Grid Search Based Tire-Road Friction Estimation

Abstract

The tire-road friction coefficient ( $\mu _{\max }$ ) 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 $\mu _{\max }$ is proposed. The observation problem is formulated as a non-convex optimization. A novelty of the framework is that the $\mu _{\max }$ 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 $\mu _{\max }$ 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 $\mu _{\max }$ 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 $\mu _{\max }$ estimation.