# Kairos: Grounded Forecasting of Presence and Directional Flow in 4D Scene Graphs

arXiv: https://arxiv.org/abs/2609.27467 · HTML: https://mlsanity.com/paper/2609.27467/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 49 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 19 of 19)

- [VINS-Mono: A Robust and Versatile Monocular Visual-Inertial State Estimator](https://mlsanity.com/paper/1708.03852/) (2017)
- [FAST-LIO2: Fast Direct LiDAR-inertial Odometry](https://mlsanity.com/paper/2107.06829/) (2021)
- [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)
- [Khronos: A Unified Approach for Spatio-Temporal Metric-Semantic SLAM in Dynamic Environments](https://mlsanity.com/paper/2402.13817/) (2024)
- [Collaborative Dynamic 3D Scene Graphs for Automated Driving](https://mlsanity.com/paper/2309.06635/) (2023)
- [3D VSG: Long-term Semantic Scene Change Prediction through 3D Variable Scene Graphs](https://mlsanity.com/paper/2209.07896/) (2022)
- [Describe Anything Anywhere At Any Moment](https://mlsanity.com/paper/2512.00565/) (2025)
- [TBD Pedestrian Data Collection: Towards Rich, Portable, and Large-Scale Natural Pedestrian Data](https://mlsanity.com/paper/2309.17187/) (2023)
- [Directional grid maps: modeling multimodal angular uncertainty in dynamic environments](https://mlsanity.com/paper/1809.00498/) (2018)
- [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)
- [Fast Online Learning of CLiFF-maps in Changing Environments](https://mlsanity.com/paper/2410.12237/) (2024)
- [NeMo-map: Neural Implicit Flow Fields for Spatio-Temporal Motion Mapping](https://mlsanity.com/paper/2510.14827/) (2025)
- [EgoMoD: Predicting Global Maps of Dynamics from Local Egocentric Observations](https://mlsanity.com/paper/2603.00167/) (2026)
- [Rheos: Modelling Continuous Motion Dynamics in Hierarchical 3D Scene Graphs](https://mlsanity.com/paper/2603.20239/) (2026)
- [Non-Parametric Modeling of Spatio-Temporal Human Activity Based on Mobile Robot Observations](https://mlsanity.com/paper/2203.06911/) (2022)

## Abstract (arXiv)

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.