## 3 Slip-Based Road Friction Monitoring
### Lateral Dynamics  
A large number of solutions have been presented in the literature in order to extend the operating range of the friction potential estimation to manoeuvres in which the vehicle lateral dynamics are excited (e.g., lane change). Such approaches present a higher flexibility and can perform an accurate grip estimation during acceleration, braking and cornering events. In other cases, the friction potential estimation is limited to cornering manoeuvres and the longitudinal dynamics are disregarded. A comprehensive discussion on pure lateral and combined (lateral and longitudinal) dynamics is presented in this subsection. The majority of the solutions proposed in the literature are predominantly model-based approaches [8; 23; 34; 43; 98; 99; 100; 101; 102; 103; 104; 105; 106; 107; 108; 109; 110; 111], and differ depending on the technical solution adopted to infer the friction potential from the parameterised friction or tyre force model (e.g., Unscented Kalman filter (UKF) [8] or Bayesian Hypothesis selection [43; 111]). Apart from this dominant group, additional solutions have been proposed using data-based [3; 112], rule-based [20], self-excitation [113], or wheel acceleration-based approaches [114]. These will be briefly discussed in the following. To start with, [PERSON] et al. [8] proposed a UKF based on a two-track vehicle model to estimate the vehicle states and augmented the vector of states with the road friction potential, modelled as a random walk variable. A simplified _Magic Formula_ tyre model was embedded into the UKF and the vehicle states and friction potential were calculated from lateral acceleration, yaw rate, and wheel speed measurements. The UKF was tested experimentally on ABS braking manoeuvres and lane change tests performed on dry asphalt and ice surfaces. In this case, the analysis was focused on limit handling manoeuvres, and additional details regarding the grip utilisation thresholds to infer the road grip were not provided. The same concept was applied in [PERSON] and [PERSON] [98]. A simplified single-track modelisation was proposed this time, and an _arctangent_ tyre model was implemented in an Extended Kalman Filter (EKF). The observer is simulated on high and low mu surfaces using  
Figure 13: Active force excitation strategy proposed by [PERSON] et al. [96]. IPG-CarMaker under limit steering inputs but grip utilisation levels are not provided. An EKF was also employed in [PERSON] et al. [102], and a _Dugoff_ type model was adopted to estimate the road friction potential. Contrary to the approached adopted by [PERSON] et al. [8], [PERSON] et al. estimated the longitudinal forces in a separated block (using a wheel rotating dynamics-based approach [53]), and limited the friction potential estimation to pure lateral dynamics events. The vehicle responses were simulated using veDYNA software and different limit double lane change manoeuvres were performed in surfaces of \(\mu_{\max}=0.9\) and \(\mu_{\max}=0.5\). Additional discussion on grip utilisation thresholds is not provided. [PERSON] et al. [101] performed the estimation of the friction potential and the tyre forces using a two-step approach, Figure 14. In first place, the tyre forces are modelled as random walk variables and estimated in addition to the vehicle planar motion states in a EKF structure using readily available CAN measurements. These estimates are then used in a second EKF structure to calculate the lateral and longitudinal tyre stiffness (\(C_{\lambda},C_{\kappa}\)), and the friction potential coefficients in the longitudinal and lateral directions \(\mu_{\max,x},\mu_{\max,y}\). In addition, a novel tyre model of reduced complexity is proposed. Simulations are carried out on high and low mu surfaces under pure braking, pure steering, and combined limit inputs. Additional braking tests were simulated under lower excitation levels and the observer experienced some difficulties to converge to the true maximum friction potential values. The same two-step approach was followed in [PERSON] et al.