Page - 32 - in Maximum Tire-Road Friction Coefficient Estimation

2 Estimation of the friction potential thedynamic reactionof either the tire or thewholevehicle, seeFigure2.10. Due to their importance for thiswork, vehicle-dynamics-basedapproacheswillbediscussed ingreater detail. Tire-related methods comprise direct measurement methods with sensors imple- mented directly in the tire tread or the wheel rim, e.g. [GH04] , [BBB+02], as well as [TSH+08], and also indirect methods that use effects such as the dependence be- tween the friction potential and the rolling sound of the tire, e.g. [ER92] and [BER92]. Tire-sound-dependent methods are very sensitive to factors other than from the friction potential. Vehicle-dynamics-based approaches Lex et al. haveproposedaclassification systemfor categorising the largenumberofpub- lishedvehicle-dynamics-basedapproaches fordetermining the frictionpotentialbasedon mathematical and physical characteristics, [LEH11]. In the proposed classification sys- tem, the mathematical methods for estimating the friction potentials are divided into algebraic, statistical, observer-based and optimization-based methods, see examples in Table 2.2. Algebraic approaches, such as Holzinger, [Hol92, p.18-46], have disadvan- tages when dealing with measurement uncertainties, because they do not integrate any observer or optimization. In this classification system, statistical approaches are also considered observer-based approaches, but they are situated within a Bayesian frame- work and thus comprise methods such as Kalman and particle filtering. Due to their significance for thiswork, someof these statisticalmethodsaredescribedbelow. Mostof the methods can be classified as either algebraic approaches or non-statistical observer- based approaches. Table 2.2 shows two examples, Ahn et al., [APT09] and Hsu et al., [HLGG06]. For other observer-based approaches, see Lex et al., [LEH11]. Optimiza- tion methods include recursive least square approaches and Fuzzy Logic as proposed by Ivanov et al., [ISAA10], or artificial neural networks (ANN) as proposed in Lex et al., [LKE13a]. The physical classification considers whetherµmax is estimated by using a direct relation with the longitudinal slip or the side slip angle, or by using another physical quantity that is related to µmax, such as the lateral acceleration and the yaw rate, as shown by Ding et al., [DT10] or the aligning torque, as shown by Hsu et al., [HLGG06]. For further examples and literature references, see also Table 2.2 and Lex et al., [LEH11]. Since many methods have been published, some exemplary methods will be mentioned that are relevant for the method proposed in this work. These mainly include methods that are directly related to slip quantities, as well as methods within the Bayesian framework, see Section 5 for a definition. 32