Accuracy Evaluation of a Lightweight Analytic Vehicle Dynamics Model for Maneuver Planning

TL;DR

This work addresses the need for fast, reliable vehicle dynamics models suitable for real-time maneuver planning in automated driving. It proposes a $C^2$ (twice continuously differentiable) vehicle dynamics model that supports both analytic extraction of trajectory parameters and forward generation from control inputs, enabling efficient integration into planning pipelines. Real-world validation includes IPG CarMaker simulations and measurements from a VW e-Golf on a closed track and public roads, revealing generally good performance with notable limitations under high slip, understeer, or sensor occlusions. The findings highlight both the practicality of the lightweight approach for constrained planning tasks and the need for extensions to handle curved road geometry and diverse vehicle types in more challenging conditions.

Abstract

Models for vehicle dynamics play an important role in maneuver planning for automated driving. They are used to derive trajectories from given control inputs, or to evaluate a given trajectory in terms of constraint violation or optimality criteria such as safety, comfort or ecology. Depending on the computation process, models with different assumptions and levels of detail are used; since maneuver planning usually has strong requirements for computation speed at a potentially high number of trajectory evaluations per planning cycle, most of the applied models aim to reduce complexity by implicitly or explicitly introducing simplifying assumptions. While evaluations show that these assumptions may be sufficiently valid under typical conditions, their effect has yet to be studied conclusively. We propose a model for vehicle dynamics that is convenient for maneuver planning by supporting both an analytic approach of extracting parameters from a given trajectory, and a generative approach of establishing a trajectory from given control inputs. Both applications of the model are evaluated in real-world test drives under dynamic conditions, both on a closed-off test track and on public roads, and effects arising from the simplifying assumptions are analyzed.

Figures (13)

• Figure 1: Overview of the main geometric parameters in the $C^2$ model at a particular point $\xi(t)$ along the trajectory $\xi$, establishing the tangent $\boldsymbol T$ and normal $\boldsymbol N$ to derive i.a. the curvature $\kappa$ and the front left wheel angle $\delta_{\text{FL}}$.
• Figure 2: A typical reversing trajectory where the path (the trajectory parametrized by arc length) has a singularity, but the trajectory's coordinates are smooth since $\|\dot\xi\|=0$ at the cusp (dashed lines in (b)). In these cases, a consistent heading direction can be defined via \ref{['eq:tfill']}.
• Figure 3: Selected simulation results from icmc of a BMW 118i driving on the Hockenheimring race track, simulated in IPG CarMaker. With an overall adequate accuracy between estimated and simulated parameters, notable deviations include longitudinal wheel slip in the rear wheels (arrows in (d)) during sharp accelerations of the rear-wheel drive vehicle model.
• Figure 4: Evaluations on the closed-off test track, Sec. \ref{['sec:tests-campusost']}.
• Figure 5: Overview of measured parameters (solid black) vs. $C^2$ model estimates (dashed blue) over time (a) and extracts around the two regions of strong errors (shaded) in $\delta_{\text{SWA}}^{C^2}$ and $v_{\text{lon}}^{C^2}$, which correspond with high lateral accelerations.