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Cross-Scenario Controller Parameter Transformation from Real-World Driving Data through Flow Matching

Christian Zink, Maik Pfefferkorn, Eric Lenz, Felix Kallmeyer, Rolf Findeisen

arXiv:2610.32719v1eess.SYcs.LGcs.SY

TL;DR

ACC may be disabled when its behavior feels unnatural or inconsistent with individual driving styles. This paper learns a flow-matching transport between scenario-specific ACC parameter distributions, reducing Wasserstein-2 distance to the target distribution versus a linear transformation.

  • Problem

    ACC is often rarely used or disabled because its behavior is perceived as unnatural and inconsistent with individual driving styles, while scenario coverage makes observing each driver in every situation impractical.

    Source: §I · p. 1

  • Method

    The paper learns a flow-matching vector field to transform ACC controller-parameter distributions between driving scenarios, with driver-aware coupling and profile-based conditioning variants.

    Source: §I · pp. 1–2

  • Results

    Flow matching reduces Wasserstein-2 distance to the measured target parameter distribution by roughly a factor of six compared with the linear transformation baseline.

    Source: §I · p. 2

  • Takeaways & Limitations

    Driver-consistent coupling generalizes more robustly to unseen drivers, while profile conditioning is particularly effective for drivers represented during training.

    Source: §VI · p. 8

    The approach still needs in-vehicle validation, and future work should broaden the driving scenarios and environmental conditions considered.

    Source: §VI · p. 8

Abstract

from arXiv · show

Advanced Driver Assistance Systems have become increasingly widespread, aiming to support drivers, reduce workload, and improve traffic safety. However, many systems are rarely used because their behavior feels unnatural and does not match individual driving behavior. The growing availability of large-scale, real-world human driving data enables more human-like and driver-individual assistance functions. This paper formulates the adaptation of Adaptive Cruise Control parameters as a driver-individual scenario-to-scenario transport problem, transforming controller parameters from one driving context to another. Using flow matching, we train a generative model to predict the target-scenario behavior of previously unseen drivers from only a few demonstrations in a source scenario. We compare the approach with a linear parameter-shift baseline and evaluate flow-matching variants incorporating driver-consistent coupling, driver embeddings, and classifier-free guidance based on driving profiles extracted from trajectory data using a variational autoencoder.

I. INTRODUCTION AND MOTIVATION

ACC may be rarely used or disabled when its behavior feels unnatural or mismatched with individual driving styles. The paper learns a flow-matching transformation between driving scenarios, using source-scenario observations to predict target-scenario behavior for previously unseen drivers.

I. INTRODUCTION AND MOTIVATION

  • Existing driver-specific cost-function and style-classification approaches require observing the target driver in each situation, a coverage burden across scenarios and conditions.The paper motivates transferring observed driving characteristics between scenarios instead.Source: §I · p. 1
  • The method learns a vector field that transports ACC controller-parameter distributions between externally defined scenarios while allowing drivers to behave differently within the same scenario.Scenarios can reflect environmental, road, traffic, or relative-velocity conditions.Source: §I · p. 1
  • With only a few source-scenario observations, the learned transformation predicts how a previously unseen driver would behave in a target scenario without target-scenario observations.The paper focuses on slow- and fast-approach ACC maneuvers, while stating that the underlying problem is not limited to ACC or automated driving.Source: §I · p. 1
  • Flow matching transports empirical source and target distributions through an ordinary differential equation, here applied in the low-dimensional parameter space of an interpretable controller.The paper contrasts this with common noise-to-data generation and emphasizes retaining closed-loop structure for analysis, simulation, and validation.Source: §I · pp. 1–2
  • Flow matching reduces Wasserstein-2 distance to the measured target parameter distribution by roughly a factor of six compared with the linear transformation baseline.The proposed β-VAE profiles provide a conditioning signal, and prototype-consistency alignment is reported as more suitable than a standard autoencoder or β-VAE.Source: §I · p. 2

II. PROBLEM FORMULATION

The study represents each approach maneuver with parameters of a longitudinal PD ACC controller, identified from real-world trajectories. Slow and fast approaches define the source and target parameter distributions for scenario transformation.

II. PROBLEM FORMULATION

  • A longitudinal PD controller represents each approach maneuver by the parameter vector θ = [KP, KD]⊤, with parameters identified from the measured closed-loop response.The ACC acceleration uses distance and relative-velocity errors, with minimum distance defined from ego speed and desired time headway.Source: §II · p. 2
  • Slow and fast approach scenarios are distinguished by initial relative velocity, and their parameter distributions define the source and target of the transformation.The objective is to preserve driver-specific behavior while learning how controller parameters change across scenarios.Source: §II · p. 2

III. DATASET AND DATA PREPROCESSING

  • The naturalistic field dataset contains over 16,000 measurements from more than 170 drivers across around 30 combustion-engine vehicles and three models.Measurements span two years and more than 30 countries, with anonymous driver identifiers supporting driver-specific maneuver aggregation.Source: §III · p. 2
  • The analyzed approaches are manual driving because the vehicles had no ACC or other driver-assistance systems; radar and a front camera detected the preceding vehicle.The sensors provide relative velocity and confirm the preceding vehicle.Source: §III · p. 2

1) Preprocessing:

  • Preprocessing retained maneuvers with ego speed at least 20 m s−1 at detection, a preceding vehicle within ±2 m s−1 of its mean speed, and a common initial distance of 120 m.The initial distance was chosen because no significant ego-velocity change was observed beyond it.Source: 1) Preprocessing · p. 2
  • Signals were resampled at 10 Hz and velocity, acceleration, and relative velocity were smoothed with a fourth-order Butterworth low-pass filter at 2 Hz.The filter was applied forward and backward to avoid phase distortion; distance was obtained by integrating filtered relative velocity.Source: 1) Preprocessing · pp. 2–3

2) Filtering:

Filtering selects comparable approach maneuvers and divides them into slow and fast scenarios. Controller parameters are then identified from trajectories, and flow-matching variants differ in how they represent driver style.

2) Filtering:

  • The desired steady-state time headway THWset was restricted to 0.9–3 s to exclude gaps considered unsafe or unrepresentative of car-following.The value is measured at the end of each maneuver, once steady following is reached.Source: 2) Filtering · p. 3
  • Initial relative velocity was restricted to −12 to −4 m s−1 to make approach conditions comparable, with −12 m s−1 the minimum observed and −4 m s−1 the maximum at which active intervention is needed.Source: 2) Filtering · p. 3
  • Only the six drivers with the most maneuvers were retained, contributing 83, 45, 41, 33, 35, and 34 maneuvers, respectively.Source: 2) Filtering · p. 3

3) Scenario-Based Parameter Identification:

  • Slow approaches use initial relative velocities from −5 to −4 m s−1, while fast approaches use −12 to −8 m s−1.These subsets define the scenarios used for the remainder of the study.Source: 3) Scenario-Based Parameter… · p. 3
  • For each trajectory, a quasi-Newton numerical method solves a nonlinear least-squares fit between simulated closed-loop response and measured behavior to identify θ = [KP, KD]⊤.The resulting vectors form point clouds in PD parameter space.Source: 3) Scenario-Based Parameter… · p. 3

IV. SCENARIO-TO-SCENARIO PARAMETER TRANSFORMATION USING FLOW MATCHING

  • The flow-matching variants differ in how driving style enters: coupling constrains source–target sample pairing, while driver embedding and CFG condition the vector field on identity or a β-VAE profile.Coupling and conditioning act on different parts of the model and can be combined.Source: §IV · p. 3

A. Flow Matching

Flow matching transports the slow-approach parameter distribution toward the fast-approach distribution using a learned vector field. The coupling choice determines which source and target samples are paired during training, including whether pairs preserve driver identity.

A. Flow Matching

  • The learned time-dependent neural vector field transports probability mass from a source distribution to a target distribution through an ordinary differential equation.A probability path linearly interpolates between source sample x0 and target sample x1.Source: A. Flow Matching · p. 3
  • Here, the source distribution contains slow-approach ACC parameters and the target distribution contains fast-approach parameters, rather than noise and generated data.At inference, integrating the learned field from t = 0 to t = 1 transports a source sample toward the target distribution.Source: A. Flow Matching · p. 3

1) Coupling:

  • Pooled coupling pairs source and target samples independently across the population, so a pair can combine different drivers and the field captures population-level transport.Source: 1) Coupling · pp. 3–4
  • Driver-consistent coupling pairs samples from the same uniformly selected driver, giving drivers equal weight rather than weighting by their number of recordings.This allows drivers with fewer approaches to contribute equally and avoids bias toward drivers with many recordings; neither coupling variant supplies identity as a network input.Source: 1) Coupling · p. 4

2) Driver Embedding:

The model conditions the vector field on a learnable embedding of the driver identity.

2) Driver Embedding:

  • A learnable 8-dimensional embedding represents driver identity without imposing an artificial ordering and can encode behavioral similarity.Its dimension was chosen to balance expressiveness against added parameters given the small number of drivers.Source: 2) Driver Embedding · p. 4
  • The vector field is conditioned on the driver embedding when trained with the flow-matching objective.The supplied passage names this objective but does not provide further detail.Source: 2) Driver Embedding · p. 4
  • The text identifies data(x1) as the driver-specific component of equation (8).The supplied passage does not further explain this component.Source: 2) Driver Embedding · p. 4

3) Classifier-Free Guidance:

Classifier-free guidance steers flow matching toward a driver profile extracted from approach trajectories. The proposed profile model aims to separate driver style from maneuver-specific information and support single-approach inference.

3) Classifier-Free Guidance:

  • With classifier-free guidance, the model learns conditional and unconditional vector fields by randomly replacing the driver-profile condition with a null token during training.The profile z is extracted by a β-VAE; the null token is used with probability 0.4.Source: 3) Classifier-Free Guidance · p. 4

1) Requirements:

  • Profiles must distinguish drivers rather than maneuvers and place multi-approach and single-approach estimates in a shared latent space.This shared space allows a driver represented by multiple training maneuvers to be characterized from one observed approach at inference.Source: 1) Requirements · p. 4

2) Overview of the architecture:

  • Direct autoencoder and β-VAE profiles were dominated by maneuver-specific characteristics, so trajectories from the same driver did not map consistently to a common latent region.The proposed transformer-based β-VAE with a set-aggregator provides context to both its VAE head and decoder but does not reconstruct that context, encouraging z to capture driver-specific rather than maneuver-specific characteristics.Source: 1) Requirements · p. 4, 2) Overview of the architecture · p. 4
  • The Set-Path aggregates 20 approaches per driver, while the Single-Path aligns each individual trajectory’s representation with the corresponding set-level prototype.This makes trajectory-specific profiles available as conditioning signals for classifier-free guidance.Source: 2) Overview of the architecture · p. 5

3) Model components:

The profile model combines shared trajectory encoding, permutation-invariant set aggregation, a VAE head, and a context-conditioned decoder. Prototype consistency aligns profiles inferred from single approaches with those inferred from driver-level sets.

3) Model components:

  • A shared transformer encoder embeds each approach, and a two-layer transformer set-aggregator pools the unordered embeddings into an order-invariant driver representation.The aggregator uses a learned attention query to pool the set elements.Source: 3) Model components · p. 5
  • The VAE head maps the pooled representation and averaged context to a diagonal Gaussian posterior, whose mean supplies the deterministic profile for flow matching.The posterior is regularized toward a standard normal prior using KL divergence.Source: 3) Model components · p. 5
  • The approach decoder reconstructs each trajectory from its latent representation while conditioned on that approach’s context.The context and latent representation form a conditioning token broadcast across the trajectory horizon.Source: 3) Model components · p. 5
  • A prototype-consistency loss pulls single-approach embeddings toward fixed set-level prototypes, with stop-gradient making the Set-Path define the target geometry.Reconstruction and KL objectives train the aggregator on multi-element sets.Source: 3) Model components · p. 5

4) Latent Space and Training:

Flow matching more closely reproduces the measured fast-approach parameter distribution and trajectory than a uniform linear shift. The evaluation also reports driver-discriminative latent profiles and notes that the transformation comparison is in-sample.

4) Latent Space and Training:

  • 0.93 five-fold random-forest accuracy and 0.42 silhouette score indicate driver-discriminative single-trajectory profiles in a shared latent space.The passage attributes the consistency between set-based and per-trajectory profiles to Set-Path–Single-Path prototype-consistency training.Source: 4) Latent Space and Training · p. 6, Figure 3 · p. 6

V. EVALUATION AND RESULTS

  • The comparison of flow-matching methods with the linear baseline is in-sample because all drivers are included in training.The evaluation separately analyzes generalization to previously unseen drivers.Source: §V · p. 6

A. Applicability of Flow Matching

  • The linear shift preserves the source distribution’s size and orientation, whereas flow matching transports regions to overlap the target more closely in location and shape.The comparison starts from slow-approach parameters and targets the measured fast-approach distribution.Source: A. Applicability of Flow Matching · p. 6, Figure 4 · p. 6
  • 54% lower maximum absolute relative-distance error than the linear shift; flow matching’s error was 2.03 m versus 4.43 m.The selected illustrative trajectory also followed the measured fast-approach reference more closely with flow-matching parameters.Source: A. Applicability of Flow Matching · p. 6, Figure 5 · p. 6

B. Systematic Evaluation of Flow Matching

The systematic evaluation compares generated and measured parameter distributions using Wasserstein-2 and complementary first- and second-moment diagnostics, with Wasserstein-2 as the primary criterion.

B. Systematic Evaluation of Flow Matching

1) Distances:

  • Mean deviation Δµ and covariance deviation ∥ΔΣ∥F isolate agreement in distribution location and shape, respectively.The covariance measure captures spread and orientation.Source: 1) Distances · p. 7
  • Wasserstein-2 is the primary criterion because it compares complete distributional geometry, while mean and covariance deviations diagnose location and shape discrepancies.A smaller W2 indicates a closer match between generated and measured distributions.Source: 1) Distances · p. 7

2) Population-averaged performance:

Across drivers, flow matching improves distribution matching over the linear transformation, with CFG plus DCC best on the pooled Wasserstein measure; driver-wise performance still varies.

2) Population-averaged performance:

  • W_norm2 falls to 0.18, roughly a sixfold reduction from the linear baseline, while Δµnorm falls from 1 to 0.05 and normalized covariance error reaches 0.18.The reported comparison indicates closer reproduction of both location and distributional shape than the linear transformation.Source: 2) Population-averaged performance · p. 7
  • CFG with DCC achieves the lowest population-averaged W_norm2 at 0.15 among the evaluated variants.Its slightly higher mean and covariance deviations do not change its ranking on the overall distribution match.Source: 2) Population-averaged performance · p. 7

3) Per-driver performance:

  • CFG, DCC, and driver embeddings consistently rank among the two best configurations across drivers, but individual-driver performance varies substantially.The reported W_norm2 ranges from 0.32 for Driver 4 to 0.55 for Driver 3; pooled evaluations are not the mean of driver-wise values.Source: 3) Per-driver performance · p. 7

C. Generalization to Unseen Drivers

For unseen drivers, driver-consistent coupling generalizes more consistently than the other tested variants. The paper concludes that flow matching captures both location and shape changes in target distributions, while in-vehicle validation remains future work.

C. Generalization to Unseen Drivers

  • The leave-one-driver-out evaluation retrained the vector field without each held-out driver, but trained the β-VAE on all drivers, yielding an optimistic estimate.Driver 5 had the closest agreement and Driver 4 the poorest agreement with measured fast-approach distributions.Source: C. Generalization to Unseen Drivers · p. 7
  • For every held-out driver, driver-consistent coupling ranked among the two configurations with the lowest normalized Wasserstein distance.The authors suggest its driver-consistent pairing may shape transport without driver-specific input.Source: C. Generalization to Unseen Drivers · p. 7

VI. CONCLUSIONS AND OUTLOOK

  • Unlike a linear transformation, flow matching captures changes in both the location and shape of the target distribution.The paper formulates controller-parameter generation as distribution transport that captures driver-specific characteristics.Source: §VI · pp. 7–8
  • Flow matching improved agreement with measured target distributions, and driver-consistent coupling generalized more robustly to unseen drivers.Profile-based conditioning was particularly effective for drivers represented during training.Source: §VI · p. 8
  • Validation across broader scenarios and environmental conditions, including in-vehicle evaluation, remains future work.The authors also identify online personalization from a limited number of observed maneuvers as a future evaluation target.Source: §VI · p. 8

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