Building a universal trajectory foundation model is a promising solution to address the limitations of existing trajectory modeling approaches, such as task specificity, regional dependency, and data sensitivity.

Spatiotemporal trajectory data is crucial for various traffic-related applications. However, issues such as device malfunctions and network instability often result in sparse trajectories that lose detailed movement information compared to their dense counterparts. Recovering missing points in sparse trajectories is thus essential. Despite recent progress, three challenges remain. First, the lack of large-scale dense trajectory datasets hinders the training of a trajectory recovery model. Second, the varying spatiotemporal correlations in sparse trajectories make it hard to generalize across different sampling intervals.

Research in trajectory forecasting (i.e., predicting where an agent will be in the future) has grown

The reason is that different types of agents have distinct behavior patterns or feasibility constraints. For example, the trajectories of on-road vehicles are restricted by roadways, traffic rules and physical constraints, while the restrictions on pedestrian behaviorsaremuchfewer. More specifically, in the first case of Figure 7, for the player of the green team in the middle, the historical steps move forward quickly, while our model can successfully predict that theplayer will suddenly stop, since heissurrounded bymanyopponents andheisnotcarrying theball. The movement ofthese particles contains twophases, corresponding totwo interaction graphs. Initially, particles are rigidly connected to each other and form a "star" shape.

Trajectory generation has recently drawn growing interest in privacy-preserving urban mobility studies and location-based service applications. Although many studies have used deep learning or generative AI methods to model trajectories and have achieved promising results, the robustness and interpretability of such models are largely unexplored. This limits the application of trajectory generation algorithms on noisy real-world data and their trustworthiness in downstream tasks. To address this issue, we exploit the regular structure in urban trajectories and propose a deep generative model based on the pathlet representation, which encode trajectories with binary vectors associated with a learned dictionary of trajectory segments. Specifically, we introduce a probabilistic graphical model to describe the trajectory generation process, which includes a Variational Autoencoder (VAE) component and a linear decoder component. During training, the model can simultaneously learn the latent embedding of pathlet representations and the pathlet dictionary that captures mobility patterns in the trajectory dataset. The conditional version of our model can also be used to generate customized trajectories based on temporal and spatial constraints. Our model can effectively learn data distribution even using noisy data, achieving relative improvements of $35.4\%$ and $26.3\%$ over strong baselines on two real-world trajectory datasets. Moreover, the generated trajectories can be conveniently utilized for multiple downstream tasks, including trajectory prediction and data denoising. Lastly, the framework design offers a significant efficiency advantage, saving $64.8\%$ of the time and $56.5\%$ of GPU memory compared to previous approaches.

Research in trajectory forecasting (i.e., predicting where an agent will be in the future) has grown

To ensure secure and dependable mobility in environments shared by humans and robots, social navigation robots should possess the capability to accurately perceive and predict the trajectories of nearby pedestrians.