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

A team of researchers from the University of Zaragoza and other institutions has introduced Rheos, a novel framework designed to solve a critical gap in robotic perception. While 3D Scene Graphs (3DSGs) excel at creating hierarchical, semantic maps of environments, and Maps of Dynamics (MoDs) track aggregate motion, Rheos merges these concepts. It embeds a dedicated 'dynamics layer' directly into the 3DSG, allowing the map to not only know *what* objects are present but also model *how* they typically move over time. This provides a continuous, semantically-grounded understanding of environmental flow, which is far more scalable and accurate than previous grid-based, discrete methods.

At its core, Rheos models motion using semi-wrapped Gaussian mixture models, which represent directional flow (like pedestrian traffic in a hallway) as a principled probability distribution with explicit uncertainty. This continuous approach outperforms the discrete histograms used in prior work. For practical, real-time use, the framework is built for efficiency. It uses reservoir sampling to manage memory, performs parallel per-cell model updates, and employs a Bayesian Information Criterion (BIC) sweep to automatically select the optimal complexity of the motion model, reducing initialization costs from quadratic to linear time. In tests on simulated pedestrian environments across four spatial resolutions, Rheos consistently outperformed discrete baselines. The team has released the implementation as open-source, paving the way for more intelligent and predictable autonomous systems.