# Learning Deep SDF Maps Online for Robot Navigation and Exploration

**Authors:** Gadiel Sznaier Camps, Robert Dyro, Marco Pavone, Mac Schwager  
**arXiv:** [2207.10782](https://arxiv.org/abs/2207.10782)  
**Date:** 2022-07-21  
**Summary page:** https://www.summarizepaper.com/en/paper/2207.10782v2/

## Key points

- The paper proposes an algorithm for LiDAR-equipped robots to autonomously build and navigate within a high-fidelity 3D map.
- The system learns a 3D map from incoming LiDAR data incrementally without forgetting by concatenating a set of local learned SDF maps.
- Simultaneously, the robot navigates to avoid collisions using a trajectory planner that takes the deep learned SDF map as a collision constraint function.
- The proposed approach resides at the intersection between learning implicit shape representations, SDFs for robotic mapping, and robot trajectory planning.
- Learned Implicit Shape Representations is a new trend in machine learning and computer vision where 3D shape representation is learned implicitly as a deep neural network function.
- The proposed algorithm optimizes a neural network to represent the Signed Distance Function (SDF) of the environment around its current vicinity continually.
- All cached local SDFs are concatenated through a confidence-weighted scheme to give rise to a global SDF for planning purposes.
- For planning, the algorithm uses sequential convex model predictive control (MPC) which optimizes dynamically feasible trajectories for the robot while enforcing no collisions with obstacles mapped in the global SDF.
- The study shows that their online mapping algorithm produces higher-quality maps than existing methods for online SDF training.
- They showcase their combined mapper and planner running online in WeBots simulator - navigating autonomously without collisions in an unknown environment.
- Overall, this study presents an effective solution for autonomous navigation in complex environments using LiDAR-equipped robots by combining deep learning-based mapping with MPC-based trajectory planning algorithms.

## Summary

The paper proposes an algorithm for LiDAR-equipped robots to autonomously build and navigate within a high-fidelity 3D map. The system learns a 3D map from incoming LiDAR data incrementally without forgetting by concatenating a set of local learned SDF maps. Simultaneously, the robot navigates to avoid collisions using a trajectory planner that takes the deep learned SDF map as a collision constraint function. The proposed approach resides at the intersection between learning implicit shape representations, SDFs for robotic mapping, and robot trajectory planning. Learned Implicit Shape Representations is a new trend in machine learning and computer vision where 3D shape representation is learned implicitly as a deep neural network function. Works that exemplify this trend include deep SDFs, learned continuous occupancy functions, and NeRFs. The proposed algorithm optimizes a neural network to represent the Signed Distance Function (SDF) of the environment around its current vicinity continually. When the SDF network quality saturates, it caches a copy of the network along with a learned confidence metric and initializes a new SDF network to continue mapping new regions of the environment. All cached local SDFs are concatenated through a confidence-weighted scheme to give rise to a global SDF for planning purposes. For planning, the algorithm uses sequential convex model predictive control (MPC) which optimizes dynamically feasible trajectories for the robot while enforcing no collisions with obstacles mapped in the global SDF. The study shows that their online mapping algorithm produces higher-quality maps than existing methods for online SDF training. In addition, they showcase their combined mapper and planner running online in WeBots simulator - navigating autonomously without collisions in an unknown environment. Overall, this study presents an effective solution for autonomous navigation in complex environments using LiDAR-equipped robots by combining deep learning-based mapping with MPC-based trajectory planning algorithms.