# Rheos: Modelling Continuous Motion Dynamics in Hierarchical 3D Scene Graphs

arXiv: https://arxiv.org/abs/2603.20239 · HTML: https://mlsanity.com/paper/2603.20239/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 29 references that are in the map.
- First posted on arXiv 9 Mar 2026.

## Builds on (most cited first, 14 of 14)

- [Hydra: A Real-time Spatial Perception System for 3D Scene Graph Construction and Optimization](https://mlsanity.com/paper/2201.13360/) (2022)
- [3D Dynamic Scene Graphs: Actionable Spatial Perception with Places, Objects, and Humans](https://mlsanity.com/paper/2002.06289/) (2020)
- [Kimera: from SLAM to Spatial Perception with 3D Dynamic Scene Graphs](https://mlsanity.com/paper/2101.06894/) (2021)
- [Foundations of Spatial Perception for Robotics: Hierarchical Representations and Real-time Systems](https://mlsanity.com/paper/2305.07154/) (2023)
- [TASKOGRAPHY: Evaluating robot task planning over large 3D scene graphs](https://mlsanity.com/paper/2207.05006/) (2022)
- [Hierarchical Representations and Explicit Memory: Learning Effective Navigation Policies on 3D Scene Graphs using Graph Neural Networks](https://mlsanity.com/paper/2108.01176/) (2021)
- [Collaborative Dynamic 3D Scene Graphs for Automated Driving](https://mlsanity.com/paper/2309.06635/) (2023)
- [OpenGraph: Open-Vocabulary Hierarchical 3D Graph Representation in Large-Scale Outdoor Environments](https://mlsanity.com/paper/2403.09412/) (2024)
- [Hydra-Multi: Collaborative Online Construction of 3D Scene Graphs with Multi-Robot Teams](https://mlsanity.com/paper/2304.13487/) (2023)
- [Crowd against the machine: A simulation-based benchmark tool to evaluate and compare robot capabilities to navigate a human crowd](https://mlsanity.com/paper/2104.14177/) (2021)
- [Pedestrian-Robot Interactions on Autonomous Crowd Navigation: Reactive Control Methods and Evaluation Metrics](https://mlsanity.com/paper/2208.02121/) (2022)
- [Aion: Towards Hierarchical 4D Scene Graphs with Temporal Flow Dynamics](https://mlsanity.com/paper/2512.11903/) (2025)
- [Bayesian Floor Field: Transferring people flow predictions across environments](https://mlsanity.com/paper/2208.10851/) (2022)
- [EgoMoD: Predicting Global Maps of Dynamics from Local Egocentric Observations](https://mlsanity.com/paper/2603.00167/) (2026)

## Built on by (most cited first, 2 of 2)

- [EgoNeMo: Transferable Map of Pedestrian Dynamics via Egocentric LiDAR Scan](https://mlsanity.com/paper/2609.06195/) (2026)
- [Kairos: Grounded Forecasting of Presence and Directional Flow in 4D Scene Graphs](https://mlsanity.com/paper/2609.27467/) (2026)

## Abstract (arXiv)

3D Scene Graphs (3DSGs) provide hierarchical, multi-resolution abstractions that encode the geometric and semantic structure of an environment, yet their treatment of dynamics remains limited to tracking individual agents. Maps of Dynamics (MoDs) complement this by modeling aggregate motion patterns, but rely on uniform grid discretizations that lack semantic grounding and scale poorly. We present Rheos, a framework that explicitly embeds continuous directional motion models into an additional dynamics layer of a hierarchical 3DSG that enhances the navigational properties of the graph. Each dynamics node maintains a semi-wrapped Gaussian mixture model that captures multimodal directional flow as a principled probability distribution with explicit uncertainty, replacing the discrete histograms used in prior work. To enable online operation, Rheos employs reservoir sampling for bounded-memory observation buffers, parallel per-cell model updates and a principled Bayesian Information Criterion (BIC) sweep that selects the optimal number of mixture components, reducing per-update initialization cost from quadratic to linear in the number of samples. Evaluated across four spatial resolutions in a simulated pedestrian environment, Rheos consistently outperforms the discrete baseline under continuous as well as unfavorable discrete metrics. We release our implementation as open source.