AnyNav: Visual neuro-symbolic friction learning for off-road navigation

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 learning in a self-supervised manner for real-world settings, we adopt the imperative learning paradigm, where a bilevel optimization framework leverages physics-based optimization for training the friction network. This explicit incorporation of physical reasoning substantially improves generalization across terrains, vehicle types, and operating 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.