Page - 100 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

B. Vehicle Dynamics xs ys′β x ′Fw y ′Fw s F const=zFw ‖Fw‖ maxF ∞F0dF X ′Fw const=zFw (a) (b) Figure B.2.: (a) Tyre characteristics for pure longitudinal or lateral tyre forces for con- stant tyre load wFz and (b) combined longitudinal and lateral tyre forces with generalized slip s, both according to [Hir09] In TMsimple, the pure longitudinal or lateral tyre forcewF ′ is described by wF ′=K sin [ B ( 1−e−|X|A ) sign(X) ] . (B.10) The variableX in eq. (B.10) is the corresponding slip quantity. For the longitudinal force, the slip readsX=sx, see eq. (B.9). In the lateral direction, the slip is defined as X=α, according to eq. (B.3). The parametersK,B andA are described in eq. (B.11), and fig. B.2(a) shows the physical parametersFmax,F∞ and dY0. K=Fmax B=pi−arcsin ( F∞ Fmax ) (B.11) A= 1 dY0 KB For thecombined lateral and longitudinal tyre forces, the side slipangleα is transformed to have the same unit as the longitudinal slip sx reaching the same initial stiffnes of the characteristics. The transformation is done using sy= α G(Fz) , (B.12) where theweighting factor isdefinedasG(Fz) = dFx0(wFz) dFy0(wFz) . Using the transformationde- scribed ineq. (B.12), thegeneralizedslipvector is introduced,whichreadss= [ sx sy ]T , 100