# On-Board Road Friction Estimation Technique for Autonomous Driving Vehicle-Following Maneuvers
## 7 Performance Analysis
In so doing, the collision is safely avoided (see Figure 7), but higher acceleration and jerk can be appreciated during the braking until the stop, as shown in Figure 8. It is also worth to note that, when the emergency braking maneuver is commanded from AEB, than the ABS is responsible ensuring that the longitudinal slips of the tires are regulated to the optimal reference value \(\lambda^{*}\) returned by the friction estimator module as described in Section 4 (see Figure 8b-d). In order to clearly appreciate the enhancement of the here proposed grip-aware driving functionalities with respect to classical ACC, AEB and ABS strategies, the above maneuver has been repeated without leveraging the knowledge of the actual road-grip. Results in Figure 9 disclose that in this case the ACC is still capable of tracking the velocity references, while ensuring a desired gap that obviously depends only from the actual vehicle velocity, namely \(d_{des}(t)=d_{0}+\widetilde{v}_{H}v(t)\). However, when the leading vehicle performs the emergency hard brake, the safety distance results to be too small, the AEB is activated too late and it is impossible to avoid the collision that, hence, occurs at the time instant \(t=154\) s with a velocity of \(v\simeq 10\) m/s = 36 km/h. A further investigation of the achievable performance has been performed in the case when vehicles are moving in variable environmental conditions, i.e., the actual grip changes in time due to different climatic condition that have to be faced during travelling. Specifically, vehicle drives from dry asphalt to wet road, i.e., the actual maximum road grip starts from \(\mu=1\) and than decreases, into two steps, until \(\mu=0.5\) (see Figure 10c). The initial dynamic condition of the vehicles match the ones chosen in the previous driving scenario. Figure 9: Driving Functionalities without on-board road-grip estimate: vehicle-following and hard emergency braking. (**a**) Time-history of the current distance gap, \(d\), and of the desired one, \(d_{des}\). (**b**) Time-history of the ego velocity \(v\) and leader velocity \(v_{lead}\). Results depicted in Figure 10 show how the on-line road-grip estimate is performed with good precision (always below 1% at steady state). Furthermore, as the road grip decreases the safe distance is correctly adapted in order to provide a safer spacing with respect to the current adhesion (see Figure 10a) and the predictive ACC correctly tracks the reference values without any constraints violation. As in the previous driving scenario, at the time instant a \(t=150\) s an emergency situation emerges inducing the hard braking maneuver. Also in this case the combination of the grip-aware AEB and ABS is able of ensuring a safe stopping without collision. Final exemplar results refer to a typical Stop & Go scenario where continuous smooth accelerations and decelerations occur due to traffic congestion. In order to better assess  
Figure 10: Road-Grip aware Driving Functionalities in case of varying \(\mu\): vehicle-following and hard emergency braking. **(a)** Time-history of the current distance gap, \(d\), and of the desired one, \(d_{des}\). **(b)** Time-history of the ego velocity \(v\) and leader velocity \(v_{lead}\). **(c)** On-board road-grip estimate, \(\mu(t)\) vs. \(\tilde{\mu}\). the collision risk and the safety margins during traffic jam, we leverage the following well-known non-dimensional collision-index \(\gamma(t)\)[34]:  
\[\gamma(t)=\frac{d(t)-d_{br}}{d_{w}-d_{br}}, \tag{69}\]  
where \(d(t)\) is the actual distance between the vehicles, \(d_{br}\) is the breaking critical distance and \(d_{w}\) is the warning critical distance. Note that the above index witnesses the possibility of an incoming crash due to the current driving situation. Specifically, when it is positive and greater than the unity a safe situation is detected, while, if it is below the unity, a possible dangerous scenario is signalized.