Autonomously navigating off-road terrain at high speed demands accurate control, which often relies on dynamics models that capture complex interactions between the robot and terrain. In off-road regimes, terrain interaction is a major component of the vehicle's dynamics. Prior work attempts to capture this effect by training learned models of the vehicle's dynamics, conditioned on its perception of the local environment. However, said conditioning is often overly simplistic, ignoring the spatial structure of the dynamics problem. Our approach, SpatialBEV, exploits this spatial structure. At each step, we query the bird's-eye-view (BEV) features around the predicted state, conditioning the next prediction on current geometric and semantic cues. We additionally present a benchmarking approach that mines a dataset's most difficult scenarios. On datasets collected across seasons, SpatialBEV reduces prediction error by 17.1%, compared to physics-based and learned baselines. We further evaluate on hardware on high-speed ($\geq$10 m/s) and geometrically challenging courses with a 25.3% reduction in maximum cross-track error. More details can be found at https://theairlab.org/spatial-bev-dynamics .

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