Page - 57 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

5.1. Path Prediction CG β rrα frα ICR fl rl x0 y0 zωv rrW rrv frv R frW flW flv rlα rlv rlW xwfr ywfr lrα lδ rδ xwfl ywfl ywrl xwrl xwrr ywrr br 2 br 2 xv yv v Figure 5.1.: Coordinate systems at all four wheels of the vehicle reads κay = vay vv2x . (5.2) If the wheel speeds are available, the curvature can be estimated using the difference between the wheel speeds of the left and right wheel at a non-driven axle. This method only works if the longitudinal slip and the side slip angle at the considered wheels are small. Figure 5.1 shows the speeds at the four wheel points and the corresponding coordinatesystems. Assumingsmall sideslipangles, thespeedsat thewheelpointsequal the speed in the x-direction of the corresponding coordinate system, e.g. αrl 1rad leads to ‖vrl‖≈wrlvx. The longitudinal speeds of the rear wheels and the CG read wrlvx= vvx− br 2 vωz, (5.3) wrrvx= vvx+ br 2 vωz and (5.4) vvx=R vωz. (5.5) Thevariableswrlvx andwrrvx are the longitudinal speedsat theWrl andWrr-points, vvx is the longitudinal vehicle speed at CG, vωz is the yaw rate of the vehicle, and br is the track width at the rear axle, which is the non-driven axle. Solving eqs. (5.3) to (5.5) for 1 R leads to κ∆v= 2(wrlvx−wrrvx) br (wrlvx+wrrvx) . (5.6) 57