A Framework for Lane-Change Maneuvers of Connected Autonomous Vehicles in a Mixed-Traffic Environment

Abstract

In the transition era towards connected autonomous vehicles (CAVs), the sharing of the roadway by CAVs and human-driven vehicles (HDVs) in a mixed-traffic stream is expected to pose safety and flow efficiency concerns even though CAVs may tend to adopt rather conservative maneuvering policies. Unfortunately, this will likely cause HDV drivers to unduly exploit such conservativeness by driving in ways that imperil safety. A context of this situation is lane-changing by the CAV, a potential major source of traffic disturbance at multi-lane highways that could impair their traffic flow efficiency. In dense, high-speed traffic conditions, it will be extremely unsafe for the CAV to change lanes without cooperation from neighboring vehicles in the traffic stream. To help address this issue, this paper developed a framework through which connected HDVs (CHDVs) could cooperate to facilitate safe and efficient lane-changing by the CAV. A numerical experiment was carried out to demonstrate the efficacy of the framework. The results indicated the CAVs’ lane-changing feasibility and the overall duration of the lane-changing if the CAV carries out that maneuver. It was observed that throughout the lane-changing process, the safety of not only the CAV but also of all neighboring vehicles, was promoted through the framework’s collision avoidance mechanism. The overall traffic flow efficiency was analyzed in terms of the ambient level of CHDV–CAV cooperation. Overall, the results of the study present evidence of how CHDV–CAV cooperation can help enhance the overall system efficiency.

1. Introduction

After the introduction of connected autonomous vehicles (CAVs) on public roads, there will likely exist not only dedicated lanes for CAVs at certain locations but also shared lanes where CAVs and human-driven vehicles (HDVs) will co-exist in a mixed-traffic stream. In the transition period (the time between the CAVs introduction and their full market penetration), mixed traffic on shared lanes will be prevalent as infrastructure agencies may be unable to raise the funding needed to provide dedicated lanes at all locations. It is anticipated that even though CAVs may tend to adopt rather conservative maneuvering policies in deference to HDVs, such sharing of the roadway will pose concerns related to safety and flow efficiency. In this introduction, we discussed safety and efficiency issues in the era of mixed traffic, the challenges associated with CAV lane-changing, and the prospective benefits of vehicle connectivity in addressing these challenges. We demonstrated that the safety and efficiency of a mixed-traffic stream can be enhanced using a cooperative control framework that accounts for CHDVs drivers’ intentions to cooperate with the CAV with whom they share the road space.

1.1. Safety in the Mixed-Flow Era

The recent literature has stated that autonomous vehicles (AVs) will profoundly impact the safety performance of transportation systems. This is an important expectation, given that traffic-related accidents are the second leading cause of death between the ages of 5 and 29, and the third leading cause of death between the ages of 30 and 44 [1]. According to a report from the National Highway Traffic Safety Administration, the potential of AVs to save lives and reduce injuries is particularly welcome due to the realization that 94% of serious crashes are due to human error [2]. Autonomous driving is expected to remove or at least mitigate human error and thereby reduce crashes [3,4]. This can be most effective when the market penetration of the AVs is 100%. However, the transition phase of HDVs to AVs (and thus, the specter of mixed-traffic streams) will last longer than most stakeholders expected [5]. The Volvo CEO Hakan Samuelsson stated that it would be “irresponsible” to put AVs on the road if they were not sufficiently safe, because that would erode trust among the public and regulators [6]. Consistent with his statement, it can be argued that on-road AVs should (and will) be “sufficiently” safe. However, this could cause the AV to behave too conservatively in the mixed-traffic stream. Such concern is well-justified, because the conservative control policies adopted by AVs may likely cause HDVs to unduly exploit the AV conservativeness by driving in ways that imperil safety. In other words, realizing the tolerant nature of AV operations, HDVs may undertake driving behaviors (for example, texting) and maneuvers (for example, keeping small headways) that are inherently less safe than they would do in an all-HDV traffic environment. One such example is Google’s self-driving car which experienced a crash because an HDV violated stopping regulations at a stop sign [7]. Such HDV behavior may be deliberate and conscious or may be due to risk compensation. A specific context of this situation is lane-changing by the AV, as we discussed in the next section of this paper.

1.2. AV Lane-Changing Challenge

The lane-changing maneuver is critical to road safety as 40% of freeway accidents occur in ramp areas [8]. A freeway-exiting vehicle located in the fast lane will need to perform multi-lane-changing maneuvers to get to the ramp, which can be extremely unsafe for HDVs and much more so for AVs. AVs (at least in their current stage of development) lack the dexterity of human drivers; therefore, their operations need to be conservative in order to be safe. Unfortunately, such conservative behavior would not only leave AVs more vulnerable to aggressive human drivers but could also inhibit the interpretability of drivers’ intentions. In a recent analysis of California traffic incidents involving AVs, Favarò et al. [9] found that in 57% of crashes, the AV was rear-ended by a human driver. Evidently, vehicle automation cannot eliminate all the human errors from the system. In the context of mixed-traffic operations, human error can be classified as: (a) Type I, where human error is endogenously related to the vehicle and can be addressed by completely removing humans from the vehicle control; and (b) Type II, where the human error is exogenously related to the ego vehicle, in other words, the human error is from neighboring vehicles in the traffic stream and cannot be easily addressed by minimizing the human–vehicle interaction [10]. In the research area of AV lane-changing maneuver, most of the literature has focused on how AVs perform “sufficiently” safe [11,12,13] but did not account for the risk faced by AVs emanating from other HDVs in the traffic stream. In short, they focused only on Type I human error but did not address Type II human error.

Figure 1 presents two examples of dense traffic where the AV needs to perform a mandatory lane-changing maneuver to a target lane [14]. When there are connected AVs (CAV) on the target lane, the ego AV (the AV that is seeking to change lanes) prospectively requests (through connectivity) the cooperation of these neighboring CAVs so that it can changes lane smoothly. On the other hand, when there is dense HDV traffic on the target lane, it is difficult for a conservative AV to change lanes without the HDVs’ cooperation. This is an issue of significant concern because lane-changing maneuvers represent a major cause of traffic disturbance at multi-lane freeways [15], and low efficiency lane-changing maneuvers cause traffic flow disruptions in the sections in the vicinity of the ramp [14,16,17]. Therefore, it can be hypothesized that AV–HDV cooperation (through connectivity) can help address AV lane-changing anxiety. Additionally, any such cooperation framework actualized via a centralized control of the local traffic flow could help enhance road traffic safety.

1.3. The Potential Safety Benefits of Connectivity

Connectivity is the capability of vehicles to communicate and share information with other systems (such as vehicles, infrastructure, roadside unit, etc.) through various relatively short- and long-range connectivity technologies [18,19]. As a sibling technology, connectivity plays a key role in magnifying the capabilities and benefits of vehicle automation. Through connectivity, automated vehicles will be able to communicate with other vehicles (V2V) or infrastructures (V2I) [20] over communication ranges that exceed the limited range of their on-board sensors. In situations involving hazardous roadway conditions, drivers of connectivity-equipped vehicles can receive warning notifications and alerts through V2X connectivity. In the United States, the NHTSA duly recognizes that connectivity is a promising technology that can prevent 615,000 crashes and, thereby, significantly reduce the number of fatalities and serious injuries associated with highway crashes [2]. Furthermore, a core aspect of the USDOT’s intelligent transportation system research program is the Connected Vehicle Research Initiative [21]. With the help of connectivity capabilities, cooperation between vehicles during their operational maneuvers, including lane-changing and car-following, can be enhanced [22,23,24,25]. In other words, in a mixed-traffic stream consisting of HDVs and CAVs, the CAV lane-changing maneuvers can be made safer and smoother if the vehicles in the traffic stream are connected. Moreover, by equipping AVs and HDVs with connectivity, the safety of neighboring vehicles can be promoted.

1.4. Fostering Centralized Cooperative Control Using Model Predictive Control (MPC)

Connectivity capabilities can help realize cooperative control, for example, where a centralized control platform is made to control (via override) the speeds of vehicles in the traffic stream of interest. This can be considered an extension of the cooperative adaptive cruise control (CACC) concepts as discussed in Milanés et al. [26]. In a complex environment where multiple vehicles interact with each other, decentralized control might yield a situation where decisions will likely be based on incomplete information. On the other hand, centralized control that combines global information in the system may yield a superior overall performance [27]. Typically, centralized control problems involve multiple constraints, and MPC has been shown to be effective for solving motion planning problems with multiple constraints [28,29,30,31,32]. Thus, MPC is used in designing the cooperative control framework.

1.5. Cooperation Intention of Human Drivers with Connectivity

Vehicle manufacturers and other stakeholders in the automobile industry recognize the value of connectivity and seek ways to incorporate connectivity with HDVs [21,33]. Compared with other sensing and short-range communication technologies, including light detection and ranging (LiDAR) and video, connectivity has several advantages [10]. First, V2V connectivity, which can be realized through smartphone or simple Bluetooth technology, has already been accepted by drivers [34,35]. Second, connectivity technology has a larger service range [36]. Third, V2V connectivity is not prone to locational occlusion or inclement weather and therefore allows drivers to receive roadway information in advance even without a clear line of sight [37,38]. Finally, connectivity is less expensive and, therefore, more affordable and practical for installation on vehicles [39]. For all its merits, however, there are a few issues associated with connectivity. The benefits of connectivity can be realized only when human drivers comply with the information transmitted through connectivity [40]. Additionally, the effect of connectivity (and therefore its merits) is expected to differ among drivers because different drivers respond differently to information received from external sources [41]. In other words, different drivers may have different intention levels for cooperation. For this reason, it is not just important but also imperative, for purposes of practicality, to investigate the impact of different levels of cooperation intention of the connected HDVs (CHDVs) on the performance of the proposed cooperative control framework.

To address the gaps in the literature, this paper used MPC theory to formulate a cooperative control framework that incorporates connectivity and automation. The framework is applied to help CAVs in mixed traffic to undertake lane-changing successfully, and such success is measured in terms of safety and efficiency. These benefits pertain to not only the CAV and nearest CHDVs but also other vehicles in the outerneighborhood of the lane-change location. The framework is duly cognizant of human drivers as it considers the cooperative intention of the human drivers as an important factor. CHDVs refer to human-driven vehicles that have connectivity capability and therefore communicate with the CAV and with each other. In this study, we considered several different combinations of the CHDVs’ cooperative intention levels and locations.

This paper was organized as follows: Section 2 describes the problem formulation of the cooperative control framework. Section 3 introduces the controller design and detailed mathematical control models. Section 4 presents and analyzes the simulation results. Section 5 summarizes the study and offers concluding remarks.

2. Problem Formulation

Consider a CAV on a highway segment that needs to change lanes from a current lane to a target lane. The reason for the intended lane change could be a construction work zone or an accident located on the same lane downstream. Ideally, the CHDVs on the target lane cooperate with the CAV (through communication) by creating a gap through which the CAV can merge and thereby change lanes successfully. However, the cooperative intention of the CHDV human drivers will not always be 100%. The effect of the different levels of the CHDV’s cooperative intention, as well as their different locations, need to be considered in any lane-change control framework. Throughout the lane-changing process, it is vital that the control framework guarantees a certain minimum level of safety in terms of the relative distance and relative velocity between any vehicle pair. Therefore, throughout the lane-changing process, the changing of relative distances and relative velocities among each vehicle pair (CAV–CHDV and CHDV–CHDV) will influence the centralized control framework’s decisions. This framework controls the acceleration and deceleration rates of the CHDVs on the target lane, in order to create a safe gap based on the safety requirements and efficiency. The problem settings and control framework are introduced in subsequent subsections.

2.1. Problem Settings

As stated above, the control framework considers both the cooperative intention and relative position of the CHDVs on the target lane. Figure 2 presents an example of the combination of CHDVs’ cooperative intention levels and relative positions. The target vehicle of interest (the CAV that needs to change lanes) is termed the target connected and autonomous vehicle (TCAV). Two cooperative levels are considered and indicated by different colors: green vehicles are those which actively cooperate, while grey vehicles are those that are less active in cooperating. Additionally, two relative positions are considered: the vehicles within the blue-outlined square area are the vehicles that are close to the TCAV, which are defined as immediate neighbors of the TCAV, and the vehicles in the yellow-outlined square area but not in the blue-outlined square area are the vehicles that are relatively further away from the TCAV, which are defined as outer neighbors of the TCAV. Both vehicle types are located in the connectivity range of the TCAV. Based on their positions, the CHDVs can be further categorized as PHDVs (CHDVs that precede the TCAV) and FHDVs (CHDVs that follow the TCAV). The planned trajectory of the TCAV’s lane change needs to consider the immediate neighboring CHDVs in terms of their longitudinal positions along the same lane: the ending longitudinal position of the TCAV lane-change trajectory ($x_e^{TCAV}$) needs to be within the future ending longitudinal positions of the immediate neighboring CHDVs $(x_e^{FHDV}<x_e^{TCAV}<x_e^{PHDV}, FHDV, PHDV\in \left\{immediate neighbors\right\}$).

As shown in Figure 2, in the lane-changing situation, crashes most likely happen between the lane-changing vehicle and vehicles in the target lane that are neighboring to it (particularly between the lane-changing vehicle and its immediate neighboring vehicles). Once the collision between the lane-changing vehicle and the immediate neighboring vehicles takes place on the target lane, secondary crashes can be triggered (between immediate neighboring vehicles and outer neighboring vehicles). Therefore, the control framework needs to consider different vehicle interactions: (a) TCAV–immediate neighboring vehicles, and (b) immediate neighboring vehicles–outer neighboring vehicles.

Table 1. Abbreviations and Terms.

Abbreviations/Terms	Explanations
CAV	Connected and Autonomous Vehicle
TCAV	Target Connected and Autonomous Vehicles (lane-changing vehicle)
CHDV	Connected Human-Driven Vehicle
HDV	Human-Driven Vehicle
FHDV	Following Human-Driven Vehicle
PHDV	Preceding Human-Driven Vehicle
Immediate Neighboring	Nearest neighboring vehicles of TCAV in the connected range
Outer Neighboring	Outer neighboring vehicles of TCAV in the connected range

lists the abbreviations and terms used in this paper.

2.2. Assumptions

This study was based on several assumptions:

(1)

The initial bumper-to-bumper headway is set based on the initial velocity.

(2)

The planned trajectory in each time step is a cubic polynomial curve [42].

(3)

The TCAV’s lane-changing trajectory is planned based on the future end position of the FHDV and PHDV in the immediate neighboring location.

(4)

The CHDVs (FHDVs and PHDVs) on the target lane are the controlled vehicles, which perform the lane-keeping maneuver with their acceleration/deceleration controlled by the central platform.

(5)

The velocities of all the vehicles in the system are normally distributed.

(6)

The dynamic and static features of the vehicles are considered the same.

(7)

The state of the controlled vehicles includes two parts: (a) longitudinal positions, (b) velocity.

Researchers established that using a buffer area to represent the vehicle is an appropriate way to minimize vehicle crashes in the analysis [43,44]. In this research, we used a circular buffer area. As shown in Figure 3, to avoid collision, there should be no overlapping or tangential contact between the buffer circles.

3. Methodology

In this section, we introduced the cooperative control framework based on the MPC method. Then we formulated the detailed CAV lane-changing trajectory planning model and the model for the controlled CHDVs motion. Then we discussed, in detail, the optimization problem of the MPC control framework.

3.1. Control Framework

The cooperative control framework was designed particularly to control the acceleration/deceleration of CHDVs in the target lane to assist the TCAV’s lane-changing maneuver. Thus, as shown in Figure 4, two major parts were included in the control framework:

• Lane-changing trajectory planning model for TCAV, which was formulated based on two considerations: (a) lane-changing trajectory and (b) velocity.
• MPC control models for CHDVs on the target lane, which guarantees the crash avoidance of the local system by considering vehicles’ interactions. The inputs are the current states of the CHDVs (longitudinal positions, velocity) and the TCAV’s current lane-changing information of (trajectory, velocity). The outputs are the CHDVs’ acceleration or deceleration rates.

More complex constraints in terms of the CHDV and CAV system dynamics, control efforts, longitudinal positions, velocities, and comfort levels were considered under different conditions using constraint sets. The MPC controller was applied based on its ability to handle multiple constraints [45,46]. The ending position of the planned trajectory of the TCAV needs to be within the ending positions of the immediate neighboring FHDV and PHDV. Thus, the motion-planning of the TCAV considers the range of the CHDVs’ positions. After generating the planned trajectory and velocity, the MPC will control the acceleration or deceleration of the CHDVs to avoid crashes based on two safety requirements: (a) velocity (for FHDVs, the velocity needs to be strictly less than the TCAV’s, while for PHDVs, the velocity needs to be strictly greater than the TCAV’s); (b) bumper-to-bumper distance (for all the CHDVs, they need to keep the bumper-to-bumper distance greater than the safety distances to any of their neighbors). Thus, the trajectory and velocity of the TCAV is regarded as an important reference for the controlled decisions for the CHDVs in terms of crash avoidance. In the proposed MPC controller, cooperative intentions are associated with constraints. Velocity constraints are soft constraints while bumper-to-bumper constraints are hard constraints. Both actively and inactively cooperating CHDVs strictly satisfy the bumper-to-bumper distance constraints. On the other hand, the situation is different in the case of velocity: the velocity of each actively cooperating CHDV strictly satisfies the safety requirements throughout the process. However, for CHDVs that are less actively cooperating, the velocity is allowed to exceed the limit to a specified degree δ. The detailed controller design is introduced in the following subsections.

3.2. TCAV Trajectory Planning Model

Motion planning consists of (a) trajectory planning and (b) speed profile generation. The planned trajectory at each time step is represented by a cubic polynomial curve ($y\left(x\right)=ax+b{x}^2+c{x}^3$) with the second smoothness [42].

$$y_t\left(x_t\right)=-tan{\theta }_t^i+\frac{2x_t^{e}tan{\theta }_t^i-3y_t^e}{{\left(x_t^e\right)}^2}{x}_t^2+\frac{2y_t^e-x_t^{e}tan{\theta }_t^i}{{\left(x_t^e\right)}^3}{x}_t^3$$

(1)

In Equation (1), ($x_t,y_t$) is the position of the TCAV at time $t$. $x_t$ and $y_t$ are the longitudinal and latitudinal positions of the TCAV, respectively. $x_t^e$ represents the ending logitudinal position of the TCAV, which is decided by the rollover-free boundary as well as the future ending positions of the CHDVs (discussed in a subsequent section of this paper) in the immediate neighboring location of the TCAV. $\theta$ represents the course angle of the TCAV, which is the angle between the moving direction and the x-axis. ${\theta }_t^i$ is the initial moving direction angle at time step $t$. The final position’s course angle equals to zero (${\theta }_e=0$; $y_t^{\prime }\left(x_t^e\right)$ = 0). The rollover-free boundary is calculated based on Yang et al.’s model [42]:

$$x_n^f=\frac{6y_t^e{v}_t^i}{\sqrt{6y_t^e{a}_s^r}}$$

(2)

where $y_t^e$ represents the ending latitudinal position, and $v_t^i$ represents the initial velocity towards moving direction at time step $t$. The $a_s^r$ is the boundary latitudinal acceleration, and the value is set as $6.958$ m/s², which is based on Sun and Wang’s research on lane-changing lateral acceleration [47].

The speed profile is generated with the purpose of completing the lane-changing in as short time as possible. The velocity profile of the TCAV can be calculated based on the ending position. When the rollover-free boundary is considered as an appropriate ending position, the proper longitudinal acceleration can be represented as:

$$a=\frac{2\left(\frac{6y_t^e{v}_t^i}{\sqrt{6y_t^e{a}_s^r}}-v_t^i\tau \right)}{{\tau }^2}$$

(3)

where $\tau$ is the length of a single time step. If we assume the highest longitudinal acceleration rate is $a_{max}$, then the appropriate aggressive longitudinal acceleration can be represented as $min\left\{a,a_{max}\right\}$. Based on the acceleration, the aggressive velocity of the time step $t$ is therefore $v_n^i+min\left\{a,a_{max}\right\}\tau$.

To ensure safety, the final longitudinal position of the planned lane-changing trajectory needs to consider both the future ending positions of the CHDVs and the rollover-free condition. Figure 5 presents the detailed trajectory planning process. With the initial condition of the CAV and CHDVs’ (longitudinal positions, velocity), the CAV lane-change trajectory and the ending position are generated through a cubic polynomial model considering the rollover-free condition (Equation (1)). To ensure the safety among the CAV and CHDVs, at each time step, the planned lane-changing trajectory compares the rollover-free ending positions: $\left(x_f^r,\infty \right)$ with the ending positions of the immediate neighboring FHDV and PHDV ($e_{FHDV1},e_{PHDV1}$). The moving direction angle and longitudinal distance of each time step will change accordingly based on the CHDVs’ final positions, until the lane-change maneuver is completed. However, when the situation is not suitable for implementing a lane-changing maneuver, the TCAV waits for the next available gap.

3.3. Controlled CHDVs Motion Model

The CHDVs in this research refer to only those HDVs with connectivity. The controller can control only their longitudinal acceleration/deceleration and velocity but not their lateral movements. The motion model for each time step can be represented as a discrete-time model:

$$x\left(k+1\right)=x\left(k\right)+v\left(k\right)\tau +\frac{1}{2}a\left(k\right){\tau }^2$$

(4a)

$$y\left(k+1\right)=y\left(k\right)=c$$

(4b)

$$v\left(k+1\right)=v\left(k\right)+a\tau$$

(4c)

The symbol $c$ represents the constant latitudinal positions of the CHDVs. The motion model can be written in a compact form as:

$$\overline{x}\left(k+1\right)=A\overline{x}\left(k\right)+Bu\left(k\right)$$

(5a)

$$y\left(k+1\right)=C\overline{x}\left(k\right)$$

(5b)

$$for: \overline{\mathit{x}}\left(\mathit{k}\right)=\left[\begin{array}{c}x\left(k\right)\\ v\left(k\right)\end{array}\right], \mathit{A}=\left[\begin{array}{cc}1& \tau \\ 0& 1\end{array}\right], \mathit{B}=\left[\begin{array}{c}\frac{1}{2}\tau \\ \tau \end{array}\right]$$

(5c)

When $C$ is equal to $I_2$, the MPC controller can predict the states of the system in multiple sampling times to form a more accurate decision. $N_p$ represents the prediction horizon, which is the number of future control intervals that MPC evaluates. $N_c$ represents the control horizon, which is the number of control actions to optimize the control interval. The control horizon falls between 1 and the prediction horizon $N_p$. However, short control horizons may degrade the control performance. Thus, in this study, the relation between $N_p$ and $N_c$ is set to be $N_p=N_c+1$. The predicted outputs through the control interval can be written as

$$\overline{x}\left(k+1\right)=A\overline{x}\left(k\right)+Bu\left(k\right)$$

(6a)

$$\overline{x}\left(k+2\right)=A^2\overline{x}\left(k\right)+ABu\left(k\right)+Bu\left(k+1\right)$$

(6b)

…

$$\overline{x}\left(k+N_c\right)=A^{N_c}\overline{x}\left(k\right)+A^{N_c-1}Bu\left(k\right)+\cdots +Bu\left(k+N_c-1\right)$$

(6c)

$$\overline{x}\left(k+N_p\right)=A^{N_p}\overline{x}\left(k\right)+A^{N_p-1}Bu\left(k\right)+\cdots +\left(AB+B\right)u\left(k+N_c-1\right)$$

(6d)

The output sequence and input sequence can be represented in a more compact form, as

$$\mathit{X}\left(\mathit{k}+\mathbf{1}\right)={\left[\begin{array}{c}\overline{x}\left(k+1\right)\\ \overline{x}\left(k+2\right)\\ \overline{x}\left(k+3\right)\\ ⋮\\ \overline{x}\left(k+N_p\right)\end{array}\right]}_{N_p\times 1} \mathit{U}\left(\mathit{k}\right)={\left[\begin{array}{c}u\left(k\right)\\ u\left(k+1\right)\\ u\left(k+2\right)\\ ⋮\\ u\left(k+N_c-1\right)\end{array}\right]}_{N_c\times 1}$$

(7)

Based on the output and input sequence, the system prediction can be written as $X\left(k+1\right)=M_x\overline{x}\left(k\right)+M_{u}U\left(k\right)$, where

$${\mathit{M}}_{\mathit{x}}={\left[\begin{array}{c}A\\ A^2\\ \begin{array}{c}⋮\\ A^{N_c}\end{array}\\ A^{N_p}\end{array}\right]}_{N_p\times 2}{\mathit{M}}_{\mathit{u}}={\left[\begin{array}{cccc}B& 0& \cdots & 0\\ AB& B& \cdots & 0\\ ⋮& ⋮& \ddots & ⋮\\ A^{N_c-1}B& A^{N_c-2}B& \cdots & B\\ A^{N_p-1}B& \cdots & \cdots & \left(A+1\right)B\end{array}\right]}_{2N_p\times N_c}$$

(8)

3.4. Optimization Problem Associated with the MPC Controller

The MPC controller considers the relative position of the TCAV and its neighboring CHDVs. As discussed previously, there are various classes of vehicle-to-vehicle interactions that need to be considered. For the CHDVs in an immediate neighboring location, both the interactions with the TCAV and the interactions with outer neighboring CHDVs are considered. While for CHDVs in the outer neighboring location, only the interactions with the CHDVs in their neighboring area (the immediate neighboring CHDVs) are considered. The objective is to control the CHDVs and TCAV to cooperatively complete the lane-changing process while avoiding the collision of any vehicles in the system. If the feasibility cannot be satisfied at the first attempt, the TCAV will stand by and the CHDVs will be controlled to adjust their velocities to create the gap to make it feasible for the lane-change process to commence. The objective functions are formulated differently in terms of the location of the CHDVs. Moreover, the constraints for the following vehicles (FHDVs) and the preceding vehicles (PHDVs) are different.

The objective function of the CHDVs in the immediate neighboring location consists of the tracking of the TCAV, control inputs, velocity soft constraints, and comfortableness measure (or, Jerk). $r(.)$ is the lane-changing information of the TCAV used as reference in the optimal control problem, and $P,Q,R$ are the weight parameters in the cost function. The control variables are $\overline{u}$, which represents the deceleration/acceleration, and $\overline{\delta }$, which represents velocity soft constraints (i.e., velocity is allowed to exceed the limit to a specified degree $\overline{\delta }$. For example, the safety velocity is supposed to be strictly smaller than $v_s$, but with soft constraints, the velocity can be smaller than $v_s+\overline{\delta }$):

$$J_1=\underset{\overline{u},\overline{\delta }}{\min }{\displaystyle \sum }_{k=1}^{N_p}\Vert \overline{x}\left(k+n\right)-r{\left(k+n\right)\Vert }_Q^2+{\displaystyle \sum }_{k=1}^{N_c}\Vert \overline{u}{\left(k+n-1\right)\Vert }_R^2+\Vert \overline{\delta }{\left(k+n-1\right)\Vert }_P^2+Jerk$$

(9)

$s.t.\left(n=1,\dots ,N_p\right)$

$$\overline{x}\left(k+n\right)=A\overline{x}\left(k+n-1\right)+B\overline{u}\left(k+n-1\right)$$

(10)

$$d_{max}\le \overline{u}\left(k+n-1\right)\le a_{max}$$

(11)

Equation (10) represents the system equation, and $d_{max}$, $a_{max}$ in Equation (11) represent the maximum deceleration and acceleration rates. Moreover, the comfort (lack of jerk) is considered. CHDVs give up their speed to cooperate with the TCAV, and in practice, the comfort (or, lack of jerk) that is associated with the deceleration/acceleration is an important factor that influences the CHDV driver’s compliance with the CAV controller recommendations. Jerk has a significant impact on the safety and comfort of passengers. The jerk cost function considers the change of the acceleration/deceleration through the control horizon:

$$J={{\displaystyle \int }}_{t_0}^{t_f}{\displaystyle \sum }_{i=1}^m{\tilde{u}}_i{}^{2}dt$$

(12a)

In this research, we considered using the prediction horizon as $N_p=5$, control horizon as $N_p=N_c-1=4$ to ensure the sufficient condition of the system stability after the control efforts, which are based on previous research [10]. The difference between the control inputs can be represented in a compact form, as follows:

$${\left[u_1,u_2,u_3,u_4\right]}^T\mathit{C}\left[\begin{array}{c}{u}_1\\ u_2\\ u_3\\ u_4\end{array}\right], \mathit{C}=\left[\begin{array}{cccc}1& -1& 0& 0\\ -1& 2& -1& 0\\ 0& -1& 2& -1\\ 0& 0& -1& 1\end{array}\right]$$

(12b)

For the CHDV that follows the TCAV on the target lane, the constraints can be described as follows:

$$\overline{x}\left(k+n\right)-r\left(k+n\right)\le \left[\begin{array}{c}-l_1\\ \overline{\delta }\left(k+n-1\right)\end{array}\right] for:k=1, \dots , N_c$$

(13a)

$$\overline{x}\left(k+n\right)-r\left(k+n\right)\le \left[\begin{array}{c}-l_1\\ 0\end{array}\right] for:k=N_p$$

(13b)

$$\overline{x}\left(k+n\right)-r\left(k+n\right)\ge \left[\begin{array}{c}\sqrt{4R^2-{\left(l_y^{\overline{x}}\left(k+n\right)-l_y^r\left(k+n\right)\right)}^2}\\ -\overline{\delta }\left(k+n-1\right)\end{array}\right]$$

(13c)

$$\overline{u}\left(k+n-1\right)\ge \frac{2\left(l_2-\Delta x\left(k+n-1\right)\right)}{{\tau }^2}+d_{max}$$

(13d)

For the CHDV that precedes the TCAV on the target lane, the constraints are different:

$$\overline{x}\left(k+n\right)-r\left(k+n\right)\ge \left[\begin{array}{c}{l}_1\\ -\overline{\delta }\left(k+n-1\right)\end{array}\right] for:k=1, \dots , N_c$$

(14a)

$$\overline{x}\left(k+n\right)-r\left(k+n\right)\ge \left[\begin{array}{c}{l}_1\\ 0\end{array}\right] for:k=N_p$$

(14b)

$$r\left(k+n\right)-\overline{x}\left(k+n\right)\ge \left[\begin{array}{c}\sqrt{4R^2-{\left(l_y^{\overline{x}}\left(k+n\right)-l_y^r\left(k+n\right)\right)}^2}\\ \overline{\delta }\left(k+n-1\right)\end{array}\right]$$

(14c)

$$\overline{u}\left(k+n-1\right)\le a_{max}+\frac{2\left(\Delta x\left(k+n-1\right)-l_2\right)}{{\tau }^2}$$

(14d)

$r\left(k+n\right)$ represents the state of the TCAV, which includes the longitudinal location and the velocity. $\Delta x\left(k+n-1\right)$ in Equations (13d) and (14d) represents the state difference between the CHDV in the immediate neighboring location ($\overline{x}\left(k+n-1\right)$) and CHDV in the outer neighboring location ($\widehat{x}\left(k+n-1\right)$). Thus,$\Delta x\left(k+n-1\right)$ equals to $\overline{x}\left(k+n-1\right)-\widehat{x}\left(k+n-1\right)$. The TCAV tracking in the objective function penalizes aggressive control actions. Moreover, the large control efforts will be penalized. The cooperative intention is shown through $\overline{\delta }\left(k+n-1\right)$, which denotes the violation allowance of the bound in the velocity constraint. Furthermore, the distance constraints (13a), (13b), (14a), and (14b) are applied to guarantee the safe requirements of longitudinal distance. $l_1$ represents the safety requirements in terms of longitudinal distance between the TCAV and immediate neighboring CHDVs. $l_2$ represents the safety requirements of longitudinal distance between the immediate neighboring CHDVs and the outer neighboring CHDVs. Additionally, the crash avoidance constraints (13c) and (14c) are applied to ensure safety by avoiding the tangent situations of the circle buffer areas. $R$ indicates the radius of the circle buffers. Constraints (13d) and (14d) are used to illustrate the relationship between the CHDVs on the target lane that are in the different locations. Those constraints help avoid any imminent secondary collision between CHDVs that neighbor each other.

The objective function of outer neighboring CHDVs is similar to that for the previous case except that the reference used here is $\overline{x}(.)$, which represents the immediate neighboring CHDVs’ information.

$$J_2=\underset{\widehat{u},\widehat{\delta }}{\min }{\displaystyle \sum }_{k=1}^{N_p}\Vert \widehat{x}\left(k+n\right)-\overline{x}{\left(k+n\right)\Vert }_Q^2+{\displaystyle \sum }_{k=1}^{N_c}\Vert \widehat{u}{\left(k+n-1\right)\Vert }_R^2++\Vert \widehat{\delta }{\left(k+n-1\right)\Vert }_P^2+Jerk$$

(15)

$s.t.\left(n=1,\dots ,N_p\right)$

$$\widehat{x}\left(k+n\right)=A\widehat{x}\left(k+n-1\right)+B\widehat{u}\left(k+n-1\right)$$

(16)

$$d_{max}\le \widehat{u}\left(k+n-1\right)\le a_{max}$$

(17)

The constraint set of the outer neighboring CHDVs in the following position of immediate neighboring CHDVs is

$$\widehat{x}\left(k+n\right)-\overline{x}\left(k+n\right)\le \left[\begin{array}{c}-l_2\\ \overline{\delta }\left(k+n-1\right)\end{array}\right]for:k=1,\dots ,N_c$$

(18a)

$$\widehat{x}\left(k+n\right)-\overline{x}\left(k+n\right)\le \left[\begin{array}{c}-l_2\\ 0\end{array}\right]for:k=N_p$$

(18b)

For the outer neighboring CHDVs in the preceding position of immediate neighboring CHDVs on the target lane, the constraints, which are different from those above, are

$$\widehat{x}\left(k+n\right)-\overline{x}\left(k+n\right)\ge \left[\begin{array}{c}{l}_2\\ -\widehat{\delta }\left(k+n-1\right)\end{array}\right]for:k=1,\dots ,N_c$$

(19a)

$$\widehat{x}\left(k+n\right)-\overline{x}\left(k+n\right)\ge \left[\begin{array}{c}-l_2\\ 0\end{array}\right]for:k=N_p$$

(19b)

The constraints (18a), (18b), (19a), and (19b) are imposed to help maintain a safe longitudinal distance between the neighboring CHDVs at different locations. $l_2$ represents the safety distance between the CHDVs in the immediate neighboring location and the outer neighboring location.

4. Simulations and Results

Simulation experiments were carried out under different sets of conditions. The key points considered in the simulations were

• The initial state of the CHDV on the target lane: this consisted of the initial longitudinal location and initial velocity.
• The cooperative levels of the CHDV: this was categorized as active cooperation vs. inactive cooperation.
• The connectivity proportions of the HDVs: this was categorized as active cooperation vs. non-cooperation.
• Multiple lane-changing simulations: more than one lane-change maneuver was considered.

Based on these considerations, there existed several different combinations of initial state in the simulations. The combinations could be placed into different categories in terms of the percentage of actively cooperating CHDVs and their positions (FHDV or PHDV). In this section, the influence of the cooperative level and location is discussed in detail. Moreover, the type that had a larger influence on the system efficiency served as the focus in the simulation in terms of feasibility and overall lane-changing time.

The simulation was implemented using MATLAB, with the following parameter setup: maximum deceleration rate, $d_{max}$ = −5.08 m/s²; maximum acceleration rate, $a_{max}$ = 5.08 m/s²; maximum longitudinal acceleration rate through lane-changing maneuver, $a_{max}^L$= 3.024 m/s²; time interval for each time step, τ = 0.2 s; reference TCAV trajectory and velocity r; longitudinal safety distance requirement, $l_1$ = 5 m; longitudinal safety distance requirement, $l_2$= 10 m; vehicle length, $l_v$ = 4 m; radius of vehicles’ buffer circle, $l_r$ = 3 m; lane width, $l_w$ = 3.7 m; weight parameter, P = 15; weight parameter, Q = 10; weight parameter, R = 10; prediction horizon, $N_p=5$; and control horizon $N_c=4$. The prediction horizon $N_p=5$ was based on the sufficient condition for stability mentioned in a previous study [10]. A rate of −5.08$\mathrm{m}/{\mathrm{s}}^2$ is the maximum longitudinal deceleration of the human driver to prevent an emergency situation [48]. $P,Q,R$ are defined appropriately to have the objective function as a convex function. In order to have a dense traffic on the target lane, four vehicles were considered in all the simulation experiments: two vehicles in the immediate neighboring location and the other two vehicles in the outer neighboring location. Moreover, their initial location was decided by the bumper-to-bumper distance based on their initial velocities. The vehicle length was 4 m, and the radius of the circle buffer area was defined as 3 m (the diameter of the circle buffer area was 6 m).

4.1. Percentage of Actively-Cooperating CHDVs

As mentioned previously, the CHDV at different locations can choose the level at which they seek to cooperate with CAVs. The number of actively cooperating CHDVs in the system influences the performance of the control framework. The nature and complexity of the optimization problem depends on the combination of the number and locations (immediate neighboring, outer neighboring) of the actively cooperating CHDVs. In this section, the performance of the control framework is evaluated using two matrices: (a) an initial feasibility under different situation in terms of the actively cooperating CHDVs, and (b) multiple lane-changing process times under the different combinations.

In Figure 6, there are three different combinations of actively cooperating CHDVs (which are indicated by green-colored cars in the figure). Figure 6a presents a low percentage (0%) of actively cooperating CHDVs), and Figure 6b presents the case where 50% are actively cooperating CHDVs; here, there exists several different combinations in terms of the CHDVs’ positions. Thus, in the experiment, we tested two cases; first, 50% are actively cooperating CHDVs in the following position (50% actively cooperating CHDVs are FHDVs), and, second, 50% are actively cooperating CHDVs in the preceding position (50% actively cooperating CHDVs are PHDVs). Figure 6c presents the highest percentage (100%) of actively cooperating CHDVs.

4.2. Feasibility of Different Percentage of Actively Cooperating CHDVs

The performance of the control framework varies by the different combinations of the percentage of actively cooperating CHDVs. One of the important factors that needs to be considered is feasibility (which indicates whether the CAV can lane change or not at a certain time). From previous research, lane change has been identified as the main operations context that influences the efficiency of freeway traffic operations, particularly at locations near the ramp area [14]. For example, when the lane-changing process is not feasible, the CAV will be unable to lane change directly; in other words, the CAV needs to wait for an available gap before it can carry out the lane-changing maneuver. This will cause low efficiency or even traffic flow congestion upstream of the CAV. However, if the feasibility can be satisfied, the CAV can change lanes immediately without significant impairment to the efficiency of other vehicles.

The cooperative control framework lends such infeasible situations a second chance by adjusting the CHDVs’ acceleration/deceleration rates. In the meantime, the CAV will keep waiting for the CHDVs to create the gap by maintaining the original speed. Thus, the initial feasibility will reach a higher level because of the “waiting–adjusting” strategy. Moreover, when multiple lane changes are considered, the connection between two lane-change processes will need to consider the “waiting–adjusting” strategy as well because the feasibility of the second lane-change process is uncertain.

Figure 7 presents four sub-figures under the different combinations. Figure 7a shows the actively cooperating CHDVs at 0%, the feasibility rates are low, particularly when the standard deviations of the velocities are high. Figure 7b,c have the actively cooperating CHDVs at 50% but in different locations (following vs. preceding the TCAV). The feasibility rates are improved under both situations. Figure 7d is when the number of actively cooperating CHDVs is at 100%, and it is observed that the feasibility rates improved significantly. There is a common pattern in all the sub-figures: the larger the standard deviation, the lower the feasibility rate. However, the change of the average speed of all the vehicles seems have less influence on feasibility. Therefore, it can be inferred that the relative velocities among the vehicles are important determinants of the system feasibility.

Furthermore, the feasibilities under different cooperative combinations were found to differ significantly. When the percentage of actively cooperating CHDVs was the highest, the average feasibility was at its maximum, that is, 94%. This is because active cooperation gives a higher chance for the CAV to maintain the current state and wait for a feasible situation created by the neighboring CHDVs. The feasibility when there is no actively cooperating CHDVs was 35%. In the situations where the percentage of actively cooperating CHDVs was 50%, the average feasibility rate was approximately 68%, which still represents an improvement compared to the situation where there was 0% actively cooperating CHDVs. Under the situations where the FHDV is feasible but the PHDV is not feasible, the actively cooperating PHDV will be easy to adjust to be feasible, to reach a feasibility rate of as much as 77%. However, in situations where the PHDV is feasible and the FHDV is not feasible, it will not be able to easily adjust the actively cooperating FHDV to be feasible. Moreover, the feasible rate is 59%. Thus, in the situation where the FHDV is not feasible, it is more difficult for the CAV to commence the lane-changing maneuver.

4.3. Multiple Lane-Changing Duration under Different Situations

Feasibility is a key factor in evaluating different cooperative combinations. However, it cannot reflect the relationship between a lane-changing cooperative combination and its efficiency. A straightforward way to do this is to analyze the total time for the lane-changing process. Such efficiency is an important evaluation metric of the control framework performance. In the simulations in this research, we focused on more than one lane-changing maneuver (Figure 8).

The total lane-changing process time is the sum of the two lane-changing maneuvers’ duration and the possible waiting time before each lane-changing maneuver starts. Figure 9 presents the total lane-changing process time with different percentages of actively cooperating CHDVs. Considering the double lane change, we obtained four different combinations: 0% of vehicles are actively cooperating CHDVs during both lane changes, 50% are actively cooperating CHDVs during both lane changes, 50% are actively cooperating CHDVs during one lane change and 100% are actively cooperating CHDVs during the second lane change, 100% are actively cooperating CHDVs in both lane changes.

In the simulation, in the case of 100% of the vehicles being actively cooperating CHDVs, the CHDVs are assigned larger rates of acceleration/deceleration compared to the case where 0% of the vehicles are actively cooperating CHDVs. Moreover, the waiting time for the CAV is set as 2 s (that is, 20-time steps for CHDVs to adjust their locations and speeds). In reality, when the mandatory lane change is caused by an emergency situation such as a sudden lane drop, an approaching construction work zone, or queue-jumping to veer off the road [49], waiting time needs to be considered. With regard to normal conditions without connectivity and cooperation, the waiting time can be within the range of 2.9 to 5.6 s (depending on the condition) [50]. However, by using the cooperation framework based on connectivity technology, emergency situations can be addressed efficiently with shorter waiting time (2 s). Typically, the lane-changing maneuver time takes 2 s. Therefore, a single lane-changing process time for a normal vehicle is between 4.9 and 7.6 s. Here, we consider the double lane-change process. Therefore, cases where the total lane-changing process time is larger than 10 s are not acceptable for our cooperation framework.

As shown in Figure 9a, when there are 0% actively cooperating CHDVs in the system for both lane-changing maneuvers, 56% of the cases have a total lane-changing process time as more than 10 s, which are shown as the dark area. In Figure 9b, the cases that have a total lane-changing as more than 10 s is lower (42%), which means 58% of the cases can complete the double lane change within 10 s. When one of the lane-changing processes has 50% of actively cooperating CHDVs and the other has 100% of actively cooperating CHDVs (Figure 9c), the cases of short lane-change time improve to 67%. It was observed that a higher percentage of actively cooperating CHDVs translates into a larger “high-efficiency” area (light-colored grids). However, when the percentage of actively cooperating CHDVs reaches 100% for the lane-changing maneuver across both lanes (Figure 9d), it is difficult to earn further improvement of the control performance. Specifically, because the standard deviation of the dark area is too high, it is difficult for the control framework to yield further improvements. Additionally, there are common patterns that can be observed across the results for the different combinations: generally, the higher the standard deviation, the lower the efficiency. The highest efficiency focuses on the initial condition where the velocity distribution has a small standard deviation, and the range of the mean velocity is 55 to 70 mph.

Furthermore, the location of the actively cooperating CHDVs will also affect the performance of the control framework. Figure 10a shows the situation where actively cooperating CHDVs are immediate neighbors of the TCAV, Figure 10b shows the situation where actively cooperating CHDVs are outer neighbors of the TCAV. The efficiency (total travel time) of Figure 10a is apparently higher than the Figure 10b. The cases of efficient lane-changing maneuvers take 67% when the actively cooperating CHDVs are immediate neighbors. However, the efficient lane-changing maneuvers take 56% when the actively cooperating CHDVs are outer neighbors.

4.4. Proportion of Human Driver Connectivity in Cooperative Control Framework

According to NHTSA in 2017, there is a published rule that requires all new vehicles to have Vehicle-to-Vehicle (V2V) communication capabilities. It is expected that vehicle manufacturers will phase the technology into their fleets over a few years, with all new vehicles being required to “talk” to each other by 2023 [51]. However, in the current era, there is still a long way to go in the realization of full connectivity of HDVs in the traffic stream, and therefore, vehicles without connectivity will not be able to receive any information or instructions (which means, they are non-cooperative). These vehicles may affect the performance of the cooperative control framework. Moreover, the locations and proportions of the non-cooperative HDVs may have different effects that need to be analyzed in detail.

In this paper, scenarios with different proportions of non-cooperative HDVs at different locations were analyzed. In Figure 11, the green-colored vehicles represent cooperative vehicles, and the white-colored vehicles represent non-cooperative vehicles. The figure presents three scenarios with different proportions of non-cooperative vehicles: 100% non-cooperative vehicles, 50% non-cooperative vehicles at preceding locations or following locations, and 0% non-cooperative vehicles.

In this study, a car-following model was used to describe the movement of non-cooperative vehicles in the cooperative control framework. The lane-changing TCAV can only observe the motion information (direction, speed and acceleration) without any cooperation from the HDVs. To analyze the effect of non-cooperative vehicles on the cooperative control framework performance, lane-changing feasibility was calculated under different proportions of non-cooperative vehicle.

Figure 12 presents the results of the proposed cooperative control framework under different proportions of non-cooperative vehicles. Figure 12a shows the performance of the cooperative control framework when there is 0% non-cooperative vehicles. In other words, all the vehicles are cooperative vehicles. Therefore, the feasibility rate is high (average is 94%) under this situation. However, as shown in Figure 12d, when the amount of non-cooperative vehicles is at 100%, it was observed that the feasibility rates dropped significantly (average was 28%), particularly in situations where the standard deviation of the vehicle velocity was large and mean velocity was high. Figure 12b,c have the non-cooperative CHDVs at 50% in different locations ((b) is preceding and (c) is following the TCAV). The feasibility rates are improved under both situations compared to Figure 12d: 63% for non-cooperative vehicles in the preceding positions and 71% for non-cooperative vehicles in the following positions.

It is observed that if the non-cooperative vehicles are FHDVs, the TCAV cannot find a feasibility gap while changing lanes in 29% of the. If the non-cooperative vehicles are PHDVs, the chance of failing to find a gap is 37%. This is because for the situations where the FHDV is feasible but the PHDV is not feasible, the actively cooperating PHDV will be easy to adjust to be feasible, while in situations where PHDV is feasible and FHDV is not feasible, it will not be able to easily adjust the actively cooperating FHDV to be feasible. Thus, the vehicles in the following positions have larger effects on the lane-changing feasibility of the TCAV. Furthermore, compared with the situations where all vehicles are cooperative, the chance of failing to find a gap is quite large. When the non-cooperative vehicles inactively cooperate, the chance of failing to finding a gap while lane-changing is as low as 23%, and when the vehicles actively cooperate, the chance of failing to find a gap is further reduced to 6%.

5. Conclusions

This paper focused on the challenges that AVs will encounter during the mixed-flow era. Previous studies on HDV lane-changing have ascertained that these maneuvers, as high speed situations, tend to be inherently unsafe and have low efficiency. It is expected that the safety issues associated with this problem will be exacerbated in the mixed-flow era where both HDVs and CAVs share the traffic stream. The expectation is that it will be much more difficult for the AV to carry out lane-change maneuvers because HDVs will perceive the on-road AVs as “sufficiently” safe devices that will react to avoid or mitigate any unsafe driving by the HDV. Even though such perceptions may cause the HDV drivers to engage in uncooperative driving behavior, they can hardly be faulted for making such assumptions in the first place because AVs will likely be programmed and controlled to drive rather conservatively. This paper formulated a cooperative control framework for connected HDVs to cooperate with the CAV to help them carry out safe and efficient lane-changing maneuvers. The cooperative control framework was based on the vehicle automation and V2V connectivity. The underlying theory of the framework, MPC control, was used to address the multi-car interactions and multiple constraints in the CHDVs optimal motion planning. An important consideration in the developed cooperative control framework is the level at which the human driven vehicles are expected to cooperate with the CAVs, and their different initial locations just before the CAV’s prospective lane change. Despite their connectivity capabilities, CHDVs, after all, are only “human” as they are operated by human drivers whose cooperation will profoundly influence the performance of the control framework. Therefore, consideration of the cooperative level of the various CHDVs in the traffic stream is of utmost importance. In the control framework design, we used two different levels to represent HDV-driver compliance: inactive cooperation and active cooperation. We designed the optimization problem in the MPC controller based on the level of cooperation as well as the initial locations of the HDVs. We also assumed that the human driver of any CHDV would not accept a certain threshold level of speed change abruptness. This ensures a certain level of passenger comfort in the controlled CHDVs and is represented by the jerk cost function in the optimization problem.

In the simulation part, the performance of the cooperative control framework was considered from two perspectives: first, the initial feasibility under different percentages of actively cooperating CHDVs and, second, the total process time for the bi-lane change in the simulation. From the results, we observed that a higher percentage of actively cooperating CHDVs in the system translate into a higher rate of lane-changing feasibility. With regard to the lane-changing process duration, we observed that when the percentage of actively cooperating CHDVs is higher, the efficiency of those cases (which is reflected by the total lane-changing process time) increases. Clearly, the level of active cooperation of the CHDVs is of critical importance to the successful performance of a lane-change maneuver. We also observed that the locations of the actively cooperating CHDVs influences the performance of the lane-changing maneuver: when the actively cooperating CHDVs are in the immediate neighboring location of the TCAV, the efficiency of the lane change is higher. It was also noted, in different situation settings and runs, that the feasibility of lane-changing maneuvers is affected by the locations of the actively cooperating CHDVs. It was determined that the following HDV (FHDV) affects the feasibility rate to a larger extent compared to the preceding HDV (PHDV). Similar cases were also found in situations where some vehicles are non-cooperating. In addition, compared to the situations with connectivity, our simulations showed that vehicles without connectivity will decrease the feasibility of the TCAV.

The proposed framework was designed to address the CAV lane-changing challenge at dense and high-speed traffic environments such as freeways. To address lane-changing challenges in all traffic environments including urban roadways, the framework structure, inputs, and parameters will need to be modified. CAV lane-changing at urban roads can be expected to be characterized by more complicated vehicle interactions and road designs such as signalized intersections and roundabouts. Therefore, the optimization aspect of the cooperative control framework will need to include additional constraints to capture these interactions and design features. In future efforts to address these road environments, simulation platforms such as SUMO and VISSIM can be used to test the efficacy of the cooperative control framework developed in this study. This can be done under various combinations of non-cooperative vehicles, and actively and inactively cooperating vehicles.

This research demonstrates the benefits of the CHDV–CAV cooperative network to the CAV in the mixed-traffic stream and the importance of the cooperation (via compliance) of CHDVs in the neighborhood of the CAV. A network of actively cooperating vehicles in the neighborhood of the CAV will yield high efficiency not only for CAVs but for the overall system, including CHDVs.