Grid Search Based Tire-Road Friction Estimation

Abstract

The tire-road friction coefficient (µ 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 µ max is proposed. The observation problem is formulated as a non-convex optimization. A novelty of the framework is that the µ 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 µ 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 µ 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 µ max estimation.

Tire Road Friction Coefficient Estimation: Review and Research Perspectives

“…On the other hand, methods using state observers are often reported such as extended Luenberger observer [85], online gradient descent algorithm [86], nonlinear observer [87,88], high-order sliding mode observer [89], etc. The observer-based approach usually has a certain range of applicability, and an adaptive observer [90,91] for all road conditions was proposed to solve this problem.…”

Tire Slip H∞ Control for Optimal Braking Depending on Road Condition

“…These estimations are then used to calculate the longitudinal slip on each wheel and for the model used by the controller. To simplify the algorithm, the TRFC is supposed to be obtained by some estimation method [ 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ] and the optimal tire slip that maximizes the braking force is calculated by means of the Burckhardt friction model. Finally, the controller generates the necessary braking pressure for each wheel in order to minimize the error between the optimal and current longitudinal slip.…”

“… Scheme of the control architecture implemented in Simulink and CarSim [ 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ]. …”

“…The main contributions are: The proposed controller is able to make the tire slip follow a given reference based on the TRFC, resulting in a small reference error and good transient response, guaranteeing system stability. Since the estimation of the TRFC is not the focus of this article, it is assumed to be known for making use of any of the most recent literature algorithms [ 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ]. The braking forces are maximized depending on road condition.…”

Detection of Surface Defects in Ceramic Tiles With Complex Texture

“…Because the relative dimension of the input feature Qi is low and the computational complexity is small, the grid search method is used to determine the C and g values [35].…”