheme is further employed for the triaxial FTS to achieve fast and accurate trajectory tracking. The developed triaxial FTS is comprehensively demonstrated by fabricating a hexagonal spherical micro-lens array with each lenslet generated within 0.24&#x00A0;s. The practical error for the spatial trajectory tracking was within <inline-formula><tex-math notation="LaTeX">$ \pm$</tex-math></inline-formula>30&#x00A0;nm, and good surface quality with a form error of 63.66&#x00A0;nm and surface roughness of <i>Sa</i>=2.05&#x00A0;nm is achieved.

A novel voxel-particle energy approach to predict 3D microscopic fracture surface of porous geomaterials and fracture permeability modeling

Characterizing and predicting 3D microscopic fractures are rarely reported due to the challengeable difficulty to determine its spatial trajectories. In this study, a double threshold segmentation algorithm is proposed to obtain 3D microstructure models of porous geomaterials by X-ray computing tomography (CT) images. A novel voxel-particle energy (VPE) approach is proposed to predict 3D fracture characteristics, and fracture permeability modeling is conducted. Results show that excellent agreements are found between the experimental and numerical results, showing the accuracy of proposed VPE method. As dynamic viscosity increases, microscopic fracture permeability increases. Microscopic fracture permeability decreases with increasing input pressure, and it increases with increasing voxel scale. The proposed VPE method provides an effective tool to predict 3D cracks and its spatial trajectories, which is helpful for the deep resource and underground space development.

Optimal temperature trajectory for tubular reactor using physics informed neural networks

Numerical approaches to solve partial differential equations (PDEs) governing the physical systems are very time consuming, and it limits their applications in online decision making. These physical systems can be modeled using a Neural network, and a nonlinear mapping can be obtained by capturing the knowledge represented by the PDEs governing the physical system. Such a Physics Informed Neural Network (PINN) generates a solution in a closed analytical form that maps the inputs of the PDE to its solution. In this paper, we exploit the advantage of obtaining this closed analytical form of solution for substantially easing the step of inverting such models for optimization. We demonstrate this capability by obtaining the optimal spatial temperature trajectory of a representative tubular reactor model to maximize the reactor yields. The PINN model was seen to accurately capture the dynamics of the tubular reactor governed by second order PDEs with spatial variables and temperature parameters as inputs. The results of modeling and optimization were compared with the finite difference method (FDM) of solving PDEs and were found to be computationally superior to the latter. The computational time taken by the PINN framework to obtain the optimal trajectory was significantly less than the traditional FDM method without compromising accuracy. Such approaches can supersede traditional methods where the governing physical models are computationally expensive and facilitate online decision making through the use of PINNs.

Understanding children's cycling route selection through spatial trajectory data mining

A sustainable alternative transportation mode to address growing transportation and environmental stress is cycling, which is eco-friendly and healthy for humans. Improving the quality of the bicycling experience is crucial for increasing bicycle use. Good bicycling experience is more critical for child bicyclists because they are less experienced and need more space for error. Therefore, a scientific assessment of child bicyclist perception of selected route safety, comfort, and environment is of great interest. Finding an effective way to learn child bicyclist behavior and help them reduce cycling risk is necessary. In response to this need, we utilize a data mining model to develop a methodology for measuring children's bicycling route safety conditions by evaluating multiple road safety-related features. The proposed method uses a set of route features representing the situation of street environments extracted from state data and first-hand children’s bicycle trajectory data collected using Global Positioning Systems (GPS) from volunteer children bicyclists. A random forest (RF), a well-known classifier, is adopted to predict child bicyclists' behavior. We extract the different route segments between children’s selected routes and the shortest path to learn the child bicyclists' behavior and use the selected best features to interpret their changing cycling behavior. The result shows that children bicyclists' behavior could be analyzed by giving trajectory and nearby road safety situation data. Our model achieves a promising accuracy with an average rate of 92% over multiple scenarios, demonstrating the proposed method's feasibility and the effectiveness of selected features. In addition, we compare our feature effectiveness with the state's generated road safety score data to evaluate the feature robustness. Our features outperform the safety score feature with an average of 10% improvement in prediction accuracy. Furthermore, our method proposes a model framework that can be applied to different study regions and adult bicycling behavior learning.

An online method for robust target tracking using a wireless sensor network

This work addresses the target tracking problem using a wireless sensor network (WSN). A set of sensors is randomly deployed to continuously monitor the moving targets, with their spatial trajectories already known but with estimated temporal trajectories and thus, possible delays and advances. The network has to transfer the data collected by the sensors to a base station, with hop-communication between the sensors. Previous works focused on the computation of a robust activation schedule which is passively tracking the targets (i.e., with no reaction to the actual behavior of the targets) by just activating sensors according to the pre-computed schedule. It has a maximized stability radius which is the guarantee on the maximal delay or advance of the targets it can cover, however it loses some targets whenever a delay or advance is beyond the value of its stability radius. Consequently, it is observed in many instances that a target is lost despite being in the range of a fully functioning WSN. A major novelty of the present work is to propose an online method that actively reacts to the delays and advances of the targets to extend the coverage offered by the robust schedule. The proposed method both detects the delays and advances beyond the stability radius, and constantly modifies the schedule to cover the targets as long as possible, at a computational cost that remains acceptable in a real-life application. It lets the WSN monitor the targets despite delays and advances that may not be covered by the guarantee of the stability radius. The second major novelty of our work is the introduction of the dynamic stability radius; it is a guarantee on the greatest delay or advance that can be covered by an online scheduling method. It is, by definition, greater than or equal to the classical stability radius but it is dynamically recomputed such that this guarantee increases over time. Our online method is dynamically optimizing the dynamic stability radius, meaning that each online decision is made so that the WSN has increasing capacities to cover the targets over time. Numerical experiments show that the online method proposed in this work offers more robustness than the previous works, with a dynamic stability radius that improves significantly over the stability radius from previous works, and that increases over time. Experiments also highlight the possibility to use such a method in a real-time context because of its fast computation time.

Pitch Angle Error Measurement Technology for Track and Control Equipment Based on Trajectory

Due to the large support span of the pitching mechanism of the Fork-arm antenna pedestal of large phased array track and control equipment, the antenna array was deflected downward by its self-weight load. When measuring the pitch angle error, the pitch axis and the normal pointing angle of the array fluctuated, which significantly interfered with the evaluation results of common measuring methods for pitch angle error such as electronic goniometer. In view of the above problems, this paper proposed a pitch angle error measurement technology of track and control equipment based on motion trajectory. In this method, Target point for measurement was set in the appropriate area of the end face of the array skeleton, and the laser tracker was used to track and capture the spatial coordinates and trajectory of the target point in the process of pitching motion. The geometric model of the pitch angle algorithm was constructed based on the circular motion trajectory, which eliminated the influence of the fluctuation of the pitch axis and the normal pointing angle of the array on the pitch angle. The pitch angle error algorithm and data processing model were established, and the programmed rapid calculation and evaluation of the pitch angle deviation of track and control equipment were realized.

Four-dimensional digital design to prediction of the real-time functional rehabilitation in the esthetic zone

Recent developments in digital technology and materials have improved the accuracy and efficiency of tracking and recording mandibular motion, with various methods being described. The present article describes a digital workflow with complete and accurate 3-dimensional spatial trajectories of mandibular motion to direct the design of lingual restorations. The workflow allowed the lingual curvature of the restoration to conform with the distinctive trajectory of mandibular protrusion.

Dynamic Analysis of a Delta Parallel Robot with Flexible Links and Joint Clearances

Delta robot is a lightweight parallel manipulator capable of accurately moving heavy loads at high speed and acceleration along a spatial trajectory. This intensive dynamic process may have a significant impact on the end-effector trajectory precision and motor behavior. The paper highlights the influence on the dynamic behavior of a Delta robot by considering individual and combined effects of clearances and friction in the spherical joints, as well as the flexibility of the rod elements. The CAD modeling of the Delta robot and its motion simulation on a representative spatial trajectory where the maximum allowed values of speed and acceleration are reached were performed using the Catia and Adams software packages. The obtained results show that the methods used were successfully applied and the effects are mutually interconnected, but not cumulative.

Inland Vessel Travel Time Prediction via a Context-Aware Deep Learning Model

Accurate vessel travel time estimation is crucial for optimizing port operations and ensuring port safety. Existing vessel travel time prediction models primarily rely on path-finding algorithms and corresponding distance/speed relationships to calculate travel time. However, these models overlook the complex nature of vessel travel time, which is influenced by multiple traffic-related factors such as collision avoidance, shortest path selection, and vessel personnel performance. The lack of consideration for these specific aspects limits the accuracy and applicability of current models. We propose a novel context-aware deep learning approach for inland vessel travel time prediction. Firstly, we introduce a complex network that captures vessel–vessel interaction contexts, providing valuable traffic environment information as an input for the deep learning model. Additionally, we employ a convolutional neural network to extract spatial trajectory information, which is then integrated with interaction contexts and indirect context information. In the vessel travel time prediction procedure, we utilize a long short-term memory network to capture the temporal dependence within consecutive channel sections’ fused multiple context feature sets. Extensive experiments incorporating historical data from the Wuhan section of the Yangtze River in China demonstrate the superiority of our proposed model over classical models in predicting vessel travel time. Importantly, our model accounts for the specific traffic contexts that had previously been overlooked, leading to improved accuracy and applicability in inland vessel travel time prediction.

An Adaptive Control Method with Disturbance Estimation for Underwater Manipulation

In this paper, an adaptive control scheme with disturbance estimation is proposed for the station keeping and trajectory tracking of an underwater vehicle-manipulator system (UVMS) in a task space. The control of UVMSs encounters time-varying and lumped disturbances introduced by the motion of the manipulator and currents. The proposed control scheme includes an observer to identify disturbances without introducing additional sensors. Using state-of-the-art UVMS control technologies, it alleviates the restriction of the feedforward control applied to the UVMS. In addition, the proposed control scheme is not designed based on the worst case. In other words, the robustness of the controller is not achieved at the price of performance, and the performance of the controller can be recovered in the absence of disturbance. Meanwhile, the controller can also realize quick responses to attenuating disturbance and closed-loop stability when encountering an unexpected disturbance. The effectiveness of the proposed control scheme was demonstrated by a series of spatial trajectory tracking experiments under various disturbances. A limitation of this study is that the proposed control scheme is specialized for the underwater manipulation of UVMSs.

Development and Experimental Studies of a Method Based on a Reference Control Signal Generating System for Redundant Serial Manipulators

The paper presents the design and experimental study of a synthesis method based on reference signal generation systems. The method can be used for all actuators of redundant manipulators. The aforementioned systems aim to save the dynamic control accuracy of the working tools of serial manipulators when they move along arbitrary spatial trajectories, taking into account restrictions in all degrees of freedom and special cases of their link positions. The maintenance of the control accuracy could be ensured by eliminating the reach of all degrees of freedom of manipulators to their limits and to indicated special positions, characterized by an ambiguity when solving the inverse kinematic problems of various serial manipulators. This is in addition to preventing the reach of their working tools to the boundaries of the working area due to the use of a redundant degree of freedom when approaching the indicated undesirable positions. The experimental studies performed in this paper confirm the efficiency of the proposed method and allow accurate characteristics to be obtained.

Analysis of the influence of detouring obstacle avoidance behavior on unidirectional flow

A pedestrian’s active obstacle avoidance behavior has an important impact on crowd safety in heterogeneous crowd movements, but how it affects the movement of individuals and crowd is not yet clear. This study proposes a detour anisotropic social force model (DASFM) that considers active obstacle avoidance behavior for future collision prediction. DASFM prioritizes moving obstacle pedestrians based on velocity obstacle (VO) and combines the anisotropic social force model (ASFM) to achieve the dynamic process of pedestrian active obstacle avoidance behavior. The results show that DASFM enables individuals to safely overtake while avoiding fluctuations in pedestrian speed and distance between pedestrians. The model improved abnormal “strip group” crowd aggregation, individual jostling, and congestion found in other models. It has effective performance in spatial distribution, trajectory, density evolution, and time consumption of crowd movement in unidirectional flow under open conditions. The fundamental diagram generated by DASFM in unidirectional flow under periodic boundary conditions tends to be consistent with the observations and experimental results of other researchers. Instantaneous flow analysis shows that overtaking behavior alleviates local congestion in the low-density crowd and promotes the slow flow of the high-density crowd. However, overtaking behavior also exacerbates the stop-and-go waves of the high-density crowd, posing a threat to crowd safety. This study not only effectively realizes the simulation of overtaking behavior among individuals and crowds, but also discovers the impact patterns of overtaking behavior on low- or high-density crowd. Therefore, measures should be taken to control individual overtaking behavior in high-density crowd to prevent the production of stop-and-go waves.

A Study of Spatio-Temporal Differentiation Characteristics and Driving Factors of Shaanxi Province’s Traditional Heritage Villages

The spatial distribution of traditional villages is a key factor for rural revitalization and sustainable development. However, the rapid expansion of cities has resulted in the disappearance and decline of many traditional villages. Therefore, for the protection of traditional villages, it is necessary to analyze the spatio-temporal differentiation characteristics and driving factors. In this study, a total of 500 traditional villages were selected in Shaanxi Province. With the support of spatial analysis tools such as ArcGIS and Geo-detector, the spatial differentiation and its driving factors were analyzed. It was found that traditional villages showed a three-core distribution mode, indicating a typical aggregation distribution of tendency. In Shaanxi, the directional evolution of traditional villages was characterized by a spatial and temporal trajectory toward the north, and then towards the south. In addition, traditional villages existed in areas with underdeveloped economies, far from the cities and close to water sources, with an elevation over 500 m and a slope less than 25°. Traditional villages in Shaanxi Province are experiencing uneven spatio-temporal evolution due to regional cultural differences and uneven economic development in southern, central, and northern areas. It is possible to provide strategies for the development, protection, and utilization of traditional villages and promote the development of rural revitalization based on the traditional villages.

ADEPT: Autoencoder with differentially expressed genes and imputation for robust spatial transcriptomics clustering

Advancements in spatial transcriptomics (ST) have enabled an in-depth understanding of complex tissues by quantifying gene expression at spatially localized spots. Several notable clustering methods have been introduced to utilize both spatial and transcriptional information in the analysis of ST datasets. However, data quality across different ST sequencing techniques and types of datasets influence the performance of different methods and benchmarks. To harness spatial context and transcriptional profile in ST data, we developed a graph-based, multi-stage framework for robust clustering, called ADEPT. To control and stabilize data quality, ADEPT relies on a graph autoencoder backbone and performs an iterative clustering on imputed, differentially expressed genes-based matrices to minimize the variance of clustering results. ADEPT outperformed other popular methods on ST data generated by different platforms across analyses such as spatial domain identification, visualization, spatial trajectory inference, and data denoising.

Arbitrary Spatial Trajectory Reconstruction Based on a Single Inertial Sensor

Compared with vision, infrared rays, and ultrasonic positioning technologies, the signal acquisition of portable inertial sensors is not affected by the external environment, such as light and occlusion. Therefore, motion tracking based on inertial signals is a promising complement. However, accurate trajectory reconstruction based on inertial sensors is a great challenge due to the intrinsic and measurement errors, especially the drift error that exacerbates the accumulative error in trajectory calculation. To address this challenge, we propose a new trajectory reconstruction method, Geometric Dynamic Segmental Reconstruction (GDSR), where we treat the movement trajectory as a combination of basic trajectories. To this end, we design a temporal and spatial interaction segmentation approach to decompose the trajectory into basic segments by combining the dynamic feature of IMU signals with the spatial morphological feature of motion. Accordingly, we design a geometrical model library with undetermined parameters to match these segments. For precise parameter prediction, we propose an extra-supervised learning method that integrates different prediction tasks into one framework, which can not only expand training samples but also enable different subtasks to compete with each other, thus improving the parameter prediction accuracy of each subtask, thereby accurately approximating the trajectory segments. To quantify the trajectory reconstruction accuracy, we propose the Fréchet Spline Sliding Error (FSSE) and Length Error Ratio (LER) to evaluate curve similarity. The range of FSSE is [0, 2], where 0 means that the two curves have the same shape. The range of LER is [1, +∞], where 1 means that the two curves have the same length. We test different IMUs in two experimental scenarios and one public available data set. In all the three tests, the FSSE of the GDSR method is less than 0.09, and the LER is less than 1.31, which is significantly better than all the comparison methods.