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.
