Accurate dynamics models are essential for model-based robotic control, yet nominal Euler--Lagrange models often become inaccurate in the presence of payload variation, unmodeled coupling, friction, aerodynamic effects, and changing operating conditions. Most learning-based correction methods improve prediction accuracy by introducing a single additive residual, but do not preserve the internal mechanical structure of Euler--Lagrange systems. This leads to models that do not preserve symmetry, positive-definiteness, or the coupling between inertia and velocity-dependent terms, which can result in physically inconsistent predictions and reduced reliability when embedded in model-based controllers. We propose a structure-preserving residual learning framework that decomposes model mismatch into an inertia correction, the corresponding induced Coriolis term, and a generalized-force residual. The mechanical component is learned under physical constraints, while the disturbance-sensitive component is represented through a sparse history-dependent latent interaction model and adapted online using Bayesian linear regression. This separation preserves key mechanical structure while restricting adaptation to the part of the dynamics most affected by changing conditions. Experiments across multiple robotic platforms, including mobile, aerial, and manipulator systems, show that the proposed method improves dynamics prediction and trajectory tracking under coupled and time-varying dynamics. These results highlight the value of combining structured residual modeling, compact latent interaction selection, and selective online adaptation for real-world model-based control.

翻译：精确的动力学模型是基于模型的机器人控制的关键，然而名义上的欧拉-拉格朗日模型在负载变化、未建模耦合、摩擦、空气动力学效应以及运行条件改变时往往变得不准确。多数基于学习的修正方法通过引入单一加性残差来提高预测精度，但并未保留欧拉-拉格朗日系统的内部机械结构。这导致模型无法保持对称性、正定性，以及惯性项与速度相关项之间的耦合关系，从而可能在嵌入基于模型的控制器时产生物理上不一致的预测，并降低可靠性。我们提出一种结构保持的残差学习框架，将模型失配分解为惯性修正、相应的诱导科里奥利项以及广义力残差。机械分量在物理约束下进行学习，而对扰动敏感的分量则通过稀疏历史依赖的潜交互模型表示，并利用贝叶斯线性回归实现在线自适应。这种分离既保留了关键的机械结构，又将自适应限制在受条件变化影响最大的动力学部分。在多种机器人平台（包括移动机器人、空中机器人和机械臂系统）上的实验表明，所提方法在耦合和时变动力学条件下改善了动力学预测和轨迹跟踪性能。这些结果凸显了结构化残差建模、紧凑潜交互选择以及选择性在线自适应相结合在实际基于模型控制中的价值。