Tire Road Friction Coefficient Estimation for Individual Wheel Based on Two Robust PMI Observers and a Multilayer Perceptron

The tire-road friction coefficient (TRFC) is critical to the control of assisted and autonomous vehicles. However, direct measurement of TRFC by existing sensors is impossible. In this paper, we aim to develop a scheme to estimate TRFC based on the mathematical model and measurable vehicle states. To address this issue, we first develop a vehicle dynamics model and a wheel rotation dynamics model. Based on the two models, we propose two robust proportional multiple-integral (PMI) observers for the longitudinal and lateral tire-force estimation. To reduce the conservative of conventional $H_{\infty}$ observer, a novel optimization problem is formulated and solved by particle swarm optimization (PSO) algorithm to determine the observer gain. Next, an multilayer perceptron (MLP) is trained to estimate TRFC from the estimated tire forces, slip rate, and slip angle. However, based on data analysis, we find that the tire forces are not sensitive to the TRFC when the slip ratio and slip angle are relatively low, and these data frames would degrade the performance of MLP. To balance the performance and generalization ability of MLP, we determine the threshold for slip ratio and slip angle to exclude the insensitive data frames and train the MLP with the remaining data. Finally, the proposed scheme is verified under different scenarios. The simulation results demonstrate that the proposed method could estimate the TRFC more accurately than the traditional method. Furthermore, the proposed method has the advantage that its estimation does not depend on the initial states.