Beyond the Plane: Coupling Planar Vehicle Dynamics with Three-Dimensional Road Geometry

2026-08-10

AI Summary

This study addresses the limitation of conventional two-dimensional vehicle dynamics models in accurately capturing the influence of three-dimensional road geometries—such as banked racetracks—on vehicle behavior, which hampers the fidelity of autonomous driving simulations. To overcome this, the authors propose a lightweight coupling approach that integrates road-induced forces and moments into an efficient 2D framework through coordinate transformation, explicit 3D road geometry modeling, and tire normal force computation. This method enables, for the first time, high-fidelity interaction between standard 2D dynamics models and complex 3D road surfaces without sacrificing computational efficiency. Validation using real-world data from the Las Vegas Motor Speedway and synthetic tracks demonstrates that the approach faithfully reproduces realistic vehicle dynamics even under extreme conditions, significantly enhancing simulation realism. The implementation is publicly released.

Abstract

Simulation is crucial for developing and testing autonomous driving systems. In particular, the development of localization and control algorithms relies on an accurate vehicle dynamics simulation. However, most vehicle dynamics models are two-dimensional while real-world roads are three-dimensional. For example, effects from the three-dimensional road geometry on the Las Vegas Motor Speedway can increase the normal forces on the tires by more than 66% compared to the nominal load at standstill. As a result, even highly detailed planar vehicle dynamics models struggle to accurately reproduce the real vehicle's behavior. While solutions for three-dimensional vehicle dynamics exist, they are rarely adopted, computationally expensive, and complex. To address this issue, we present a novel method to couple planar vehicle dynamics models with real-world three-dimensional road geometry. We transform the planar vehicle state from the vehicle model's two-dimensional plane to its corresponding representation in three-dimensional space. Additionally, we calculate road-geometry-induced forces and moments and apply them to the planar vehicle model. We validate our approach using high-speed data recorded with a full-scale race car on the banked Las Vegas Motor Speedway. Furthermore, on synthetic tracks, we show that our method yields accurate results even in edge cases. Together, our results demonstrate that the gap between planar simulation and real-world three-dimensional roads can be closed without abandoning simpler planar models. To simplify adoption of our method, we provide the implementation as open-source software on github.com/TUMFTM/3d-road-geometry-coupling.

Problem

• vehicle dynamics
• 3D road geometry
• simulation accuracy
• autonomous driving
• planar models

Innovation

• 3D road geometry
• planar vehicle dynamics
• simulation coupling
• autonomous driving
• vehicle modeling