Page - 67 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

5.3. Object Selection 5.3.1.1. Constant Path Width With the Constant Path Width Algorithm, the trajectory is superimposed by a path with a constant width of b0, which is the simplest way to describe the predicted path, [WDS09]. A point is within the path if the condition |uj|≤ b0 (5.38) is fulfilled, where uj is the lateral coordinate of the point in the natural coordinate system. As already mentioned in eq. (5.37), an object is represented by a list of four points. There is a special case if a number of the points are outside the left path boundary and the rest of the points are outside the right boundary, e.g. |uj,fl|>b0, |uj,fr|>b0, |uj,rl|>b0 and |uj,rr|>b0 with uj,fl<0, uj,fr<0, uj,rl>0 and uj,rr>0. (5.39) Figure 5.6(a) gives an example of the special case of eq. (5.39). In such cases, an additional fifth point is added to the list of eq. (5.37) reading nsj,5 = [ min(sj,fl,sj,fr,sj,rl,sj,rr) 0 ] , (5.40) which can be described as the point with the minimum s-coordinate of the other four points and a zero u-coordinate in the natural coordinate system, see fig. 5.6(a). In this case, object j is in the predicted path. The OTF is the object with the smallest s-coordinate in the predicted path. 5.3.1.2. Non-Constant Path Width Another option is to use a Non-Constant Path Width, which should compensate for errors in the path prediction, [WDS09]. The function used is a polynomial of second order which reads b(s) =a1s 2 +a2s+a3, (5.41) where the coefficients a1 to a3 could be found using the definitions b(0) = b0, b(smax) = bmax and (5.42) db ds ∣∣∣∣ smax = 0. Figure 5.6(b) gives an example of b(s) for the parameters b0 = 2.2m, bmax= 3m and smax= 45m. Asshowninchapter5.3.1.1, theOTFcontainsthepointwiththeminimum s-coordinate fulfilling the condition |uj|<b(s). 67