# Adaptive Cruise Control with Look-Ahead Anticipation for Driving on Freeways
## 3 Evaluation of the Proposed La-ACC
### Evaluation of the Proposed La-ACC on a Single Vehicle  
At first, the influence of the maximum look-ahead horizon \(h_{\text{max}}\) on the generated acceleration by La-ACC is observed and shown in Figure 2. In this observation, the host vehicle is running at a speed of 80 km/h with a gap of 30 m from its preceding vehicle. Three different relative speeds and, for each, three distinct accelerating cases of the preceding vehicle are separately analyzed. Figure 2a shows the case when both the preceding and host vehicles are running at the same speed of 80 km/h (i.e., \(\Delta V_{\text{p}}=v_{\text{h}}-v_{\text{p}}=0\)). For instant acceleration \(a_{\text{p}}=0\) of the preceding vehicle, i.e., both vehicles are at equilibrium states, La-ACC generates zero acceleration for any look-ahead horizon (i.e., for 0 to 2 sec as shown in the horizontal axis). Note that when the look-ahead horizon \(h_{\text{la}}\) is zero, La-ACC is exactly equivalent to ACC. However, when \(a_{\text{p}}=-0.25\) or \(a_{\text{p}}=0.25\) for the same speed of both vehicles, La-ACC with a longer horizon generates acceleration by aligning to the decelerating/accelerating trend of the preceding vehicle.  
Figure 2b,c show similar cases when the preceding vehicle has a relative speed \(\Delta V_{\text{p}}=-2\) km/h and \(\Delta V_{\text{p}}=2\) km/h, respectively. Even when \(a_{\text{p}}=0\), La-ACC exhibits higher sensitivity than ACC by reflecting the look-ahead states. Often, the speed of a vehicle does not change monotonically in varying dense traffic; therefore, a long horizon may not be suitable for realizing smooth driving.  
Next, La-ACC with 1 s look-ahead horizon is evaluated by controlling a host vehicle in two typical scenarios, as shown in Figure 3. In addition, by visualizing the speed and acceleration characteristics of the host vehicle, the quality of driving is also evaluated quantitatively by measuring its performance index and fuel consumption. A typical performance index \(J(v_{\text{h}}(t),a_{\text{h}}(t))\), generally employed in the optimal vehicle control problem, is defined as the integral of the weighted driving cost as follows:  
\[J(v(t),a(t))=\int_{t=0}^{30}(w(V_{\text{max}}-v_{\text{h}}(t))^{2}+a_{\text{h} }^{2}(t))\text{d}t, \tag{17}\]  
for this evaluation of 30 s of driving. The parameters are set as \(w=0.001\) and \(V_{\text{max}}=27.78\) m/s (same as the maximum speed of the preceding vehicle). A low value of \(J\) is desired as it indicates less deviation from the desired speed and low acceleration or braking. Although \(J\) does not include the vehicle's fuel consumption, the inclusion of the square of speed deviation and the square of acceleration relates \(J\) with fuel consumption indirectly as found from various fuel consumption models, e.g., [37; 39]. In Figure 3, Scenario I shows the case when the preceding vehicle speeds up from 65 km/h to 100 km/h in 0 to 15 s, and Scenario II shows the case when the preceding vehicle slows down from 100 km/h to 80 km/h in 0 to 8 s. The instantaneous speed and acceleration characteristics of La-ACC and ACC, taken from independent simulation for the same condition, are shown by red and blue curves,  
Figure 2: Acceleration characteristics of La-ACC for varying look-ahead horizon at different speeds and accelerating conditions of the preceding vehicle. The object vehicle is at 80 km/h speed with a gap of 30 m from the preceding vehicle.  
respectively, in each scenario. The speed of the La-ACC vehicle results in less overshoot and converges earlier than the ACC vehicle. For the observed period of 30 s, La-ACC attains a better performance index and lower fuel consumption compared to ACC. Both qualitative and quantitative comparisons indicate the advantages of La-ACC over ACC.