Page - 58 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

5. Selection of the Object to Follow Table 5.1.: Comparison of the different curvature estimation algorithms according to [WDS09] Situation κωz κay κ∆v κδ Robust at low vehicle speeds ◦ −− − ++ Robust at high vehicle speeds ◦ ++ − − Another possible way to calculate the curvature is to use the linear Single-Track Model (STM), as described in appendix B.1. According to [HW10], the required lateral tyre forces can be calculated out of the second and third line of eq. (B.1) for quasistatic cornering when vωz= v v R . Due to simplifications 3 and 4 in appendix B.1, eq. (B.2) can be rewritten as wfFy=−fcy ( −δ+β+ lf R ) (5.7) for the front tyres and wrFy=−rcy ( β− lr R ) (5.8) for the rear tyres. Therefore, the required steering angle δ for a given vehicle speed vv can be calculated using δ(vv) = lf+ lr R︸ ︷︷ ︸ δA + m vv 2 (lf+ lr)R ( lr 2fcy − lf 2rcy ) , (5.9) where δA is the linearisation of the Ackermann steering angle describing the steering angle at low speeds, when the vehicle moves around ICR-A. According to [WDS09], eq. (5.9) can be solved to κδ= δ( lf+ lr+ mv2x lf+lr ( lr 2fcy − lf2rcy )). (5.10) Table 5.1 shows a comparison of the different algorithms described in eqs. (5.1), (5.2), (5.10) and (5.10) and evaluates them for high and low vehicle speeds. Since the se- lected algorithm should work in both speed ranges, the algorithm based on the yaw rate described in eq. (5.1) is the best compromise. For a given curvature, the predicted trajectory should be calculated in the vehicle co- ordinate system at time step k, (vkx,vky). To this end, two different approaches are available. The first one, described in [WDS09], is to calculate the trajectory using the parabola βyˆ= κ 2 d2, (5.11) where βyˆ is they-coordinate of the trajectory at a given distanced= √ βxˆ2 +βyˆ2 in the (βx,βy)-coordinate system. Figure 5.2 shows the newly introduced (βx,βy)-coordinate 58