Physics-informed machine learning for lugre-based tire force prediction in high-performance autonomous vehicles

Abstract

Accurate prediction of tire forces is fundamental to vehicle dynamics simulation, state estimation, and control, particularly for robotics and autonomous driving systems operatingunder uncertain road conditions. Tire–road friction exhibits strong nonlinearities, transient behavior, and hysteresis, making it difficult to model using either purely physics-based or purely data-driven approaches. Furthermore, friction properties cannot be reliably inferred from perception alone, as visually similar surfaces may correspond to substantially different grip conditions. This thesis proposes a Physics-Informed Machine Learning framework for tire force prediction based on the LuGre friction model. The LuGre formulation is embedded as a structured, differentiable component within a stochastic dynamical system, capturing slipdependent friction dynamics and internal frictional memory. Neural network components are used to learn model parameters and unmodeled effects directly from data while preserving physical consistency. Tire forces and latent friction states are treated as internal variables and are inferred implicitly through vehicle motion rather than being directly supervised. Model parameters are learned by maximizing the likelihood of observed vehicle trajectories using differentiable stochastic rollouts implemented via Euler–Maruyama integration.The model is evaluated using vehicle trajectory data generated in the BeamNG.Tech simulation environment, which provides an effective validation platform due to its combination of high-fidelity vehicle dynamics and soft-body physics, enabling the representation of deformation, force propagation, weight transfer, and detailed contact interactions. Performance is assessed through trajectory rollout accuracy, force–slip behavior, hysteresis characteristics, and uncertainty analysis across a range of driving conditions. Results demonstrate that the proposed physics-informed approach produces physically plausible tire force behavior and stable long-horizon predictions, while improving robustness compared to purely data-driven models. The framework provides a principled approach for integrating physical tire models with modern learning techniques, with direct relevance to robotics, autonomous vehicles, reduced-order and learning-based vehicle dynamics simulation, and to model-based optimal control methods for limit handling due to its structured and differentiable formulation.