# Adaptive Cruise Control with Look-Ahead Anticipation for Driving on Freeways
## 2 Look-Ahead Anticipatory Scheme of Adaptive Cruise Control
### Review of an Existing ACC  
The model of a commercially used ACC system is reviewed briefly according to [22; 23] for the convenience in developing its look-ahead scheme. The model is developed based on experimental data taken from the ACC equipped vehicles on test runs [22]. Acceleration of the host vehicle with ACC for regulating the gap or cruising was modeled as a function of the state (i.e., position and speed) of the host vehicle and the state of its preceding vehicle, if it exists within a specified range of \(R_{\text{th}}\). Acceleration decided by ACC at time \(t\) can generally be provided by a function \(f_{\text{acc}}\) as follows:  
\[a_{\text{h}}(t) =f_{\text{acc}}(z_{\text{h}}(t),z_{\text{p}}(t))\] \[=\left\{\begin{array}{ll}f_{\text{free}}(v_{\text{h}}(t)),&\text{ for }x_{\text{p}}(t)-x_{\text{h}}(t)>R_{\text{th}},\\ f_{\text{regu}}(z_{\text{h}}(t),z_{\text{p}}(t)),&\text{ otherwise,}\end{array}\right. \tag{2}\]  
where the functions \(f_{\text{free}}(\cdot)\) and \(f_{\text{regu}}(\cdot,\cdot)\) represent the decisions in the cruising mode and the gap-regulating mode, respectively. They are defined as follows:  
\[f_{\text{free}}(v_{\text{h}})= k_{0}(v_{\text{ref}}-v_{\text{h}}), \tag{3}\] \[f_{\text{regu}}(z_{\text{h}},z_{\text{p}})= k_{1}(x_{\text{p}}-x_{\text{h}}-d_{0}+t_{\text{hw}}v_{\text{h}})\] \[+k_{2}(v_{\text{p}}-v_{\text{h}}), \tag{4}\]  
where \(d_{0}\) is a constant, \(t_{\text{hw}}\) is the set time headway, \(k_{0}\), \(k_{1}\), and \(k_{2}\) are gains, and \(v_{\text{ref}}\) is the reference speed set by the driver.  
By minimizing the difference between experimental and simulated speeds using model (4) in the gap regulating mode (i.e., for \(x_{\text{p}}-x_{\text{h}}\leq R_{\text{th}}\)), the gains are approximated as \(k_{1}=0.23\) s\({}^{-2}\) and \(k_{2}=0.07\) s\({}^{-1}\)[22]. For a smooth transition from the cruising mode (i.e., for \(x_{\text{p}}-x_{\text{h}}>R_{\text{th}}\)) to the gap regulating mode by quickly reducing the speed error, a new mode called approaching mode is considered in [23]. The approaching mode starts when the gap falls within twice as large as the desired gap (i.e., \(x_{\text{p}}-x_{\text{h}}-d_{0}<2t_{\text{hw}}v_{\text{h}}\)). When gap and speed errors simultaneously become smaller than 0.2 m and 0.1 m/s, respectively, the regulating mode starts. In the approaching mode, the gains of (4) are tuned as \(k_{1}=0.04\) s\({}^{-2}\) and \(k_{2}=0.8\) s\({}^{-1}\). Gain \(k_{0}\) for the cruising mode is chosen at 0.4 s\({}^{-1}\), which falls within the typical range found in various ACC systems [23]. The desired gap including vehicle length \(d_{0}\) between vehicles at standstill is considered zero in [22] assuming that ACC is only kept active at a high speed with sufficient gaps. In order to prevent rear-end collisions with a higher clearance at low speed, \(d_{0}\) was tuned in [23] as a function of vehicle speed: at speed below 10.8 m/s, \(d_{0}=7\) m; at speed above 15 m/s, \(d_{0}=5\) m; and at speed between 10.8 m/s and 15 m/s, \(d_{0}\) is linearly tuned from 7 m to 5 m.  
In the above-described scheme, a driver has to deactivate ACC and drive manually when the host vehicle approaches a standstill vehicle or intends to change the lane in a restricted situation. A system-initiated deactivation method is also introduced to cope with the situation when there is a high risk of rear-end collisions according to a model of the safety-critical situation. Incorporating such functionality, ACC guarantees no collision in prevailing driving conditions [23].