Autonomous ground vehicles operating off-road must plan curvature-feasible paths while accounting for spatially varying soil strength and slope hazards in real time. We present a continuous state--cost metric that combines a Bekker pressure--sinkage model with elevation-derived slope and attitude penalties. The resulting terrain cost field is analytic, bounded, and monotonic in soil modulus and slope, ensuring well-posed discretization and stable updates under sensor noise. This metric is evaluated on a lattice with exact steering primitives: Dubins and Reeds--Shepp motions for differential drive and time-parameterized bicycle arcs for Ackermann steering. Global exploration is performed using Vehicle-Dynamics RRT\(^{*}\), while local repair is managed by Vehicle-Dynamics D\(^{*}\) Lite, enabling millisecond-scale replanning without heuristic smoothing. By separating the terrain--vehicle model from the planner, the framework provides a reusable basis for deterministic, sampling-based, or learning-driven planning in deformable terrain. Hardware trials on an off-road platform demonstrate real-time navigation across soft soil and slope transitions, supporting reliable autonomy in unstructured environments.
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