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FORTE: Forecasting Occupancy for Spatiotemporal Risk-Aware Planning in Dynamic Environments

Hahjin Lee, Young J. Kim

arXiv:2609.39305v1cs.RO

TL;DR

Dynamic navigation needs predictions of when and where collisions may occur, yet existing OGM methods can be inefficient and underuse temporal occupancy information in planning. FORTE combines non-autoregressive occupancy forecasting with topology-distinct path evaluation using predicted occupancy evolution. It reports improvements in prediction and navigation against state-of-the-art baselines.

  • Problem

    Existing OGM-based methods can struggle with accurate, efficient forecasting and often fail to use predicted occupancy’s temporal evolution in planning, despite the need to anticipate when and where collisions may occur.

    Source: §I · p. 1

  • Method

    FORTE predicts the full OGM horizon non-autoregressively and selects among topology-distinct paths using predicted occupancy at arrival times and its directivity.

    Source: §I · pp. 1–2

  • Results

    FORTE reports up to 215.3% higher IoU, 5.24x faster inference, and a 3.5x higher success rate versus state-of-the-art baselines.

    Source: §I · p. 2

  • Takeaways & Limitations

    Predicted occupancy evolution can inform proactive collision-aware planning across distinct path topologies without explicit object detection or tracking.

    Source: §I · p. 1

Abstract

from arXiv · show

Safe navigation in dynamic environments requires anticipating future environmental states to account for spatiotemporal risks, specifically when and where collisions may occur. To this end, occupancy grid map (OGM) prediction has been widely adopted as an effective approach. However, existing OGM-based navigation methods often struggle to achieve accurate and efficient forecasting and fail to fully exploit the temporal information in predicted OGMs during planning. To address these challenges, we propose FORTE, a navigation framework that directly exploits the spatiotemporal evolution of predicted occupancy from the perspectives of spatiotemporal occupancy overlap and occupancy directivity. Based on these properties, FORTE evaluates multiple topology-distinct paths and selects the suitable one without explicit object detection or tracking. To support online planning, we formulate a latent diffusion model-based OGM predictor that generates the entire forecast horizon in a non-autoregressive manner while maintaining temporal consistency through temporal shift modules. Extensive evaluations demonstrate that FORTE outperforms state-of-the-art baselines. For prediction, FORTE achieves up to 215.3% higher IoU and 5.24x faster inference; for navigation, it yields up to a 3.5x higher success rate.

I. INTRODUCTION

FORTE integrates predicted occupancy’s spatiotemporal evolution into planning over topology-distinct paths, while using non-autoregressive forecasting to support online planning. The paper reports gains in both prediction and navigation performance.

I. INTRODUCTION

  • OGM prediction forecasts occupied regions directly on a grid without explicit detection or tracking, but existing methods still face accuracy and efficiency challenges.Autoregressive forecasting can further reduce inference efficiency.Source: §I · p. 1
  • Existing OGM-based navigation often treats predictions as static maps, losing timing and occupancy direction that can affect path choice and contribute to freezing.A single high-level path can also confine the local planner to an unfavorable local optimum around a moving obstacle.Source: §I · p. 1
  • FORTE evaluates multiple topology-distinct guidance paths using predicted occupancy at estimated arrival times and its directivity, without explicit object detection or tracking.The selected path guides a local planner; efficient forecasting supports online updates.Source: §I · pp. 1–2
  • FORTE uses a latent diffusion model to generate the full future OGM horizon at once, with temporal shift modules maintaining motion consistency across prediction steps.The approach treats the future OGM sequence as a video and predicts non-autoregressively.Source: §I · pp. 1–2
  • Up to 215.3% higher IoU, 5.24× faster inference, and a 3.5× higher success rate versus state-of-the-art baselines are reported for FORTE.The prediction improvements and navigation success-rate improvement are reported across the respective tasks.Source: §I · p. 2

II. RELATED WORK

Prior work spans dynamic navigation, occupancy forecasting, and topology-driven planning, but the cited approaches leave challenges in temporal occupancy use, efficient stochastic prediction, or practical integration.

A. Navigation in Dynamic Environments

  • Dynamic-navigation methods incorporate predicted obstacle trajectories or scene states, but some do not exploit temporal information, while world models face computational and vision-centric integration limits.Object-level methods use predicted trajectories as planning constraints; scene-level methods incorporate future environmental states without explicitly modeling individual obstacles.Source: A. Navigation in Dynamic Environments · p. 2

B. Occupancy Grid Map Prediction

  • OGM forecasting progressed from ConvLSTM and flow-based methods to stochastic predictors, but mobile-robot methods can be blurry or slow and often reduce predictions to spatial planning costs.The cited stochastic driving methods are described as difficult to deploy on resource-constrained mobile robots.Source: B. Occupancy Grid Map Prediction · p. 2

C. Topology-Driven Planner

  • Topology-driven planners explore distinct navigation behaviors, while FORTE combines topology-driven planning with stochastic occupancy forecasting to account for predicted environmental changes and uncertainty.Prior methods cited here use crowd gaps, winding number, or space-time trajectories based on constant-velocity motion estimates.Source: C. Topology-Driven Planner · p. 2

III. PROBLEM FORMULATION

The formulation considers online mobile-robot planning from recent LiDAR-derived occupancy maps and predicted future maps. It distinguishes observed, predicted, and planning-frame occupancy along the forecasting and planning pipeline.

III. PROBLEM FORMULATION

  • At each time step, the robot uses its current OGM and predicted future OGMs to plan online toward a navigation goal in an environment with static and dynamic obstacles.The recent τ observations predict the next τ maps at intervals of ∆t, spanning a horizon of τ∆t.Source: §III · p. 2
  • The notation distinguishes past observed OGMs aligned to a prediction frame, future OGMs predicted there, and predictions transformed into the current robot frame for planning.These stages are denoted by ¯o, ˆo, and ˜o, respectively.Source: §III · p. 2

A. OGM Prediction

  • Past scans in their different local frames are aligned to a common reference frame before constructing the OGM sequence used for prediction.The common prediction frame is ˆFt+1.Source: A. OGM Prediction · p. 2
  • The implementation uses one occupancy channel, 64×64 grids, a 10-step horizon at 0.1-second intervals, and 0.1-meter cells.These settings are reported for the implementation.Source: A. OGM Prediction · p. 2
  • The pipeline forecasts OGMs from recent LiDAR scans and robot states, then evaluates topology-distinct guidance paths using predicted occupancy evolution before sending the selected path to the local planner.The planning costs include arrival-time and directivity costs.Source: Figure 1 · p. 3
  • The predictor models future OGMs from aligned scans, then transforms the predicted sequence from its prediction frame into the current planning frame.The model pθ produces ˆot+1:t+τ in ˆFt+1; before planning, the sequence is transformed to Fcur.Source: A. OGM Prediction · p. 3

B. TSR Planning

TSR evaluates topology-distinct guidance paths against predicted occupancy, while the prediction pipeline aligns scans and forecasts future occupancy for planning.

B. TSR Planning

  • Given a reference path and current OGM, TSR forms feasible, topology-distinct guidance paths toward laterally sampled local goals, scores them against predicted occupancy at estimated arrival times, and selects a path for the local planner.Path selection also minimizes unnecessary switching between topology classes across planning cycles.Source: B. TSR Planning · p. 3

IV. OGM PREDICTION

  • The prediction cycle aligns past scans, forecasts future occupancy, and transforms the predicted OGMs into the current robot frame.These are the three components of the described forecasting pipeline.Source: §IV · p. 3

A. Scan Alignment

  • FORTE estimates only the one-step-ahead frame and aligns all past scans there, avoiding repeated future-frame alignment and reducing dependence on long-horizon frame estimates.Repeated alignment can increase computational cost, while long-horizon estimation errors can spatially misalign predictions.Source: A. Scan Alignment · p. 3

B. LDM Predictor

The LDM predictor forecasts the full OGM horizon non-autoregressively, using temporal shift modules to maintain consistency across steps. Before planning, forecasts are aligned to the robot’s current frame.

B. LDM Predictor

  • The LDM generates all τ future OGM steps non-autoregressively and uses temporal shift modules to exchange latent channels between adjacent steps, supporting temporal consistency.Static maps and ConvLSTM motion features condition the U-Net; its decoded latent sequence produces the forecast.Source: B. LDM Predictor · p. 3
  • At inference, Gaussian noise is denoised by a U-Net conditioned on static-map and motion features, then decoded into the future OGM sequence.The static map represents persistently observed structures, while the ConvLSTM features represent recent occupancy changes.Source: B. LDM Predictor · p. 3

C. OGM Grid Transformation

  • Before each planning cycle, predicted OGMs are transformed from the forecast frame into the current robot frame to spatially align them with the planner’s environment.The transformation interpolates logits under the relative frame transformation, converts them back to probabilities, and sets cells outside the valid overlap to zero.Source: C. OGM Grid Transformation · p. 4

V. TOPOLOGY-DRIVEN SPATIOTEMPORAL RISK AWARE PLANNER

The TSR planner evaluates topology-distinct paths against predicted occupancy at estimated arrival times and selects a path using spatiotemporal risk. It samples local goals within the forecast horizon and retains one representative per approximate topology class.

V. TOPOLOGY-DRIVEN SPATIOTEMPORAL RISK AWARE PLANNER

  • TSR evaluates topology-distinct guidance paths using predicted occupancy at estimated arrival times and occupancy directivity, then selects a path while reducing oscillatory switching between topology classes.The selected guidance path is followed by the downstream local planner.Source: §V · p. 4

A. Local Goal Sampling

  • Local goals are sampled from free-space segments of a lateral line at a lookahead distance covering the robot’s maximum travel over the prediction horizon.The number of samples per segment is proportional to its length.Source: A. Local Goal Sampling · p. 4

B. Candidate Guidance Paths with Distinct Topology

  • A fast approximate topology check groups geometrically different paths by whether sampled occupied cells separate them, retaining one representative path per class.The check casts opposite-direction rays parallel to the local goal line from sampled occupied cells.Source: B. Candidate Guidance Paths with… · p. 4

C. Spatiotemporal Risk Evaluation

  • Each path point is paired with a forecast OGM layer using estimated arrival time, producing a space-time representation for risk evaluation.Arrival-time indices are clipped to the prediction horizon; Fig. 2 illustrates occupancy peaks connected across adjacent path points for directivity evaluation.Source: C. Spatiotemporal Risk Evaluation · pp. 4–5, Figure 2 · p. 5

1) Arrival-Time Cost:

Arrival-time cost assesses occupancy where the robot is expected to reach each path point, rather than treating spatial overlap alone as collision risk.

1) Arrival-Time Cost:

  • Spatial overlap does not necessarily imply collision risk because the robot and occupancy may reach the same location at different times.The arrival-time cost therefore evaluates occupancy at each point when the robot is expected to arrive.Source: 1) Arrival-Time Cost · p. 5
  • The cost uses the occupancy cost at each path point in its corresponding predicted OGM layer.The OGM layer is selected for the estimated time the robot reaches that point.Source: 1) Arrival-Time Cost · p. 5
  • This timing-based penalty avoids rejecting paths that overlap occupied space spatially but remain feasible in space and time.It penalizes a path only when its points are predicted occupied at the robot’s arrival.Source: 1) Arrival-Time Cost · p. 5

2) Directivity Cost:

Directivity cost complements arrival-time cost by capturing occupancy motion along a path without explicit object tracking. The total risk cost combines both terms with adjustable relative weights.

2) Directivity Cost:

  • Arrival-time cost may capture only a single overlap point even when collision risk increases as an occupied region approaches, motivating a separate directivity cost.Directivity uses the temporal order of occupancy peaks along the path to distinguish approaching from receding occupancy.Source: 2) Directivity Cost · p. 5
  • Occupancy peaks are local maxima above a fixed threshold in the predicted occupancy sequence at each path point.Peaks at adjacent path points are linked when their prediction-step indices differ by no more than the temporal window size; each link is characterized by signed speed and occupancy cost.Source: 2) Directivity Cost · p. 5
  • Earlier peaks at farther points and later peaks nearer the robot indicate approaching occupancy and increase directivity cost, while the reverse ordering reduces it.The cost favors paths through spaces expected to be vacated and avoids regions expected to be occupied by approaching obstacles.Source: 2) Directivity Cost · p. 5

3) Total Cost:

  • Total spatiotemporal risk combines arrival-time and directivity costs, with separate weights controlling their relative contributions.Source: 3) Total Cost · p. 5

D. Path Selection

TSR reuses a previous guidance path when its risk remains acceptable, otherwise considering a same-topology route before selecting the lowest-risk candidate. The experiments evaluate prediction and navigation against several baselines.

D. Path Selection

  • TSR retains the previous guidance path while its risk is acceptable, reducing oscillatory switching between topology classes.If its risk exceeds the threshold, the planner considers alternatives.Source: D. Path Selection · p. 5
  • The planner reuses the pruned and extended previous path when its risk is at most η; otherwise, it tests a same-topology path before choosing the minimum-risk candidate.The selected path guides the local planner.Source: D. Path Selection · pp. 5–6
  • Figure 3 plots test-set average IoU, SSIM, and NMI across 10 prediction steps, with curves averaged over 8 stochastic samples.Source: Figure 3 · p. 6

VI. EXPERIMENTS

  • Experiments evaluate prediction on a dataset and navigation in simulated and real-world environments.Source: §VI · p. 6

A. Experimental Setup

  • The prediction comparison includes SCOPE, SCOPE++, SO-SCOPE, and VDT; navigation comparisons include SCOPE-based methods and HEIGHT, with DWA and ART-TEB as FORTE local planners.VDT is excluded from navigation experiments because its inference latency limits real-time applicability.Source: A. Experimental Setup · p. 6

B. OGM Prediction Results

FORTE is evaluated on OGM prediction and navigation in simulation and real-world settings. It improves prediction results and outperforms navigation baselines in simulation, with additional success in two real-world corridor scenarios.

B. OGM Prediction Results

  • Prediction is evaluated on 17,000 OGM-Turtlebot2 test samples over 10 future steps using IoU, SSIM, and NMI.Source: B. OGM Prediction Results · p. 6
  • At longer horizons, FORTE improves IoU by up to 215.3% and SSIM by 22.14%; it has the lowest inference time, approximately 5.24× faster than VDT.FORTE also outperforms competing methods in NMI; the authors associate higher NMI with cleaner occupancy distributions from iterative denoising.Source: B. OGM Prediction Results · p. 6

C. Navigation Results in Simulation

VII. CONCLUSION

Prediction and navigation experiments show improved performance, with ablations supporting contributions from the TSR planner and directivity cost. The current framework also has motion-range and joint-optimization limitations.

VII. CONCLUSION

  • Experiments demonstrate improved prediction accuracy and navigation performance, while ablations support the TSR planner’s and directivity cost’s contribution to navigation success.Source: §VII · p. 8
  • The conventional local planner limits the framework’s range of robot motions, including backward motion.Source: §VII · p. 8
  • Prediction and planning use forecasted OGMs but are not jointly optimized.Source: §VII · p. 8
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