Neural Networks Based Road-Tire Friction Coefficient Estimation Using Fiala Tire Model and Kalman Filter

In this paper an algorithm for friction coefficient estimation is presented by using the robotic system dynamic model and feed forward neural networks (FFNN). The system is a robotic vehicle with articulated suspension (RVAS). The Fiala tire model is investigated and modeled. Then the road and robotic vehicle data is generated that represent the working environment required for neural networks training and validation. The input and output data pairs are prepared to estimate the road tire friction coefficient based on the inputs of tire forces (longitudinal, lateral, and vertical), slip angle, slip ratio, and wheel angular speed. The data is divided into two parts, one for training and the other for validation. For each FFNN design (number of neurons), the training process is repeated 50 times for each design to ensure error saturation. The training and validation tests are executed based on the root mean square error (RMSE) as the main performance measure. It is found that a FFNN of size 19 neurons can estimate the road tire friction coefficient effectively. The training results RMSE 12.87% and validation results RMSE 13.09%. Moreover, a detailed study of the uncertainties effect is executed up to 30% of each input to the FFNN.