Improvement of Traction Force Estimation in Cornering through Neural Network

Abstract

<div>Accurate estimation of traction force is essential for the development of advanced control systems, particularly in the domain of autonomous driving. This study presents an innovative approach to enhance the estimation of tire–road interaction forces under combined slip conditions, employing a combination of empirical models and neural networks. Initially, the well-known Pacejka formula, or magic formula, was adopted to estimate tire–road interaction forces under pure longitudinal slip conditions. However, it was observed that this formula yielded unsatisfactory results under non-pure slip conditions, such as during curves. To address this challenge, a neural network architecture was developed to predict the estimation error associated with the Pacejka formula. Two distinct neural networks were developed. The first neural network employed, as inputs, both longitudinal slip ratios of the driving wheels and the slip angles of the driving wheels. The second network utilized longitudinal slip ratios of the driving wheels and longitudinal and lateral accelerations of the vehicle as inputs. The training of the neural networks was performed using data from straight-line accelerations, circuit maneuvers, and a sinus steering maneuver. Both neural networks were designed as multi-output networks capable of simultaneously estimating longitudinal force errors for both driving wheels. The estimator was tested by making two laps on the Hockenheim circuit in the opposite direction. The initial root mean square error (RMSE) was substantially reduced using corrective neural networks. These findings affirm the effectiveness of the neural network-based approach in improving traction force estimation under combined slip conditions, overcoming the limitations of the Pacejka formula in cases of non-pure slip, thereby paving new avenues for the implementation of more advanced and secure vehicle control systems.</div>