Page - 61 - 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 as δi|k(i) =      δke δ˙k δk i∆t for δ˙k δk≤0 and δk [ 1+q ( 1−e− δ˙k qδk i∆t )] for δ˙k δk>0, (5.18) where q is a tuning parameter. The condition δ˙k δk≤ 0 means that the steering wheel angle δk and its velocity δ˙k have opposite signs. This could be interpreted as“steering out of the corner”. The other condition δ˙k δk> 0 means that both quantities have the same sign, meaning“steering in the corner”. For long prediction horizons, meaning the limit i→∞, the function values read lim i→∞ δi|k= { 0 for δ˙k δk≤0 and (1+q)δk for δ˙k δk>0. (5.19) In eq. (5.19) it can be seen that q scales the maximum value of the steering angle. Aditionally, eq. (5.18) ensures a smooth transition from the measured to the predicted values for δ and δ˙, meaning for i= 0, δ0|k = δk and δ˙0|k = δ˙k. Figure 5.3 shows an example of a measurement for the steering wheel angle δSW and the steering wheel velocity δ˙SW. Both graphs show the measurement until the time tk = 56s as solid black graphs and the predicted values in grey. Additionally, the future measurements are displayed as dashed graphs. However, at the time of the prediction, they were not available. It is impressive that the predicted values for δ and δ˙ seem to be a good input for the algorithm. In chapter 5.1.2, the input for the linear STM is the steering wheel angle δk for the whole path prediction. In comparison, the predicted values depicted in fig. 5.3 match the measured data very well, which leads to the conclusion that the prediction algorithm for the steering wheel angle delivers good results. If the parameter q of eq. (5.18) is set to small values, then the steering angle will stay nearly constant for the case δ˙kδk>0. For q= 0.05, it will only increase 5% from the initial value of δk, for the limit i→∞. The parameter q has to be found iteratively with simulations, which shows that low values give the best results. 5.1.4. Evaluation of Path Prediction Algorithms To evaluate the different path prediction algorithms, the predicted trajectory has to be transformed into the global coordinate system. The transformation reads  0xˆi|k0yˆi|k 0ψˆi|k   ︸ ︷︷ ︸ 0zˆi|k =   0xk0yk 0ψk   ︸ ︷︷ ︸ 0zk +   cos(0ψk) −sin(0ψk) 0sin(0ψk) cos(0ψk) 0 0 1     vkxˆi|kvkyˆi|k vkψˆi|k   ︸ ︷︷ ︸ vkzˆi|k +, (5.20) where 0ψk is thevehicleheading in theglobal coordinate systemat time tk, as illustrated infig.5.2. Thevector 0zˆi|kdescribes thepredictedpositionandorientationof thevehicle 61