用神经算子预测运动规划价值函数，实现零样本超分辨率与高效路径规划。
Generalizable Motion Planning via Operator Learning
- 将价值函数逼近建模为从代价函数到价值函数的算子学习，基于Eikonal PDE框架。
- 在16倍训练分辨率下仍保持高精度，3D场景中优于现有神经价值预测方法。
- 提出ε-一致启发式，使A*和RRT*规划节点数减少30%，路径接近最优。
本文提出一种规划神经算子（PNO），用于预测运动规划问题的价值函数。将价值函数近似重构为从代价函数空间到价值函数空间的单一算子学习任务，该算子由Eikonal偏微分方程（PDE）定义。因此，尽管模型仅在粗分辨率下使用有限样本训练，仍具备神经算子的零样本超分辨率特性。我们在MovingAI lab的2D城市数据集上实现了16倍训练分辨率下的精确价值函数逼近；在iGibson建筑数据集的3D场景中，对比了最先进的神经价值函数预测器；并展示了4自由度机械臂的最优规划能力。最后，研究了利用PNO输出作为启发式函数加速运动规划。理论上证明，通过引入归纳偏置层，确保价值函数满足三角不等式，从而保证启发式函数ε-一致性。实验显示，相比经典规划方法（A*、RRT*），该启发式使MovingAI lab 2D城市数据集上的节点访问量减少30%，同时获得接近最优的路径长度。
原文摘要 · Abstract (English)
In this work, we introduce a planning neural operator (PNO) for predicting the value function of a motion planning problem. We recast value function approximation as learning a single operator from the cost function space to the value function space, which is defined by an Eikonal partial differential equation (PDE). Therefore, our PNO model, despite being trained with a finite number of samples at coarse resolution, inherits the zero-shot super-resolution property of neural operators. We demonstrate accurate value function approximation at $16\times$ the training resolution on the MovingAI lab's 2D city dataset, compare with state-of-the-art neural value function predictors on 3D scenes from the iGibson building dataset and showcase optimal planning with 4-DOF robotic manipulators. Lastly, we investigate employing the value function output of PNO as a heuristic function to accelerate motion planning. We show theoretically that the PNO heuristic is $ε$-consistent by introducing an inductive bias layer that guarantees our value functions satisfy the triangle inequality. With our heuristic, we achieve a $30\%$ decrease in nodes visited while obtaining near optimal path lengths on the MovingAI lab 2D city dataset, compared to classical planning methods ($A^\ast$, $RRT^\ast$).
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