Page - 32 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

2. Adaptive Cruise Control 10−20− 10 2000 1 0 1 0 1 40−80− 40 800 6− 03− 3 ms sss f mf tc c rd tf vf hd d sd a haza 100 0 20 0 0 2 [m/s]r˙e [m]re20− 100− 2− 4− (a) (b) mf: much faster f: faster ss: same speed s: slower ms: much slower vf: very far tf: too far rd: right distance c: close tc: too close ha: hard acc. a: accelerate za: zero accel. sd: slight dec. d: decelerate hd: hard dec. ]2[m/sdesa [m]re [m/s]r˙e Figure 2.19.: (a) Membership functionsµ and (b) resulting outputades for a fuzzy ACC lower level controller of [Ga¨c12] variables. For ACC systems, the fuzzy variables are the inter-vehicle distance and speed errors, er and er˙ of eqs. (2.23) and (2.24), and the desired acceleration ades. In his thesis [Ga¨c12], Ga¨chter defined a set of membership functions µ, which are depicted in fig. 2.19(a). An error of er =−30m cannot be clearly assigned to one membership function µier, see fig. 2.19(a). It results in µtc(−20) = 0.396 and µc(−20) = 1. All the other membership functions of the position error µier equal zero. This fuzzy as- signment (i.e. all the values between zero and one are possible for each membership function) gives the method its name, [Ada09a]. The membership function for a speed error of er˙ = 4m/s is µf(4) = 1. The operation, called aggregation, provides a logical connection between µier and µier˙. Ga¨chter used the logical and, which can be math- ematically described as minimum function, µtc,f = min{µtc(−20),µf(4)}= 0.396 and µc,f = min{µc(−20),µf(4)}= 1. This operation is carried out for all possible 25 com- binations of µier and µier˙. Table 2.2 shows the control rules in matrix form. There, it can be seen that both membership functions µtc,f and µc,f correspond to the slight 32