Planning under Noise with Neural Operators

TL;DR

The paper presents PUN, a neural operator that learns value fields for planning in uncertain environments with varying geometries. It uses reflecting boundary conditions on obstacles and a goal-specific Dirichlet condition to improve signal propagation, and leverages a modified Monte Carlo solver to compute fields without mesh-based discretization. The model learns to predict these fields from noisy, partially converged simulations, enabling fast inference with bounded local search.

Why It Matters

Robust motion planning under noise is critical for robotics in real-world environments with unknown layouts. PUN enables efficient, scalable planning across high-dimensional spaces without requiring re-computation for each new scenario, reducing both time and computational cost. This approach supports reliable navigation in complex, dynamic settings where traditional planners struggle with noise and geometry variation.

Key Findings

• Using reflecting Neumann conditions on obstacles improves value signal propagation compared to zero-Dirichlet conditions, leading to more accurate value field estimation.
• Extending the Walk on Stars Monte Carlo solver to higher dimensions enables mesh-free PDE solution, avoiding the need for explicit configuration-space discretization.
• Learning from noisy, partially converged Monte Carlo labels allows PUN to predict high-quality value fields rapidly at inference, achieving superior success rates and speed across multiple noise levels and dimensions.