用神经网络学习导航函数，零样本适配新环境，保安全且高效。
Neural Navigation Functions for Zero-Shot Generalizable Motion Planning
- 基于椭圆规划结构，用数据驱动方式学习局部微分方程系数。
- 在未见环境中实现零样本迁移，性能优于直接预测值函数的方法5倍。
- 适合需要高安全性与强泛化能力的机器人路径规划场景。
我们提出神经导航函数（Neural-NF），一种可零样本迁移至未知环境几何结构的可反应式导航函数。Neural-NF 将数据驱动适应嵌入到结构化的椭圆规划器中，导航目标被学习，而规划器结构通过构造保持不变。具体地，由内在拉普拉斯导出的特征被映射为局部偏微分方程（PDE）系数，求解所得边界值问题后，可在每个目标域上生成全局一致的值函数。对于任意可接受的学习模型，所生成策略均保证无碰撞、单调下降，并在目标处达到全局最小值。该方法对任意参数设置都具有线性可解的最优控制解释。实验表明，Neural-NF 在多样环境间实现强零样本迁移，相比直接预测值函数的模型，性能提升最高达5倍。
原文摘要 · Abstract (English)
We introduce Neural Navigation Functions (Neural-NF), a learned reactive navigation function capable of zero-shot transfer across unseen environment geometries. Neural-NF places data-driven adaptation within a structured elliptic planner, where the navigation objective is learned while planner structure is preserved by construction. Specifically, intrinsic Laplacian-derived features are mapped to local PDE coefficients, and solving the resulting boundary value problem produces a globally consistent value function on each target domain. For every admissible learned model, the resulting policy is collision-free, provides monotonic descent and a global minimum at the goal by construction. This admits a linearly-solvable optimal-control interpretation for any parameter setting. Empirically, Neural-NF achieves strong zero-shot transfer across diverse geometries and outperforms learned planners that directly predict the value function by up to a $5\times$ improvement.
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