Estimation of the Tire-Road Interaction Forces by using Pacejka’s Formulas with Combined Slips and Camber Angles

The growing market demand for highly automated and autonomous vehicles and the need to equip vehicles with ever higher standards of comfort, safety and performance requires knowledge of physical quantities that are often difficult or expensive to measure directly. The absence of direct sensors, the difficulty of implementation, and their cost have led researchers to identify alternative solutions that allow estimating the physical quantity of interest by aggregating other available information. The interaction forces between tire and road are among the most significant. Given that the dynamics of a vehicle are strongly linked to the forces exchanged between the tire and the road, their knowledge is fundamental in the development of control systems aimed at improving performance in terms of handling, road holding or comfort. This paper presents a new technique for the estimation of tire-road interaction forces based on the integration of models and measures. A Central Difference Kalman filter was applied to a Double Track Model. The non-linear Kalman filter allowed us to handle the non-linearity of the system. The tire-road interaction was modelled through Pacejka's magic formulas that into account the combined longitudinal and lateral slips and the camber angle. This version made it possible to carry out complex and realistic manoeuvres. The realized estimator also considers the influence of lateral and longitudinal load transfers and aerodynamic forces in the three spatial directions. The Camber angle used in this observer was estimated through neural networks. The measures used are longitudinal velocity, yaw rate, longitudinal slip and wheel steering angles.