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

2 min read

3D scene graphs track individual agents but say little about how people usually move through a place. Maps of Dynamics (MoDs) do, but on uniform grids with no semantics. Rheos adds a dynamics layer to a hierarchical scene graph: each navigational node keeps a semi-wrapped Gaussian mixture over heading and speed, a continuous distribution with explicit uncertainty. It builds on Aion, which first combined MoDs with scene graphs using discrete direction histograms. To run online, each node keeps a bounded buffer by reservoir sampling, nodes update in parallel, and a Bayesian Information Criterion sweep picks the number of mixture components, which cuts initialisation cost from quadratic to linear in the number of samples.

Findings

  • In a simulated pedestrian environment at four spatial resolutions, Rheos beats the Aion histogram baseline on mean log predictive density, with the largest gains at fine resolution where histograms are sparsest.
  • It also wins on mean predictive probability, a discrete metric that favours histograms.
  • Ablation against the original mean-shift initialisation: mean-shift collapses to one component in 92% of cells (146 of 158), while the BIC sweep averages 2.17 components per node against 1.11. The BIC sweep takes longer per update but stays within the configured update interval.
  • Code is open source.

Limits

  • Simulation only, one pedestrian environment.
  • The flow model takes observed motion as given. How errors in detecting and tracking people would affect it is not tested.

Relevance

Kairos, from the same first author, later forecasts presence and directional flow in 4D scene graphs; Rheos is the earlier, mapping-only step, so it is the place to start for flow in scene graphs. It answers a different “dynamic” from dynamic-scenes, which is mostly about objects that move or vanish: here the map learns habitual motion, which matters for long-term-autonomy in places shared with people. For a team, per-node mixtures are compact enough to merge across robots, though the paper does not try.