Page - 64 - 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 5.2. Natural Coordinates This chapter introduces natural coordinates that are beneficial in the mathematical treatment of the object selection algorithms in chapter 5.3. For the selection of the OTF, the position of each object relative to the predicted path has to be found. Figure 5.4 illustrates a situation with two target objects, a truck and a car. The reference point is measured by the Radio Detection and Ranging (RADAR) sensor in the sensor coordinate system with the position vector ssj = [ sxj syj ]T for the j-th object. The same point has the coordinates nsj = [ sj uj ]T in the natural coordinate system (s,u) with its origin in the CG of the ego vehicle. The s-component is measured along the predicted path, and the u-component is measured perpendicular to the predicted path. In general, the predicted path is given with a number of ipoints in the vehicle coordinate system. Figure 5.5 illustrates the predicted path at time tk with four points ( xˆi−1|k , yˆi−1|k ) to ( xˆi+2|k , yˆi+2|k ) and three measured points (vxj,vyj), (vxr,vyr) and (vxt,vyt) in the vehicle coordinate system. For the calculation of the natural coordinates of that point, the point (vxq,j,vyq,j) has to be found first. In the presented case, it does not matter if the calculation is done in the vehicle, sensor or global coordinate system. Hence, the index for the coordinate system is left for further considerations. The equations for two straight lines are set up that read σi: [ xq,j yq,j ] = [ xˆi|k yˆi|k ] +ki,jpi and (5.27) ηi: [ xq,j yq,j ] = [ x1 y1 ] +mi,jni, (5.28) where thescalarquantitieski,j andmi,j are theunknowns. Thestraight lineσi isparallel to the longitudinal coordinate for the i-thpathelement, andηi corresponds to the lateral coordinate. The vectors pi and ni are defined by pi= [ pi,x pi,y ] = [ xˆi+1|k− xˆi|k yˆi+1|k− yˆi|k ] and (5.29) ni= [−pi,y pi,x ] . (5.30) Equations (5.27) to (5.30) can be solved for ki,j. If ki,j ∈ [0,1], then the coordinates (xq,j,yq,j) could be found using eq. (5.27). The lateral distance to the path reads dj= √ (xj−xq,j)2 +(yj−yq,j)2. (5.31) 64