Real Trajectory Research Articles

Simulating human mobility with a trajectory generation framework based on diffusion model

Most mobility modeling methods are designed to solve specific tasks, leading to questions regarding their deficiency in generalizability. Inspired by the bloom of foundation models, we proposed a Trajectory Generation framework based on the Diffusion Model (TrajGDM) to capture the universal mobility pattern in a trajectory dataset by learning the trajectory generation process. The process is modeled as a step-by-step uncertainty-reducing process, in which a deep learning network with a novel training method is proposed to learn from the process. We compared the proposed trajectory generation method with six baselines on two public trajectory datasets. The results showed that the similarity between the generated and real trajectory movements measured by the Jensen-Shannon Divergence improved significantly on both datasets. Moreover, we applied zero-shot inferences on two basic trajectory tasks: trajectory prediction and trajectory reconstruction. The accuracy improved by a maximum of 25.6% on two tasks. The universal mobility pattern that is suitable for solving multiple trajectory tasks is verified, inferring the strong generalizability of our model. Finally, the study provides insights into artificial intelligence’s understanding of human mobility by exploring the way the model maps the trajectory in the latent space into reality.

Trajectory modeling via random utility inverse reinforcement learning

We consider the problem of modeling trajectories of drivers in a road network from the perspective of inverse reinforcement learning. Cars are detected by sensors placed on sparsely distributed points on the street network of a city. As rational agents, drivers are trying to maximize some reward function unknown to an external observer. We apply the concept of random utility from econometrics to model the unknown reward function as a function of observed and unobserved features. In contrast to current inverse reinforcement learning approaches, we do not assume that agents act according to a stochastic policy; rather, we assume that agents act according to a deterministic optimal policy and show that randomness in data arises because the exact rewards are not fully observed by an external observer. We introduce the concept of extended state to cope with unobserved features and develop a Markov decision process formulation of drivers decisions. We present theoretical results which guarantee the existence of solutions and show that maximum entropy inverse reinforcement learning is a particular case of our approach. Finally, we illustrate Bayesian inference on model parameters through a case study with real trajectory data from a large city in Brazil.

High-statistics pedestrian dynamics on stairways and their probabilistic fundamental diagrams

Staircases play an essential role in crowd dynamics, allowing pedestrians to flow across large multi-level public facilities such as transportation hubs, shopping malls, and office buildings. Achieving a robust quantitative understanding of pedestrian behavior in these facilities is a key societal necessity. What makes this an outstanding scientific challenge is the extreme randomness intrinsic to pedestrian behavior. Any quantitative understanding necessarily needs to be probabilistic, including average dynamics and fluctuations. To this purpose, large-scale, real-life trajectory datasets are paramount.In this work, we analyze the data from an unprecedentedly high statistics year-long pedestrian tracking campaign, in which we anonymously collected millions of trajectories of pedestrians ascending and descending stairs within Eindhoven Central train station (The Netherlands). This has been possible thanks to a state-of-the-art, faster than real-time, computer vision approach hinged on 3D depth imaging, sensor fusion, and YOLOv7-based depth localization. We consider both free-stream conditions, i.e. pedestrians walking in undisturbed, and trafficked conditions, unidirectional/bidirectional flows. We report on Eulerian fields (density, velocity and acceleration), showing how the walking dynamics changes when transitioning from stairs to landing. We then investigate the (mutual) positions of pedestrian as density changes, considering the crowd as a “compressible” physical medium. In particular, we show how pedestrians willingly opt to occupy fewer space than available, accepting a certain degree of compressibility. This is a non-trivial physical feature of pedestrian dynamics and we introduce a novel way to quantify this effect. As density increases, pedestrians strive to keep a minimum distance d≈0.6m (two treads of the staircase) from the person in front of them. Finally, we establish first-of-kind fully resolved probabilistic fundamental diagrams, where we model the pedestrian walking velocity as a mixture of a slow and fast-paced component (both in non-negligible percentages and with density-dependent characteristic fluctuations). Notably, averages and modes of velocity distribution turn out to be substantially different. Our results, of which we include probabilistic parametrizations based on few variables, are key towards improved facility design and realistic simulation of pedestrians on staircases.

Generative adversarial network for car following trajectory generation and anomaly detection

Car-following trajectory generation and anomaly detection are critical functions in the sensing module of an automated vehicle. However, developing models that capture realistic trajectory data distribution and detect anomalous driving behaviors could be challenging. This paper proposes ‘TrajGAN’, an unsupervised learning approach based on the Generative Adversarial Network (GAN) to exploit vehicle car following trajectory data for generation and anomaly detection. The proposed TrajGAN consists of two modules, an encoder-decoder Long Short-Term Memory (LSTM)-based generator and an LSTM-multilayer perceptron (MLP) based discriminator, whose former component is used to generate vehicular car following trajectories and the latter one is for trajectory anomaly detection. By letting these two modules game with each other in training, we can simultaneously achieve robust trajectory generators and anomaly detectors. Trained with the Next Generation Simulation (NGSIM) dataset, TrajGAN can generate realistic trajectories with a similar distribution of training data and identify a manifold of anomalous trajectories based on an anomaly scoring scheme. Simulation results indicate that the proposed approach is efficient in reproducing artificial trajectories and identifying anomalous driving behaviors.

Data-Driven Predictive Control and MPC: Do we achieve optimality?

In this paper, we explore the interplay between Predictive Control and closed-loop optimality, spanning from Model Predictive Control to Data-Driven Predictive Control. Predictive Control in general relies on some form of prediction scheme on the real system trajectories. However, these predictions may not accurately capture the real system dynamics, for e.g., due to stochasticity, resulting in sub-optimal control policies. This lack of optimality is a critical issue in case of problems with economic objectives. We address this by providing sufficient conditions on the underlying prediction scheme such that a Predictive Controller can achieve closed-loop optimality. However, these conditions do not readily extend to Data-Driven Predictive Control. In this context of closed-loop optimality, we conclude that the factor distinguishing the approaches within Data-Driven Predictive Control is if they can be cast as a sequential decision-making process or not, rather than the dichotomy of model-based vs. model-free. Furthermore, we show that the conventional approach of improving the prediction accuracy from data may not guarantee optimality.

Maritime trajectory mining: An automatic zones of interests discovery and annotation framework⋆

As global traffic continues to grow, the identification of areas of particular significance, known as Zones of Interest (ZOI), becomes crucial for optimizing transportation systems and analyzing mobility patterns. In the maritime domain, effective ZOIs discovery is essential for enhancing route planning, improving safety measures, and managing resources efficiently. Within the context of trajectory mining, these ZOIs provide valuable insights into movement behaviors and operational efficiencies. In this paper, we present a framework for discovering and annotating ZOIs within maritime trajectories. The proposed approach involves processing raw positional data to initially identify candidate ZOIs, which are subsequently refined using contextual information. By leveraging real georeferenced vessels trajectories, collected from thousands of commercial ships, this framework proposes a structure of elements that will be implemented as part of the TNTM French project. While this research contributes to maritime field by providing a method for ZOIs discovery and annotation, it can be generalized to various application domains that may leverage of mobility data analytics.

Enhancing digital health services: A machine learning approach to personalized exercise goal setting.

The utilization of digital health has increased recently, and these services provide extensive guidance to encourage users to exercise frequently by setting daily exercise goals to promote a healthy lifestyle. These comprehensive guides evolved from the consideration of various personalized behavioral factors. Nevertheless, existing approaches frequently neglect the users' dynamic behavior and the changing in their health conditions. This study aims to fill this gap by developing a machine learning algorithm that dynamically updates auto-suggestion exercise goals using retrospective data and realistic behavior trajectory. We conducted a methodological study by designing a deep reinforcement learning algorithm to evaluate exercise performance, considering fitness-fatigue effects. The deep reinforcement learning algorithm combines deep learning techniques to analyze time series data and infer user's exercise behavior. In addition, we use the asynchronous advantage actor-critic algorithm for reinforcement learning to determine the optimal exercise intensity through exploration and exploitation. The personalized exercise data and biometric data used in this study were collected from publicly available datasets, encompassing walking, sports logs, and running. In our study, we conducted the statistical analyses/inferential tests to compare the effectiveness of machine learning approach in exercise goal setting across different exercise goal-setting strategies. The 95% confidence intervals demonstrated the robustness of these findings, emphasizing the superior outcomes of the machine learning approach. Our study demonstrates the adaptability of machine learning algorithm to users' exercise preferences and behaviors in exercise goal setting, emphasizing the substantial influence of goal design on service effectiveness.

Conditional-TimeGAN for Realistic and High-Quality Appliance Trajectories Generation and Data Augmentation in Nonintrusive Load Monitoring

Conditional-TimeGAN for Realistic and High-Quality Appliance Trajectories Generation and Data Augmentation in Nonintrusive Load Monitoring

Generative artificial intelligence model for simulating structural brain changes in schizophrenia.

Recent advancements in generative artificial intelligence (AI) for image generation have presented significant opportunities for medical imaging, offering a promising way to generate realistic virtual medical images while ensuring patient privacy. The generation of a large number of virtual medical images through AI has the potential to augment training datasets for discriminative AI models, particularly in fields with limited data availability, such as neuroimaging. Current studies on generative AI in neuroimaging have mainly focused on disease discrimination; however, its potential for simulating complex phenomena in psychiatric disorders remains unknown. In this study, as examples of a simulation, we aimed to present a novel generative AI model that transforms magnetic resonance imaging (MRI) images of healthy individuals into images that resemble those of patients with schizophrenia (SZ) and explore its application. We used anonymized public datasets from the Center for Biomedical Research Excellence (SZ, 71 patients; healthy subjects [HSs], 71 patients) and the Autism Brain Imaging Data Exchange (autism spectrum disorder [ASD], 79 subjects; HSs, 105 subjects). We developed a model to transform MRI images of HSs into MRI images of SZ using cycle generative adversarial networks. The efficacy of the transformation was evaluated using voxel-based morphometry to assess the differences in brain region volumes and the accuracy of age prediction pre- and post-transformation. In addition, the model was examined for its applicability in simulating disease comorbidities and disease progression. The model successfully transformed HS images into SZ images and identified brain volume changes consistent with existing case-control studies. We also applied this model to ASD MRI images, where simulations comparing SZ with and without ASD backgrounds highlighted the differences in brain structures due to comorbidities. Furthermore, simulating disease progression while preserving individual characteristics showcased the model's ability to reflect realistic disease trajectories. The results suggest that our generative AI model can capture subtle changes in brain structures associated with SZ, providing a novel tool for visualizing brain changes in different diseases. The potential of this model extends beyond clinical diagnosis to advances in the simulation of disease mechanisms, which may ultimately contribute to the refinement of therapeutic strategies.

PUTS: Privacy-Preserving and Utility-Enhancing Framework for Trajectory Synthesization

Vehicle trajectory data is essential for traffic management and location-based services. However, publishing real-life trajectory data has been challenging because vehicle trajectories contain users' sensitive information. Differential privacy addresses such problems by publishing a synthetic version of the input dataset, but existing works always assume the real-world data is absolutely accurate. This assumption no longer holds in trajectory data because it typically contains errors due to inaccurate positioning services, which leads to poor performance of data synthesized by such trajectories. Even worse, existing works may generate unrealistic trajectories due to their coarse data synthesis methods, resulting in low practical utility or even inability to handle complex tasks. In this paper, we propose a <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</u> rivacy-preserving and <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U</u> tility-enhancing framework for <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</u> rajectory <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</u> ynthesization ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PUTS</i> ). Our framework mitigates the impact of data errors in trajectories on differential privacy mechanisms, by exploiting map-matching techniques and real-world road network structure. In <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PUTS</i> , a two-layer approach from path to trajectory synthesis is proposed to not only guarantee the reality of synthetic trajectories, but also scale up <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PUTS</i> in real-world applications. Extensive experiments on real-world datasets show that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PUTS</i> significantly outperforms existing methods in terms of utility in a range of real-world applications.

The simulation model uses the HIL method applied for studying the motion of 6 degrees of freedom of container ships

This article presents the construction of a hardware-in-the-loop (HIL) simulation model to research and test trajectory controllers for container ships. The proposed model consists of a 3D virtual control object and a real trajectory controller. The virtual object is a 3D dynamic model built based on 6 degrees of freedom (6-DOF) equations, technical records of the ship, and Unity software. Meanwhile, the controller is built using Matlab/Simulink software. The controller and control object communicate with each other using the Modbus TCP/IP protocol with a physical Ethernet link. Besides, the proposed model also fully includes the main turbulence components of the environment affecting the ship that many previous studies on ship trajectory control have ignored. The test results show that the model operates reliably, and accurately, and can be applied to research and test trajectory controllers for ships.

Research on Path Planning for Unmanned Surface Vessels Based on AIS Data

To address the issues of poor endpoint convergence and suboptimal path quality in global path planning for unmanned surface vessels (USVs), this paper proposes an endpoint-convergence oriented improved genetic algorithm based on AIS data. Firstly, utilizing a genetic algorithm with an endpoint-convergence objective function, a set of paths with strong endpoint convergence is selected. Secondly, to overcome the limitations of a single optimization algorithm, a multi-objective path planning approach is employed using a genetic algorithm, thereby improving the distance and trajectory smoothness in global path planning for unmanned ships. Finally, the planned paths are evaluated by comparing them with the real paths from AIS data. The simulation results demonstrate that the proposed method outperforms other traditional algorithms in terms of average path turn count and turn angle, reducing them by an average of 35.41% and 35.72%, respectively. Moreover, the proposed method exhibits the smallest error compared to the real trajectories, with an average reduction of 18.26%. These results validate the effectiveness and rationality of the proposed approach in improving path quality, reducing path turn count, and achieving better alignment with actual trajectories.

Trajectory Vorticity - Computation and Visualization of Rotational Trajectory Behavior in an Objective Way.

Trajectory data consisting of a low number of smooth parametric curves are standard data sets in visualization. For a visual analysis, not only the behavior of the individual trajectories is of interest but also the relation of the trajectories to each other. Moving objects represented by the trajectories may rotate around each other or around a moving center. We present an approach to compute and visually analyze such rotational behavior in an objective way. We introduce trajectory vorticity (TRV), a measure of rotational behavior of a low number of trajectories. We show that it is objective and that it can be introduced in two independent ways: by approaches for unsteadiness minimization and by considering the relative spin tensor. We compare TRV against single-trajectory methods and apply it to a number of constructed and real trajectory data sets, including drifting buoys in the Atlantic, midge swarm tracking data, pedestrian tracking data, pigeon flocks, and a simulated vortex street.

Federated and Online Dynamic Spectrum Access for Mobile Secondary Users

Users in dynamic spectrum access (DSA) with federated reinforcement learning (FRL) autonomously access channels, avoiding centralized coordination and protecting users’ privacy. However, existing FRL-based DSA mechanisms are limited to ideal network states, i.e., assuming that channel states and users’ interference relationships are unchanged. Besides, users should upload intermediate results simultaneously for federated aggregation. The above conditions are impractical for mobile users since their network states and locations are unstable. Meanwhile, newly connected users have to train their models through local data with numerous computing resources since global models are unsuitable for them. We propose FRDSA, an FRL-based secure and lightweight channel selection mechanism in DSA for mobile users under dynamic network states. An independent channel selection environment with a virtual group strategy is presented to avoid interference between users under unstable channel states. Furthermore, an asynchronous parameter aggregation method in FRDSA dynamically adjusts the aggregation factors without users simultaneously uploading intermediate results. Simulations based on real trajectory data show that FRDSA significantly reduces approximately 60% interference between mobile users under unstable network states. Newly connected users can directly apply the well-trained global model to access channels autonomously instead of retraining a model, effectively reducing mobile users’ computing resource requirements.

The simulation model uses the HIL method applied for studying the motion of 6 degrees of freedom of container ships

This article presents the construction of a hardware-in-the-loop (HIL) simulation model to research and test trajectory controllers for container ships. The proposed model consists of a 3D virtual control object and a real trajectory controller. The virtual object is a 3D dynamic model built based on 6 degrees of freedom (6-DOF) equations, technical records of the ship, and Unity software. Meanwhile, the controller is built using Matlab/Simulink software. The controller and control object communicate with each other using the Modbus TCP/IP protocol with a physical Ethernet link. Besides, the proposed model also fully includes the main turbulence components of the environment affecting the ship that many previous studies on ship trajectory control have ignored. The test results show that the model operates reliably, and accurately, and can be applied to research and test trajectory controllers for ships.

Robot kinematics analysis and trajectory planning based on artificial potential field method

Abstract In order for a robot to complete a given task, it must first be made to autonomously reach a specified target location, so optimizing the robot path trajectory planning is a prerequisite for the use of robots. In this paper, for the two problems of the traditional artificial potential field method of target unreachable and local optimization, we first improve the repulsive potential field function so that the robot’s gravitational force and repulsive force are zero at the target position and then construct the robot kinematic analytical model by setting the virtual target point away from the local minimum value point. On this basis, the improved algorithm is used to compare simulation experiments in three environments with the real trajectory planning test in the showroom. In the climate “near the obstacle of the target point” and the pure U-shaped area environment, the robot of the traditional APF algorithm cannot reach the target point. However, the algorithm in this paper reaches the target point in all three environments, with a time taken of only 21, 33, and 42 seconds, respectively. In the real trajectory planning of the showroom, the improved algorithm in this paper reaches the target point quickly and accurately, with a total path trajectory length of 77.7835m, a time of 43 seconds, and a total turning angle of 793°. This paper provides an effective method for planning robot path trajectories in a complex and variable environment.

GNN-RM: A trajectory completion algorithm based on graph neural networks and regeneration modules

Data about vehicle trajectories assumes a crucial role in applications such as intelligent connected vehicles. However, missing values resulting from sensors and other factors frequently affect real trajectory data. Currently, it is challenging to utilize trajectory completion methods to generate accurate real-time results at an affordable computing cost. This paper proposes GNN-RM, a trajectory completion algorithm based on graph neural networks and regeneration modules, encompassing feature extraction, subgraph construction, spatial interaction graph, and trajectory regeneration modules. The feature extraction algorithm extracts influential data as feature vectors based on certain conditions and organizes these feature vectors into different subgraphs according to categories. The spatial interaction graph constructed through graph neural networks extracts spatial interaction features between vehicles and the environment, while the regeneration modules constructed by multi-head attention mechanisms extract temporal features of vehicles, thereby completing the missing trajectories. The experimental results demonstrate that GNN-RM can achieve higher trajectory completion accuracy with fewer input parameters than multiple baseline models.

ПІДГОТОВКА МОДЕЛЮВАННЯ ФРЕЗЕРНОЇ ОБРОБКИ ДЕТАЛІ,ВСТАНОВЛЕНОЇ У ФРАКТАЛЬНИХ ЛЕЩАТАХ

The article is a publication of scientific and methodical character. The article is devoted to the preparation of a virtual experiment of milling processing of a complex profile part, which is installed in a fractal vice. It was determined that fractal vices are presented on the technological equipment market in a very limited range. At the same time, the cost of fractal vices is unreasonably high. The cost is commensurate with the cost of the milling machine itself. However, modeling the processing of a part mounted in a fractal vise is of considerable academic interest. Fractal vices use Pascal's law on the plane (with some assumptions). The mathematical model proposed earlier was further developed. The model is flat and consists of a system of three differential equations of the second order. The equations describe plane-parallel and torsional movements of the part. Selected main parameters and their recommended values for the mathematical model of the processing process. At this stage, the main goal of the virtual experiment is to compare the set and real trajectories of the milling cutter. Also, the goal is to analyze the influence of parameters of elastic-damping elements, clamping force, etc. on the result. A matrix of options for conducting a virtual experiment is proposed. The matrix provides a large number of possible movements of the cutter relative to the part (simple, complex, locked, unlocked). It was determined that the matrix of options allowsfor a large number of possible processing options. From this set, several options are selected, the most suitable for further modeling and comparison with the results of a natural experiment. It is believed that the technological system "machine –vice –tool –workpiece" is a closed dynamic system with negative feedback. However, it is necessary to investigate the behavior of the system without feed-back and compare it with the rest of the experiments

Predicting micro/nanoscale colloidal interactions through local neighborhood graph neural networks

Understanding interparticle interactions has been one of the most important topics of research in the field of micro/nanoscale materials. Many significant characteristics of such materials directly stem from the way their building blocks interact with each other. In this work, we investigate the efficacy of a specific category of Machine Learning (ML) methods known as interaction networks in predicting interparticle interactions within colloidal systems. We introduce and study Local Neighborhood Graph Neural Networks (LN-GNNs), defined according to the local environment of colloidal particles derived from particle trajectory data. The LN-GNN framework is trained for unique categories of particle neighborhood environments in order to predict interparticle interactions. We compare the performance of the LN-GNN to a baseline interaction network with a simpler architecture and to an Instance-Based ML algorithm, which is computationally more expensive. We find that the prediction performance of LN-GNN measured as an average normalized mean absolute error outperforms the baseline interaction network by a factor of 2–10 for different local neighborhood configurations. Furthermore, LN-GNN’s performance turns out to be very comparable to the instance-based ML framework while being an order of magnitude less expensive in terms of the required computation time. The results of this work can provide the foundations for establishing accurate models of colloidal particle interactions that are derived from real particle trajectory data.

Vehicle Speed and Position Estimation considering Microscopic Heterogeneous Car-Following Characteristics in Connected Vehicle Environments

This paper proposes a method for estimating the speed and position of unsampled vehicles using sampled data from connected automated vehicles (CAVs). The determination of vehicle speed and position on the road is a challenging and crucial task, as they can effectively reflect traffic flow characteristics and contribute to traffic state estimation and intersection signal timing optimization. Connected automated vehicles have the capability to upload their own trajectory data while also capturing trajectory data of surrounding vehicles through onboard sensors. Therefore, this paper proposes a novel approach to estimate the speed and position of unsampled vehicles. Firstly, using real vehicle trajectory data, the correlation between the velocity of following vehicles and the velocity of leading vehicles under different densities is analyzed, leading to the development of a velocity estimation model incorporating a speed correction factor. Secondly, the correlation between time headway, the rate of change of following vehicle acceleration, and traffic density is examined. To address the issue of heterogeneous behavior in vehicle following described by the Intelligent Driver Model (IDM), a real-time optimization model for estimating vehicle position by optimizing IDM parameters is proposed. The velocity estimation model and the position estimation model are summarized as two nonlinear optimization problems. Finally, the proposed method is validated using actual vehicle trajectory data. Experimental results demonstrate that when the number of connected automated vehicles (CAVs) is 2, the proposed method reduces the average absolute error by 30.73% and the standard deviation of the average absolute error by 42.8% compared to a linear model-based speed estimation method under different density conditions. Compared to a method that estimates vehicle position by calibrating desired gaps, the proposed method reduces the average absolute error by 38.2% and the standard deviation of the average absolute error by 41.7% under different density conditions. Furthermore, the proposed method exhibits good practicality under different CAV penetration rates.