融合Hermite插值与PINN的空间电磁捕获刚体动力学建模与预测

Rigid-Body Dynamics Modeling and Prediction for Space Electromagnetic Capture via Hermite Interpolation and Physics-Informed Neural Networks

摘要: 空间电磁捕获过程中刚体运动状态受到电磁场、质量参数及初始条件等多因素耦合作用影响，其动力学响应具有显著的非线性特征。传统物理信息神经网络通常利用单一网络直接学习完整动力学映射关系，不仅需要拟合系统中的平滑变化趋势，还需刻画电磁吸附阶段的局部强非线性行为，导致模型训练复杂度较高，并限制了预测精度的进一步提升。针对上述问题，本文提出一种融合物理约束插值与PINN的协同预测方法。首先，根据空间电磁捕获动力学响应中普遍存在的趋势项与非线性扰动项特征，将目标状态分解为线性趋势部分和非线性残差部分；随后利用Hermite插值构建动力学响应的连续趋势项预测模型，实现目标轨迹的基线估计；在此基础上，引入PINN学习由电磁耦合作用、姿态变化及动力学约束引起的非线性残差项，并通过牛顿–欧拉方程构建物理约束损失函数，实现非线性动力学行为的精确刻画；最终将插值预测结果与PINN残差输出进行融合，获得目标状态的高精度预测结果。

Abstract: The dynamic response of rigid bodies during space electromagnetic capture is governed by the coupling effects of electromagnetic fields, mass properties, and initial operating conditions, resulting in highly nonlinear motion characteristics. Conventional Physics-Informed Neural Networks typically employ a single neural network to learn the complete dynamic mapping, requiring the model to simultaneously capture both smooth trend behaviors and strong nonlinear responses occurring during the electromagnetic attraction process. Such a learning paradigm increases training complexity and limits predictive performance. To address this issue, this paper proposes a collaborative prediction framework that integrates physics-constrained interpolation with PINN. The proposed method decomposes the dynamic response into a linear trend component and a nonlinear residual component. First, a Hermite interpolation model is employed to reconstruct the continuous trend term of the motion trajectory and provide a baseline prediction. Subsequently, a PINN is introduced to learn the nonlinear residual dynamics induced by electromagnetic coupling effects, attitude variations, and rigid-body dynamic interactions. Newton-Euler equations are incorporated into the loss function to ensure physical consistency of the residual prediction. The final dynamic state is obtained by fusing the interpolated trend prediction with the nonlinear residual estimated by the PINN.