# On-Board Road Friction Estimation Technique for Autonomous Driving Vehicle-Following Maneuvers
## 7 Performance Analysis  
The co-simulation platform described in Section 6 has been exploited to assess the effectiveness of the proposed grip-aware functionalities. The illustrative results, reported in the following, refer to a vehicle-following process along a typical motorway where the ego vehicle moves with an initial velocity of \(v(0)=30\) m/s, having an initial space gap \(d(0)=90\) m from its predecessor (leader) that moves with an initial speed of \(v_{lead}(0)=20\) m/s. The leader is a human-driven vehicle emulated through SUMO, whose realistic velocity profile accounts for both speed limits and driver imperfection parameters (details on how to model the human-drivers via SUMO can be found in [62] and references therein). Further characteristics parameters of the road scenario, as well as the ones for the controller, are summarized in Table 1.  
Figure 6: Co-simulation Platform. The first exemplar driving scenario refers to vehicles moving in the presence of heavy rain, with actual road grip \(\mu=0.5\). Due to the presence of an obstacle, at the time instant \(t=150\) s the leading vehicle performs a sudden hard-brake inducing the maximum deceleration allowed by the road grip, i.e., \(\mu g\). Results in Figure 7 show how leveraging the on line estimation of the actual road condition (reported in Figure 7c), the ego vehicle is able to safely perform the velocity tracking while always preserving the desired safe space gap about \(d_{des}(t,\tilde{\mu})\), depending on the grip estimate. In addition, it is worth to note that the emergency brake is safely performed and vehicles correctly reach the required standstill distance when they finally stops without colliding. According to the theoretical derivation, the Predictive ACC also guarantees both acceleration and jerk of the ego vehicle fulfill the comfort constraints until the leading vehicle performs the hard brake at time instant \(t=150\) s (see Figure 8). Indeed, from this time instant the ACC tries to handle this hazardous braking maneuver, but the necessity of hard deceleration leads to the activation of the AEB, which hence commands the maximum braking torque to be imposed, obviously ignoring the comfort constraints which have less priority w.r.t. the safety. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Value** \\ \hline \(m\) & vehicle mass & 1521 [kg] \\ \(I_{z}\) & chassis moment of inertia & 2875 [kg \(\cdot\) m\({}^{2}\)] \\ \(I_{f}\) & distance c.o.g.-front axle & 1.2 [m] \\ \(I_{r}\) & distance c.o.g.-rear axle & 1.6 [m] \\ \(C_{x}\) & longitudinal drag coefficient & 0.28 \\ \(I_{w}\) & wheel moment of inertia & 1 [kg \(\cdot\) m\({}^{2}\)] \\ \(R_{r}\) & wheel radius & 0.315 [m] \\ \(h\) & height c.o.g. & 0.54 [m] \\ \hline \(\tau\) & driveline constant & 0.05 [s] \\ \(\widetilde{\tau}_{H}\) & headway time & 1.1 [s] \\ \(d_{0}\) & minimum spacing & 2 [m] \\ \(T_{s}\) & ACC sampling time & 0.1 [s] \\ \(H_{p}\) & ACC prediction horizon & 15 \\ \(H_{c}\) & ACC control horizon & 15 \\ \(\Delta u_{min}\) & ACC minimum control & \(-0.1\) [m/s\({}^{2}\)] \\ \(\Delta u_  
Figure 8: Road-Grip aware Driving Functionalities: vehicle-following and hard emergency braking. Time-history of the ego-vehicle acceleration (**a**), jerk (**c**), front tire (**b**) and rear tire (**d**) longitudinal slip ratios. Figure 7: Road-Grip aware Driving Functionalities: 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. \(\widetilde{\mu}\).