# Safe Navigation using Neural Radiance Fields via Reachable Sets

arXiv: https://arxiv.org/abs/2604.26899 · HTML: https://mlsanity.com/paper/2604.26899/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2026.

## Built on by (most cited first, 1 of 1)

- [SE(3) Neural Potential Fields for 6-DoF Trajectory Planning Directly from Images Without Explicit 3D Reconstruction](https://mlsanity.com/paper/2609.24864/) (2026)

## Abstract (arXiv)

Safe navigation in cluttered environments is an important challenge for autonomous systems. Robots navigating through obstacle ridden scenarios need to be able to navigate safely in the presence of obstacles, goals, and ego objects of varying geometries. In this work, reachable set representations of the robot's real-time capabilities in the state space can be utilized to capture safe navigation requirements. While neural radiance fields (NeRFs) are utilized to compute, store, and manipulate the volumetric representations of the obstacles, or ego vehicle, as needed. Constrained optimal control is employed to represent the resulting path planning problem, involving linear matrix inequality constraints. We present simulation results for path planning in the presence of numerous obstacles in two different scenarios. Safe navigation is demonstrated through using reachable sets in the corresponding constrained optimal control problems.