Lateral Velocity Model for Vehicle Parking Applications

TL;DR

This work tackles the challenge of lateral velocity estimation in automated parking, where consumer-grade sensors lack a direct lateral-velocity measurement. It introduces a lightweight two-parameter lateral velocity law based on yaw rate, $v_{y,r} = - x_{\rho} \omega_z$, and derives a physically meaningful link to steering via $\beta_r = - \dfrac{x}{L - x_{\rho}} \tan\delta_f$, enabling a robust and calibratable solution for low-speed parking. By integrating this law into an extended Kalman filter and performing a parameter-disturbance analysis, the authors show that small offsets of the zero-slip point ($Δx$) can significantly affect localization, and provide explicit error bounds. Experimental results on nine parking maneuvers (including reverse perpendicular cases) demonstrate that the proposed approach reduces lateral-velocity estimation errors and improves parking localization accuracy, achieving substantially lower trajectory errors than the zero-slip baseline. The method is especially impactful for consumer-grade platforms where extensive vehicle-specific calibration is impractical, and it lays the groundwork for online parameter estimation to further enhance robustness during the transition from parking to normal driving.

Abstract

Automated parking requires accurate localization for quick and precise maneuvering in tight spaces. While the longitudinal velocity can be measured using wheel encoders, the estimation of the lateral velocity remains a key challenge due to the absence of dedicated sensors in consumer-grade vehicles. Existing approaches often rely on simplified vehicle models, such as the zero-slip model, which assumes no lateral velocity at the rear axle. It is well established that this assumption does not hold during low-speed driving and researchers thus introduce additional heuristics to account for differences. In this work, we analyze real-world data from parking scenarios and identify a systematic deviation from the zero-slip assumption. We provide explanations for the observed effects and then propose a lateral velocity model that better captures the lateral dynamics of the vehicle during parking. The model improves estimation accuracy, while relying on only two parameters, making it well-suited for integration into consumer-grade applications.

Figures (11)

• Figure 1: Lateral velocity model resulting from a shift between the rear axis and the point $P_0$ where the zero-side-slip assumption holds.
• Figure 2: Evaluated side-slip behavior during low-speed maneuvering with fitted lines for forward (blue) and reverse driving (gray). The vehicle is driving a dedicated calibration maneuver to obtain these clean results.
• Figure 3: Single-track model with side-slip angle $\beta$, velocity vector $\hbox{\boldmath$\mathbf{v}$}$, yaw rate $\omega_z$, lever arms to the front $l_f$ and rear $l_r$, slip-angles $\beta_i$, steering angle $\delta_f$ and tire forces $F_{y,i}$
• Figure 4: Two-track model at the front axis, where additional side-slip and thus tire force $\Delta F$ is being generated. This is caused by the deviation from Ackermann steering, that would minimize the slip angle at each tire.
• Figure 5: Effect of Ackermann deviation on side-slip angle (red). The normal Ackermann behavior is depicted as well (blue).