Grid Search based Tire-road Friction Estimation

The tire-road friction coefficient ( μmax ) is an important input for vehicle dynamics control system and automated driving modules. However, reliable and accurate measurement of this parameter is difficult and costly in mass-produced vehicles and thus estimation is necessary. In this research, an innovative optimization based framework to estimate μmax is proposed. The observation problem is formulated as a non-convex optimization. A novelty of the framework is that the μmax can be accurately estimated in real time together with side slip angle as a by-product without requiring a good initial guess for the non-convex optimization. A key observation is that the time derivative of μmax and side slip angle can be assumed as zero and computed based on measurement, respectively. This allows the observed variables to be updated at a relatively low frequency w.r.t. the solution of the optimization problem. During the interval between each two neighbouring updating time, the observer estimates the μmax and side slip angle by integrating sensor information based on the last update. To find the global optima approximately, a grid search method is implemented for solving non-convex optimization. The estimation results from the proposed observer and a linearization based observer (lbo) are finally compared under various tire-road conditions with simulations and experiments. The results showed that 1) the proposed observer can always guarantee stability in a wide range of vehicle operations while lbo cannot. 2) w.r.t. root mean square of estimation error, the proposed observer performs overall better than lbo in μmax estimation.