# Multi-Resolution 3D Mapping with Explicit Free Space Representation for Fast and Accurate Mobile Robot Motion Planning

arXiv: https://arxiv.org/abs/2010.07929 · HTML: https://mlsanity.com/paper/2010.07929/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [FindAnything: Open-Vocabulary and Object-Centric Mapping for Robot Exploration in Any Environment](https://mlsanity.com/paper/2504.08603/) (2025)
- [Probabilistic Point Cloud Modeling via Self-Organizing Gaussian Mixture Models](https://mlsanity.com/paper/2302.00047/) (2023)
- [SOLVR: Submap Oriented LiDAR-Visual Re-Localisation](https://mlsanity.com/paper/2409.10247/) (2024)
- [SeMLaPS: Real-time Semantic Mapping with Latent Prior Networks and Quasi-Planar Segmentation](https://mlsanity.com/paper/2306.16585/) (2023)
- [GIRA: Gaussian Mixture Models for Inference and Robot Autonomy](https://mlsanity.com/paper/2307.00071/) (2023)
- [From Distances to Trajectories: Real-Time Signed Distance Function Mapping and Distance-Accelerated Motion Planning for UAVs](https://mlsanity.com/paper/2607.19306/) (2026)
- [OctWorld: Long-Range World-Consistent Video Generation with Octree-Based 3D Mapping](https://mlsanity.com/paper/2609.03919/) (2026)
- [LAPS: Improving Incremental LiDAR Mapping using Active Pooling and Sampling for Neural Distance Fields](https://mlsanity.com/paper/2605.15496/) (2026)

## Abstract (arXiv)

With the aim of bridging the gap between high quality reconstruction and mobile robot motion planning, we propose an efficient system that leverages the concept of adaptive-resolution volumetric mapping, which naturally integrates with the hierarchical decomposition of space in an octree data structure. Instead of a Truncated Signed Distance Function (TSDF), we adopt mapping of occupancy probabilities in log-odds representation, which allows to represent both surfaces, as well as the entire free, i.e. observed space, as opposed to unobserved space. We introduce a method for choosing resolution -- on the fly -- in real-time by means of a multi-scale max-min pooling of the input depth image. The notion of explicit free space mapping paired with the spatial hierarchy in the data structure, as well as map resolution, allows for collision queries, as needed for robot motion planning, at unprecedented speed. We quantitatively evaluate mapping accuracy, memory, runtime performance, and planning performance showing improvements over the state of the art, particularly in cases requiring high resolution maps.