## 3 Slip-Based Road Friction Monitoring
### Tyre Self-Alignment Torque
Nevertheless, the validation of the observer is performed on a single-track planar dynamics model, and therefore additional conclusions regarding the observer performance on a high-fidelity vehicle model cannot be extracted. A tyre-SAT-based friction estimator developed by Centro Ricerche Fiat (CRF) is also reported in the European project Friction [104] and in Koskinen [23]. The observer is described as a model-based algorithm in which tyre SAT and \"standard\" vehicle signals are employed to compute \(\mu_{\text{max}}\). Additional technical details are not provided. Authors remark that a certain lateral excitation is required to perform the estimation. Specifically, a friction utilisation threshold \(\mu=0.3\) is reported in these works as necessary to estimate the friction potential on a high mu road. This excitation threshold is also found in the Intelligent Vehicle Safety System (IVSS) project [36; 37]. In this case, it is argued that a correlation between the tyre SAT stiffness and the road grip potential can be established, following an analogy with the slip slope approach presented in the longitudinal dynamics section. Different experimental tests are performed on dry asphalt, snow, and ice. Overall, a 0.3 G excitation level is reported as necessary to guarantee an accurate friction potential estimation. In [PERSON] et al. [9] the _Magic Formula_ type model was employed to infer the road friction potential from the tyre SAT and the axle lateral slip. Specifically, the authors employed a random-walk EKF to estimate the axle lateral, longitudinal and vertical forces and vehicle planar motion states from signals readily available on the CAN bus of modern vehicles. The front axle lateral forces, in addition to the angle steered by the front wheels and the steering tie rod forces, were employed to estimate the individual tyre SATs from a Neural Network structure, Figure 19. The NN training was carried out using simulation data from a multi-body simulation model. Finally, the road friction potential \(\mu_{\text{max}}\) was obtained from a _Magic Formula_ tyre model using an interpolation algorithm and the pair \((\alpha_{f},\tau_{a})\). Despite the fact that several simulation results are presented in the multi-body simulation software MSC ADAMS the analysis is focused on the observer accuracy, and further conclusions on grip utilisation levels could not be extracted. To conclude with the model-based approaches, solutions employing the friction similarity method presented in [67] have been found in [35; 121]. [PERSON] et al. [121] integrated an UKF to estimate the vehicle planar motion states and a tyre-road friction estimator in a hybrid fashion. In this case, the maximum tyre SAT approach introduced in [118] is employed to estimate the road grip potential during medium  
Figure 19: Estimation structure described in [PERSON] et al. [9]. Figure adapted by the authors from [9]. lateral slip levels. For higher excitations, a full sliding model is considered. Fishhook manoeuvres are simulated in Carsim at three different road friction levels: high mu, low mu, and mixed mu. As additional manoeuvres at lower excitation levels (e.g., slalom) are not provided it is not possible to establish a fair comparison with the results described in [118]. [PERSON] et al. [35] presented an EKF observer to estimate the road friction potential from yaw rate, speed, steering wheel angle and EPS current measurements. Specifically, a simplified single-track yaw-sideslip vehicle model was employed in the EKF to estimate the vehicle planar motion states and the road friction potential, modelled as a random-walk variable. A simplified suspension and steering kinematics model was employed to translate the total axle alignment torque to the tyre SAT, neglecting the jacking torques at each wheel, assuming that cancel each other. The authors proposed a sigma-modification method in order to keep the road friction potential estimates within realistic limits.