# A Graph-Based Method for Tactical Planning of Lane-Level Driving Tasks in the Outlook Region
## 7 Simulation
### Baseline Model  
The AV-IDM determines the lateral and longitudinal accelerations of the ego vehicle based on all vehicles within the surrounding region. The model can also make lane-change decisions, but it does not generate lane-change trajectories; instead, it guides the vehicle's lane change directly through acceleration. The lateral acceleration output \(a_{Lat}^{Eff}\) is shown in the following equation:  
\[a_{Lat}^{Eff}=a_{Lat}^{Call}+a_{Lat}^{Disc}, \tag{12}\]  
where \(a_{Lat}^{Coll}\) denotes the lateral acceleration component for avoiding obstacles and \(a_{Lat}^{Disc}\) denotes the lateral acceleration component for discretionary lateral movements, i.e., lane changes. In AV-IDM, \(a_{Lat}^{Disc}\) is calculated by a function calibrated with the NGSIM dataset which has the following form:  
\[a_{Lat}^{Disc}=f\left(s_{Front^{\prime}}^{Eff},s_{Rarr^{\prime}}^{Eff},s_{Lift ^{\prime}}^{Eff},s_{Right}^{Eff},SF\right), \tag{13}\]  
Figure 7: Simulation framework.  
where \(s_{Front}^{Eff}\), \(s_{Rear}^{Eff}\), \(s_{Left}^{Eff}\), \(s_{Right}^{Eff}\) denote the effective distances of obstacles in the front, rear, left, and right area relative to the ego vehicle and \(SF\) denotes the ratio of the actual speed of the ego vehicle to its desired speed. It can be seen that AV-IDM is a typical model for determining lane-change intention based on the ego vehicle's surrounding region. Considering that [29] does not specify the required lateral acceleration for lane keeping, the optimal preview lateral acceleration model [40] is introduced to generate the lateral acceleration for following the target lane's centerline. Therefore, the adjusted lateral acceleration takes the following form:  
\[\begin{cases}a_{Lat}^{Eff}=a_{Lat}^{Coll}+a_{Lat}^{Disc},\ if\ \left|a_{Lat}^{Disc} \right|\geq a_{0}\\ a_{Lat}^{Eff}=a_{Lat}^{Coll}+a_{Lat}^{Lane},\ if\ \left|a_{Lat}^{Disc} \right|<a_{0}\end{cases}, \tag{14}\]  
where \(a_{0}\) denotes the threshold for triggering lane-change behavior. If \(a_{0}\) is set too high, the vehicle will not be able to respond to promptly to external conditions. Conversely, if \(a_{0}\) is set too low, the vehicle may become overly sensitive and lose stability. In the simulation, \(a_{0}\) is set to 0.2 m/s\({}^{2}\). Equation (14) is used in the baseline model to control the lateral acceleration of the ego vehicle. For the proposed model, the lateral acceleration is calculated as follows:  
\[\begin{cases}a_{Lat}^{Eff}=a_{Lat}^{Coll}+a_{Lat}^{LC},\ if\ LC=true\\ a_{Lat}^{Eff}=a_{Lat}^{Coll}+a_{Lat}^{Lane},\ if\ LC=false\end{cases}, \tag{15}\]  
where \(LC\) denotes whether a lane change is needed at the moment, which is directly determined by the lane-level driving task; \(a_{Lat}^{LC}\) denotes the desired lateral acceleration for lane changing, and by referring to the reasoning process in [29], it can be determined by the following equations:  
\[a_{Lat}^{LC}=a_{Lat}\left[1-\left(\frac{v_{Lat}}{v_{Lat}^{\prime}}\right)^{ \delta}\right], \tag{16}\]  
\[v_{Lat}^{\prime}=\frac{d_{Lat}}{t_{{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{ \it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{ it{\it{ it{       }}}}}}}}}}}}}}}}}} \]  
where \(a_{Lat}\) denotes the maximum lateral acceleration of the ego vehicle, which can be determined based on the parameter set in [29]; \(v_{Lat}^{\prime}\) denotes the expected average speed during the lane-changing process; \(d_{Lat}\) denotes the lateral distance that needs to be moved for lane changing, which can be approximately equal to the lateral distance between the centerlines of two lanes; and \(\delta\) denotes the acceleration exponent, with a higher value leading to more aggressive vehicle acceleration. Equations (16) and (17) are jointly used to execute the lane-changing task based on the output of the proposed model.