# On-Board Road Friction Estimation Technique for Autonomous Driving Vehicle-Following Maneuvers
## 2 Related Work  
ADAS for the safe automatic driving mostly tackles the stabilization of the chassis longitudinal motion and the actuation of the emerging braking via a wide variety of control techniques. Among others, Model Predictive Control (MPC) has been effectively used in [24; 25; 26; 27; 28] in order to synthesize an ACC system. Regarding the AEB, typically event-based controllers have been realized through a continuous evaluation of the braking distance [29; 30] or the collision time [31]. Alternative formulations can be found in [32], where the authors classify the collision risk upon the definition of potential fields, or in [33] where an impedance controller is synthesized, thus resulting in a time based controller. Some ADAS combine ACC and AEB strategies for multiple driving situations: in [34] a Linear Quadratic Regulator (LQR) works jointly with a Time-To-Collision (TTC)-based logic and in [35] a Proportional-Integral-Derivative (PID)-based velocity control embeds a continuous time collision avoidance mechanism with the aim of reducing excessive jerk. More complex architectures can be found in [36; 37], where nonlinear MPC and reinforcement learning formulations have been designed for safely steering the longitudinal vehicle's dynamics. Attempts to account for the road conditions into specific ADAS driving features have only recently been developed; research of the tire-road friction estimation is a topic that has been extensively addressed and the study is continuing to this day. According to [38], it is possible to divide the different approaches on friction estimation into two main groups: experiment-based and model-based approaches. The experimental based methods use additional sensor measurement as optical or acoustic sensors and cameras to evaluate the friction based on the fact that wet asphalt is dark grey with a higher clarity of texture than dry asphalt [39]. The disadvantages associated with this category lie in the high frequency of these sensors get dirty, and therefore distort the results. In addition, the vehicles are generally not equipped with the sensors mentioned above and are difficult to maintain. With regard to the model-based group, the friction information is evaluated thanks to the mathematical models describing the vehicle system and its subsystems, starting from the information, measured by the sensors installed on the vehicle. Such methodology has demonstrated to be able to evaluate the actual grip in the most environmental condition, but not the potential grip. In [40], the authors experimentally evaluate a set of parameters, as peak friction, interaction shape and curvature factors, for different road environmental condition (dry, snow, ice) to estimate the tire stiffness. Then a run-time switch selects the set of parameters in memory corresponding to the current stiffness of the tire, leading to evaluate the potential grip. The limit of this approach is dictated by the number of parameters to be stored in the memory, able to describe the different asphalt conditions [41]. Differently from the [40], the friction peak value has been researched imposing relatively large magnitudes of braking/accelerating or steer inputs to achieve sufficient variations in tires' dynamic responses. To this purpose, a different speed control logics have been developed for the front and rear wheels in order to identify the stiffness and the tire road friction coefficient without severely influencing vehicle forward speed. However, these maneuvers may not be practical in every vehicle operating condition, as in [42], in which the tire-road friction estimator has been activated when the vehicle reached constant speeds. The latest methodology belonging to model-based approaches is the slip-slope [43], based on the assumption that in small slip ranges the correlation between slip and \(\mu\) could be represented by a linear function, and at higher values of slip ratio the normalized longitudinal interaction force is assumed to saturate.