Estimation of vehicle sideslip, tire force and wheel cornering stiffness

Baffet, Guillaume; Charara, Ali; Lechner, Daniel · 2009 · Crossref

DOI: 10.1016/j.conengprac.2009.05.005

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Summary

This paper addresses the challenge of estimating critical vehicle dynamics variables—specifically tire-road forces, vehicle sideslip angle, and wheel cornering stiffness—which are essential for enhancing active safety systems like electronic stability programs but are not directly measurable in standard vehicles. The authors propose a two-block estimation process that relies solely on sensors already integrated into modern cars, such as yaw rate, longitudinal and lateral accelerations, steering angle, and angular wheel velocities. The method is designed to be robust against variations in road friction, a common source of error in vehicle dynamics modeling. The estimation process is divided into two sequential blocks. The first block employs a Sliding-Mode Observer (SMO) based on a single-track vehicle model to estimate longitudinal and lateral tire forces and yaw rate. This observer models force evolution as constant ($\dot{F}=0$), ensuring that force estimates remain independent of tire-road parameters and thus robust to friction changes. The second block utilizes an Extended Kalman Filter (EKF) to estimate the vehicle sideslip angle and wheel cornering stiffness. This block incorporates a "linear adaptive force model," which adds a readjustment variable to the standard linear tire-force model to correct for errors caused by varying road friction. The EKF’s variance-covariance matrices are dynamically adjusted based on the vehicle's state to ensure accurate stiffness estimation only when lateral dynamics are sufficient. Experimental validation was conducted using a Peugeot 307 equipped with dynamometric hubs and Correvit sensors to provide ground-truth measurements of tire forces and sideslip angles. The tests included slalom and roundabout maneuvers on dry asphalt. The SMO demonstrated high accuracy, with normalized mean errors for tire forces and yaw rate remaining below 6% across both tests. The EKF was compared against a standard linear model observer (ORL). While the ORL failed to maintain accuracy when cornering stiffness parameters were artificially varied, the adaptive EKF maintained consistent estimation performance regardless of stiffness settings. The EKF normalized mean errors for rear sideslip angle ranged from 4.4% to 8.1%, and the estimated cornering stiffness values converged quickly once lateral dynamics became significant. The study concludes that the proposed two-block estimation process provides accurate and robust estimates of vehicle dynamics variables using only standard sensor inputs. By decoupling force estimation from friction-dependent parameters and employing an adaptive model for stiffness, the method effectively handles road friction variations. This approach offers a viable solution for improving the reliability of active safety systems by providing precise real-time data on tire forces and sideslip angles without requiring specialized hardware.

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• steering pattern