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Accurately understanding and predicting the future trajectories of pedestrians around autonomous vehicles is a major challenge. Due to the uncertainty and diversity of pedestrian trajectories, current research focuses on the multimodality of trajectory prediction. Currently, multimodal pedestrian prediction methods mainly use deep generative networks to generate mutually independent trajectories through independent sampling strategy, thus focusing on modes with a large number of samples. Moreover, deep generative networks are black-box models that are entirely data-driven and cannot effectively explain trajectory generation. In addition, current research lacks an effective measure for each trajectory. Therefore, in our paper, we propose a physics constrained pedestrian trajectory prediction with probability quantification. We divide multimodal trajectory prediction into two phases: trajectory generation phase and trajectory selection phase. During the trajectory generation phase, rather than directly predicting trajectories, we incorporate a differential constraint module to ensure that the generated trajectories adhere to pedestrian motion laws. This approach enhances the interpretability of the model prediction process. Subsequently, we generate a set of candidate trajectory proposals with specific correlations through the correlated sampling module. During the trajectory selection phase, a probability selection module is proposed to establish explicit probability distributions for the candidate trajectory proposals and to select the proposal with the highest probability as the final output. Extensive experiments on a public real-world pedestrian trajectory dataset show that our proposed model exhibits significant advantages over existing models in multimodal trajectory prediction, which not only effectively reduces the error but also mitigates mode collapse. Moreover, we provide probabilities for each trajectory to better capture the model uncertainty and provide more comprehensive information for downstream decision-making systems. • Implemented differential constraints to regulate pedestrian behavior. • Proposed a correlation sampling method to mitigate modal collapse. • We propose an efficient probabilistic measurement mechanism. [ABSTRACT FROM AUTHOR]

Autonomous vehicles offer significant advantages for transportation systems, particularly in enhancing traffic safety. To achieve this goal, it is crucial to comprehensively understand and predict the future trajectories of pedestrians in proximity to autonomous vehicles. Many contemporary approaches for predicting pedestrian trajectories heavily rely on neural networks, especially recurrent neural networks. However, these approaches do not explicitly incorporate the dynamics of pedestrian movement and instead rely on data-driven black-box models. Consequently, these models may fall short in terms of interpretability and fail to adhere to the fundamental principles of kinematics. In response to these limitations, our work introduces an innovative model for pedestrian trajectory prediction grounded in neural differential constraints. We aim to investigate temporal changes in pedestrian state variables, such as position and speed, using neural networks. During the prediction process, the output of the neural network is governed by differential equations. This approach ensures that the generated trajectories align with the fundamental principles of physics, harnessing the combined power of neural networks and physics-based pedestrian motion models. Furthermore, our research endeavors to develop a cohesive framework that seamlessly integrates pedestrian movement patterns with the influence of ego-vehicles, while also considering potential destinations to inform future trajectory planning. We conducted extensive experiments on two publicly available real-world datasets to assess the effectiveness of our model in enhancing prediction accuracy and providing coherent explanations of pedestrian motion, comparing it to state-of-the-art methods. • Differential equations can restrict trajectories to adhere to physical principles. • Pedestrian-vehicle movement is converted to image coordinate system for modeling. • Enhance prediction accuracy by precisely estimating a pedestrian's potential goal. [ABSTRACT FROM AUTHOR]