Uncertainty-aware Accurate Elevation Modeling for Off-road Navigation via Neural Processes

Terrain elevation modeling for off-road navigation aims to accurately estimate changes in terrain geometry in real-time and quantify the corresponding uncertainties. Having precise estimations and uncertainties plays a crucial role in planning and control algorithms to explore safe and reliable maneuver strategies. However, existing approaches, such as Gaussian Processes (GPs) and neural network-based methods, often fail to meet these needs. They are either unable to perform in real-time due to high computational demands, underestimating sharp geometry changes, or harming elevation accuracy when learned with uncertainties. Recently, Neural Processes (NPs) have emerged as a promising approach that integrates the Bayesian uncertainty estimation of GPs with the efficiency and flexibility of neural networks. Inspired by NPs, we propose an effective NP-based method that precisely estimates sharp elevation changes and quantifies the corresponding predictive uncertainty without losing elevation accuracy. Our method leverages semantic features from LiDAR and camera sensors to improve interpolation and extrapolation accuracy in unobserved regions. Also, we introduce a local ball-query attention mechanism to effectively reduce the computational complexity of global attention by 17\% while preserving crucial local and spatial information. We evaluate our method on off-road datasets having interesting geometric features, collected from trails, deserts, and hills. Our results demonstrate superior performance over baselines and showcase the potential of neural processes for effective and expressive terrain modeling in complex off-road environments.