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Act Natural! Extending Naturalistic Projection to Multimodal Behavior Scenarios

Hamzah I. Khan, David Fridovich-Keil

TL;DR

This work addresses the challenge of achieving naturalistic, predictable behavior for autonomous agents in human environments by extending unimodal naturalistic projection to multimodal scenarios. It introduces a data-driven representation where time-indexed naturalistic behavior at each moment is modeled as a union of convex hulls, learned from observed trajectories through clustering and hull construction, and couples this with a mixed-integer optimization to project arbitrary trajectories into the learned set while preserving dynamics. Key contributions include (i) a multimodal naturalistic set identification framework, (ii) an online trajectory projection method that enforces naturalistic constraints via binary selection of convex hulls, and (iii) comprehensive experiments on inD and rounD datasets across curved roads, intersections, and roundabouts, with analysis of runtime-accuracy tradeoffs. The approach provides a practical, interpretable, data-efficient alternative to purely data-hungry imitation-learning methods, enabling real-time planning that respects human-like behavior in complex driving scenarios.

Abstract

Autonomous agents operating in public spaces must consider how their behaviors might affect the humans around them, even when not directly interacting with them. To this end, it is often beneficial to be predictable and appear naturalistic. Existing methods for this purpose use human actor intent modeling or imitation learning techniques, but these approaches rarely capture all possible motivations for human behavior and/or require significant amounts of data. Our work extends a technique for modeling unimodal naturalistic behaviors with an explicit convex set representation, to account for multimodal behavior by using multiple convex sets. This more flexible representation provides a higher degree of fidelity in data-driven modeling of naturalistic behavior that arises in real-world scenarios in which human behavior is, in some sense, discrete, e.g. whether or not to yield at a roundabout. Equipped with this new set representation, we develop an optimization-based filter to project arbitrary trajectories into the set so that they appear naturalistic to humans in the scene, while also satisfying vehicle dynamics, actuator limits, etc. We demonstrate our methods on real-world human driving data from the inD (intersection) and rounD (roundabout) datasets.

Act Natural! Extending Naturalistic Projection to Multimodal Behavior Scenarios

TL;DR

This work addresses the challenge of achieving naturalistic, predictable behavior for autonomous agents in human environments by extending unimodal naturalistic projection to multimodal scenarios. It introduces a data-driven representation where time-indexed naturalistic behavior at each moment is modeled as a union of convex hulls, learned from observed trajectories through clustering and hull construction, and couples this with a mixed-integer optimization to project arbitrary trajectories into the learned set while preserving dynamics. Key contributions include (i) a multimodal naturalistic set identification framework, (ii) an online trajectory projection method that enforces naturalistic constraints via binary selection of convex hulls, and (iii) comprehensive experiments on inD and rounD datasets across curved roads, intersections, and roundabouts, with analysis of runtime-accuracy tradeoffs. The approach provides a practical, interpretable, data-efficient alternative to purely data-hungry imitation-learning methods, enabling real-time planning that respects human-like behavior in complex driving scenarios.

Abstract

Autonomous agents operating in public spaces must consider how their behaviors might affect the humans around them, even when not directly interacting with them. To this end, it is often beneficial to be predictable and appear naturalistic. Existing methods for this purpose use human actor intent modeling or imitation learning techniques, but these approaches rarely capture all possible motivations for human behavior and/or require significant amounts of data. Our work extends a technique for modeling unimodal naturalistic behaviors with an explicit convex set representation, to account for multimodal behavior by using multiple convex sets. This more flexible representation provides a higher degree of fidelity in data-driven modeling of naturalistic behavior that arises in real-world scenarios in which human behavior is, in some sense, discrete, e.g. whether or not to yield at a roundabout. Equipped with this new set representation, we develop an optimization-based filter to project arbitrary trajectories into the set so that they appear naturalistic to humans in the scene, while also satisfying vehicle dynamics, actuator limits, etc. We demonstrate our methods on real-world human driving data from the inD (intersection) and rounD (roundabout) datasets.
Paper Structure (33 sections, 23 equations, 11 figures, 1 table)

This paper contains 33 sections, 23 equations, 11 figures, 1 table.

Figures (11)

  • Figure 1: (top) Given a multimodal behavior dataset $\mathcal{D}{}$, our method first generates a naturalistic behavior set by computing nonconvex time-indexed sets. Each nonconvex set is represented by the union of a set of convex hulls which are formed by clustering the trajectory states at each time. Then, we project arbitrary trajectories into this set to make the behaviors more naturalistic. (bottom) Demonstration of our method on a roundabout scenario. Observe that the polygons cover the entry and exit lanes, as well as regions around the roundabout. Subsequently, the projected trajectories (shown in red) more closely align with human data. Figure is rotated for presentation.
  • Figure 2: \ref{['fig:inD-r1-hull2d']} and \ref{['fig:inD-r1-clusters2d']} depict naturalistic behavior sets generated using two different methods for recording 1 of the inD dataset. Both methods capture the tendency of human drivers to drive on the outside of the curve without explicit modeling. Projecting a straight trajectory into the naturalistic behavior set results in similar trajectories with both methods, that capture these human tendencies.
  • Figure 3: An analysis of the behavior of vehicles traveling eastward along the road in recording 22 of the inD dataset, without explicit modeling. \ref{['fig:inD-r22-hull2d-f245']} depicts a large set spanning most of the relevant path and which may not be as useful for understanding human-like behavior. The method used in \ref{['fig:inD-r22-clusters2d-f245']} breaks up the naturalistic behavior set and exposes areas where vehicles tend to slow or stop for other agents. We identify the number of clusters by inspecting \ref{['fig:inD-r22-trajectory-plots']}.
  • Figure 4: A legend for rounD, recording 0 (frames 96 and 304).
  • Figure 5: unimodal khan2024actnatural
  • ...and 6 more figures

Theorems & Definitions (3)

  • Remark 1: Inspirations from Approaches to Forward Reachability
  • Remark 2: Difference from khan2024actnatural
  • Remark 3: Modifying \ref{['eq:binary-sum']} to Improve Computational Efficiency