Stochastic vehicle handling prediction using a polynomial chaos approach

One fundamental difficulty in understanding the physics of the off-road traction and in predicting vehicle performance is the indeterminacy of certain important parameters on the interface between tyre and terrain/road surface, for instance, the slip ratio, the slip angle, the normal forces, and the friction coefficients. It is not possible to accurately capture the effect of such uncertainties on the tyre behaviour (resultant force and moments) using a deterministic model. In addition, current measuring techniques have certain limitations and sometimes non-negligible measurement errors could be a source of relatively rough approximations in estimating some important parameters involved in vehicle dynamics simulations and control algorithms. In this study, mathematical tools to quantify the impact of uncertainties in tyre-terrain interface on vehicle handling were employed. We treated the uncertainty in key parameters associated with the tyre-road interface using a polynomial chaos approach. Two of the most popular semi-empirical models for predicting the pneumatic tyres performance under steady-state and transient conditions, the Friction Ellipse Model (FEM) and the Magic Formula Model (MFM), were selected to be extended from the deterministic to a stochastic workframe, to account for the uncertainties in the tyre-terrain friction coefficient, the slip ratio, the slip angle, and the normal forces in the contact patch. The modelling approach presented in this paper was able to capture the stochastic nature of parameters of interest and to predict the response of the system under those uncertainties, in an effort to provide a better understanding and a more realistic prediction of the tyre-terrain interaction than a deterministic formulation. To illustrate the application of the stochastic tyre-road models on vehicle dynamics, they were simulated in conjunction with a bicycle-car model.