## 3 Slip-Based Road Friction Monitoring
### Lateral Dynamics
[PERSON] and G\(\ddot{\text{o}}\)hlich [110] employed a Bayes-based estimator in combination to a General Regression Neural Network (GRNN) estimator. Specifically, the GRNN is employed during low excitation levels (\(|\alpha|<0.05\), \(|\lambda|<0.02\)), while the Bayes-based estimator is employed at high slip values. Finally, acceleration-braking and lane change simulations performed in Carsim are presented. Further conclusions regarding grip utilisation levels are difficult to extract. Alternative approaches have been proposed in the literature apart from the model-based solutions described previously. To start with, a data-based approach was proposed by [PERSON] et al. [112]. This time authors presented a back-propagation (BP) Neural Networks structure to estimate the road friction potential from wheel speed, tyre longitudinal slip, yaw rate, longitudinal and lateral acceleration, and steering wheel angle values. A two-hidden-layer structure composed of ten neurons each is trained from simulation data obtained with veDYNA vehicle dynamics simulation software. Authors highlight that the approach still presents significant drawbacks (e.g., estimation may become inaccurate if the simulation model employed during the NN training does not match the real vehicle) and further improvements are to be performed. In the paper by [PERSON] and [PERSON] [3] an observer composed of three Neural Network structures is proposed to estimate the friction potential. In particular, RLS is  
Figure 16: Estimation structure proposed by [PERSON] et al. [99]. Figure adapted by the authors from [99]. applied to extract the maximum road grip from a linear interpolation model. In order to avoid large errors during reduced excitation levels (e.g., straight-line driving) the estimation is carried when a certain lateral acceleration level is present (\(|a_{y}|>1.5\) m/s\({}^{2}\)). Overall, grip utilisation levels ranging from 40 to 80% are required to estimate the road friction potential. In [PERSON] et al. [114] a novel approach based on the three-axis wheel accelerations is provided. A parametric model of the form  
\[ \begin{bmatrix}\dot{a}_{x}^{i}\\ \dot{a}_{y}^{i}\end{bmatrix} = \begin{bmatrix}\mu_{x}^{i}\\ \mu_{y}^{i}\end{bmatrix} (\dot{a}_{z}^{i}+g)=\theta^{T}\phi \tag{47}\]  
is proposed to estimate the friction utilised by each tyre. Individual wheel accelerations are obtained from the vehicle body accelerations, which are measured using a six-degree-of-freedom (6-DoF) inertial motion unit, and RLS and Gradient Estimator (GE) are applied to estimate the vector of parameters \(\theta=[\mu_{x},\mu_{y}]\). The authors validated the proposed grip utilisation observer under emergency braking manoeuvres on dry asphalt. Despite the fact that it is indicated that the friction potential can be calculated from the friction consumption level additional results in this line are not provided. A tyre model-less approach was presented by [PERSON] et al. in [20]. In this case, the grip utilisation levels during braking \(\mu_{abs}\), driving \(\mu_{tsc}\), and cornering \(\mu_{ayc}\) manoeuvres are employed in a signal fusion fashion to obtain a \"comprehensive\" road friction estimate (\(\mu_{comp}\)), defined as  
\[\mu_{comp}=\frac{k_{1}\mu_{abs}+k_{2}\mu_{tsc}+k_{3}\mu_{ayc}}{k_{1}+k_{2}+k_{3}} \tag{48}\]  
where \(k_{1},k_{2},k_{3}\) are certainty factors computed from the tyre slips and the chassis accelerations. A rule-based approach is presented in order to update the friction estimates during braking and cornering manoeuvres only when the utilised friction is closed to the maximum road friction level. A Fuzzy logic controller is adopted to achieve the previous task during driving events. Experimental results were reported on dry asphalt, packed-snow, and icy roads for emergency braking manoeuvres, lane change, hard acceleration, slalom, and steady-state cornering driving. Overall, the validation of the algorithms focuses on limit handling manoeuvres, and additional conclusions on low excitation levels cannot be extracted.