## 3 Slip-Based Road Friction Monitoring
### Tyre Self-Alignment Torque
The proposed estimator was validated experimentally in a mu-jump transition (asphalt \(\mu_{\text{max}}=0.9\) to basalt tile \(\mu_{\text{max}}=0.2\)). The results evidenced an accurate detection of the mu transition under a reduced lateral excitation level (\(|a_{y}|<2\) m/s\({}^{2}\)). Regarding tyre model-less approaches, relevant works have been presented in [10; 124; 125; 126; 127; 128]. To start with, [PERSON] and [PERSON] [10] presented a data-based approach using Neural Networks to estimate the road friction potential. Specifically, two NN were concatenated to recognise the road grip potential: the first to estimate the tyre forces in the three axes and tyre SAT when fed by the steering wheel angle, forces on the king pin, force on the steering link and suspension inclination angle. The second NN was aimed at estimating the wheel slip and friction potential from the outputs of the preceding structure. A grip utilisation threshold (\(\mu=0.3\)) was set to limit the friction potential estimation to situations in which a certain excitation is present. The NN was trained with data from surfaces of \(\mu_{\text{max}}=0.8\) and \(\mu_{\text{max}}=0.3\). In a second step, data not included on the training dataset were employed to validate the estimation structure. Despite accurate results are obtained, only a reduced number of test cases are presented, and therefore a more comprehensive analysis regarding the extrapolation ability of the proposed NN cannot be assessed. In addition to this work, the authors provided further details regarding the NN structures on [68]. An alternative tyre model-less approach was proposed by [PERSON] et al. in [124] to detect slippery road segments. In this case, steering torque thresholds corresponding to a high mu asphalt road are defined for different vehicle speeds. At each time step, the current steering wheel torque measured by the EPS system is compared to the dynamic thresholds representative of high-mu situations. If significant differences are appreciated, the low mu road flag is triggered, and the EPS steering friction is augmented slightly with the aim to maintain a constant steering effort. Moreover, the authors proposed an additional algorithm to detect off-road segments from the wheel speed fluctuations. In this case, it is pursued to have more robustness against kick forces induced by the irregularities rather than the detection of the road grip potential. As the detection of \(\mu_{\text{max}}\) is not the main aim of this work, additional results or discussion on this topic is not provided. Other tyre model-less works have focused on providing a relative measurement of the remaining road friction, known as the lateral grip margin (LGM), and defined as \(LGM=\mu_{\text{max}}-\mu\), rather than trying to estimate the real value of \(\mu_{\text{max}}\)[125; 126; 38; 119]. [PERSON] et al. [38] defined the LGM as:  
\[LGM=\frac{\tau_{cur}}{(\partial\tau/\partial\alpha)_{0}\cdot\alpha}=1-\frac{F _{y}}{\mu_{\text{max}}F_{z}} \tag{51}\]  
where \(\tau_{cur}\) is the current tyre SAT and \(\partial\tau/\partial\alpha\) is the tyre SAT stiffness. In brief, the LGM is defined as the ratio between the tyre SAT measured on high mu conditions and the current tyre SAT (assuming that the tyre lateral slip remains within the tyre SAT linear limits), Figure 20.  
In [38] a modular structure is presented to estimate the tyre SAT from the EPS signals, and the tyre lateral slip required to compute the LGM is calculated with a single-track yaw-body slip observer. The authors provided an interesting analysis regarding the sensitivity of the LGM to the grip utilisation level. Specifically, the authors evidence that the LGM presents an earlier sensitivity to low-mu surfaces compared to other metrics such as the yaw rate deviation. [PERSON] et al. [119,125] continued with this research line. The authors enhanced the previous approach to account for the influence of the longitudinal forces.