分析力学和图神经网络的轨迹预测方法

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Title:

Trajectory prediction methods based on analytical mechanics and graph neural networks

作者:

李明晗, 肖阳, 邢向磊

哈尔滨工程大学 智能科学与工程学院, 黑龙江 哈尔滨 150001

Author(s):

LI Minghan, XIAO Yang, XING Xianglei

College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China

关键词:

轨迹预测; 图神经网络; 拉格朗日力学; 交互作用力; 深度学习; 多层感知机; 运动学模型; 分析力学

Keywords:

trajectory prediction; graph neural networks; Lagrangian mechanics; interaction force; deep learning; multi-layer perceptron; kinematic model; analytical mechanics

分类号:

TP391.41

DOI:

10.11992/tis.202501020

摘要:

轨迹预测旨在通过分析智能体的历史运动数据来预测轨迹。然而，现有深度学习方法因忽略物理约束和运动规律导致可解释性不足。针对此问题，提出一种融合分析力学与图神经网络的轨迹预测模型，利用图神经网络、卷积神经网络和图注意力机制提取目标时空动态特征，结合欧氏距离和相对运动推断交互力，并引入拉格朗日力学对动力学过程和约束进行建模，以生成符合物理规律的轨迹。在Spring-balls数据集上的实验表明，模型在5球10帧短期预测中精度提升14.29%。在更具挑战性的50帧长期预测中，5球和10球场景下的精度分别提升6.25%和4.81%。此外，在人体运动预测中，该模型平均多关节位置误差(mean per joint position error，MPJPE)均优于主流方法，验证了其在长期预测中的更高精度和有效性。

Abstract:

Trajectory prediction seeks to forecast the future motion of intelligent agents by analyzing their past trajectories. While deep learning methods have been demonstrated to capture complex features, they frequently neglect physical constraints, thereby constraining interpretability. To address this, a trajectory prediction model is proposed that integrates analytical mechanics with graph neural networks (GNNs). The model combines GNNs, convolutional neural networks, and graph attention to extract spatiotemporal dynamics, infers interaction forces from Euclidean distance and relative motion, and incorporates Lagrange mechanics to enforce physical laws. Experiments on the Spring-balls dataset demonstrate the superior performance of the proposed model in comparison to traditional models, exhibiting a 14.29% accuracy gain in 10-frame short-term prediction for the 5-ball case and improvements of 6.25% and 4.81% in 50-frame long-term scenarios. In the domain of human motion prediction, our model demonstrates a reduction in mean position error (MPJPE) when compared to prevailing approaches for a wide range of actions. This finding signifies enhanced long-term accuracy and validates the efficacy of the model.