# Learning Deep SDF Maps Online for Robot Navigation and Exploration

arXiv: https://arxiv.org/abs/2207.10782 · HTML: https://mlsanity.com/paper/2207.10782/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2022.

## Built on by (most cited first, 5 of 5)

- [ReKep: Spatio-Temporal Reasoning of Relational Keypoint Constraints for Robotic Manipulation](https://mlsanity.com/paper/2409.01652/) (2024)
- [Neural Fields in Robotics: A Survey](https://mlsanity.com/paper/2410.20220/) (2024)
- [MergeNet: Explicit Mesh Reconstruction from Sparse Point Clouds via Edge Prediction](https://mlsanity.com/paper/2407.11610/) (2024)
- [Implicit 3D scene reconstruction using deep learning towards efficient collision understanding in autonomous driving](https://mlsanity.com/paper/2506.15806/) (2025)
- [Inspection Planning Primitives with Implicit Models](https://mlsanity.com/paper/2510.07611/) (2025)

## Abstract (arXiv)

We propose an algorithm to (i) learn online a deep signed distance function (SDF) with a LiDAR-equipped robot to represent the 3D environment geometry, and (ii) plan collision-free trajectories given this deep learned map. Our algorithm takes a stream of incoming LiDAR scans and continually optimizes a neural network to represent the SDF of the environment around its current vicinity. When the SDF network quality saturates, we cache a copy of the network, along with a learned confidence metric, and initialize a new SDF network to continue mapping new regions of the environment. We then concatenate all the cached local SDFs through a confidence-weighted scheme to give a global SDF for planning. For planning, we make use of a sequential convex model predictive control (MPC) algorithm. The MPC planner optimizes a dynamically feasible trajectory for the robot while enforcing no collisions with obstacles mapped in the global SDF. We show that our online mapping algorithm produces higher-quality maps than existing methods for online SDF training. In the WeBots simulator, we further showcase the combined mapper and planner running online -- navigating autonomously and without collisions in an unknown environment.