High Performance Vehicle Dynamics Model for Autonomous Driving Simulation

Raffael Düll,
Shubham Khatri,
Teodor Rotaru,
Felix Sievers

under supervision by
Dr. Stefan Sicklinger (AUDI AG)
M.Sc. with honors Friedrich Menhorn (TUM)

Introduction

Vehicle Dynamics Simulations are a crucial part of an autonomous driving framework. Typically, these are performed using commercial Multibody Dynamics (MBD) packages, which have unacceptable performance for a real-time application. This project focused on tackling this problem through the development of a high-performance vehicle dynamics simulation tool.

The developed tool is based on the Arbitrary Lagrangian-Eulerian (ALE) formulation implemented using the high-performance library Intel MKL. The tool also contains an MBD implementation using these libraries for benchmarking purposes. It also provides the flexibility to use several time integration schemes. These schemes were tested and compared in terms of accuracy and performance.

The designed ALE model provides the flexibility to simulate general road profiles and is capable of handling a non-analytical formulation of non-rigid components of the vehicle. Further, the model offers the flexibility to use a non-analytic external field resulting in generalisation comparable to an MBD formulation.

Models

Fig.1: Scheme of the MBD model

An MBD formulation for the car was done. The model was simplified by considering the suspensions and the tyres as nonlinear springs with damping. MBD formulation of the car was done with 30 DOF as shown in Fig. 2.

MBD model was simplified with ALE formulation for performance improvements, by removing the rotational springs (see Fig. 3). We decouple the total motion of the body in a composition of Lagrangian and Eulerian frames. Hence the total motion of the body is described by the motion of Eulerian Frame in the Lagrangian Frame plus the localized changes in the body w.r.t. to Eulerian Frame, as shown in Fig. 4.

Fig.2: Resulting Physical system with the assumptions taken in account for ALE modelling

Fig.3: Example of Lagrangian-Eulerian frame for uniform circular motion

This ALE formulation was generalized for arbitrary road profile and can take into account nonlinear functions for stiffnesses and damping.
One disadvantage of the ALE formulation is that it cannot handle explicit time integration schemes. Therefore, the Backward Euler and Backward Differentiation Formula (BDF2) were used. On the other hand, the MBD formulation can handle all implicit and explicit formulations.

Results

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Fig.4: Position of the Z-component of the centre of gravity of the main vehicle body on a straight road profile with fixed tyres road conditions under the effect of gravity and constant velocity, dt=0.001 sec

Based on energy conservation laws, we validated the correctness of the MBD method. For ALE we observed that the x-y plane of the car follows the trajectory, while for the vertical direction ALE shows similar oscillations as for MBD. The differences in the oscillations, shown in Fig.4, arise due to the introduced simplification, i.e., decoupling and removal of the rotational springs.

For MBD we observed that the explicit Runge-Kutta 4th order provides the best performance without compromising the accuracy. Similarly, for ALE the corresponding method is BDF-2. Comparing these two methods, ALE provides a speedup of about 3.

Github repository: EVAA

Project report: Report