cs.ROMar 7, 2026

Efficient Trajectory Optimization for Autonomous Racing via Formula-1 Data-Driven Initialization

Authors: Samir Shehadeh, Lukas Kutsch, Nils Dengler, Sicong Pan, Maren Bennewitz

Organizations: University of Bonn, Germany · Lamarr Institute for Machine Learning and Artificial Intelligence and the Center for Robotics, Bonn, Germany

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Abstract

Trajectory optimization is a central component of fast and efficient autonomous racing. However practical optimization pipelines remain highly sensitive to initialization and may converge slowly or to suboptimal local solutions when seeded with heuristic trajectories such as the centerline or minimum-curvature paths. To address this limitation, we leverage expert driving behavior as a initialization prior and propose a learning-informed initialization strategy based on real-world Formula1 telemetry. To this end, we first construct a multi-track Formula1 trajectory dataset by reconstructing and aligning noisy GPS telemetry to a standardized reference-line representation across 17 tracks. Building on this, we present a neural network that predicts an expert-like raceline offset directly from local track geometry, without explicitly modeling vehicle dynamics or forces. The predicted raceline is then used as an informed seed for a minimum-time optimal control solver. Experiments on all 17 tracks demonstrate that the learned initialization accelerates solver convergence and significantly reduces runtime compared to traditional geometric baselines, while preserving the final optimized lap time.

Figures & tables

Fig. 1: Overview of our proposed learning-informed initialization method. First, expert Formula 1 telemetry (left) is used to train a geometric raceline predictor that captures structural properties of near-optimal racing behavior. The predicted raceline then serves as an initialization for a minimum-time trajectory optimization solver. Finally, the resulting optimized trajectory is transferred to a RoboRacer [ 10 ] platform (right), demonstrating robustness to domain shift from full-scale Formula 1 data to a 1:10 autonomous racing system operating on an initially unknown map.
Fig. 2: The racing track is described by a centerline parameterized by the arc length, with track boundaries and racelines expressed as lateral offsets relative to this reference.
TrackSourceSeasonDriver
BakuAC2025Max Verstappen
BarcelonaAC2025Oscar Piastri
COTAAC2025Max Verstappen
HungaroringAC2025Charles Leclerc
ImolaAC2025Max Verstappen
InterlagosAC2025Lando Norris
TABLE I: Used racetracks for raceline reconstruction and dataset generation. Track geometries were obtained from the Assetto Corsa racing simulation (AC) and the TUM Racetrack Database (TUM) 2 . Melbourne 2024 was used due to race-wide rain conditions in 2025.
Fig. 3: Network architecture for raceline prediction. History and future windows are encoded using dilated temporal convolutional networks and fused with the target window via convolutional and multi-head temporal attention layers. The fused features are flattened and processed by an MLP to predict a raceline, which is subsequently used as initialization seed for a minimum-time optimizer.
Fig. 4: Neural network training behavior and qualitative raceline prediction results. (a) Training and validation loss curves show stable convergence and similar trends, indicating good generalization without overfitting. (b–d) Predicted racelines (green) compared to the reconstructed expert Formula 1 raceline (blue) and the track centerline (black dashed) on representative circuits (Spielberg, Monza, and COTA). The predicted trajectories closely follow the expert racing line, particularly in corner entry and exit regions, while clearly deviating from the geometric centerline, demonstrating that the network captures expert driving structure from track geometry alone. On COTA the deviation is slightly higher, due to the long straights before the curve where acceleration profiles are difficult to predict.
MethodRMSE [m]MAE [m]
CL (Centerline)3.07 ±\pm 0.612.57 ±\pm 0.55
MC (Min Curve)3.12 ±\pm 0.722.57 ±\pm 0.61
F1-NN (Ours)3.02 ±\pm 0.692.45 ±\pm 0.63
TABLE II: Mean geometric deviation with respect to the reconstructed expert raceline (F1-GT) across all 17 tracks of our dataset. RMSE and MAE are computed in the Frenet frame using the lateral offset d(s)d(s) . Although the geometric improvement of F1-NN over CL is moderate, this small structural offset proves crucial for improving initialization quality in nonlinear minimum-time trajectory optimization. Notably, geometric agreement alone does not fully explain optimization performance, highlighting that initialization quality depends on structural properties beyond simple pointwise deviation.
Init.Iter. ↓\downarrowOpt. Time [s] ↓\downarrowGen. Time [s] ↓\downarrowTotal Runtime [s] ↓\downarrowLap Time [s] ↓\downarrow
CL521.6 ±\pm 149.0149.5 ±\pm 47.5–149.5 ±\pm 47.585.70 ±\pm 11.20
MC483.1 ±\pm 112.1136.2 ±\pm 38.7121.4 ±\pm 50.3257.6 ±\pm 63.485.26 ±\pm 11.17
F1-NN (Ours)434.5 ±\pm 103.1 ∗123.4 ±\pm 40.5 ∗0.63 ±\pm 0.1 †124.0 ±\pm 40.5 ∗†85.22 ±\pm 11.21 ∗
F1-GT400.1 ±\pm 67.6112.3 ±\pm 26.2–112.3 ±\pm 26.285.14 ±\pm 11.13
TABLE III: Comparison of initialization strategies for minimum-time optimization. Reported are the mean and standard deviation of solver iterations, optimized lap time, optimization runtime, initialization generation time, and total runtime across all evaluated tracks. Lower values indicate improved efficiency and solution quality. CL denotes the centerline, MC the minimum-curvature trajectory, F1-NN the raceline predicted by our neural network, and F1-GT the reconstructed Formula 1 ground-truth trajectory. ∗ indicates statistical significance compared to CL ( p<0.05p<0.05 ), and † indicates statistical significance compared to MC ( p<0.05p<0.05 ).
Init.Lap Time [s]Speed [m/s]Lat. Err [m]
CL7.090 ±\pm 0.0613.504 ±\pm 1.0100.165 ±\pm 0.155
F1-NN (Ours)6.640 ±\pm 0.069 ∗3.672 ±\pm 1.014 ∗0.109 ±\pm 0.075 ∗
TABLE IV: Real-world RoboRacer evaluation comparing centerline (CL) and our proposed F1-NN initialization. Reported are mean ±\pm standard deviation across 10 autonomous laps. Lat. Err denotes the lateral tracking error between the planned raceline and the executed vehicle trajectory. ∗ indicates statistically significant improvement over CL ( p<0.01p<0.01 ).
Fig. 5: Qualitative example of the optimized raceline on the RoboRacer test track. The F1-NN-initialized trajectory (red) follows smooth cornering arcs resulting in high speed and trackability.

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