Real-Time Tire–Road Friction Coefficient Estimation for Four-Wheel-Independent-Drive Electric Vehicles Using a Piecewise Gain-Scheduled Observer and Neural Networks

Four-wheel-independent-drive electric vehicles are gaining increasing research attention due to their comprehensive dynamic performance. Real-time tire–road friction coefficient information contributes to the development of adaptive control algorithms and active safety control systems for such vehicles. However, traditional tire models widely adopted in existing estimation methods may fail to match practical tire characteristics accurately. Furthermore, lateral velocity serves as a critical state variable for tire–road friction coefficient estimation, whereas existing lateral velocity observers using low-cost inertial measurement unit sensors suffer from degraded estimation performance under complex driving maneuvers. To address the above challenges, this paper proposes a three-stage friction coefficient estimation framework. Firstly, vehicle lateral velocities are estimated via a piecewise gain-scheduled observer using inertial measurement unit measurements. Secondly, tire slip ratios are calculated based on the observed lateral velocities; meanwhile, the longitudinal, lateral and vertical forces of each tire are reconstructed. Lastly, tire force and slip information under combined slip conditions are acquired, and a multilayer perceptron neural network is established to achieve individual tire–road friction coefficient estimation. The simulation results verify the numerical feasibility and preliminary effectiveness of the proposed estimation method under ideal simulation conditions.