# Adaptive Cruise Control for Cut-In Scenarios Based on Model Predictive Control Algorithm
## 2 Cut-In Scenario Classification and Cut-In Possibility Quantification
### Quantification of Cut-In Possibility Based on Lateral Distance and Lateral Relative Velocity
#### 2.3.1 Lateral Distance Criterion  
When a nearby vehicle performs a cut-in maneuver, the continuous change of the nearby vehicle's lateral displacement is the most intuitive. The driver's judgment of the cut-in vehicle is generally based on whether the lateral distance of the nearby vehicle has an impact on the current driving trajectory of the host vehicle. As shown in Figure 6, if the nearby vehicle's body and the host vehicle's body overlap in the longitudinal direction, the driver will take measures to adjust the vehicle, according to the driving state of the two vehicles. Therefore, cut-in possibility is determined according to a change in the vehicle's lateral distance.  
As the lateral displacement of a nearby car increases, the cut-in possibility of the vehicle becomes greater. The cut-in possibility is the greatest when the body of the nearby vehicle overlaps with the body of the host vehicle in the longitudinal direction. Therefore,  
Figure 5: Determination of potential cut-in vehicles.  
Figure 6: Vehicle’s body overlap.  
the cut-in possibility of the nearby vehicle is quantified as the value of [0,1] according to the vehicle's lateral distance.  
\[P_{cutin\_d_lat}\in[0,1] \tag{5}\]  
where \(P_{cutin\_d_lat}\) is the cut-in possibility based on lateral distance. When \(P_{cutin\_d_lat}=1\), it is considered that the nearby vehicle will definitely cut in. On the contrary, when \(P_{cutin\_d_lat}=0\), it is considered that the nearby vehicle cannot cut in. In addition, because the lateral distance of the nearby vehicle is positively related to the cut-in possibility, the sigmoid function is selected to link the lateral displacement with the cut-in possibility.  
\[P_{cutin\_d_lat}=\left\{\begin{array}{ll}\frac{1}{1+e^{-1}d_{lat}+e}\;d_{ lat}\in[-H,0]\\ \frac{1}{1+e^{\lambda_{lat}+e}}\;d_{lat}\in[0,H]\end{array}\right. \tag{6}\]  
where \(d_{lat}\) is the lateral distance of the nearby vehicle, \(a\) and \(b\) are both parameters that are related to the width of the lane line and the width of the host vehicle.  
As the relative lateral distance decreases, the cut-in possibility of the nearby vehicle increases gradually. When the nearby vehicle body and the host vehicle body have any overlap in the longitudinal direction, \(P_{cutin\_d_lat}=1\), and is regarded as cut-in behavior. The cut-in possibility based on lateral distance \(P_{cutin\_d_lat}\) and lateral distance \(d_{lat}\) are shown in Figure 7.  
As shown in Figure 7, the ordinate is the cut-in possibility based on lateral distance \(P_{cutin\_d_lat}\), the abscissa is the lateral distance of nearby vehicle, \(d_{lat}\), \(W_{egg}\) is the width of the vehicle, and \(H\) is the width of the lane. As shown in Figure 7a, with the lateral distance of a nearby vehicle decreases, the cut-in possibility, \(P_{cutin\_d_lat}\), becomes greater. When a nearby vehicle shifts laterally until it overlaps with the host vehicle body in the longitudinal direction and touches the red dotted line in Figure 7a, the cut-in probability is considered to be 1, which means \(P_{cutin\_d_lat}=1\) when \(d_{lat}\leq(1/2)W_{h}\).  
Figure 7: Cut-in possibility based on relative lateral distance.