This paper presents a safe, efficient, and agile ground vehicle navigation algorithm for 3D off-road terrain environments. Off-road navigation is subject to uncertain vehicleterrain interactions caused by different terrain conditions on top of 3D terrain topology. The existing works are limited to adopt overly simplified vehicle-terrain models. The proposed algorithm learns the terrain-induced uncertainties from driving data and encodes the learned uncertainty distribution into the traversability cost for path evaluation. The navigation path is then designed to optimize the uncertainty-aware traversability cost, resulting in a safe and agile vehicle maneuver. Assuring real-time execution, the algorithm is further implemented within parallel computation architecture running on Graphics Processing Units (GPU).

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