Off-road traversability is direction-dependent and vehicle specific, yet most global maps assign a single isotropic cost to each location. Existing learned estimators are also commonly trained independently for each vehicle; this preserves vehicle-specific behavior but prevents vehicles from sharing common terrain representations. DGT-MAP addresses both limitations through a self-supervised framework that learns global, directional, and vehicle-conditioned traversability costmaps from RGB-D observations and locomotion signals. A shared multi-task backbone learns common terrain features across training vehicles while vehicle-specific prediction heads preserve platform-dependent responses. At inference, DGT-MAP produces a heading-indexed costmap that can be used by a direction-aware planner. We evaluate DGT-MAP in simulation by integrating it into a Hybrid A* navigation stack and measuring downstream task success on challenging terrains, including slopes that are traversable downhill but not uphill and a ridge obstacle that is traversable by some vehicles, but not by others. Across evaluated tasks, DGT-MAP achieves the highest or tied-highest navigation success rate when compared against geometric, binary, and learned direction-agnostic baselines.

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