# On-Board Road Friction Estimation Technique for Autonomous Driving Vehicle-Following Maneuvers
## 3 Problem Statement and Control Architecture  
Consider a front-wheel driven vehicle where the propulsion is obtained through an electric engine. Moreover assume the vehicle is equipped with proprioceptive sensors for the measurement of its state variables (e.g., chassis velocity, acceleration, yaw rate, and tires' angular velocities), as well as with exteroceptive sensors (e.g., radar, camera, lidar, or a combination of these) for the sensing of the external environment and for the mapping of external obstacles (details on sensing technologies can be found in [44] and the corresponding references). The aim of this work is to describe a methodology capable to perform the autonomous vehicle-following process in a safe, controlled and comfortable manner even in poor weather conditions, like ice, snow and heavy rain, starting from the information available thanks to a computationally cost effective model-based tire-road friction coefficient technique. The data from proprioceptive sensors are collected in run-time, processed with the physical model-based estimator and, then, employed in loop with a vehicle control logic. From the point of view of the control, the objective is to develop grip-aware functionalities in order to improve driving performance and safety, starting from the strategies for ACC, AEB and ABS longitudinal maneuvers, leveraging the on-board estimation of the road conditions. To achieve the above mentioned tracking capability, the ACC system has not only to safely adjust the ego-vehicle speed to approach the velocity of the leading vehicle, but it has also to keep the vehicle spacing to an expected value \(d_{des}\) that must be adaptable on the base of the estimated road grip, as:  
\[d(t)\to d_{des}(t,\mu), \tag{1}\] \[\Delta v(t)\to 0, \tag{2}\]  
where \(v(t)\) is the ego vehicle velocity measured on-board by proprioceptive sensors, while \(d(t)\) is the distance between the ego vehicle and the leading one and \(\Delta v(t)\) is the relative velocity w.r.t. the leading \(v_{lead}\), computed leveraging the on-board exteroceptive sensors. Here, the grip-aware desired space gap \(d_{des}\) can be set according to the following the headway time rule [45]:  
\[d_{des}(t,\mu)=d_{0}+\tau_{H}(\mu)v(t), \tag{3}\]  
where \(d_{0}\) is the constant spacing at standstill and \(\tau_{H}(\mu)\) is the headway time to be properly adapted on the base of the road friction coefficient to be on-line estimated. In order to further reduce the risks of crashes, the ACC works jointly with the AEB that, sharing the same on-board sensors, continuously monitors the area in front of the car, automatically detects a risk and hence activates the vehicle braking system (via the ABS, Anti Brake-locking System) decelerating the vehicle with the purpose of avoiding or mitigating a possible collision. It follows that, unlike the ACC, the AEB is activated only when a collision index highlights the possibility of a crash. Here, we exploit the well-known TTC index [46] and the AEB is hence activated if its value is under some threshold depending on the estimate road conditions, as:  
\[TTC=-\frac{d(t)}{\Delta v(t)}<TTC_{th}(\mu),\quad\text{being }\Delta v(t)<0. \tag{4}\]  
When the emergency braking is requested by the AEB, the maximum torque is applied to the wheels via the ABS control chain. The wheel actuation systems decreases the longitudinal slip value, thus generating a braking force on the chassis. However, if the slip ratio is below the optimal value, depending on the actual road condition, the dynamics could become unstable with a consequent lock of the wheels. It follows that an efficient control strategy for automatic safe braking during emergency has to adapt the optimal slip value on the base of the estimation of the grip in order to enhance the performance of the ABS, and thus of the overall vehicle.