Lateral and Longitudinal Tire Force Prediction Using Soft Computing

While first-principles models derived from physics laws can often approximate the system behavior, it remains difficult sometimes to capture non-physically derived behavior. The empirical formula designed by Pacejka, is among the different models of the literature that are presented to describe the tire behavior for roads with surface roughness, This formula has no physical basis and its mathematical expression is obtained from intuition and experience, but it fits well the reality of the tires. The difficulty of estimating the longitudinal and lateral forces for a broad range of tires can be solved using artificial intelligence. In this paper, both the longitudinal force as a function of longitudinal slip, s, and the lateral force as a function of the lateral slip α. Both forces are estimated using tools from artificial intelligence, where fuzzy and neural network approaches are used, excluding the need to estimate them from empirical formula. To enhance the accuracy of the performance of the estimator, we present a method for optimizing membership functions using particle swarm optimization (PSO) algorithm, resulting in a fuzzy estimator that try to synthesize the magic formula for certain models of tires. A trained neural network is the other proposal in this paper, in which techniques from machine learning is used to realize an intelligent tire systems able to estimate these forces. Simulation results are reported, compared and discussed.