Page - 65 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

5.2. Natural Coordinates CG x0 y0 xs,xv yv ys jljw ju js jxs jys ru rs fl,j fr,j rr,j rl,j Figure 5.4.: Natural coordinates The sign ofuj can be found using uj=dj for n T i [ xj−xq,j yj−yq,j ] >0 and (5.32) uj=−dj for nTi [ xj−xq,j yj−yq,j ] <0. (5.33) The condition in eq. (5.32) shows that the vector ni and the vector from the point (xq,j,yq,j) to (xj,yj) have the same direction, while in the condition of eq. (5.33) they have opposite directions. In the example given in fig. 5.4, the lateral coordinates are uj< 0 and ur> 0. The longitudinal coordinate sj is the distance along the predicted path from CG to the point (xq,j,yq,j). There is a special case if ki,r> 1 and ki+1,t< 1, see points (xr,yr) and (xt,yt) in fig. 5.5. For this case, the coordinates are found using ki,r= 1 for the point (xr,yr) andki+1,t= 0 for the point (xt,yt), if the points are within the left part of the grey marked area. Usingki+1,t= 0 means that the straight linesσi+1 andηi+1 are used to find the coordinates for the point (xt,yt). To check if the points are within the grey area, the angle between the i-th and i+1-th trajectory segment have to be found using αi= arccos ( pTipi+1 ‖pi‖‖pi+1‖ ) . (5.34) The following conditions describe how to choose whether the point is in the left part of the grey area or in the right part. arctan ( (ki,r−1)‖pi‖ |ur| ) < αi 2 (5.35) leads to the left part, and arctan (−ki+1,t‖pi+1‖ |ut| ) < αi 2 (5.36) 65