Understanding human motion is fundamental to the development of intelligent systems capable of seamless interaction with people. Trajectory prediction is a critical component in domains, such as intelligent transportation, surveillance, and human–robot collaboration. However, accurately forecasting human movement remains a significant challenge due to its inherently uncertain and multimodal nature. In this work, we propose a deep neural network that models agent dynamics and predicts future trajectories by representing them as a probabilistic multimodal distribution. To effectively capture the stochasticity of human behavior, our method employs a score-based diffusion model that learns to generate realistic trajectory samples by denoising latent representations. In addition, we introduce a novel social attention mechanism designed to model complex interagent interactions, further improving predictive performance. We validate our approach in both pedestrian and marine vessel trajectory datasets, demonstrating its superior ability to capture social dynamics and forecast diverse plausible future outcomes. Extensive experiments and ablation studies confirm the robustness, generalizability, and accuracy of our framework in varied real-world environments.

The safety of navigation is critical in areas with heavy and complex traffic. Accurate prediction of the future trajectory of ships is crucial, especially in encounter situations where conventional navigational devices are prone to high uncertainty and risk due to their limitations. Unfortunately, kinematic models and data-driven methods suffer from numerous issues, such as poor performance, intricate architecture, and reduced interpretability. In response, this article introduces a novel approach, driven by automatic identification system (AIS) data, to enhance the efficacy of ship encounter trajectory prediction. It revolves around encounter classification, wherein the invaluable insights of seamanship play a pivotal role in identifying and categorizing legitimate encounters into three distinct types. This categorization forms the foundation for developing a probability-based classification model, in conjunction with a hybrid predictor that amalgamates a kinematics-based model and a neural network-based model. Historical AIS data collected in Oslofjord, Norway, are utilized in this study, and experiments have been conducted to assess the performance of the proposed method through real cases. The results substantiate the promise of the classification model and underscore the exceptional predictive capabilities of the hybrid approach. This superiority is attributed to the synergistic effects arising from the integration of its constituent models.

Machine learning (ML) has been actively adopted in Linear Programming (LP) and Mixed-Integer Linear Programming (MILP), whose potential is hindered by instance scarcity. Current synthetic instance generation methods often fall short in closely mirroring the distribution of original datasets or ensuring the feasibility and boundedness of the generated data — a critical requirement for obtaining reliable supervised labels in model training. In this paper, we present a diffusion-based LP/MILP instance generative framework called MILP-FBGen. It strikes a balance between structural similarity and novelty while maintaining feasibility/boundedness via a meticulously designed structure-preserving generation module and a feasibility/boundedness-constrained sampling module. Our method shows superiority on two fronts: 1) preservation of key properties (hardness, feasibility, and boundedness) of LP/MILP instances, and 2) enhanced performance on downstream tasks. Extensive studies show two-fold superiority that our method ensures higher distributional similarity and 100% feasibility in both easy and hard datasets, surpassing current state-of-the-art techniques.

Navigation safety is of paramount importance in areas with heavy and complex maritime traffic. Any ship navigating such a scenario should be able to foresee the future positions of other ships and adjust its path accordingly to avoid collisions. However, predicting future trajectories is a very challenging problem due to many possible future trajectories from the inherent uncertainty and the complex interaction dynamics between different ships. In this article, we propose a deep generative model based on the conditional variational autoencoder framework to learn marine vessel movement and predict future trajectories. The model is able to produce a multimodal probability distribution over future trajectories and model the complex interactions between vessels. Experiments are performed in two-vessel encounter scenarios from real-world automatic identification system data. The proposed model outperforms the baseline methods, including both kinematics-based and data-driven methods. The trajectories predicted by the proposed model are also analyzed to demonstrate the effectiveness of the model.

To decrease the risk of collisions and ensure safe navigation, an Automatic Identification System (AIS) was developed to broadcast real-time ship states information, such as ship position and sailing speed. Due to the real-time characteristic of AIS data, it, hence, has been widely used to construct a data-driven model for ship trajectory prediction, which can provide onboard decision support for navigators. However, data provided by AIS is sometimes partially missing or simply wrong. Poor quality of AIS data can degrade the performance of data-driven models and lead to large uncertainty in the predicted ship positions. Therefore, this paper proposes a hybrid model to reduce uncertainty by integrating the multi-output Gaussian process (MOGP) model predictions and historical trajectory information. Historical trajectories provide useful prior knowledge to calibrate the performance of MOGP model predictions. This model is built through three steps: 1) extracting historical ship trajectory information from the route that a ship is following; 2) predicting ship positions with a data-driven predictor built by an MOGP; and 3) obtaining a trajectory by knowledge fusion of historical information and predicted results. The experiment shows the proposed hybrid model outperforms other data-driven models and has small errors and uncertainty quantification of the ship position prediction. Especially for the 6-minute position prediction, its RMSE is over 100 meters smaller than other methods.

In recent years, maritime operations have become more technologically demanding due to the more complex working condition and stricter safety requirements. The need to improve the performance of human-machine cooperation in navigation through a more intelligent system in path planning, while taking into account the human factors, is more and more urgent. In this paper, a model predictive control (MPC) optimization scheme is proposed for collision-free path planning taking into account the ship dynamics and International Regulations for Preventing Collisions at Sea (COLREGS) explicitly. It utilizes three potential fields which are designed based on COLREGS and the experience of navigators. Different tuning parameter sets are tested in a single encounter scenario including give-way, head-on and overtaking, and multiple ship encounter with 5 target ships is evaluated. The simulation shows promising results where the own ship can perform evasive action according to different encounter types following COLREGS Rule 13-15 and achieve the target positions while maintaining a safe distance during the collision avoidance period. The shortest distances between the own ship and target ships in multiple encounter scenario are all larger than 250m, which further proves the effectiveness of the algorithm.