# Sampling-free obstacle gradients and reactive planning in Neural Radiance Fields (NeRF)

arXiv: https://arxiv.org/abs/2205.01389 · HTML: https://mlsanity.com/paper/2205.01389/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 10 references that are in the map.
- First posted on arXiv 3 May 2022.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Vision-Only Robot Navigation in a Neural Radiance World](https://mlsanity.com/paper/2110.00168/) (2021)
- [Voxblox: Incremental 3D Euclidean Signed Distance Fields for On-Board MAV Planning](https://mlsanity.com/paper/1611.03631/) (2016)
- [Riemannian Motion Policies](https://mlsanity.com/paper/1801.02854/) (2018)
- [NeuralBlox: Real-Time Neural Representation Fusion for Robust Volumetric Mapping](https://mlsanity.com/paper/2110.09415/) (2021)

## Built on by (most cited first, 6 of 6)

- [CROSSFIRE: Camera Relocalization On Self-Supervised Features from an Implicit Representation](https://mlsanity.com/paper/2303.04869/) (2023)
- [RGB-Only Reconstruction of Tabletop Scenes for Collision-Free Manipulator Control](https://mlsanity.com/paper/2210.11668/) (2022)
- [Semantically-aware Neural Radiance Fields for Visual Scene Understanding: A Comprehensive Review](https://mlsanity.com/paper/2402.11141/) (2024)
- [One-Shot Neural Fields for 3D Object Understanding](https://mlsanity.com/paper/2210.12126/) (2022)
- [Unified Linear Parametric Map Modeling and Perception-aware Trajectory Planning for Mobile Robotics](https://mlsanity.com/paper/2507.09340/) (2025)
- [Path Planning in Physically Viable World Models](https://mlsanity.com/paper/2607.00673/) (2026)

## Abstract (arXiv)

This work investigates the use of Neural implicit representations, specifically Neural Radiance Fields (NeRF), for geometrical queries and motion planning. We show that by adding the capacity to infer occupancy in a radius to a pre-trained NeRF, we are effectively learning an approximation to a Euclidean Signed Distance Field (ESDF). Using backward differentiation of the augmented network, we obtain an obstacle gradient that is integrated into an obstacle avoidance policy based on the Riemannian Motion Policies (RMP) framework. Thus, our findings allow for very fast sampling-free obstacle avoidance planning in the implicit representation.