# Semantic OcTree Mapping and Shannon Mutual Information Computation for Robot Exploration

arXiv: https://arxiv.org/abs/2112.04063 · HTML: https://mlsanity.com/paper/2112.04063/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2021.

## Built on by (most cited first, 16 of 16)

- [Learning Generalizable Feature Fields for Mobile Manipulation](https://mlsanity.com/paper/2403.07563/) (2024)
- [SPINE: Online Semantic Planning for Missions with Incomplete Natural Language Specifications in Unstructured Environments](https://mlsanity.com/paper/2410.03035/) (2024)
- [Deep Reinforcement Learning-based Large-scale Robot Exploration](https://mlsanity.com/paper/2403.10833/) (2024)
- [Air-Ground Collaboration for Language-Specified Missions in Unknown Environments](https://mlsanity.com/paper/2505.09108/) (2025)
- [Multimodal LLM Guided Exploration and Active Mapping using Fisher Information](https://mlsanity.com/paper/2410.17422/) (2024)
- [Evidential Semantic Mapping in Off-road Environments with Uncertainty-aware Bayesian Kernel Inference](https://mlsanity.com/paper/2403.14138/) (2024)
- [Understanding while Exploring: Semantics-driven Active Mapping](https://mlsanity.com/paper/2506.00225/) (2025)
- [Ella: Embodied Social Agents with Lifelong Memory](https://mlsanity.com/paper/2506.24019/) (2025)
- [Active Exploration based on Information Gain by Particle Filter for Efficient Spatial Concept Formation](https://mlsanity.com/paper/2211.10934/) (2022)
- [Interactive Semantic Map Representation for Skill-based Visual Object Navigation](https://mlsanity.com/paper/2311.04107/) (2023)
- [Uncertainty-aware Semantic Mapping in Off-road Environments with Dempster-Shafer Theory of Evidence](https://mlsanity.com/paper/2405.06265/) (2024)
- [Build Once, Monitor Continuously: Persistent Semantic Mapping via Autonomous Exploration and Open-Vocabulary Object Updates](https://mlsanity.com/paper/2409.15493/) (2024)
- [Belief Consistency Between Foundation-Model Evidence and Geometric Perception in Persistent Robotic Maps](https://mlsanity.com/paper/2606.00318/) (2026)
- [SGE: Semantically-Guided Exploration for Unstructured Environments via Image-Space Waypoint Sampling](https://mlsanity.com/paper/2608.29315/) (2026)
- [Multi-Scale Semantic Mapping in Urban Environments via Observation Calibration and Policy Dependence Regularization](https://mlsanity.com/paper/2609.34833/) (2026)
- [Uncertainty-Aware RL-Controlled Adaptive 3D Mapping](https://mlsanity.com/paper/2610.00188/) (2026)

## Abstract (arXiv)

Autonomous robot operation in unstructured and unknown environments requires efficient techniques for mapping and exploration using streaming range and visual observations. Information-based exploration techniques, such as Cauchy-Schwarz quadratic mutual information (CSQMI) and fast Shannon mutual information (FSMI), have successfully achieved active binary occupancy mapping with range measurements. However, as we envision robots performing complex tasks specified with semantically meaningful concepts, it is necessary to capture semantics in the measurements, map representation, and exploration objective. This work presents Semantic octree mapping and Shannon Mutual Information (SSMI) computation for robot exploration. We develop a Bayesian multi-class mapping algorithm based on an octree data structure, where each voxel maintains a categorical distribution over semantic classes. We derive a closed-form efficiently-computable lower bound of the Shannon mutual information between a multi-class octomap and a set of range-category measurements using semantic run-length encoding of the sensor rays. The bound allows rapid evaluation of many potential robot trajectories for autonomous exploration and mapping. We compare our method against state-of-the-art exploration techniques and apply it in a variety of simulated and real-world experiments.