Graph-DDL: A Goal-Directed Deep Learning Framework Integrating Spatial-Temporal Graph Neural Networks with Asymptotically Stable Dynamical Systems for Pedestrian Trajectory Prediction

Abstract

Pedestrian trajectory prediction plays a critically important role in autonomous driving and robot navigation. In recent years, deep learning models have achieved notable progress in this field; however, they often lack interpretability in their predictions, making it difficult to ground the results in physical laws or social norms. Recent studies have proposed a dynamics-based deep learning (DDL) framework that integrates asymptotically stable dynamical systems into Transformer models to address these issues. Nevertheless, Transformer architectures in federated crowd settings suffer from the limited capacity to capture complex spatial interaction information among pedestrians. To overcome this limitation, this paper presents a novel framework, Graph-DDL, which combines a Spatial-Temporal Graph Neural Network (ST-GNN) with asymptotically stable dynamical systems. We construct dynamic adjacency matrices that encode relative distance and relative velocity between pedestrians, replacing the conventional static interaction representations with physically grounded dynamic interaction graphs. Leveraging the inherent properties of the Transformer architecture, we redesign the spatial interaction mechanism to build a goal-directed Transformer backbone. Specifically, a novel coupling scheme is designed that integrates "relative distance" based proximity graphs with "relative velocity" based dynamic adjacency matrices, enabling realistic pedestrian collision avoidance and interaction behavior modeling. By incorporating asymptotic stability constraints, the ST-GNN outputs are guaranteed to produce stable, well-defined control trajectories. Experimental validation confirms that Graph-DDL maintains convergence assurance while yielding significant improvements in open-space crowd scene displacement and prediction accuracy, endowing the model with physical interpretability and social norm compliance.