# Adaptive Cruise Control with Look-Ahead Anticipation for Driving on Freeways
## 2 Look-Ahead Anticipatory Scheme of Adaptive Cruise Control
### Anticipatory Feature with ACC  
It has been intensively investigated that the predictive control of vehicles can provide improved driving behavior. In such predictive control schemes, using the predicted future states of the preceding vehicle, the optimal control input is obtained in such a manner that the vehicle can avoid any aggressive acceleration in subsequent time. In order to incorporate such predictive features in the existing ACC, a simple look-ahead scheme of making anticipatory driving decisions with negligible computation cost is proposed. The term _look-ahead_ refers to making the appropriate plan by anticipating what will occur in the future. For the sake of simplicity, the proposed look-ahead anticipatory scheme of ACC is referred to as _La-ACC_, henceforth, in the paper. In particular, as illustrated in the conceptof the proposed La-ACC in Figure 1, the relative states of both the host and preceding vehicles are determined for a short look-ahead horizon \(h_{\text{la}}\), and using such a predicted state, the standard decision function of ACC is used to take a control action. Specifically, for a look-ahead horizon \(h_{\text{la}}(t)\), the control decision of the proposed La-ACC is described by a function \(f_{\text{lacc}}\) as follows:  
\[a_{\text{h}}(t) = f_{\text{lacc}}(z_{\text{h}}(t),z_{\text{p}}(t),\bar{a}_{\text{p} }(t)) \tag{5}\] \[= f_{\text{acc}}(z_{\text{h}}(t+h_{\text{la}}(t)),\bar{z}_{\text{p} }(t+h_{\text{la}}(t))),\]  
where \(\bar{a}_{\text{p}}(t)\) denotes the estimated average acceleration of the preceding vehicle in the horizon, \(z_{\text{h}}(\cdot)=[\bar{x}_{\text{h}}(\cdot),\bar{v}_{\text{h}}(\cdot)]^{\top}\) and \(z_{\text{p}}(\cdot)=[\bar{x}_{\text{p}}(\cdot),\bar{v}_{\text{p}}(\cdot)]^{\top}\) denote the respective look-ahead states of the host and preceding vehicles. Specifically, they are obtained as follows. \[\bar{v}_{\text{h}}(t+h_{\text{la}}(t)) = v_{\text{h}}(t), \tag{6}\] \[\bar{v}_{\text{p}}(t+h_{\text{la}}(t)) = v_{\text{p}}(t)+\bar{a}_{\text{p}}(t)h_{\text{la}}(t),\] (7) \[\bar{x}_{\text{h}}(t+h_{\text{la}}(t)) = x_{\text{h}}(t)+v_{\text{h}}(t)h_{\text{la}}(t),\] (8) \[\bar{x}_{\text{p}}(t+h_{\text{la}}(t)) = x_{\text{p}}(t)+v_{\text{p}}(t)h_{\text{la}}(t)+0.5\bar{a}_{\text {p}}(t)h_{\text{la}}^{2}(t). \tag{9}\]  
La-ACC given by (5) uses the gains and parameters of the original ACC but with the predicted relative states of the host and the preceding vehicles. At low speeds with a short gap, a long look-ahead horizon may cause undesired oscillations, since the acceleration of the preceding vehicle is often uncertain and noisy. Therefore, the look-ahead horizon \(h_{\text{la}}\) is tuned dynamically as follows:  
\[h_{\text{la}}(t)=\left\{ \begin{array}{ll}h_{\text{max}}\beta^{-1}v_{\text{ h}}(t),&\text{if }v_{\text{h}}(t)\leq\beta,\\ h_{\text{max}},&\text{otherwise},\end{array} \right. \tag{10}\]  
where \(\beta\) is a constant, and \(h_{\text{max}}\) is the maximum look-ahead horizon in second. Depending on speed \(v_{\text{h}}\), look-ahead horizon \(h_{\text{la}}\) is tuned linearly from 0 to \(h_{\text{max}}\) when the speed varies from 0 to \(\beta\). Such tuning at a low speed helps avoid any oscillatory decision due to the presence of the preceding vehicle at a short gap. The key parameter of this look-ahead approach is the acceleration of the preceding vehicle \(\bar{a}_{\text{p}}(t)\). In the case of connected-cooperative driving, such information can be provided directly by the preceding vehicle. In the traditional unconnected driving scenario considered in this study, \(\bar{a}_{\text{p}}(t)\) is estimated by using the recent speeds of the preceding vehicle according to a _conditional persistence prediction_ technique [30].