Estimation of Tire-Road Forces and Vehicle Sideslip Angle

Baffet, Guillaume; Charara, Ali; Lechner, Daniel · 2008 · Crossref

DOI: 10.5772/5531

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Summary

This paper addresses the challenge of estimating critical vehicle dynamic variables—specifically longitudinal and lateral tire-road forces, velocity, sideslip angle, and wheel cornering stiffness—to enhance vehicle safety and handling control systems like Electronic Stability Programs. Since these variables are often unmeasurable in standard vehicles due to technical and economic constraints, the authors propose a novel two-block estimation process that relies solely on standard sensor measurements (yaw rate, accelerations, steering angle, and wheel velocities). The approach separates vehicle body dynamics from tire-road interface dynamics to improve robustness against friction variations. The methodology employs two Extended Kalman Filters (EKFs). The first observer ($O_{1,4w}$) uses a four-wheel vehicle model combined with a random walk force model to estimate tire forces and yaw rate. To address observability issues where individual wheel forces cannot be differentiated, the system estimates force sums for front and rear axles, distributing them based on vertical load transfer calculations. The second observer ($O_{2,LAM}$) utilizes a single-track model and a linear adaptive tire-force model to estimate the sideslip angle and correct for cornering stiffness variations. This adaptive model introduces a readjustment variable to account for changes in tire-road friction, unlike fixed linear models. The authors validate the local observability of both systems using Lie derivative analysis. Experimental validation was conducted on a Peugeot 307 equipped with high-precision sensors, including GPS, dynamometric hubs, and a Correvit sensor for ground-truth sideslip and velocity data. The test involved acceleration, slalom maneuvers at 12 m/s, and deceleration. The first observer ($O_{1,4w}$) demonstrated rapid convergence and high accuracy, with normalized mean and standard deviation errors below 7% for force estimations, even with incorrect initial conditions. The second observer ($O_{2,LAM}$) was compared against a fixed linear model observer ($O_{rl}$). While $O_{rl}$ failed to provide accurate sideslip estimates when cornering stiffness parameters varied, $O_{2,LAM}$ maintained robust performance with consistent normalized mean errors of approximately 7% across different stiffness settings. The study concludes that the two-block estimation process effectively decouples force estimation from sideslip angle calculation, offering significant advantages for vehicle control systems. The first block provides accurate force estimates without requiring an explicit tire model, while the second block ensures robust sideslip angle estimation despite variations in road friction. These findings support the integration of adaptive tire-force models in vehicle dynamics observers to improve safety system reliability under varying driving conditions. Future work aims to expand the validity domain by incorporating roll, vertical dynamics, and elasto-kinematics.

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• steering pattern