Low speed does not always guarantee safety in off-road driving. For instance, crossing a ditch may be risky at a low speed due to the risk of getting stuck, yet safe at a higher speed with a controlled, accelerated jump. Achieving such behavior requires path planning that explicitly models complex motion dynamics, whereas existing methods often neglect this aspect and plan solely based on positions or a fixed velocity. To address this gap, we introduce Motion-aware Traversability (MAT) representation to explicitly model terrain cost conditioned on actual robot motion. Instead of assigning a single scalar score for traversability, MAT models each terrain region as a Gaussian function of velocity. During online planning, we decompose the terrain cost computation into two stages: (1) predict terrain-dependent Gaussian parameters from perception in a single forward pass, (2) efficiently update terrain costs for new velocities inferred from current dynamics by evaluating these functions without repeated inference. We develop a system that integrates MAT to enable agile off-road navigation and evaluate it in both simulated and real-world environments with various obstacles. Results show that MAT achieves real-time efficiency and enhances the performance of off-road navigation, reducing path detours by 75% while maintaining safety across challenging terrains.

翻译：低速行驶并不总能保证越野驾驶的安全性。例如，低速穿越沟渠可能因陷车风险而存在危险，但以较高速度进行受控的加速跳跃则可能是安全的。实现此类行为需要路径规划明确建模复杂的运动动力学，而现有方法往往忽略这一方面，仅基于位置或固定速度进行规划。为填补这一空白，我们引入了运动感知可通行性表示，以明确建模基于实际机器人运动的地形成本。MAT不是为可通行性分配单一标量分数，而是将每个地形区域建模为速度的高斯函数。在在线规划过程中，我们将地形成本计算分解为两个阶段：(1) 通过单次前向传播从感知中预测与地形相关的高斯参数，(2) 通过评估这些函数（无需重复推理）高效更新根据当前动力学推断出的新速度对应的地形成本。我们开发了一个集成MAT的系统以实现敏捷的越野导航，并在模拟和真实环境中使用各种障碍物对其进行了评估。结果表明，MAT实现了实时效率，并提升了越野导航性能，在保持具有挑战性地形安全性的同时，将路径绕行减少了75%。