Off-road navigation is critical for a wide range of field robotics applications from planetary exploration to disaster response. However, it remains a longstanding challenge due to unstructured environments and the inherently complex terrain-vehicle interactions. Traditional physics-based methods struggle to accurately capture the nonlinear dynamics underlying these interactions, while purely data-driven approaches often overfit to specific motion patterns, vehicle geometries, or platforms, limiting their generalization in diverse, real-world scenarios. To address these limitations, we introduce AnyNav, a vision-based friction estimation and navigation framework grounded in neuro-symbolic principles. Our approach integrates neural networks for visual perception with symbolic physical models for reasoning about terrain-vehicle dynamics. To enable self-supervised learning in real-world settings, we adopt the imperative learning paradigm, employing bilevel optimization to train the friction network through physics-based optimization. This explicit incorporation of physical reasoning substantially enhances generalization across terrains, vehicle types, and operational conditions. Leveraging the predicted friction coefficients, we further develop a physics-informed navigation system capable of generating physically feasible, time-efficient paths together with corresponding speed profiles. We demonstrate that AnyNav seamlessly transfers from simulation to real-world robotic platforms, exhibiting strong robustness across different four-wheeled vehicles and diverse off-road environments.

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