Page - 97 - 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 B.1. Lateral Vehicle Dynamics The Single-Track Model (STM), illustrated in fig. B.1, is frequently used to model the lateral dynamics of the vehicle for controller design. It was introduced by Riekert et al. in the year 1940, [RS40]. According to [HW10], the simplifications for this model are that 1. both wheels of each axle are located at the centre line of the vehicle, 2. the Center of Gravity (CG) height equals zerohCG= 0, 3. only small lateral accelerations vay≤4m/s2 occur, 4. the steering angle is small δ 1rad, and 5. the longitudinal vehicle speed vvx is constant. In general, the equation of motion for the STM of fig. B.1 reads  m 0 00 m 0 0 0 vIzz     vv˙xvv˙y vω˙z   =m   vωz vvy−vωz vvx 0   +2   vfFx+vrFx vfFy+vrFy vfFy lf−vrFy lr   , (B.1) wheremdescribes the vehicle mass and vIzz the moment of inertia of the vehicle around the vz-axis. The state variables vvx, vvy and vωz are the translatoric and rotational speedsofthevehicle inthe(0x,0y)planeoftheglobalcoordinatesystem. Thedimensions lf and lr are the distancesbetween theCGandthe frontand rear axle. Thewheel forces