NeSAM: Neuro-Symbolic Kinodynamics with Soil Adaptation for Off-Road Mobility

Off-road mobility requires autonomous mobile robots to generalize across heterogeneous vehicle fleets and continuously changing terrain conditions. Existing cross-vehicle adaptation approaches generally assume flat terrain, while terrain-aware kinodynamic models often require platform-specific data collection and retraining. To this end, we propose VertiAKD, a unified framework for transferring and adapting off-road kinodynamic knowledge across diverse vehicles on geometrically and semantically complex terrain simultaneously. VertiAKD learns a shared mobility representation that jointly encodes vehicle configurations, trajectory transitions, and local elevation and semantic terrain features. Given limited data from a novel vehicle operating on unseen terrain, VertiAKD identifies the most relevant mobility descriptors and transfers their knowledge to initialize a terrain-aware kinodynamic model via function encoders, which is then periodically refined online from streaming observations without gradient-based retraining. We evaluate VertiAKD in the Verti-Bench simulator, built on the Chrono multi-physics engine, and on five physical configurations of the Verti-4-Wheeler platform. With only one minute of new trajectory data and associated terrain features, VertiAKD reduces long-horizon prediction error by up to 34.52% over direct mobility descriptor transfer across diverse unseen vehicle configurations and 94.43% over competing baselines. We further demonstrate robust closed-loop trajectory tracking in both simulation and physical experiments, highlighting the effectiveness of terrain-aware cross-vehicle knowledge transfer for accurate modeling and reliable off-road navigation.

Autonomous driving in off-road environments presents significant challenges due to the dynamic and unpredictable nature of unstructured terrain. Traditional kinodynamic models often struggle to generalize across diverse geometric and semantic terrain types, underscoring the need for real-time adaptation to ensure safe and reliable navigation. We propose VertiAdaptor (VA), a novel online adaptation framework that efficiently integrates elevation with semantic embeddings to enable terrain-aware kinodynamic modeling and planning via function encoders. VA learns a kinodynamic space spanned by a set of neural ordinary differential equation basis functions, capturing complex vehicle-terrain interactions across varied environments. After offline training, the proposed approach can rapidly adapt to new, unseen environments by identifying kinodynamics in the learned space through a computationally efficient least-squares calculation. We evaluate VA within the Verti-Bench simulator, built on the Chrono multi-physics engine, and validate its performance both in simulation and on a physical Verti-4-Wheeler platform. Our results demonstrate that VA improves prediction accuracy by up to 23.9% and achieves a 5X faster adaptation time, advancing the robustness and reliability of autonomous robots in complex and evolving off-road environments.

Reinforcement learning for off-road navigation requires extensive vehicle-terrain interaction data, which are costly to collect in high-fidelity simulation. World models offer a promising alternative by replacing simulator roll-outs during policy optimization. However, an off-road world model must condition state transitions on exteroceptive terrain information, which proprioception alone does not provide. This challenge is further amplified by the need to model both rigid and deformable terrain, where data-driven and physics-based approaches offer complementary strengths. We propose Verti-WM, a physics-aided exteroceptive world model that recurrently fuses a frozen Transformer for rigid terrain and a neuro-symbolic terramechanics model for deformable terrain. Elevation and semantic observations queried from a supplied map at each predicted pose condition fusion, enabling six-degree-of-freedom rollouts for policy optimization without further simulator access. Verti-WM reduces prediction error by 34.6% and 21.7% over data-driven and physics-based baselines, respectively. Policies trained entirely within Verti-WM achieve comparable task success rates while reducing computation time by 23.6X relative to direct training in the high-fidelity simulator. We further validate Verti-WM using real-world data, enabling policy optimization within learned real-world kinodynamics and achieving a 80% success rate on the Verti-4-Wheeler platform, compared with 40% for direct sim-to-real transfer.