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Combining Evasive and Braking Reactions for Safety Reference Models in Automated Vehicles

Riccardo Donà, Konstantinos Mattas, Biagio Ciuffo

arXiv:2609.29738v1cs.RO

TL;DR

C&C driver benchmarks inform ADS minimum capabilities, while safety reference models commonly use braking despite research into evasive and combined maneuvers. This paper combines fuzzy longitudinal braking and lateral lane-change logic in a sequential reference model. In high-speed cut-in scenarios, it improves on braking-only models, approaches evasive strategies’ avoidance capability, and retains impact-speed mitigation when avoidance is not feasible.

  • Problem

    C&C driver thresholds inform ADS minimum capabilities, while safety reference models most commonly consider braking despite research into evasive lane changes and combined maneuvers.

    Source: §I · p. 1

  • Method

    FSM-H combines longitudinal Proactive Fuzzy Safety with the lane-change Criticality Fuzzy Safety formulation to model sequential braking and evasive steering.

    Source: A. Fuzzy Safety Models · p. 2, §I · p. 2, §IV · p. 5

  • Results

    In high-speed cut-in scenarios, FSM-H substantially improves on braking-only models, approaches purely evasive strategies’ avoidance capability, and reduces impact speed when avoidance is infeasible.

    Source: §IV · p. 6

  • Takeaways & Limitations

    Explicitly modeling maneuver sequencing yields a more behaviorally plausible safety envelope while retaining a modular, explainable, low-computation model for scenario-based ADS assessment.

    Source: §IV · p. 6

Abstract

from arXiv · show

Computational models of careful and competent human drivers are essential for scenario-based evaluation of automated driving systems (ADS). However, most existing safety reference models primarily focus on longitudinal braking, neglecting the role of evasive steering in human collision avoidance. This paper proposes a hybrid Fuzzy-Safety Model (FSM-H) that integrates longitudinal mitigation and lateral avoidance within a unified behavioral framework. The braking component is governed by Proactive Fuzzy Safety (PFS) metrics, representing the erosion of longitudinal safety margins, while the steering component is driven by Criticality Fuzzy Safety for lane-change (CFS-LC), capturing lateral conflict severity and maneuver feasibility. A finite-state architecture models the sequential escalation from nominal driving to braking and, when necessary, to evasive steering, incorporating perception-reaction time and lane-check delays to reflect human decision processes. The model is evaluated in reconstructed high-criticality cut-in scenarios and compared with braking-only and steering-only reference strategies. Results show that the hybrid approach expands the preventability envelope while maintaining behavioral plausibility and computational tractability. The proposed framework provides a transparent and explainable human reference model suitable for simulation-based ADS safety benchmarking and regulatory assessment.

I. INTRODUCTION

Careful and Competent (C&C) driver models set an important benchmark for ADS safety, but the benchmark’s threshold affects minimum capabilities and market readiness. This paper proposes a hybrid braking-and-evasive-steering reference model to represent human responses more plausibly in safety-critical situations.

I. INTRODUCTION

  • The C&C threshold helps determine an ADS’s minimum capabilities and readiness for market introduction.C&C models are used in simulation-based ADS assessment, where computational efficiency and accurate driving dynamics also matter.Source: §I · p. 1
  • Existing C&C models span cognitive and equation-based approaches, braking or evasive-steering maneuvers, and scenarios such as cut-ins, cut-outs, and car-following,,,,,,.Models are also distinguished by the scenarios they can handle.Source: §I · p. 1
  • Safety reference models commonly assess instantaneous risk with surrogate safety metrics, then apply a mitigation strategy, most often braking after a reaction time.Evasive lane changes and combined braking-and-swerving strategies are also being investigated.Source: §I · p. 1, Figure 1 · p. 1
  • The paper combines the FSM with its lane-change extension to model sequential braking and evasive steering, aiming to reflect human behavior rather than set an unrealistic ADS benchmark,.Crash investigations using event data recorders indicate that drivers usually brake before undertaking an evasive maneuver.Source: §I · pp. 1–2

A. Fuzzy Safety Models

The FSM uses fuzzy safety metrics to assess longitudinal conflict and modulate braking, while FSM-LC adapts the framework to evasive lane changes. Both use safety distances and maneuver-specific criticality logic.

A. Fuzzy Safety Models

  • PFS sets the distance needed for a full stop if the leader brakes; CFS sets the distance needed to match a slower leader’s speed under acceleration constraints.Together, the metrics define a safety envelope whose violation triggers modulated braking.Source: A. Fuzzy Safety Models · p. 2
  • FSM assigns zero criticality beyond the SAFE distance, full criticality below the UNSAFE threshold, and linearly interpolates between them.This fuzzy transition contrasts with hard-threshold triggering and supports a modulated reaction.Source: A. Fuzzy Safety Models · p. 2
  • When PFS alone triggers, braking ranges from 0–100% of comfortable deceleration; when CFS triggers, full maximum deceleration is available.Source: A. Fuzzy Safety Models · p. 2
  • FSM-LC replaces FSM braking with evasive lane changing: PFSLC measures full-lane-change safety distance, while CFS-LC targets displacement sufficient to clear the obstacle.The full lane-change time is based on a jerk-limited kinematic model.Source: A. Fuzzy Safety Models · pp. 2–3
  • FSM-LC has shorter safety distances than FSM, reflecting the shorter time needed for evasive maneuvering as speed increases.Source: A. Fuzzy Safety Models · p. 3

B. Hybrid Model Realization

FSM-H combines FSM braking logic with FSM-LC lane-change logic in a sequential response, escalating from braking to evasive steering when mitigation is insufficient.

B. Hybrid Model Realization

  • FSM-H couples FSM’s PFS braking logic with FSM-LC’s CFS-LC lane-change logic.The model reuses the FSM/FSM-LC structure.Source: B. Hybrid Model Realization · p. 3
  • PFS typically activates before CFS-LC, producing initial braking before steering when longitudinal mitigation does not restore safety.This sequence reflects reported driver behavior and escalating response intensity.Source: B. Hybrid Model Realization · p. 3
  • After reaction time τ, FSM-H applies PFS · bego,comf braking and waits an additional τcheck lane before considering evasive steering.The lane-check delay is aligned with crash data, although it was not precisely calibrated in this paper.Source: B. Hybrid Model Realization · p. 3
  • If CFS-LC remains zero, FSM-H retains PFS braking; if steering begins, braking is removed to avoid unrealistically aggressive or dynamically unfeasible combined actions.The reaction logic is represented by equations (7) for longitudinal dynamics and (8) for lateral dynamics.Source: B. Hybrid Model Realization · p. 3
  • The modular FSM/FSM-LC design makes FSM-H straightforward to realize while supporting modulated braking-to-steering behavior.FSM-H parameters mirror those of FSM and FSM-LC for fair comparison and are reported in Table I.Source: B. Hybrid Model Realization · p. 3, Table I · p. 3

C. Simulation benchmark suite

The simulation benchmark suite explores high-speed cut-in scenarios from UN Regulation 157 Annex 3, using a broad parameter sweep rather than modeling naturalistic driving exposure.

C. Simulation benchmark suite

  • The benchmark uses high-speed cut-in scenarios from UN Regulation 157 Annex 3, implemented in an openly available simulation suite.The suite is available at https://github.com/ec-jrc/JRC-FSM.Source: C. Simulation benchmark suite · p. 3
  • Fig. 3 presents the FSM-H reaction mechanism used in the benchmark model.Source: Figure 3 · p. 4
  • The sweep covers ego speeds of 70–130 km/h, target speeds of 10–120 km/h, lateral cut-in speeds of 0.25–2.5 m/s, and initial distances of 5–120 m.It investigates 75,600 parameter combinations using independent uniform sampling.Source: C. Simulation benchmark suite · p. 4
  • Only scenarios above 70 km/h are considered because evasive maneuvers are no longer the most effective obstacle-avoidance maneuver at slower speeds.The parameter sweep is intended for deterministic exploration, not to represent naturalistic driving exposure.Source: C. Simulation benchmark suite · p. 4

A. Illustrative Scenario Analysis

In the illustrative hard cut-in, FSM collides while FSM-LC and FSM-H avoid collision through different reaction strategies.

A. Illustrative Scenario Analysis

  • The original FSM model resulted in a collision at 4.7 s, whereas the other two models safely addressed the scenario using different strategies.Source: A. Illustrative Scenario Analysis · p. 4
  • FSM-H initially decelerates at −4 m/s², then switches to evasive steering at 2.2 s when CFS-LC triggers and braking is reset.Source: A. Illustrative Scenario Analysis · p. 4
  • The hard cut-in example uses ego speed 130 km/h, target speed 50 km/h, initial distance 50 m, and lateral speed 1 m/s.Fig. 4 presents the models’ cut-in analysis and criticality metrics for this scenario.Source: Figure 4 · p. 4

B. Aggregated Performance Comparison

Across the cut-in simulation, FSM-H improves the crash-reduction benchmark over FSM, though it trails FSM-LC; many cases are handled with braking alone, while delayed steering can hurt in highly critical cases.

B. Aggregated Performance Comparison

C. Switching Dynamics and Escalation Behavior

FSM-H switches from braking to steering at a median TTC of 3.08 s, close to previously reported driver intervention thresholds.

C. Switching Dynamics and Escalation Behavior

IV. SUMMARY AND CONCLUSIONS

FSM-H combines braking and steering in a sequential safety-reference strategy intended to reflect careful and competent human driving. In high-speed cut-in simulations, it approaches purely evasive avoidance while retaining impact-speed mitigation, with maneuver sequencing shaping the preventability–severity trade-off.

IV. SUMMARY AND CONCLUSIONS

  • FSM-H combines longitudinal PFS logic with lateral CFS lane-change logic to implement sequential mitigation consistent with observed human driving behavior.Source: §IV · p. 5
  • FSM-LC has the lowest overall crash rate, while FSM-H offers comparable avoidance, greater behavioral coherence with EDR findings, and a slight crash-frequency increase primarily linked to the lane-check delay.The initial braking phase partly compensates for reduced preventability through speed reduction.Source: §IV · pp. 5–6
  • Even when collision avoidance is infeasible, FSM-H reduces kinetic energy before impact and has a lower median impact speed than FSM-LC.Source: §IV · p. 6
  • FSM-H's median switching TTC of approximately 3.0 s aligns with previously reported thresholds for driver intervention in critical scenarios.Source: §IV · p. 6
  • The preventability boundary reflects interactions among reaction time, mitigation sequencing, and dynamic constraints, making FSM-H more behaviorally plausible than single-maneuver models.Source: §IV · p. 6
  • FSM-H substantially improves on braking-only reference models and achieves avoidance capabilities close to purely evasive strategies while retaining impact-speed mitigation when avoidance is infeasible.Source: §IV · p. 6
  • The model retains the original FSM's modular, explainable, low-computational structure for large-scale scenario-based assessment and regulatory use.Further work will extend conflict typologies, examine parameter sensitivity, and validate switching against naturalistic driving data.Source: §IV · p. 6
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