Beyond the Plane: Coupling Planar Vehicle Dynamics with Three-Dimensional Road Geometry
2026-08-10 • Robotics
Robotics
AI summaryⓘ
The authors explain that using flat (2D) vehicle models to simulate cars on real, bumpy 3D roads leads to inaccuracies, especially in how forces on tires are calculated. They created a new method that links simple flat vehicle models with detailed 3D road shapes to better mimic real driving conditions without making the simulation too complicated or slow. They tested their method with real race car data from the Las Vegas Motor Speedway and on computer-generated tracks, showing improved accuracy. Their method makes it easier to simulate vehicles realistically while keeping models simple, and they shared their code publicly for others to use.
vehicle dynamicsplanar models3D road geometrysimulationlocalizationcontrol algorithmstire forcesautonomous drivingLas Vegas Motor Speedwayopen-source software
Authors
Simon Sagmeister, Phillip Pitschi, Nico Haja, Markus Lienkamp
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.