Kairos: Grounded Forecasting of Presence and Directional Flow in 4D Scene Graphs
Organizations: University of Turku, Finland · Instituto Tecnol´ogico de Arag´on (ITA) and the University of Zaragoza, Spain · University of Zaragoza, Spain · Centre for Artificial Intelligence, Zürich University of Applied Sciences, Winterthur, Switzerland
Abstract
Long-term autonomy in human-populated environments requires anticipating whether and how people will move at times a robot has not yet observed. Existing representations of pedestrian motion face a tradeoff: they either forecast future activity, reducing each location to a scalar rate, or model the full directional distribution, holding it fixed in time. We present Kairos, a predictive directional-flow memory that extends a hierarchical 3D scene graph (3DSG) to a 4D scene graph (4DSG). Every observed voxel of the reconstructed geometry stores a directional mixture and a presence rate, and spectral predictors forecast, for any future query time, both the probability that people are present and the full directional distribution of their motion. Pairwise flow dependence between adjacent voxels supports conditional queries, and per-voxel predictive variances yield calibrated credible intervals that tighten as observations accumulate. We evaluate Kairos on three real pedestrian environments: a robot-collected campus dataset, a shopping mall, and a station concourse recorded continuously for eleven months. Its learned state remains consistent under loop-closure corrections, and its forecasts are competitive with dedicated occupancy and flow models trained on the full detection stream, although Kairos learns from only the small fraction available to a patrolling robot. Finally, we validate the representation on a downstream encounter-probability planning task, where plans computed over the Kairos forecasts encounter more people than plans computed over any time-invariant map at an equal success rate. We provide the code at https://github.com/IacopomC/kairos.
Figures & tables
| Required properties | Additional capabilities | ||||||||
| Family | Method | Flow Representation | Forecast | Index | Warp | Online Fit | Flow Coupling | Presence | Forecast Uncertainty |
| Discrete MoD | Cond. Transition Maps [ 6 ] | transitions | — | grid | — | — | implicit | — | — |
| CLiFF-map [ 7 ] | SW-GMM | — | grid | — | — | kernel imp. | — | — | |
| Dir. Grid Maps [ 8 ] | von Mises mixture | — | grid | — | — | — | — | — | |
| FreMEn [ 2 ] , FrOctoMap [ 5 ] | — | occupancy | grid | — | ✓ | — | binary | — | |
| STeF-Map [ 17 ] | 8-bin histogram | bin value | grid | — | ✓ | — | — | — | |
| Dataset | Extent | Train / Test | Candidate periods | Primary role |
| TBD | min over mo. | / days | s | flow prediction, cost |
| ATC | days over yr | / days | h | flow, sparse coverage, loop closure, coupling |
| HB | mo. continuous | / days | h | presence, periodicity, coupling |
| TBD | ATC | H | ||||||||||||||||
| MLPD | MLPD | MLPD | ||||||||||||||||
| Method | Cov. | H | S | J | CRPS | MAE | Cov. | H | S | J | CRPS | MAE | Cov. | H | S | J | CRPS | MAE |
| Uniform (reference) | — | — | — | — | — | — | ||||||||||||
| CLiFF-map [ 7 ] | ||||||||||||||||||
| STeF-Map [ 17 ] | — | — | — | — | — | — | — | — | — | |||||||||
| Aion [ 16 ] | — | — | — | — | — | — | — | — | — | |||||||||
| Method | CRPS [ CI] | H MLPD |
| STeF-Map [ 17 ] | ||
| Aion [ 16 ] | ||
| Kairos (ours) |
| Per detection | Per node | ||||
| Odometry | H | J | CRPS | ( ∘ ) | (%) |
| Drift-free | — | — | |||
| Uncorrected | |||||
| Loop closure | |||||
| s | s | s | s | s | ||||||||
| Regime | Model | MLPP | MLPP | MLPP | Rel | Res | MLPP | Rel | Res | MLPP | Rel | Res |
| Embodied m FoV | Constant base rate | |||||||||||
| Kairos (no dwell) | ||||||||||||
| Kairos (static rate) | ||||||||||||
| Kairos | ||||||||||||
| Full visibility | Constant base rate | |||||||||||
| mean std [ms] | med [ms] | p95 [ms] | ||
| Base 3DSG | Frontend total | |||
| Backend optimization | ||||
| Flow dynamics | Per frame (10 Hz) | |||
| Cell update (per det.) | ||||
| Sharing (per neighborhood) | ||||
| Coupling (per frame it runs) |
| HB | ATC | |||||
| Information source | Succ. | Med. [s] | Enc. | Succ. | Med. [s] | Enc. |
| None (wait) | ||||||
| None (random walk) | ||||||
| Static rate | ||||||
| FreMEn | ||||||
| Kairos | ||||||
| Regime | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | All |
| Embodied ( m FoV) | ||||||||||||||||||||
| Full visibility |
| TBD | ATC | HB | ||||||||||
| Method | sparse | medium | dense | global | sparse | medium | dense | global | sparse | medium | dense | global |
| detections | ||||||||||||
| Reference | ||||||||||||
| Sharing | ||||||||||||
| TBD | ATC (emb.) | ATC (full) | HB (emb.) | HB (full) | |||||||
| Pairs | Coupling | J | MAE | J | MAE | J | MAE | J | MAE | J | MAE |
| All | Fixed alignment prior | ||||||||||
| Learned coupling | |||||||||||
| Learned, by | |||||||||||
| ATC | HB | |||||||
| Cov. 68 | Cov. 95 | ECE | Sharp. | Cov. 68 | Cov. 95 | ECE | Sharp. | |
| Speed | ||||||||
| Weights | ||||||||
Appendix figures & tables10 assets
Supplementary material from the paper’s appendix.
Appendix
| Dataset | Environment | Time Span | Rate |
| ATC [ 1 ] | shopping mall | 84 days / 1 yr | 10 Hz |
| Eindhoven [ 48 ] | train platform | 60 days | 10 Hz |
| Havlíčkův Brod [ 39 ] | station concourse | 11 months, 24/7 | 1 Hz |
| Pardubice [ 39 ] | station concourse | 11 months, 24/7 | |
| TBD [ 38 ] | university hall | 213 min/16 scenes | 10 Hz |
| Edinburgh [ 49 ] | university hall | 7 months | 9 Hz |
| within slot | across slots | |||
| Dataset | med | 5th/95th | ||
| TBD | / | |||
| ATC | / | |||
| HB | / | |||
| Regime | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | All |
| Embodied ( m FoV) | |||||||||||||
| Full visibility |
| Hour | 00 | 01 | 02 | 03 | 04 | 05 | 06 | 07 | 08 | 09 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 |
| Embodied ( m field of view) | ||||||||||||||||||||||||
| Constant base rate | ||||||||||||||||||||||||
| Kairos (static rate) | ||||||||||||||||||||||||
| Kairos | ||||||||||||||||||||||||
| Full visibility | ||||||||||||||||||||||||
| Constant base rate | ||||||||||||||||||||||||
| s | s | s | s | s | ||||||||
| Regime | Model | MLPP | MLPP | MLPP | Rel | Res | MLPP | Rel | Res | MLPP | Rel | Res |
| Embodied m FoV | Constant base rate | |||||||||||
| Kairos (no dwell) | ||||||||||||
| Kairos (static rate) | ||||||||||||
| Kairos | ||||||||||||
| Full visibility | Constant base rate | |||||||||||
| Dataset | Crossings | Windows | Epi. share | Cov. 95 |
| ATC [ 1 ] | ||||
| HB [ 39 ] | ||||
| ATC [ 1 ] | HB [ 39 ] | |||||||
| Cov. 68 | Cov. 95 | ECE | Sharp. | Cov. 68 | Cov. 95 | ECE | Sharp. | |
| Constant aleatoric prior | ||||||||
| Adapted aleatoric variance | ||||||||
Spatiotemporal Forecasting
Spatiotemporal forecasting predicts how quantities change across locations and time, from traffic and weather to disease and environmental systems.
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