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.

翻译：在越野环境中运行的自主地面车辆必须实时规划曲率可行的路径，同时考虑空间变化的土壤强度和坡度危险。我们提出了一种连续状态-成本度量，该度量将Bekker压力-沉陷模型与基于高程的坡度及姿态惩罚项相结合。所得地形成本场在土壤模量和坡度方面具有解析性、有界性和单调性，确保了在传感器噪声下离散化的适定性和更新的稳定性。该度量在具有精确转向基元的栅格上进行评估：针对差速驱动的Dubins和Reeds-Shepp运动，以及针对阿克曼转向的时间参数化自行车模型弧线。全局探索通过车辆动力学RRT*执行，而局部修复则由车辆动力学D* Lite管理，从而实现毫秒级重规划且无需启发式平滑。通过将地形-车辆模型与规划器分离，该框架为可变形地形中的确定性规划、基于采样的规划或学习驱动规划提供了可复用的基础。在越野平台上的硬件试验展示了穿越软土和坡度变化的实时导航能力，为无结构环境中的可靠自主性提供了支持。