A Graph-Based Method for Tactical Planning of Lane-Level Driving Tasks in the Outlook Region

Abstract

Road traffic regulations usually require that a vehicle can only move one lane during one lane change and must turn on the turn signal before changing lanes. Under such constraints, if automated vehicles can plan multiple lane-change maneuvers at one time, then not only adjacent lanes but also farther lanes can be selected as target lanes when making decisions. This would help improve the driving performance in multi-lane scenarios. Many current lane-selection or lane-change methods focus on the surrounding region of the ego vehicle, usually only considering adjacent lanes as potential target lanes. This paper proposes a new tactical functional model that attempts to perform lane-level driving task planning and decision-making over a road area far beyond the surrounding region of the ego vehicle. We refer to this road area as the “outlook region”. In this functional model, the decision-making of lane-level driving tasks will take the overall performance within the outlook region as the goal, rather than pursuing the optimal single lane-change maneuver. The proposed method is implemented using a directed graph-based approach and simulation tests are conducted. The results show that the proposed method helps improve the driving performance of automated vehicles in multi-lane scenarios.

1. Introduction

Automated driving is regarded as one of the main development directions of the automotive industry due to its great potential in aspects of safety and efficiency [1,2,3,4]. Automated lane-selection and lane-change functions are key components of automated driving systems. For a long time in the future, automated vehicles will coexist with human-driven vehicles on the road. Compliance with road traffic rules is crucial for automated vehicles, especially when it comes to lane changes. Traffic regulations often stipulate that a vehicle can only move one lane at a time during a lane change and must turn on the turn signal several seconds before initiating the lane-change action. Under such regulatory constraints, if a vehicle wishes to move to a lane farther away from its current lane, it would need to perform multiple lane changes (more than two). For instance, as shown in Figure 1, if a vehicle wants to enter a faster-moving lane, it would require at least two lane changes. In this scenario, the first lane change may even have a negative impact on travel efficiency. Many current studies on automated lane selection or lane changes typically only consider the surrounding region within a limited range, which is usually used to consider interactions with other vehicles, and these methods usually search for optimal strategies within the scope of a single lane-change maneuver. This can easily cause the vehicle to fall into in local optimum situations in multi-lane scenarios and fail to find potentially better strategies.

Furthermore, the aforementioned limitations also reveal the parts of the driving task hierarchical architecture commonly reflected in many research papers which can be further improved. Referring to the earliest driving task model proposed by John A. Michon [5,6], the entire driving task can be divided into three levels: strategic, tactical, and operational. For automated driving, the strategic-level tasks mainly refer to navigation, i.e., planning the route for vehicle travel in the road network, including the lane-level route when entering and exiting intersections, while the tactical-level tasks include more detailed and specific driving behaviors such as deciding whether to overtake, change lanes, or adjust speed [7]. However, when a vehicle is traveling on a road segment, a series of related lane-change maneuvers caused by local traffic represent the local lane-level path expected by the driver or the automated driving system. This corresponds to the lane-level driving tasks located between the existing strategic- and tactical-level tasks, as shown in Figure 2. This issue is rarely mentioned in current research.

This paper attempts to propose a tactical planning method for lane-level driving tasks. According to research [8,9,10,11,12], the duration of a single lane change by human drivers generally falls within the range of 1 s to 16 s, with an average of around 5 s to 7 s. Adding the time required to signal with the turn indicator, the spatial span of the driving tasks, which can contain multiple lane changes, far exceeds the surrounding region of the ego vehicle. In this spatial span, the impact of collision safety on the decision-making outcome is small. Therefore, this paper attempts to construct a standalone lane-level driving task planning module whose considered driving environment encompasses a larger road region. In this paper, this “larger road region” is called the “outlook region”, and its spatial coverage should be sufficient to accommodate several potential lane change maneuvers of the vehicle.

Thanks to recent advancements in vehicle networking and intelligent transportation systems [13,14], vehicles can obtain real-time environmental information beyond the field of view of on-board sensors through other connected vehicles or roadside units, without being affected by obstacles. This provides a foundation for environment perception in the outlook region. Meanwhile, many studies have already begun exploring real-time estimation [15,16] and even short-term prediction [17] of lane-level traffic flow states. Considering that minor fluctuations in the motion states of individual distant vehicles do not significantly impact a driver’s decisions, while traffic flow states, which represent collective vehicle motion, are more stable, this paper attempts to characterize the driving environment of the outlook region using high-resolution traffic flow data. This approach also avoids the need to predict the motion states of numerous vehicles in the outlook region. The proposed lane-level driving task planning method can also be viewed as a potential application for future lane-level traffic state prediction methods.

In summary, the main contributions of this paper are summarized as follows:

The tactical planning function in existing driving task architectures has been further decomposed and the concept of lane-level driving tasks is clarified;

The concept of an “outlook region” is applied to the lane-selection strategies of automated vehicles, with decision-making aimed at optimizing the overall efficiency of multiple lane change maneuvers. This can improve the driving performance of automated vehicles in multi-lane scenarios.

By representing the driving environment within the outlook region in the form of high-resolution traffic flow, the need for long-term predictions of the motion states of numerous traffic vehicles is avoided.

We implement the proposed model base on a directed graph planning algorithm and build several test scenarios in Virtual Test Drive (VTD) for simulation and verification. The results show that the proposed method can reasonably guide an automated vehicle to drive on a multi-lane road segment.

The rest of this paper is organized as follows. Section 2 reviews the relevant research work. Section 3 defines the objectives expected to be achieved, as well as the fundamental assumptions adopted. Section 4 describes the representations of the driving environment that form the basis for planning and decision-making. Section 5 presents the modeling approaches for lane-following and lane-change maneuvers. Section 6 discusses the algorithm for solving optimal driving policies. Section 7 introduces the details of the simulation tests, while Section 8 presents the results of the simulation tests along with analysis. Finally, conclusions are given in Section 9.

2. Literature Review

Currently, there is lots of research on lane-changing decisions and lane selection. Based on how these methods consider traffic vehicles in the driving environment, they can be broadly categorized into the following classes.

The first class of methods considers only the nearest neighbor vehicles in the current lane and adjacent lanes. These methods ignore the influence of vehicles farther away on decision-making and are unable to respond in advance to upcoming traffic situations. Many existing methods adopt this approach. The earliest lane-changing model, proposed by Gipps [18] for micro-traffic simulation, uses the following speed of the ego vehicle to determine the speed advantage between the current lane and adjacent lanes. Ref. [19] calculates indicators such as traffic efficiency and energy consumption based on the state of leading vehicles in the current and adjacent lanes to select the optimal lane. Refs. [20,21] generate lane-changing intentions, considering factors such as whether the ego vehicle cannot reach its desired speed or maintain a minimum safety distance, due to the leading vehicle in the current lane. Refs. [22,23] establish an artificial potential field for leading vehicles, using lateral forces from leading vehicles in the left and right lanes to decide lane-changing behavior.

Since this approach makes it easy to represent the driving environment and build datasets, numerous machine learning methods also fall into this category. Ref. [24] uses a support vector machine to train a lane-change decision model, where the training data are extracted from the NGSIM dataset based on a predefined lane-change model. This model considers the three nearest vehicles in the current and target lanes. Refs. [25,26] employ reinforcement learning to train a lane-change decision model. In [25], the state vector includes the closest leading vehicle in all lanes, while [26] considers the eight nearest neighbor vehicles in the current and adjacent lanes.

The second class of methods considers all vehicles within a certain range in the current lane and adjacent lanes. Refs. [27,28] use reinforcement learning to train lane-change models, with state representations that include all vehicles within 50–60 m ahead. Ref. [29] develops a two-dimensional IDM algorithm to calculate lane-change intentions based on the relative distances to surrounding vehicles. Refs. [30,31] propose an MPC-based framework that uses the motion states of all nearby vehicles in the current and adjacent lanes to make lane-change decisions, enabling the vehicle to react proactively to upcoming traffic disturbances. Ref. [32] decides lane changes based on the average speed of vehicles in different lanes within a certain distance ahead. Among these, refs. [30,31,32] assume that vehicles can obtain the motion states of traffic vehicles through V2X communication, and their driving environments cover a broader range of traffic vehicles than other models. Refs. [4,33] introduce large language models into automated driving systems. These models comprehensively understand the ego vehicle’s near-field driving environment and handle complex and extreme scenarios. However, these methods still focus on single lane-change behaviors for decision-making and do not address the issue of multiple lane changes in multi-lane scenarios.

The third class of methods does not consider traffic vehicles. Such methods typically focus on planning strategic driving tasks, i.e., lane-level navigation or route planning, such as in [34,35,36,37]. These methods usually plan lane-level routes in the entire road network based on the lane structure and traffic rules such as speed limits and prohibitions on changing lanes. They can effectively handle the problems of lane selection and multiple lane changes at intersections, but cannot respond to dynamic traffic situations on road segments.

In summary, the current research on lane-change decisions and lane selection still pays relatively little attention to tactical planning methods for lane-level driving tasks. As mentioned earlier, most methods focus solely on tactical planning within the surrounding region of the ego vehicle, and their search scope of optimal strategies is limited to single lane-change maneuvers. This tends to lead to vehicles becoming stuck in locally optimal situations in multi-lane scenarios, which is not conducive to further improving their driving performance.

3. Objectives and Assumptions

The proposed method aims to obtain lane-level driving tasks within the outlook region, which will be used to guide the vehicle to follow the lane or change lanes several times to enter the desired lane. The outlook region in this paper is defined as a spatial range covering potential multiple lane-change maneuvers of the ego vehicle which is much larger than the vehicle’s surrounding region. Decision-making within the outlook region should not involve vehicle collision issues. Lane-level driving tasks are spatially represented by several consecutive lane segments, as shown in Figure 3. In scenarios where the vehicle is traveling on a road segment, when there is only one lane segment laterally, the vehicle is expected to be in a lane-following state. When a second lane segment appears laterally, it represents the need for a lane-change maneuver.

In the method proposed in this paper, collision safety issues are not considered in the decision of lane-level driving tasks. The lane segment specified in a lane-level driving task is the region where the vehicle is expected to drive. Subsequent modules which execute the driving tasks ensure safe operation based on the local traffic situations. For situations where it is unsafe to change lanes in a timely manner, the proposed method includes an alternative path in the lane-level driving task. The alternative path only involves lane-following maneuvers. This allows the vehicle to slow down or even stop if necessary to execute the required lane change. The handling of collision safety is separated from the decision of lane-level driving task primarily due to the following two reasons:

The time required for a complete lane-changing maneuver is significantly longer than the reaction time needed to avoid a collision. Additionally, the decision-making interval for lane-level driving tasks is much larger than the computation interval for vehicle motion intention or trajectories;

The decisions of lane-level driving tasks focus on the overall performance of the vehicle’s operation within the outlook region. Under normal circumstances, interactions with individual surrounding vehicles have a relatively minor impact on this.

In the lane-change decision process of automated vehicles, several evaluation indicators are usually established, such as driving efficiency, collision risk, energy consumption, driving comfort, etc. However, in order to introduce the proposed method more clearly and concisely, only the aspects of driving efficiency and legality are considered here. The goals of the proposed method in making decisions on lane-level driving tasks are as follows:

To minimize the travel time (or maximize the average speed) that the ego vehicle takes to pass through the predefined road segment;

To ensure that the lane-change behaviors of the ego vehicle comply with traffic regulations, specifically meaning, during a single lane change, not crossing multiple lanes; activating turn signals before changing lanes; and adhering to road or lane speed limits at all times.

When establishing a driving environment model for the outlook region, the proposed method uses high-resolution traffic flow information to describe the traffic situations rather than the motion states of individual vehicles. This approach considers the following factors:

In real-world road environments, whether using on-board sensors-based or V2X (Vehicle-to-Everything)-based perception methods, it is impossible to obtain information about all vehicles on the road. Extracting traffic flow information from the perceivable traffic vehicles can effectively avoid this disadvantage.

The states of traffic flow, which represent the motion of a group of vehicles, tend to change more smoothly compared to the motion states of individual vehicles. This allows us to avoid predicting the trajectories of a large number of vehicles over an extended period.

Therefore, the assumptions adopted in this paper regarding perception are as follows:

The ego vehicle can obtain the required road information through means such as V2X (Vehicle-to-Everything) or high-definition maps, including details like the number of lanes, types of lane markings, speed limits, and so on;

The ego vehicle can obtain high-resolution traffic flow information within the outlook region through V2X-based methods. In this paper, the term “high resolution” refers to traffic flow information that can distinguish between individual lanes in the lateral direction and should have a longitudinal resolution distance equivalent to the total travel length of a vehicle during a lane-change maneuver.

4. Driving Environment Representation

The representation of the driving environment serves as the foundation for building the entire decision-making model. In the proposed method, we discretize the driving environment spatially into numerous lane cells and subsequently convert it into a directed graph to solve optimal lane-level driving tasks. Before this work, such methods have been successfully applied to navigation route planning [37] and driving trajectory planning [38], but the granularity of environmental discretization differs depending on the level of driving tasks.

Here, we define the smallest discretized unit as a “lane cell”, which is a short lane segment where internal traffic rules and traffic flow states are considered to be consistent or similar. Each lane cell corresponds to a node in the directed graph, as shown in Figure 4, and is connected via edges to other lane cells. These edges represent possible actions, i.e., lane-following or lane-change maneuvers. By assigning appropriate costs to these edges, the driver’s preferences for different driving styles, such as travel efficiency, driving risk, regulatory compliance, etc., can be represented. The optimal lane-level driving tasks can be further determined. In subsequent section, we will establish cost functions for edges representing lane-following and lane-change maneuvers based on traffic flow states and traffic regulations at each lane cell.

Regarding the size of lane cells, given that the proposed method aims to plan lane-level driving tasks, the lateral dimension can be directly equal to the lane width at that location. The choice of longitudinal dimension, on the other hand, is a crucial issue. If the longitudinal dimension is small, it can more accurately represent the lane-change position in the path, but it will also increase the number of nodes in the directed graph, thereby increasing computational overhead. Conversely, if the longitudinal dimension is large, it may fail to promptly reflect changes in traffic situations and traffic rules, thus making the vehicle’s response sluggish.

Here, all lane cells in the driving environment are denoted as $N=\left\{n_i\right\}$. The longitudinal dimension of cell $n_i$ is denoted as $∆l$, and the value of this variable represents the spatial granularity of the discretized driving environment. The traffic flow attributes at cell $n_i$ are denoted as $\left\{v_i,{\rho }_i\right\}$, which represent the traffic flow speed and density, respectively, at the location of the cell.

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.

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:

(1)$$\begin{gathered} ∆s_{k+1}=\left(V_{k+1}^2-V_k^2\right)/2a_k, \\ {s}_{k+1}={\sum }_{k+1}∆s_i, \end{gathered}$$

where $V_k,V_{k+1}$ denote two consecutive speeds in the acceleration table, $∆s_k$ 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 $s_{k+1}\ge ∆l\ge s_k,V_{acc}=V_k$.

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).

(2)$V_{dec}=\sqrt{2·{b·s}_{left}},$

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:

(3)$C_{p,q}=∆l/v_{est},$

(4)$v_{est}=min\left(V_{acc},V_{dec},V_{rule},v_{flow}\right).$

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. A statistically based lane-change duration model proposed by Tomer Toledo [9] is adopted here to estimate the time cost of lane changes for each lane cell and the cell where the vehicle will be located after the lane change. As shown in Figure 5, the entire lane-change process can be divided into two phases: the first phase involves turning on the turn signal to indicate intent and the second phase involves performing the turning action to enter the adjacent lane.

Assuming the starting cell is $n_p$ and the target unit is $n_{p+q}^{\prime }$, the cost of the lateral edge representing the lane-change maneuver can be represented as follows:

(5)$C_{p,q}=t_{light}+t_{lcd},$

where $t_{light}$ denotes the time for turning on the turn signal to indicate intent, which can be regarded as a constant; $t_{lcd}$ denotes the time for performing the lane-change action, that is, the lane-change duration in Tomer Toledo’s model. Tomer Toledo’s lane-change duration model is an empirical model obtained from a large amount of natural driving data statistics and has the following form:

(6)$\ln \left(t_{lcd}\right)=\mathit{\beta }·\mathit{X},$

where $t_{lcd}$ denotes the lane change duration, $\mathit{X}$ denotes the vector of explanatory variables, and $\mathit{\beta }$ denotes corresponding parameters. Equation (6) can be expanded as follows:

(7)$$\begin{gathered} \ln \left(t_{lcd}\right)={\beta }_0+{\beta }_1·\overline{\rho }+{\beta }_2·D+{\beta }_3·min\left[0,∆V_{front}\right]+{\beta }_4·d_{front}+{\beta }_5· \\ min\left[0,∆V_{lag,lead}\right]+{\beta }_6·max\left[0,∆V_{lag,lead}\right]+{\beta }_7·d_{lag,lead}, \end{gathered}$$

where $\overline{\rho }$ denotes the average traffic density, $D$ denotes the change direction, $∆V_{front}$ denotes the relative speed between the ego vehicle and its preceding vehicle, $∆V_{lag,lead}$ denotes the relative speed between the lead vehicle and the lag vehicle in the adjacent lane, $d_{front}$ denotes the distance between the ego vehicle and its preceding vehicle, and $d_{lag,lead}$ denotes the gap of the lead vehicle and the lag vehicle in the adjacent lane.

In the traffic flow-based environment model build in this paper, we replaced some variables in Equation (8),

(8)$\left\{\begin{array}{c}∆V_{front}\to ∆v_{self}\\ ∆V_{lag,lead}\to ∆v_{side}\\ d_{front}\to 1/{\rho }_{self}\\ d_{lag,lead}\to 1/{\rho }_{side}\end{array}\right.,$

where ${\rho }_{self}$ denotes the traffic density at current cell, ${\rho }_{side}$ denotes the traffic density at adjacent cell, $∆v_{self}$ denotes the traffic flow speed difference between the current lane cell and its preceding cell, and $∆v_{side}$ denotes the traffic flow speed difference between the adjacent cell and its preceding cell.

Combining the estimated speed $v_{est}$ with the duration of the lane-change process at each cell, the cell $n_{p+q}^{\prime }$ where the ego vehicle located when lane-changing ends can be obtained. This process can be represented with the following equations:

(9)$$\begin{gathered} v_{est}^{\prime }=\left\{\begin{array}{c}{v}_{est}|n_{p+k},t_k\le t_{light}+0.5·t_{lcd}\\ v_{est}|n_{p+k}^{\prime },t_k>t_{light}+0.5·t_{lcd}\end{array},k=0,1,2,\cdots \right., \\ ∆t_i=∆l/v_{est}^{\prime }, \\ {t}_k={\sum }_k∆t_i \end{gathered}$$

where $v_{est}^{\prime }$ denotes the expected speed of the lane-change progress and $v_{est}$ is the estimated speed obtained by Equation (4). $n_{p+k}$ denotes any cell in the current lane, while $n_{p+k}^{\prime }$ denotes any cell in the adjacent lane, $∆t_i$ represents the time for passing through the cell, $t_k$ denotes the time consumed during lane change, and if $t_k\ge C_{p,q}$, $n_{p+k}^{\prime }=n_{p+q}^{\prime }$.

When all feasible lane-following and lane-change maneuvers are represented, the directed graph containing all possible lane-level driving tasks in the outlook region can be obtained.

6. Computing the Optimal Lane-Level Driving Task

Here, we aim to obtain the lane-level driving task with the shortest travel time within the outlook region. This problem can be specifically described as finding the minimum-cost path from an entry node to any available exit node in a given directed graph. The available exit nodes correspond to the exit cells of all available lanes within the outlook region, as shown in Figure 6. In this figure, Lanes 1, 2, and 3 extend beyond the outlook region, each generating an exit node, while Lane 4 merges into the adjacent lane within the outlook region, so there is no exit node generated from this lane. This is a minimum-cost path problem in a directed graph which we solve using Dijkstra’s algorithm. During one solving process, all minimum-cost paths to all exit nodes can be obtained simultaneously. Then, the real minimum-cost path among all above paths will be selected to generated the final lane-level driving task.

The basic principle of Dijkstra’s algorithm can be described by the following equation:

(10)$C_{u,{\overline{N}}_k}=\underset{\begin{array}{c}p\in N_k\\ q\in {\overline{N}}_k\end{array}}{\min }\left\{C_{u,p}+C_{p,q}\right\},$

where $N_k\in N$ denotes all searched nodes after $k$ steps, ${\overline{N}}_k=N\setminus N_k$ denotes all unsearched nodes until $k$ steps, $u$ denotes the origin node, $p$ denotes any node in $N_k$, $q$ denotes any node in ${\overline{N}}_k$, and $C_{u,p}$ represents the cumulative cost of traveling from origin node $u$ to node $p$, while $C_{p,q}$ represents the cumulative cost of traveling from node $p$ to node $q$. $C_{p,q}$ is defined in Equations (3) and (5).

According to the cost calculation method defined in Equation (10), the lane-level driving task obtained may have one issue: it contains too many lane changes. Excessive lane-change maneuvers will reduce the likelihood of the ego vehicle successfully following the driving task and may also disrupt traffic. Therefore, the factor of lane-change times is introduced into Equation (10). The revised cumulative cost is as follows:

(11)$C_{u,{\overline{N}}_k}=\underset{\begin{array}{c}p\in N_k\\ q\in {\overline{N}}_k\end{array}}{\min }\left\{C_{u,p}+C_{p,q}+\lambda ·F\right\},$

where $F$ denotes the coefficient about direction; $F=1$ when $C_{p,q}$ represents the cost of a lateral edge and $F=0$ when $C_{p,q}$ represents the cost of a longitudinal edge. $\lambda$ denotes the coefficient about the limitation of lane-change times, which is considered as a constant here. The number of lateral edges contained in $C_{u,p}$ represents the lane-change times of the corresponding lane-level path. The more lane changes it contains, the higher extra cost it has; thus, the path will have a lower priority in the decision-making of the final lane-level driving task.

It should be noted that the lane-level driving task with the minimum cost obtained here is the task that the vehicle is expected to follow, but in actual driving, the vehicle may not be able to change lanes in time due to interference from local traffic vehicles. An alternative path is introduced into the lane-level driving task to guide the vehicle to slow down and wait at the necessary location. The alternative path only includes lane-following maneuvers, which represents the maximum distance that the vehicle can travel in the outlook region without changing lanes and will not deviate from the navigation route, as shown in Figure 3.

7. Simulation

7.1. Simulation Framework Overview

The proposed lane-level driving task planning method is simulated and tested on Virtual Test Drive (VTD) platform. The framework of the entire simulation system is shown in Figure 7. The function of the proposed model is tactical planning within the outlook region, which is a part of the overall driving task. We reference the AV-IDM [ 29] method to implement the remaining tactical planning and motion control functions to support the vehicle in completing lane changes safely in traffic environments. This method is also used as a baseline model for the comparative test. More details will be introduced in the next subsection.

In terms of perception information acquisition and driving environment construction, lane markings and speed limits on the road segment can be obtained from the OpenDRIVE map file and the status of traffic vehicles within the outlook region as well as the ego vehicle can be obtained from the RDB protocol of VTD. As mentioned earlier, the high-resolution traffic flow information is used as the decision basis in the proposed method. Here, the method from [39] is utilized to aggregate the microscopic single-vehicle data obtained from RDB into macroscopic traffic flow data.

7.2. 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:

(12)$a_{Lat}^{Eff}=a_{Lat}^{Coll}+a_{Lat}^{Disc},$

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:

(13)$a_{Lat}^{Disc}=f\left(s_{Front}^{Eff},s_{Rear}^{Eff},s_{Left}^{Eff},s_{Right}^{Eff},SF\right),$

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:

(14)$\left\{\begin{array}{c}{a}_{Lat}^{Eff}=a_{Lat}^{Coll}+a_{Lat}^{Disc},if\left|a_{Lat}^{Disc}\right|\ge a_0\\ a_{Lat}^{Eff}=a_{Lat}^{Coll}+a_{Lat}^{Lane},if\left|a_{Lat}^{Disc}\right|<a_0\end{array}\right.,$

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 $0.2 \mathrm{m}/{\mathrm{s}}^2$. 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:

(15)$\left\{\begin{array}{c}{a}_{Lat}^{Eff}=a_{Lat}^{Coll}+a_{Lat}^{LC},ifLC=true\\ a_{Lat}^{Eff}=a_{Lat}^{Coll}+a_{Lat}^{Lane},ifLC=false\end{array}\right.,$

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:

(16)$a_{Lat}^{LC}=a_{Lat}\left[1-{\left({\displaystyle \frac{v_{Lat}}{v_{Lat}^{\prime }}}\right)}^{\delta }\right],$

(17)$v_{Lat}^{\prime }={\displaystyle \frac{d_{Lat}}{t_{tcd}}},$

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.

7.3. Simulation Scenario

Two test scenarios are built for functional verification of the proposed method. Both scenarios are established on a 20 km-long road with four lanes. The difference between the two scenarios lies in the varying traffic flow speeds across the individual lanes, as illustrated in Figure 8a,b. In scenario 1, the traffic flow speed decreases gradually from the innermost to the outermost lane. In scenario 2, the innermost lane has the highest traffic flow speed, while the two middle lanes have the lowest. The ego vehicle is located in the outermost lane in both scenarios. For scenario 1, when the ego vehicle changes lanes from the outermost to the innermost lane, each lane change provides a speed advantage. This scenario will be used to test whether the proposed model and the baseline model can generate common lane-change maneuvers. For scenario 2, when the ego vehicle moves from the outermost lane to the middle lanes, it loses the speed advantage; however, moving from the middle lanes to the innermost lane allows for a significant speed advantage. This scenario will be used to test whether the model can overcome local disadvantages and produce multiple related lane-change maneuvers.

Since we have not found a method to directly control the lane-level traffic flow in VTD, the method used here is to place some controlled vehicles at very far positions in each lane to control the traffic flow. After a certain period of time from the start of the simulation, these controlled vehicles decelerate to their target speeds and enter the near range of the ego vehicle, thereby altering the states of traffic flow in each lane. In tests of the two scenarios, after the controlled vehicles decelerate for a period of time, the traffic speeds in the four lanes are as shown in Figure 9a and 9b, respectively. It can be observed from these figures that the traffic situations in each lane have transitioned from their initial states to the predefined states. The parameters for the near-range traffic simulation for the ego vehicle during the tests are shown in Figure 10.

Since the change of the traffic flow state takes a certain amount of time, at the beginning of the simulation, the ego vehicle will be restricted to the lane-following-only mode and will not be allowed to change lanes until all controlled vehicles decelerate for enough time, which means that the traffic flow in each lane approaches the predefined scenario. The tests of both of the two scenarios for the proposed model and the baseline model are repeated 5 times. In addition, it should be pointed out that in the simulation, the proposed model only performs a lane change after maintaining the turn signal for 3 s, while the baseline model follows its decision result and performs lane change immediately.

In the simulation, the outlook region is set to cover a time headway of 30 s, providing sufficient space for the ego vehicle to plan the lane-level driving task which contains maneuvers about entering the innermost lane from the outermost lane. The values of the key parameters of the proposed model are shown in the Table 1. The aggressive parameter set from AV-IDM [29] is adopted for the baseline model and the motion control module in the simulation.

8. Results and Discussion

In the test of scenario 1, the lane-change histories of the proposed model and the baseline model are shown in Figure 11a and 11b, respectively, and their driving trajectories on the road segment are shown in Figure 12a,b. Meanwhile, Figure 13 and Figure 14 compare the results of one test for both models. From Figure 11a,b, it can be observed that both the proposed model and the baseline model are capable of guiding the ego vehicle to change lanes step-by-step into the innermost lane with the highest passing efficiency. Additionally, combined with Figure 12a,b, it can be found that although there is some variation in the timing of lane changes for the same model across different tests, the overall driving trajectories within the road segment differ only slightly. The comparison in Figure 13 reveals that the proposed model initiates lane changes earlier than the baseline model, and as shown in Figure 12a, the intervals between consecutive lane changes are also shorter for the proposed model. Figure 14 indicates that these executed lane changes result in improvements to driving efficiency. These phenomena occur because the proposed model makes lane-change decisions within the outlook region, comprehensively considering traffic situations farther ahead. This allows the vehicle to react more “proactively” to upcoming traffic situations, thereby improving driving efficiency.

In the test of scenario 2, the lane change histories of the proposed model and the baseline model are shown in Figure 15a and 15b, respectively, and their driving trajectories on the road segment are presented in Figure 16a,b. Figure 17 and Figure 18 compare the test results of the two models on one occasion. From Figure 15a,b, it can be observed that the proposed model guides the vehicle to change lanes sequentially to the innermost lane over a longer period, while the baseline model keeps the vehicle in its original lane. As mentioned earlier, we intentionally created a “trap” in scenario 2: when a vehicle moves from the outermost lane to the middle lanes, it loses the advantage in speed, and only by moving into the innermost lane can it potentially regain the speed advantage. The baseline model makes lane-change decisions based solely on the surrounding vehicles in current and adjacent lanes. Therefore, under such traffic situations, it keeps the vehicle in its original lane to maintain a higher speed. The proposed model, however, decides to change lanes based on the overall driving efficiency within the outlook area, enabling the vehicle to move through three lane changes to reach the innermost lane.

The phenomenon that the proposed model guides the vehicle to change lanes only after a longer period can be explained by the traffic situations described in Figure 19 and Figure 20. Since the controlled vehicles in the innermost lane have the highest speed, which is used to generated the highest flow speed, a large gap will be formed between these vehicles after a long period of driving, as shown in Figure 19. This makes the speed advantage of the innermost lane grow more significant over time, as illustrated in Figure 20. When this advantage becomes sufficient to compensate for the speed loss caused by the first two lane changes, the proposed model generates a lane-level driving task containing three lane changes. A comparison through Figure 18 reveals that, after briefly falling behind the baseline model, the proposed model manages to overtake it.

It should be pointed out here that the proposed model had a large lag in the third test. This was due to being blocked by other vehicles while driving, which prevented it from changing lanes. Since the proposed model makes lane-change decisions based on traffic flow, such situations where it cannot promptly follow the driving task may occur. However, even in this case, the proposed model was still able to catch up and overtake the baseline model in terms of driving efficiency within a short period, as shown in Figure 18. If a lane change model with cooperative and game-theoretic functionalities is introduced in future work, the performance in such situations should be improved.

The test results from scenario 1 and 2 demonstrate that the proposed model can improve the driving performance of automated vehicles in multi-lane scenarios and can better cope with more complex traffic situations.

In all the simulation tests mentioned above, the proposed model was run in real-time on a laptop equipped with a 2.6 GHz Intel i7-6700HQ CPU. The proposed model operates on a cycle of 500 milliseconds and its time expenditure of five test rounds in scenario 1 is shown in Table 2. It can be observed that even the maximum time expenditure does not exceed 5% of the running cycle. Considering the total time it takes for a human driver to complete a lane change in real-world environments, the running cycle of the model could be extended, for example, to one second. Therefore, we believe that the model should not encounter significant computational overhead issues.

9. Conclusions

In this study, we propose a novel tactical driving task planning method for automated vehicles. The distinctive feature of the proposed method is that the output is a lane-level driving task which can contain multiple lane-change maneuvers. The planning and decision-making of the lane-level driving task take the overall driving performance in the outlook region as the goal and do not pursue the optimal individual lane-change maneuver. This tactical perspective enables automated vehicles to overcome local adversities by performing successive lane changes over time, aiming to reach a more desirable lane for enhanced overall performance.

In proposed method, the driving environment within the outlook region is characterized via high-resolution traffic flow data and the planning problem of the lane-level driving task is transformed into a classic directed graph minimum-cost path problem. The implemented method was tested in the simulation environment of VTD and benchmarked against an existing typical lane-change decision method. The results show that the proposed method improves the overall driving efficiency within the road segment and enables the ego vehicle to react earlier to upcoming traffic situations. Furthermore, the simulation results also indirectly point out that the slight difference in the timing of lane changes has little effect on the overall driving efficiency within the road segment, and the well-planned lane-level driving task is more conducive to improving the overall driving efficiency.

Currently, there still remain several unresolved issues. First, the proposed model does not consider situations where the ego vehicle is blocked by other traffic vehicles and thus unable to follow the lane-level driving task. If the proposed model is combined with a lane-change model that incorporates cooperative and game-theoretic functions, the vehicles in the target lane or the ego vehicle will be able to actively accelerate or decelerate to establish conditions for executing lane changes, which should effectively address this issue.

Another issue is that this paper aims to demonstrate the beneficial effects of planning vehicle driving schemes from the perspective of lane-level driving tasks. However, in this research, decision-making was only based on minimizing travel time under normal driving speeds. In future studies, more comprehensive factors should be incorporated into the decision-making process. For instance, when the traffic density in a specific lane is high, it may reduce the likelihood of successfully executing lane changes in subsequent modules. In such cases, the “weight” assigned to related driving schemes should be decreased. Additionally, different types of drivers may have their own preferences for various driving schemes. For example, if a section of a lane contains heavy trucks, cautious and prudent drivers would naturally prefer to avoid the nearby area to minimize driving risks, even if the corresponding lane-level driving scheme might allow for faster travel speeds. Another example is that if the expected speed of a lane-level driving scheme aligns more closely with the vehicle’s optimal economic speed or exhibits smaller speed variations, it may better suit drivers who prioritize economy or comfort. Therefore, determining the best strategy remains a complex issue, as it involves understanding the preferences of different types of occupants regarding the driving style of automated vehicles. At the same time, the construction of relevant evaluation metrics for the decision-making of lane-level driving tasks differs from previous methods based on surrounding driving environment.

Finally, the proposed planning method is based on high-resolution traffic flow data, and there are still a few problems to be addressed. In fully congested areas or at the entrance of intersections with red lights, the local traffic flow speed will fluctuate within a range close to zero. If decisions are made by simply minimizing travel time without constraints, the stability of the results will deteriorate. In other words, when the traffic flow speed in each lane is below a certain value, decisions should be made based on evaluation indicators other than travel time. On the other hand, during the simulation tests, the motion states of all traffic vehicles within the outlook region were used to calculate the traffic flow status. However, in real road environments, the penetration rate of connected vehicles is limited, which reduces the availability and quality of high-resolution traffic flow data. Nevertheless, foreseeable technological advancements in the field of intelligent transportation systems in the future could make traffic flow monitoring and detection more precise; thereby, the impact of this adverse factor would be effectively controlled.

Author Contributions

Conceptualization, Q.Z. and H.G.; Methodology, Q.Z. and H.G.; Resources, H.G.; Software, Q.Z.; Supervision, H.G.; Validation, Q.Z.; Writing—original draft, Q.Z. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1 Multiple lane changes required to enter the target lane.

Figure 2 Hierarchical framework of whole driving task. The right part indicated by the orange arrow represents the result of further decomposition of the existing tactical functions. The surrounding region primarily involves a series of functions that focus on rapid response, such as obstacle avoidance, while the outlook region focuses on the overall driving strategies the vehicle adopts to address upcoming traffic situations.

Figure 3 Spatial composition of the lane-level driving task in the proposed method.

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.

Figure 5 The modeling of lane-change maneuver.

Figure 6 Available exit nodes in the directed graph.

Figure 7 Simulation framework.

Figure 8 Expected traffic flow status in scenario 1 (a) and scenario 2 (b).

Figure 9 Actual traffic flow status in scenario 1 (a) and scenario 2 (b) in the simulation.

Figure 10 The parameter configuration of VTD’s pulk traffic.

Figure 11 The lane change histories of the proposed model (a) and the baseline model (b) in scenario 1.

Figure 12 The driving trajectories of the proposed model (a) and the baseline model (b) on the road segment in scenario 1.

Figure 13 Comparison of lane change histories of the proposed model and the baseline model in scenario 1.

Figure 14 Comparison of driving trajectories of the proposed model and the baseline model in scenario 1.

Figure 15 Lane change histories of the proposed model (a) and the baseline model (b) in scenario 2.

Figure 16 Driving trajectories of the proposed model (a) and the baseline model (b) on the road segment in scenario 2.

Figure 17 Comparison of lane change histories of the proposed model and the baseline model in scenario 2.

Figure 18 Comparison of driving trajectories of the proposed model and the baseline model in scenario 2.

Figure 19 The large gap between controlled vehicles after a long simulation time. The blue boxes in the figure mark the controlled vehicles used to generate expected traffic flow and the yellow box marks the traffic vehicle that is changing lanes. Because the controlled vehicle in the top lane (innermost lane) is set to a faster speed, after a long simulation time, it forms a larger gap with the controlled vehicles in other lanes. This will allow other traffic vehicles to change lanes and overtake, resulting in an increase in the traffic flow speed in the top lane (innermost lane).

Figure 20 Traffic flow speed in each lane after a long simulation time.

Table 1

Key parameters of proposed method in simulation.

Variable	Meaning	Value
$∆l$ (m)	longitudinal dimension of lane cell	$max\left(v,5.6\right)$
$b$$(\mathrm{m}/{\mathrm{s}}^2$)	average braking deceleration during daily driving	2.2
$t_{light}$ (s)	the time for turning on the turn signal to indicate intent	3
$\lambda$ (s)	the coefficient about the limitation of lane-change times	0.2

Table 2

The statistics of the running results from five test runs in scenario 1.

Index	Node		Edge (Longitudinal)		Edge (Lateral)		Time (ms)
	Mean	Max	Mean	Max	Mean	Max	Mean	Max
1	210	210	203	203	164.12	168	4.49	11.38
2	210	210	203	203	164.57	168	4.65	11.35
3	210	210	203	203	164.61	168	4.53	13.91
4	210	210	203	203	164.17	168	4.44	12.12
5	210	210	203	203	164.63	168	4.46	12.85

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