Sequence Of Trajectories Research Articles

GRU-IKF scene taxiing trajectory prediction model based on attention mechanism

Aircraft taxi trajectory prediction helps solve operational problems such as airport taxiing conflicts and long waiting times, ensuring airport safety while improving service levels and increasing airport throughput. In view of the fact that the performance of machine learning models depends on good data sets, a method for predicting taxi trajectories of aircraft on the ground based on attention mechanism, fusion of gated recurrent unit (GRU) and improved Kalman filter algorithm (IKF) is proposed. Firstly, three independent gated recurrent unit networks are used to capture the motion state and temporal dependency of aircraft at future moments, and the attention mechanism is introduced to enhance the ability to extract data difference features and learn the mapping relationship from input to output; then, it is fused with the improved extended Kalman filter to integrate the output results of the neural network into the state prediction and update process to improve the accuracy of the predicted trajectory sequence. Finally, the effectiveness of the model was verified using the actual taxiing trajectory of aircraft at Lukou Airport. The simulation results show that the model can effectively and accurately predict the taxiing trajectory of aircraft on the surface, with an overall mean square error of about 0.00128. Compared with the single recurrent neural network (RNN), long short-term memory network (LSTM) and GRU model, the RMSE is reduced by 72.9%and respectively 39.9%, 54.7%and the prediction time is 40 ms. It can accurately and quickly predict the taxiing trajectory, which helps to reduce the operating load of the airport surface management system.

Attention-Linear Trajectory Prediction

Recently, a large number of Transformer-based solutions have emerged for the trajectory prediction task, but there are shortcomings in the effectiveness of Transformers in trajectory prediction. Specifically, while position encoding preserves some of the ordering information, the self-attention mechanism at the core of the Transformer has its alignment invariance that leads to the loss of temporal information, which is crucial for trajectory prediction. For this reason, we design a simple and efficient strategy for temporal information extraction and prediction of trajectory sequences using the self-attention mechanism and linear layers. The experimental results show that the strategy can improve the average accuracy by 15.31%, effectively combining the advantages of the linear layer and the self-attention mechanism, while compensating for the shortcomings of the Transformer. Additionally, we conducted an empirical study to explore the effectiveness of the linear layer and sparse self-attention mechanisms in trajectory prediction.

SSRLM: A self-supervised representation learning method for identifying one ship with multi-MMSI codes

It is of great practical significance for maritime safety and shipping development to achieve “One Ship with One Maritime Mobile Service Identity (MMSI) Code” in accordance with regulations. However, the current “One Ship with Multiple MMSI Codes” violation identification method lacks practicability and generalization. Aiming at the these problems, this paper proposes a self-supervised representation learning model for the “One Ship with Multiple MMSI Codes” abnormal behavior recognition task, named SSRLM. Firstly, we construct a new dataset about “One Ship with Multiple MMSI Codes”, named HN_MulMI. Secondly, the SSRLM model learns the contextual interdependencies among different trajectory features in the HN_MulMI dataset through an unsupervised pre-training scheme, and extracts a dense vectorial representation of the ship’s motion trajectories. Finally, by using the unique characteristics of the “One Ship with Multiple MMSI Codes” trajectory sequence, the SSRLM model captures its feature dependencies through a fine-tuning scheme to accomplish the abnormal behavior detection task. Experimental results in the two scenarios of HN_MulMI test set demonstrate that the proposed model outperform the state-of-the-art models in recent years, the average precision, recall and F1-score rates is up to about 99.26% and 93.5%. Meanwhile, we also conducted comparative experiments on three public datasets to verify the generalization performance, achieving 90.31%, 93.2% and 95.14% results in the F1 score evaluation indicators, further confirming the good recognition performance of the SSLLM model. Finally, our model has been applied to the actual scene and achieved good results.

Approximation of the HJB viscosity solutions in differential inclusion optimal control with state constraint

This paper tries to investigate a differential inclusion optimal control problem with state constraint (P) through an approximation of Hamilton–Jacobi–Bellman viscosity solutions. By invoking a duality result between the control problem (P) and the upper hull of viscosity subsolutions of the HJB equation, we prove that value functions of the discrete problems are solutions of discrete Bellman equations and converge to the value function of (P). We also establish that the optimal trajectory sequence of discrete problems converges to the solution of the optimal control problem (P). The idea behind the approximation is based on Euler polygonal arcs and Subbotin's proximal aiming condition, which allows discrete trajectories to break the state constraint, evolve in its neighbourhood and then converge to it instead of staying in the state constraint set for all time.

DSDRec: Next POI recommendation using deep semantic extraction and diffusion model

Semantics play a crucial role in many AI tasks, yet the lack of high-quality textual data in LBSNs hampers deep semantic feature learning. Sparse user check-in records, characterized by significant spatial or temporal intervals (cut points), create challenges in understanding users' real mobile preferences. However, prior studies often rely on shallow semantic signals from independent textual properties and overlook these cut points when modeling spatio-temporal context. This work proposes a recommender model named DSDRec for the next POI recommendation. To alleviate the shortage of high-quality textual data in LBSNs, we take prompt engineering to freely obtain rich semantic texts (a.k.a., prompt sentences) from the discrete trajectory sequences and then use a pre-trained language model to acquire high-quality deep semantic features based on the functional prompt sentences. To mitigate the risk caused by the cut points, we propose an effective method, Spatio-Temporal Area Encoding, to depict the global spatial and temporal relationship of check-ins in trajectory. Besides, to study the potential of diffusion models in the next POI recommendation, we stacked an improved diffusion model to assist the recommender in learning more abstract interaction information. Comprehensive experiments conducted on two real-world datasets validate the competitive performance of DSDRec over previous SOTA approaches.

Data-Driven 4D Trajectory Prediction Model Using Attention-TCN-GRU

With reference to the trajectory-based operation (TBO) requirements proposed by the International Civil Aviation Organization (ICAO), this paper concentrates on the study of four-dimensional trajectory (4D Trajectory) prediction technology in busy terminal airspace, proposing a data-driven 4D trajectory prediction model. Initially, we propose a Spatial Gap Fill (Spat Fill) method to reconstruct each aircraft’s trajectory, resulting in a consistent time interval, noise-free, high-quality trajectory dataset. Subsequently, we design a hybrid neural network based on the seq2seq model, named Attention-TCN-GRU. This consists of an encoding section for extracting features from the data of historical trajectories, an attention module for obtaining the multilevel periodicity in the flight history trajectories, and a decoding section for recursively generating the predicted trajectory sequences, using the output of the coding part as the initial input. The proposed model can effectively capture long-term and short-term dependencies and repetitiveness between trajectories, enhancing the accuracy of 4D trajectory predictions. We utilize a real ADS-B trajectory dataset from the airspace of a busy terminal for validation. The experimental results indicate that the data-driven 4D trajectory prediction model introduced in this study achieves higher predictive accuracy, outperforming some of the current data-driven trajectory prediction methods.

TrajSGAN: A Semantic-Guiding Adversarial Network for Urban Trajectory Generation

Simulating human mobility contributes to city behavior discovery and decision-making. Although the sequence-based and image-based approaches have made impressive achievements, they still suffer from respective deficiencies such as omitting the depiction of spatial properties or ordinal dependency in trajectory. In this article, we take advantage of the above two paradigms and propose a semantic-guiding adversarial network (TrajSGAN) for generating human trajectories. Specifically, we first devise an attention-based generator to yield trajectory locations in a sequence-to-sequence manner. The encoded historical visits are queried with semantic knowledge (e.g., travel modes and trip purposes) and their important features are enhanced by the multihead attention mechanism. Then, we designate a rollout module to complete the unfinished trajectory sequence and transform it into an image that can depict its spatial structure. Finally, a convolutional neural network (CNN)-based discriminator signifies how “real” the trajectory image looks, and its output is regarded as a reward signal to update the generator by the policy gradient. Experimental results show that the proposed TrajSGAN model significantly outperforms the benchmarks under the MTL-Trajet mobility dataset, with the divergence of spatial-related metrics such as radius of gyration and travel distance reduced by 10%–27%. Furthermore, we apply the real and synthetic trajectories, respectively, to simulate the COVID-19 epidemic spreading under three preventive actions. The coefficient of determination metric between real and synthetic results achieves 91%–98%, indicating that the synthesized data from TrajSGAN can be leveraged to study the epidemic diffusion with an acceptable difference. All of these results verify the superiority and utility of our proposed method.

TAU: Trajectory Data Augmentation with Uncertainty for Next POI Recommendation

Next Point-of-Interest (POI) recommendation has been proven effective at utilizing sparse, intricate spatial-temporal trajectory data to recommend subsequent POIs to users. While existing methods commonly alleviate the problem of data sparsity by integrating spatial-temporal context information, POI category features, and social relationships, they largely overlook the fact that the trajectory sequences collected in the datasets are often incomplete. This oversight limits the model’s potential to fully leverage historical context. In light of this background, we propose Trajectory Data Augmentation with Uncertainty (TAU) for Next POI Recommendation. TAU is a general graph-based trajectory data augmentation method designed to complete user mobility patterns by marrying uncertainty estimation into the next POI recommendation task. More precisely, TAU taps into the global transition pattern graph to identify sets of intermediate nodes located between every pair of locations, effectively leveraging edge weights as transition probabilities. During trajectory sequence construction, TAU selectively prompts intermediate nodes, chosen based on their likelihood of occurrence as pseudo-labels, to establish comprehensive trajectory sequences. Furthermore, to gauge the certainty and impact of pseudo-labels on the target location, we introduce a novel confidence-aware calibration strategy using evidence deep learning (EDL) for improved performance and reliability. The experimental results clearly indicate that our TAU method achieves consistent performance improvements over existing techniques across two real-world datasets, verifying its effectiveness as the state-of-the-art approach to the task.

Curriculum Goal-Conditioned Imitation for Offline Reinforcement Learning

Offline reinforcement learning (RL) enables learning policies from pre-collected datasets without online data collection. Although it offers the possibility to surpass the performance of the datasets, most existing offline RL algorithms struggle to compete with behavior cloning policies in many dataset settings due to trading off policy improvement and additional regularization to address the distributional shift issue. In many cases, if one can imitate a sequence of sub-optimal sub-trajectories in data and properly <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">“stitch”</i> them toward reaching an ideal future state, it may potentially result in a more reliable policy while avoiding the difficulties that present in typical value-based offline RL algorithms. We borrow the idea of curriculum learning to embody the above intuition. We construct a curriculum that progressively imitates a sequence of sub-optimal trajectories conditioned on a series of carefully constructed future states and cumulative rewards as goals. The sub-optimal trajectories gradually guide policy learning toward reaching the ideal goal states. We name our algorithm Curriculum Goal-conditioned Imitation (CGI). Experimental results show that CGI achieves competitive performance against state-of-the-art offline RL algorithms, especially for challenging tasks with long horizons and sparse rewards.

End-to-end model-based trajectory prediction for ro-ro ship route using dual-attention mechanism.

With the rapid increase of economic globalization, the significant expansion of shipping volume has resulted in shipping route congestion, causing the necessity of trajectory prediction for effective service and efficient management. While trajectory prediction can achieve a relatively high level of accuracy, the performance and generalization of prediction models remain critical bottlenecks. Therefore, this article proposes a dual-attention (DA) based end-to-end (E2E) neural network (DAE2ENet) for trajectory prediction. In the E2E structure, long short-term memory (LSTM) units are included for the task of pursuing sequential trajectory data from the encoder layer to the decoder layer. In DA mechanisms, global attention is introduced between the encoder and decoder layers to facilitate interactions between input and output trajectory sequences, and multi-head self-attention is utilized to extract sequential features from the input trajectory. In experiments, we use a ro-ro ship with a fixed navigation route as a case study. Compared with baseline models and benchmark neural networks, DAE2ENet can obtain higher performance on trajectory prediction, and better validation of environmental factors on ship navigation.

Learning Universal Trajectory Representation via a Siamese Geography-Aware Transformer

With the development of location-based services and data collection equipment, the volume of trajectory data has been growing at a phenomenal rate. Raw trajectory data come in the form of sequences of “coordinate-time-attribute” triplets, which require complicated manual processing before they can be used in data mining algorithms. Current works have started to explore the emerging deep representation learning method, which maps trajectory sequences to vector space and applies them to various downstream applications for boosting accuracy and efficiency. In this work, we propose a universal trajectory representation learning method based on a Siamese geography-aware transformer (TRT for short). Specifically, we first propose a geography-aware encoder to model geographical information of trajectory points. Then, we apply a transformer encoder to embed trajectory sequences and use a Siamese network to facilitate representation learning. Furthermore, a joint training strategy is designed for TRT. One of the training objectives is to predict the masked trajectory point, which makes the trajectory representation robust to low sampling rates and noises. The other is to distinguish the difference between trajectories by means of contrastive learning, which makes the trajectory representation more uniformly distributed over the hypersphere. Last, we design a benchmark containing four typical traffic-related tasks to evaluate the performance of TRT. Comprehensive experiments demonstrate that TRT consistently outperforms the state-of-the-art baselines across all tasks.

Solving Robotic Trajectory Sequential Writing Problem via Learning Character's Structural and Sequential Information.

The writing sequence of numerals or letters often affects aesthetic aspects of the writing outcomes. As such, it remains a challenge for robotic calligraphy systems to perform, mimicking human writers' implicit intention. This article presents a new robot calligraphy system that is able to learn writing sequences with limited sequential information, producing writing results compatible to human writers with good diversity. In particular, the system innovatively applies a gated recurrent unit (GRU) network to generate robotic writing actions with the support of a prelabeled trajectory sequence vector. Also, a new evaluation method is proposed that considers the shape, trajectory sequence, and structural information of the writing outcome, thereby helping ensure the writing quality. A swarm optimization algorithm is exploited to create an optimal set of parameters of the proposed system. The proposed approach is evaluated using Arabic numerals, and the experimental results demonstrate the competitive writing performance of the system against state-of-the-art approaches regarding multiple criteria (including FID, MAE, PSNR, SSIM, and PerLoss), as well as diversity performance concerning variance and entropy. Importantly, the proposed GRU-based robotic motion planning system, supported with swarm optimization can learn from a small dataset, while producing calligraphy writing with diverse and aesthetically pleasing outcomes.

Visual Analysis Method for Traffic Trajectory with Dynamic Topic Movement Patterns Based on the Improved Markov Decision Process

The visual analysis of trajectory topics is helpful for mining potential trajectory patterns, but the traditional visual analysis method ignores the evolution of the temporal coherence of the topic. In this paper, a novel visual analysis method for dynamic topic analysis of traffic trajectory is proposed, which is used to explore and analyze the traffic trajectory topic and evolution. Firstly, the spatial information is integrated into trajectory words, calculating the dynamic trajectory topic model based on dynamic analysis modeling and, consequently, correlating the evolution of the trajectory topic between adjacent time slices. Secondly, in the trajectory topic, a representative trajectory sequence is generated to overcome the problem of the trajectory topic model not considering the word order, based on the improved Markov Decision Process. Subsequently, a set of meaningful visual codes is designed to analyze the trajectory topic and its evolution through the parallel window visual model from a spatial-temporal perspective. Finally, a case evaluation shows that the proposed method is effective in analyzing potential trajectory movement patterns.

How Permanent Are the Permanent Macrodipoles of Anthranilamide Bioinspired Molecular Electrets?

Dipoles are ubiquitous, and their impacts on materials and interfaces affect many aspects of daily life. Despite their importance, dipoles remain underutilized, often because of insufficient knowledge about the structures producing them. As electrostatic analogues of magnets, electrets possess ordered electric dipoles. Here, we characterize the structural dynamics of bioinspired electret oligomers based on anthranilamide motifs. We report dynamics simulations, employing a force field that allows dynamic polarization, in a variety of solvents. The results show a linear increase in macrodipoles with oligomer length that strongly depends on solvent polarity and hydrogen-bonding (HB) propensity, as well as on the anthranilamide side chains. An increase in solvent polarity increases the dipole moments of the electret structures while decreasing the dipole effects on the moieties outside the solvation cavities. The former is due to enhancement of the Onsager reaction field and the latter to screening of the dipole-generated fields. Solvent dynamics hugely contributes to the fluctuations and magnitude of the electret dipoles. HB with the solvent weakens electret macrodipoles without breaking the intramolecular HB that maintains their extended conformation. This study provides design principles for developing a new class of organic materials with controllable electronic properties. An animated version of the TOC graphic showing a sequence of the MD trajectories of short and long molecular electrets in three solvents with different polarities is available in the HTML version of this paper.

A Spraying Path Planning Algorithm Based on Point Cloud Segmentation and Trajectory Sequence Optimization

A Spraying Path Planning Algorithm Based on Point Cloud Segmentation and Trajectory Sequence Optimization

Adaptive Successive POI Recommendation via Trajectory Sequences Processing and Long Short-Term Preference Learning

Adaptive Successive POI Recommendation via Trajectory Sequences Processing and Long Short-Term Preference Learning

Stylized Crowd Formation Transformation Through Spatiotemporal Adversarial Learning

Achieving crowd formation transformations has wide‐ranging applications in fields such as unmanned aerial vehicle formation control, crowd simulation, and large‐scale performances. However, planning trajectories for hundreds of agents is a challenging and tedious task. When modifying crowd formation change schemes, adjustments are typically required based on the style of formation change. Existing methods often involve manual adjustments at each crucial step, leading to a substantial amount of physical labor. Motivated by these challenges, this study introduces a novel generative adversarial network (GAN) for generating crowd formation transformations. The proposed GAN learns specific styles from a series of crowd formation transformation trajectories and can transform a new crowd with an arbitrary number of individuals into the same styles with minimal manual intervention. The model incorporates a space–time transformer module to aggregate spatiotemporal information for learning distinct styles of formation transformation. Furthermore, this article investigates the relationship between the distribution of training data and the length of trajectory sequences, providing insights into the preprocessing of training data.

Turbofan Engine Health Assessment Based on Spatial-Temporal Similarity Calculation.

Aiming at the problem of the remaining useful life prediction accuracy being too low due to the complex operating conditions of the aviation turbofan engine data set and the original noise of the sensor, a residual useful life prediction method based on spatial-temporal similarity calculation is proposed. The first stage is adaptive sequence matching, which uses the constructed spatial-temporal trajectory sequence to match the sequence to find the optimal matching sample and calculate the similarity between the two spatial-temporal trajectory sequences. In the second stage, the weights of each part are assigned by the two weight allocation algorithms of the weight training module, and then the final similarity is calculated by the similarity calculation formula of the life prediction module, and the final predicted remaining useful life is determined according to the size of the similarity and the corresponding remaining life. Compared with a single model, the proposed method emphasizes the consistency of the test set and the training set, increases the similarity between samples by sequence matching with other spatial-temporal trajectories, and further calculates the final similarity and predicts the remaining use through the weight allocation module and the life prediction module. The experimental results show that compared with other methods, the root mean square error (RMSE) index and the remaining useful life health score (Score) index are reduced by 12.6% and 14.8%, respectively, on the FD004 dataset, and the RMSE index is similar to that in other datasets; the Score index is reduced by about 10%, which improves the prediction accuracy of the remaining useful life and can provide favorable support for the operation and maintenance decision of turbofan engines.

MMCPP: A MULTI-MODAL CONTRASTIVE PRE-TRAINING MODEL FOR PLACE REPRESENTATION BASED ON THE SPATIO-TEMPORAL FRAMEWORK

Abstract. The concept of "place" is crucial for understanding geographical environments from a human perspective. Place representation learning involves converting places into numerical low-dimensional dense vectors and is a fundamental procedure for artificial intelligence in geography (GeoAI). However, most studies ignore multi-level distance constraints and spatial proximity interactions that enable behavioral interactions between places. Furthermore, representing the temporal characteristics of these interactions in trajectory sequences poses a challenge for natural language processing and other field techniques. In addition, most existing methods rely on all modalities from inputs as they use joint training to integrate multiple modalities. To address these issues, we propose a Multi-Modal Contrastive Pre-training model for Place representation (MMCPP). Our model consists of three encoders that capture corresponding place attributes across different modalities, including point of interests (POIs), images, and trajectories. The trajectory encoder, named RodtFormer, takes fine-grained spatio-temporal trajectories as input and leverages self-attention with rotary temporal interval position embedding to simulate dynamic spatial and behavioral proximity interactions between places. By using a coordinated pre-training framework, MMCPP independently encodes place representations across different modalities and improves model reusability. We verify the effectiveness of our model on a taxi trajectory dataset using the location prediction task at next n seconds, including 30 seconds(s), 180(s), 300(s). Our results demonstrate that compared to existing embedding methods, our model is capable of learning higher-quality position representations during pre-training, leading to improved performance on downstream tasks.

Efficient Kinematic Calibration for Articulated Robot Based on Unit Dual Quaternion

Removing the parameter redundancy in the kinematic error model does improve the robustness of parameter identification. However, this does not help much on saving the calculation time on the error compensation process, which is closely related to the data structure used for representing rigid-body motion. Compared with the homogenous transformation matrix (HTM), the unit dual quaternion (UDQ) can describe the rigid-body motion in term of an array with eight entries, thus it is a conducive data structure for efficient kinematic computation. In this work, the exponential and logarithm mappings of a UDQ are defined explicitly, so that the relationship between finite and instantaneous motions is set up under the exponential coordinate. Thereafter, by defining the adjoint operator of UDQ to transform the twist under different frames, the linearized kinematic error models are built with local product-of-exponentials (POE) formula. This facilitates the upcoming parameter identification and error compensation processes. Specially, the counts of elementary operations are evaluated throughout the compensation processes, which shows the number of arithmetic operations are greatly reduced compared with using POE formula based on HTM. Additionally, the simple data structure in term of 1-D arrays saves the data dispatch time when performing adjoint operations. These make the developed model suitable for calibration of articulated robot with a long sequence of trajectories. Experiments on a 6-degree-of-freedom industrial robot validate the effectiveness of proposed approach.