Long-term Trajectory Prediction Research Articles

Control-Oriented Real-Time Trajectory Planning for Heterogeneous UAV Formations

Aiming at the trajectory planning problem for heterogeneous UAV formations in complex environments, a trajectory prediction model combining Convolutional Neural Networks (CNNs) and Long Short-Term Memory networks (LSTM) is designed, and a real-time trajectory planning method is proposed based on this model. By pre-training trajectory prediction networks for various types of UAVs, the traditional physics-based models are replaced for flight trajectory prediction. Inspired by Model Predictive Control (MPC), in the trajectory planning stage, the method generates multi-step trajectory points using an improved artificial potential field (APF) method, estimates the actual formation trajectory using the prediction network, and optimizes the trajectory through a multi-objective particle swarm optimization (MOPSO) algorithm after evaluating the planning costs. During actual flight, the optimized parameters generate trajectory points for the formation to follow. Unlike conventional path planning based on simple constraints, the proposed method directly plans trajectory points based on trajectory tracking performance, ensuring high feasibility for the formation to follow. Experimental results show that the CNN-LSTM network outperforms other networks in both short-term and long-term trajectory prediction. The proposed trajectory planning method demonstrates significant advantages in formation maintenance, trajectory tracking, and real-time obstacle avoidance, ensuring flight stability and safety while maintaining high-speed flight.

A Trajectory Prediction Method for Reentry Glide Vehicles via Adaptive Cost Function

This paper proposes a trajectory prediction method via the adaptive cost function to address the difficulties in inferring the attack intention and maneuver mode, as well as the accumulation of prediction error during the trajectory prediction of reentry glide vehicles. Firstly, the vehicle guidance task is divided into two distinct categories: conventional guidance and no-fly zone avoidance guidance. A task-matched time-varying parameter prediction model set is then constructed. Secondly, taking into account the maneuverability, guidance intent, and battlefield situation of the vehicle, an adaptive intent cost function adapted to the guidance task is proposed, which avoids the estimation failure problem caused by manually setting cost coefficients in traditional methods. Finally, long-term trajectory prediction of vehicles is achieved using Bayesian theory to infer the attack intent and parametric model with the maximum a posteriori probability. The results of the simulations demonstrate that the proposed prediction method is capable of accurately inferring the vehicle’s attack intention and parameter model, and of effectively reducing the accumulation of prediction errors and the time required for the algorithmic process compared to existing methods.

Four-Dimensional Aircraft Trajectory Prediction with a Generative Deep Learning and Clustering Approach

Medium- and long-term four-dimensional (4D) aircraft trajectory prediction (TP) is a critical technology in air traffic management (ATM). This paper addresses the issue of existing medium- and long-term TP methods that are difficult to accurately fit aircraft trajectory data distributions. We propose a 4D TP method based on K-medoids clustering and conditional tabular generative adversarial networks (CTGAN), called C-CTGAN. Comparative experiments with four long short-term memory (LSTM)-based models and the original CTGAN model show that the proposed model’s TP accuracy is significantly higher than others when predicting medium- and long-term trajectories. When using the trajectory datasets without holding and a prediction time span of 10 min, compared to the convolutional neural network (CNN)-LSTM model, the C-CTGAN model reduces the mean absolute errors (MAEs) of core trajectory parameters, such as latitude, longitude, geometric altitude, and ground speed, by 69.89, 15.00, 74.07, and 84.21%, respectively. Compared to the original CTGAN model, the MAE is reduced by 20.43, 39.09, 31.98, and 17.07%, respectively. When using the trajectory datasets with holding, compared to the CNN-LSTM model, the C-CTGAN model shows MAE reductions of 14.08, 23.68, 31.46, and 2.86%, respectively. Compared to the original CTGAN, the reduction is 34.88, 2.69, 23.16, and 73.91%, respectively.

A Novel Multimodal Long-Term Trajectory Prediction Scheme for Heterogeneous User Behavior Patterns

A Novel Multimodal Long-Term Trajectory Prediction Scheme for Heterogeneous User Behavior Patterns

Graph-driven multi-vessel long-term trajectories prediction for route planning under complex waters

Current collision avoidance algorithms used in autonomous navigation vessels are hindered by limited long-term visibility of dynamic obstacles, resulting in overly cautious and frequent avoidance maneuvers that can actually increase the risk of collisions in complex waterways. Therefore, this paper proposed a novel graph-driven multi-vessel long-term trajectory prediction method (termed GMLTP), which extends the length of real-time and accurate prediction of other vessel trajectories. GMLTP can enhance collision avoidance algorithms by enabling more anticipatory trajectory prediction, ultimately supporting real-time route planning in creating safer, more efficient, and optimized routes. Specifically, GMLTP consists of a multi-graph spatial convolution (MGSC) layer and a probability sparse (ProbSparse) self-attention Transformer. MGSC is a finer spatial interactions extractor, which supports the modeling of spatial dependency evolution on longer sequences and thus improves the perception of long-term trends, while ProbSparse self-attention Transformer is used to reduce the computation of learning long-term global time dependencies and thus extending the predictable length. Extensive experimental results indicate that GMLTP exhibits better accuracy and generalization in prediction tasks beyond 48-timesteps (each time step is 10 s), which can provide better assistance to current real-time route planning tasks.

Research on Vehicle-Driving-Trajectory Prediction Methods by Considering Driving Intention and Driving Style

With the rapid advancement of autonomous driving technology, the accurate prediction of vehicle trajectories has become a research hotspot. In order to accurately predict vehicles’ trajectory, this study comprehensively explores the impact of driving style and intention on trajectory prediction, proposing a novel prediction method. Firstly, the dataset AD4CHE was selected as the research data, from which the required trajectory data of vehicles were extracted, including 1202 lane-changing and 1137 car-following driving trajectories. Secondly, a long short-term memory (LSTM) network based on the Keras framework was constructed by using the TensorFlow deep-learning platform. The LSTM network integrates driving intention, driving style, and historical trajectory data as inputs to establish a vehicle-trajectory prediction model. Finally, the mean absolute error (MAE) and root-mean-square error (RMSE) were selected as the evaluation indicators for the models, and the prediction results of the models were compared under two conditions: not considering driving style and considering driving style. The results demonstrate that models incorporating driving style significantly outperformed those that did not, highlighting the critical influence of driving style on vehicle trajectories. Moreover, compared to traditional kinematic models, the LSTM-based approach exhibits notable advantages in long-term trajectory prediction. The prediction method that accounts for both driving intention and style effectively reduces RMSE, significantly enhancing prediction accuracy. The findings of this research provide valuable insights for vehicle-driving risk assessment and contribute positively to the advancement of autonomous driving technology and the sustainable development of road traffic.

Vehicle trajectory prediction based on cross-attention and multilevel spatio-temporal features

Accurately predicting vehicle trajectories is crucial for motion planning in autonomous driving. Some existing trajectory prediction models employ Long Short-Term Memory (LSTM) networks to encode trajectory information, but this approach may lead to information loss. Additionally, the sparsity of the grid representation may limit the model’s ability to extract vehicle interaction features. To address these issues, this paper proposes a vehicle trajectory prediction model based on cross-attention and multilevel spatio-temporal features. The proposed model incorporates a spatio-temporal feature extraction module designed to capture the dynamic evolution of vehicle states across both time and space. Furthermore, it employs a temporal cross-attention module that reuses hidden states to select spatio-temporal features closely related to the target vehicle’s historical state, thus compensating for the temporal information loss during the encoding process. Additionally, a spatial cross-attention module, informed by social context, is deployed to analyze the dynamic interactions among vehicles. This module filters spatio-temporal interaction features with a significant impact on the target vehicle’s trajectory. The model is trained and tested using the NGSIM dataset and the highD dataset. Compared with other models, the model presented in this paper shows higher prediction accuracy in long-term trajectory prediction.

Developing an Artificial Intelligence-Based Method for Predicting the Trajectory of Surface Drifting Buoys Using a Hybrid Multi-Layer Neural Network Model

Accurately predicting the long-term trajectory of a surface drifting buoy (SDB) is challenging. This paper proposes a promising solution to the SDB trajectory prediction based on artificial intelligence (AI) technologies. Initially, a scalable mathematical model for trajectory prediction is developed, transforming the challenge of predicting trajectory points into predicting velocities in eastward and northward directions. Subsequently, a four-layer trajectory prediction calculation framework (FLTPCF) is established, outlining a complete workflow for the real-time online training of marine environment data and SDBs’ trajectory prediction. Thirdly, for facilitating accurate long-term trajectory prediction, a hybrid artificial neural network trajectory prediction model, named CNN–BiGRU–Attention, integrates a Convolutional Neural Network (CNN), Bidirectional Gated Recurrent Unit (BiGRU), and Attention mechanism (AM), tuned for spatiotemporal feature extraction and extended time-series reasoning. Extensive experiments, including ablation studies, comparative analyses with state-of-the-art models like BiLSTM and Transformer, evaluations against numerical methods, and adaptability tests, were conducted for justifying the CNN–BiGRU–Attention model. The results highlight the CNN–BiGRU–Attention model’s excellent convergence, accuracy, and generalization capabilities in predicting 24, 48, and 72 h trajectories for SDBs with varying drogue statuses and under different sea conditions. This work has great potential to promote the intelligent degree of marine environmental monitoring.

An enhanced motion planning approach by integrating driving heterogeneity and long-term trajectory prediction for automated driving systems: A highway merging case study

Navigating automated driving systems (ADSs) through complex driving environments is difficult. Predicting the driving behavior of surrounding human-driven vehicles (HDVs) is a critical component of an ADS. This paper proposes an enhanced motion-planning approach for an ADS in a highway-merging scenario. This method utilizes the results of two aspects: the driving behavior and long-term trajectory of surrounding HDVs, which are coupled using a hierarchical model that is used for the motion planning of an ADS to improve driving safety. An unsupervised clustering algorithm is utilized to classify HDV drivers into two categories: aggressive and normal, as part of predicting their driving behaviors. Subsequently, a logistic regression model is employed for driving style prediction. For trajectory prediction, a transformer-based model that concentrated parallelization computations on longer sequence predictions via a self-attention mechanism is developed. Based on the predicted driving styles and trajectories of the surrounding HDVs, an intelligent decision-making strategy is utilized for ADS motion planning. Finally, real-world traffic data collected from drones on a highway ramp in Xi’an is used as a case study to train and evaluate the proposed model. The results demonstrate that the proposed approach can predict HDVs merging trajectories with a mean squared error (MSE) smaller than 0.125 at 30 s away from the merging point, outperforming existing approaches in terms of predictable duration and accuracy. Furthermore, it exhibited safety improvements by adjusting the ADS motion state in advance with good predictive power for the surrounding HDVs’ motion. For both normal and aggressive driving styles, the ADS trajectories reached optimal safety at a prediction horizon of at least 10 s and over 6.67 s, respectively, when evaluating both time-to-collision (TTC) and deceleration rate to avoid a crash (DRAC) metrics. This indicates that our proposed procedures have improved safety for AVs with long-term predictive capabilities (i.e., over 6 s) for surrounding HDVs. Interestingly, the safety performance does not continue to improve with the increase in prediction horizon once the optimal safety performance (highest TTC and lowest DRAC) has been achieved for both normal and aggressive styles. This suggests that an excessively long prediction horizon (e.g., 30 s) is not always beneficial for safety performance of ADS in our case study. When ADS encounter aggressive HDVs, having a predicted surrounding HDV trajectory can extremely reduce crash risk and maintain a safe situation. This demonstrates that planning ADS trajectories with HDV predictions has significant effects on safety, especially for aggressive driving styles as compared to normal driving styles.

Non-probability sampling network based on anomaly pedestrian trajectory discrimination for pedestrian trajectory prediction

Pedestrian trajectory prediction in first-person view is an important support for achieving fully automated driving in cities. However, existing pedestrian trajectory prediction methods still have significant shortcomings in terms of pedestrian trajectory diversity, dynamic scene constraints, and dependence on long-term trajectory prediction. We proposes a non-probability sampling network based on pedestrian trajectory anomaly recognition (ADsampler) to predict multiple possible future pedestrian trajectories. First, by incorporating pose and optical flow information, ADsampler models the multi-dimensional motion characteristics of pedestrians based on observed trajectory information and discriminates trajectory states. The sampling range in the Gaussian latent space is determined based on the recognition results. Next, velocity and yaw information of the car are introduced to model the car's motion state. A subtraction fusion network is employed to remove redundant image feature constraints in highly dynamic scenes. Finally, ADsampler utilizes a novel trajectory decoding network that combines the position encoding capability of GRU with the long-term dependency capturing ability of Transformer to decode and predict the fused features. we evaluate our model on crowded videos in the public datasets JAAD, PIE, ETH and UCY. Experiments demonstrate that the proposed method outperforms state-of-the-art approaches in prediction accuracy.

VOSTN: Variational One-shot Transformer Network for Pedestrian Trajectory Prediction

The accurate and reliable prediction of pedestrian future trajectories is of crucial significance for ensuring the safe navigation of autonomous driving systems. This paper introduces a novel approach called the Variational One-Shot Transformer Network (VOSTN) for the prediction of future trajectories within the 2D on-board domain. VOSTN presents an innovative method called the One-Shot Generation Block, which aims to generate queries simultaneously in order to predict future trajectories in a parallel manner. The utilization of the parallel prediction effectively addresses the issue of error accumulation resulting from autoregression, improves the efficiency of inference time, and enhances the precision of long-term trajectory prediction. And the cross-attention module investigates the inter-relationship between trajectory and ego-motion. Given the inherent stochasticity of pedestrian movement, we employ the Conditional Variational AutoEncoder to forecast available multimodal trajectories. Experimental results demonstrate that our model effectively exploits the information associated with trajectory and ego-motion, leading to the acquisition of more comprehensive feature representations. Moreover, our model outperforms the performance of existing methods on the two 2D on-board domain datasets. Our deterministic/multimodal prediction models show a reduction in the bounding box center final displacement error by 8% / 9% and 0.7% / 3% on PIE and JAAD, respectively, when compared to the most optimal baseline.

Decentralized policy learning with partial observation and mechanical constraints for multiperson modeling

Extracting the rules of real-world multi-agent behaviors is a current challenge in various scientific and engineering fields. Biological agents independently have limited observation and mechanical constraints; however, most of the conventional data-driven models ignore such assumptions, resulting in lack of biological plausibility and model interpretability for behavioral analyses. Here we propose sequential generative models with partial observation and mechanical constraints in a decentralized manner, which can model agents’ cognition and body dynamics, and predict biologically plausible behaviors. We formulate this as a decentralized multi-agent imitation-learning problem, leveraging binary partial observation and decentralized policy models based on hierarchical variational recurrent neural networks with physical and biomechanical penalties. Using real-world basketball and soccer datasets, we show the effectiveness of our method in terms of the constraint violations, long-term trajectory prediction, and partial observation. Our approach can be used as a multi-agent simulator to generate realistic trajectories using real-world data.

Long-Term Trajectory Prediction of Hypersonic Glide Vehicle Based on Physics-Informed Transformer

Long-Term Trajectory Prediction of Hypersonic Glide Vehicle Based on Physics-Informed Transformer

An Interacting Multiple Model for Trajectory Prediction of Intelligent Vehicles in Typical Road Traffic Scenario.

This article presents an interacting multiple model (IMM) for short-term prediction and long-term trajectory prediction of an intelligent vehicle. This model is based on vehicle's physics model and maneuver recognition model. The long-term trajectory prediction is challenging due to the dynamical nature of the system and large uncertainties. The vehicle physics model is composed of kinematics and dynamics models, which could guarantee the accuracy of short-term prediction. The maneuver recognition model is realized by means of hidden Markov model, which could guarantee the accuracy of long-term prediction, and an IMM is adopted to guarantee the accuracy of both short-term prediction and long-term prediction. The experiment results of a real vehicle are presented to show the effectiveness of the prediction method.

Long-Term Trajectory Prediction for Oil Tankers via Grid-Based Clustering

Vessel trajectory prediction is an important step in route planning, which could help improve the efficiency of maritime transportation. In this article, a high-accuracy long-term trajectory prediction algorithm is proposed for oil tankers. The proposed algorithm extracts a set of waymark points that are representative of the key traveling patterns in an area of interest by applying DBSCAN clustering to historical AIS data. A novel path-finding algorithm is then developed to sequentially identify a subset of waymark points, from which the predicted trajectory to a fixed destination is produced. The proposed algorithm is tested using real data offered by the Danish Maritime Authority. Numerical results demonstrate that the proposed algorithm outperforms state-of-the-art vessel trajectory prediction algorithms and is able to make high-accuracy long-term trajectory predictions.

Predictive hierarchical reinforcement learning for path-efficient mapless navigation with moving target

Deep reinforcement learning (DRL) has been proven as a powerful approach for robot navigation over the past few years. DRL-based navigation does not require the pre-construction of a map, instead, high-performance navigation skills can be learned from trial-and-error experiences. However, recent DRL-based approaches mostly focus on a fixed navigation target. It is noted that when navigating to a moving target without maps, the performance of the standard RL structure drops dramatically on both the success rate and path efficiency. To address the mapless navigation problem with moving target, the predictive hierarchical DRL (pH-DRL) framework is proposed by integrating the long-term trajectory prediction to provide a cost-effective solution. In the proposed framework, the lower-level policy of the RL agent learns robot control actions to a specified goal, and the higher-level policy learns to make long-range planning of shorter navigation routes by sufficiently exploiting the predicted trajectories. By means of making decisions over two level of policies, the pH-DRL framework is robust to the unavoidable errors in long-term predictions. With the application of deep deterministic policy gradient (DDPG) for policy optimization, the pH-DDPG algorithm is developed based on the pH-DRL structure. Finally, through comparative experiments on the Gazebo simulator with several variants of the DDPG algorithm, the results demonstrate that the pH-DDPG outperforms other algorithms and achieves a high success rate and efficiency even though the target moves fast and randomly.

Interaction-Aware Personalized Trajectory Prediction for Traffic Participant Based on Interactive Multiple Model

Trajectory prediction for traffic participants is a critical task for autonomous vehicles. The long-term trajectory prediction is challenging due to limited data and the dynamic characteristics of traffic participants. This paper presents an innovative interactive multiple model algorithm considering inter-vehicle interaction and driving behavior for the traffic participant's short-term and long-term trajectory prediction. The field experiment is conducted to acquire the human driver data, which is then preprocessed and analyzed with statistical methods. The clustering result of the critical gap is used to include the interactions between them, on which the gap satisfaction probability function is designed and aimed at describing the satisfaction probability of the current lane. The driving behavior is another promising candidate to improve the long-term prediction accuracy. The clustering results of the lane change duration are used to establish the lane changing models considering the driving behavior, the driving behavior probability function is designed based on the probability of each model. Then the two functions are incorporated into the adaptive transition probability matrix, where the quantitative probabilistic relations between the gap satisfaction probability and the driving behavior probability are established. The adaptive transition probability matrix is then used in the interactive multiple model algorithm. Based on the improved interactive multiple model, the personalized trajectory prediction for the traffic participant is obtained. The effectiveness of the framework is validated by simulation and field experiment.

Vehicle Trajectory Prediction Considering Driver Uncertainty and Vehicle Dynamics Based on Dynamic Bayesian Network

Vehicle trajectory prediction is a crucial but intricate problem for lateral driving assistance systems because of driver uncertainty. This article presents a probabilistic vehicle-trajectory prediction method based on a dynamic Bayesian network (DBN) model integrating the driver’s intention, maneuvering behavior, and vehicle dynamics. By selecting a most-relevant-feature vector using joint mutual information, we design a Gaussian mixture model- hidden Markov model and employ the model as a node in the DBN to identify the driver’s intention. Then, a reference path is generated using the road information. The uncertainties of drivers are captured in steering- and longitudinal-control using a stochastic driver model and a Markov chain, respectively. A vehicle dynamic model ensures that the predicted vehicle trajectory adheres to the vehicle dynamics, which improves the prediction accuracy. A particle filter is used to recursively estimate the vehicle trajectory, including position coordinates and the lateral distance from the vehicle center of gravity to the road edge. We evaluate the proposed DBN trajectory prediction method in both lane-keeping and lane-changing scenarios based on a dataset collected from a real-time dynamic driving simulator. Results show that the proposed method can achieve accurate long-term trajectory prediction.

Long-Term Trajectory Prediction Model Based on Transformer

Long-Term Trajectory Prediction Model Based on Transformer

A Probabilistic Architecture of Long-Term Vehicle Trajectory Prediction for Autonomous Driving

In mixed and dynamic traffic environments, accurate long-term trajectory forecasting of surrounding vehicles is one of the indispensable preconditions for autonomous vehicles (AVs) to accomplish reasonable behavioral decisions and guarantee driving safety. In this paper, we propose an integrated probabilistic architecture for long-term vehicle trajectory prediction, which consists of a driving inference model (DIM) and a trajectory prediction model (TPM). The DIM is designed and employed to accurately infer the potential driving intention based on a dynamic Bayesian network. The proposed DIM incorporates the basic traffic rules and multivariate vehicle motion information. To further improve the prediction accuracy and realize uncertainty estimation, we develop a Gaussian process (GP)-based TPM, considering both the short-term prediction results of the vehicle model and the driving motion characteristics. Afterward, the effectiveness of our novel approach is demonstrated by conducting experiments on a public naturalistic driving dataset under lane-changing scenarios. The superior performance on the task of long-term trajectory prediction is presented and verified by comparing with other advanced methods.