# A Graph-Based Method for Tactical Planning of Lane-Level Driving Tasks in the Outlook Region
## 5 Modeling of Lane-Following and Lane-Change Maneuvers  
In this section, the lane-following and lane-change maneuvers of the ego vehicle will be modeled based on the driving environment representation described in the previous section. These maneuvers will all be represented as edges in the directed graph. All edges are categorized into two types: longitudinal edges and lateral edges, which respectively represent lane-following maneuvers and lane-change maneuvers. According to the decision-making objectives defined in the previous section, the time consumed by either lane-following or lane-change maneuvers will be used as the cost of the edges. The time consumed for the lane-following maneuver can be represented as the time taken for the ego vehicle to travel from the starting lane cell to the adjacent cell with the estimated speed. This estimated speed primarily considers the following several factors. 1. The maximum speed \(V_{acc}\) that the ego vehicle can accelerate to within a specified distance under the current vehicle speed. Since the maximum acceleration of the vehicle at different speeds has strong non-linearity, a pre-determined acceleration table based on experimental results is used here to calculate the vehicle speed after different acceleration distances under specific initial speeds. If the vehicle has a maximum acceleration \(a_{k}\) at speed \(V_{k}\), the following equations can be approximately obtained: \[ \begin{split}\Delta s_{k+1}=\left(V_{k+1}^{2}-V_{k}^{2}\right)/2a _{k},\\ s_{k+1}=\sum_{k+1}\Delta s_{i},\end{split} \] (1) where \(V_{k},V_{k+1}\) denote two consecutive speeds in the acceleration table, \(\Delta s_{k}\) denotes the approximate distance of the vehicle accelerating from \(V_{k}\) to \(V_{k+1}\), and \(s_{k+1}\) denotes the distance required for the vehicle to accelerate from its initial speed to \(V_{k+1}\). Additionally, if \(s_{k+1}\geq\Delta l\geq s_{k},\ V_{acc}=V_{k}\). 2. The maximum speed \(V_{dec}\) at which the ego vehicle can smoothly decelerate to a stop when the current lane is about to end or merge into the adjacent lane. This value can be calculated according to the following Equation (2). \[V_{dec}=\sqrt{2\cdot b\cdot s_{left}},\] (2)  
Figure 4: The discretized driving environment and the corresponding directed graph. In the left part, each lane is longitudinally divided into multiple lane cells. Each lane cell corresponds to a node in a directed graph in the right part. Gray nodes indicate that the corresponding lane cell is unavailable for driving due to reasons such as insufficient width. The arrows connecting the nodes represent driving maneuvers, where arrows connecting nodes across different lanes signify lane-change maneuvers and others represent lane-following maneuvers. Note: To avoid the image being too cluttered, only some of the edges representing potential lane-change maneuvers are shown here. where \(s_{left}\) denotes the distance between the current cell and the end of the lane and \(b\) denotes the average braking deceleration during daily driving. 3. The regulatory speed limit \(V_{rule}\) at the current cell;
4. The traffic flow speed \(v_{flow}\) at the current cell. The estimated speed \(v_{est}\) is the minimum of the above four speeds. Then, the cost of a lane-following maneuver, when traveling from cell \(n_{p}\) to the adjacent cell \(n_{q}\), can be represented as follows:  
\[C_{p,\;q}=\Delta I/v_{est}, \tag{3}\]  
\[v_{est}=min\Big{(}V_{acc},\;V_{dec},V_{rule},v_{flow}\Big{)}. \tag{4}\]  
For the lane-change maneuver, what needs to be determined here is the duration of the lane-change process and the position after the lane change. As mentioned earlier, the proposed method isolates collision safety issues when planning lane-level driving tasks; therefore, it does not generate precise lane-change trajectories, nor is there a need for the precise location prediction of traffic vehicles.