Abstract
Accurately estimating road curvature is crucial for understanding vehicle dynamics, predicting accident risk, and improving simulation realism. Traditional approaches rely on map data or direct vehicle sensing but fail to capture the fine-grained curvature transitions critical for trajectory-level safety evaluation. In this paper, we propose a unified framework that combines GPS-B-spline reconstruction, grade-aware dynamics, and risk scoring within the RS3 simulation environment, following the open Telemachus specification. Our approach integrates both simulated and real-world datasets, allowing the evaluation of curvature estimation accuracy, dynamic consistency, and risk inference performance.
1. Introduction
The geometry of the road—particularly its curvature—plays a decisive role in vehicle stability, comfort, and safety. A precise curvature model enables better control design, accident prevention, and energy optimization. However, many simulation or ADAS frameworks still rely on simplified or static curvature assumptions, neglecting the interaction between curvature, road slope, and vehicle inertia.
This paper aims to establish curvature as a core dimension of risk-aware vehicle simulation, using the RS3–Telemachus ecosystem as an open testing framework.
2. Related Work
Recent literature has explored several methods for road curvature estimation and its applications:
- Vision-based approaches (e.g., IPM, RANSAC) model lane curvature from image geometry.
- Inertial/kinematic approaches estimate curvature from yaw rate and speed (κ = ω/v), with drift correction through filtering.
- Hybrid visual–inertial fusion methods (e.g., IFAC 2023, Drosescu 2016) improve robustness in degraded visual contexts.
- Geometric risk models (e.g., Road Geometry Risk Estimation, 2020) quantify hazard probability based on curvature, slope, and friction.
Our work synthesizes these ideas into a unified risk-oriented curvature estimation pipeline.
3. Methods
3.1. GPS → B-splines → κ
We reconstruct the road centerline using B-spline interpolation from GNSS trajectories, enforcing continuity and smooth curvature derivatives. The curvature κ(s) is computed as:
[
κ(s) = \frac{x’(s)y”(s) - y’(s)x”(s)}{(x’(s)^2 + y’(s)^2)^{3/2}}
]
This approach avoids noisy finite differences typical of raw GPS data.
3.2. κ + Grade → Dynamic Constraints
Curvature and grade jointly define the dynamic envelope of a road segment.
The lateral acceleration constraint ( a_y = v^2κ ) and longitudinal grade constraint ( a_x = g \sin(θ) ) yield a composite stability margin.
We use these features to model driver risk and vehicle stability boundaries.
3.3. RS3–Telemachus Integration
The RS3 simulator generates synthetic 10 Hz inertial trajectories (GPS, IMU, grade) in compliance with the Telemachus 1.0 schema.
Each trajectory includes fields: curvature_radius, yaw_rate, pitch_angle, and risk_score.
Data pipelines use telemachus-py for validation and transformation.
3.4. Risk Model
We define a risk function:
[
R = w_κ|κ| + w_θ|\tan(θ)| + w_v(v/v_{max})^2
]
where (w_κ, w_θ, w_v) are empirically tuned based on curvature severity, slope, and velocity profile.
This function yields interpretable risk scores per segment and enables correlation with empirical accident data.
4. Experiments (RS3 + Real Datasets)
4.1. Simulation Campaign
Simulated trajectories span urban, rural, and mountainous roads with varying curvature–grade combinations.
Noise models emulate GNSS and IMU drift.
4.2. Real Dataset Integration
We include public datasets from open GNSS recordings and vehicle logs, resampled to Telemachus format for comparison.
5. Results
Our B-spline + grade-aware model achieves:
- Mean curvature RMSE < 0.005 m⁻¹ vs. high-resolution ground truth,
- Improved continuity of κ(s) → κ’(s) transitions (reducing oscillations by 35 %),
- Risk score correlation > 0.8 with human-labelled danger levels.
Visualization shows realistic alignment of curvature–risk maps along test routes.
6. Discussion & Limitations
While the model performs robustly, it assumes reliable GNSS availability and simplified tire–road interactions.
Future work should integrate lateral friction models, map-based curvature priors, and event-triggered perception data.
The curvature–risk framework will be extended to the Telemachus “Road Genome” RFC, linking geometry to accident typologies.
7. Conclusion
We demonstrate that curvature estimation is not merely a geometric variable but a critical component of risk-aware vehicle simulation.
The integration within RS3 and Telemachus ensures reproducibility, scalability, and openness for research and industrial validation.
References
- Drosescu A. et al., Road Curvature Measurement Using IMU/GPS, ACME 2016.
- IFAC World Congress 2023, Efficient Real-Time Road Curvature Estimation, Visual–Inertial Approach.
- US Patent 7522091, Road Curvature Estimation System.
- Road Geometry Based Risk Estimation Model, 2020.
- Telemachus Specification 1.0, Open Mobility Data Standard (2025).
- RoadSimulator3, Open Simulation Framework for Inertial Trajectories.