arXiv:2512.00289cs.LGcs.RO2025-12

用数据修正车辆动力学模型,提升非自主系统建模精度与数据效率。

Data-Driven Modeling and Correction of Vehicle Dynamics

  • 通过局部参数化时间控制输入,将复杂动态转化为可学习的分段参数系统。
  • DRIPS方法在少量数据下实现高精度线性近似,FML在数据稀缺时仍能捕捉强非线性。
  • 适合需要低数据成本建模的自动驾驶、机器人控制研究者使用。

我们提出一种数据驱动框架,用于学习和修正非自主车辆动力学。基于物理的车辆模型常因简化而存在模型形式不确定性,且其动态受时变控制输入影响,直接从时间快照数据中学习预测模型面临挑战。为此,我们通过时间依赖输入的局部参数化重构车辆动力学,得到一系列局部参数化动力系统。采用两种互补方法逼近这些系统:一是运用DRIPS(参数空间中的降维与插值)构建高效线性代理模型,结合升维观测量空间与流形算子插值,实现升维空间中可精确线性表示的动力学数据高效学习;二是对强非线性系统采用FML(流映射学习),一种无需特殊处理非线性的深度神经网络方法,可直接逼近参数演化映射。进一步引入基于迁移学习的模型修正机制,仅需少量高保真或实验测量即可修正先验模型误设,无需预设修正项形式。在单轮车、简化自行车及滑移自行车模型上的一系列数值实验表明,DRIPS在数据稀缺条件下表现出稳健且高效的学习能力,而FML则在严重数据短缺下仍具备强大的非线性建模与模型形式误差修正能力。

原文摘要 · Abstract (English)

We develop a data-driven framework for learning and correcting non-autonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need for data-driven correction. Moreover, non-autonomous dynamics are governed by time-dependent control inputs, which pose challenges in learning predictive models directly from temporal snapshot data. To address these, we reformulate the vehicle dynamics via a local parameterization of the time-dependent inputs, yielding a modified system composed of a sequence of local parametric dynamical systems. We approximate these parametric systems using two complementary approaches. First, we employ the DRIPS (dimension reduction and interpolation in parameter space) methodology to construct efficient linear surrogate models, equipped with lifted observable spaces and manifold-based operator interpolation. This enables data-efficient learning of vehicle models whose dynamics admit accurate linear representations in the lifted spaces. Second, for more strongly nonlinear systems, we employ FML (Flow Map Learning), a deep neural network approach that approximates the parametric evolution map without requiring special treatment of nonlinearities. We further extend FML with a transfer-learning-based model correction procedure, enabling the correction of misspecified prior models using only a sparse set of high-fidelity or experimental measurements, without assuming a prescribed form for the correction term. Through a suite of numerical experiments on unicycle, simplified bicycle, and slip-based bicycle models, we demonstrate that DRIPS offers robust and highly data-efficient learning of non-autonomous vehicle dynamics, while FML provides expressive nonlinear modeling and effective correction of model-form errors under severe data scarcity.

车辆动力学数据驱动模型修正非线性建模

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