Abstract
To improve the driving efficiency and energy-saving characteristics for large-scale mixed traffic flows under different market penetration rates (MPRs) of intelligent and connected vehicles (ICVs) at unsignalized intersections, considering the cooperative eco-driving performance between ICVs and human-driven vehicles (HDVs) with time-varying speed characteristics, the hierarchical and distributed cooperative eco-driving architecture is first established in this paper, consisting of a cloud decision layer and a vehicle control layer. For the cloud decision layer, the multivehicle model-free adaptive predictive cooperative driving (MFAPCD) method is designed by using only the driving data of the HDVs and ICVs formation based on compact form dynamic linearization (CFDL) technique, thereby improving traffic efficiency. Furthermore, the CFDL integral terminal sliding mode predictive control (CFDL-ITSMPC) scheme is utilized to predict the time-varying driving speed of HDVs, and then, the CFDL predictive control (CFDL-PC) scheme is utilized to predict the expected control variables of ICVs formation. For the vehicle control layer, based on the anticipated driving speed obtained from the cloud decision layer, the nonlinear distributed model predictive control (NDMPC) method is utilized for distributed optimal control of each vehicle formation, to achieve optimization in terms of energy saving. Simulation results show that, compared with the signal time assignment strategy, the method can increase the average velocity by about 15.22% and decrease the average fuel consumption by about 36.43% under different MPRs and traffic volumes.
1. Introduction
The ICVs enabled by the new generation of information and communication technology can provide new ideas for solving problems such as high time consuming and poor energy saving for vehicles to pass through intersections [1]. Given the current traffic situation, the transition from today’s largely human-driven traffic to purely automated traffic will be a gradual process, with the fact that we may experience mixed traffic shortly. Therefore, in such a transitional period, it is necessary to design a driving scheme to coordinate the mixed traffic flows of ICVs and HDVs, which is of great significance for improving traffic efficiency and reducing fuel consumption.
At present, several driving efficiencies and energy-saving improvement methods have been proposed under different MPRs and traffic volumes oriented to signal-controlled intersections, such as the timing and optimization of traffic signals for cooperative driving of hybrid vehicles [2–4]. However, with the continuous improvement of the communication network infrastructure and the intelligent level of ICVs, the transportation system will be more intelligent, and the traffic lights will be replaced by the infrastructure called intersection manager. Moreover, there are also several scholars focused on a multivehicle cooperative driving method to improve the driving efficiency or energy-saving for mixed traffic flows at such nonsignal-controlled intersections. Zohdy and Rakha [5] proposed an improved cooperative adaptive cruise control (iCACC) system, and the traffic efficiency and fuel consumption of intersections under different MPRs were discussed, in which HDVs with given driving states can maintain a safe driving distance from ICVs. Qian et al. [6] proposed a priority-based coordination system with the hypothesis that the driving state of HDVs is accurately known and can maintain a safe distance from their leading ICVs to enhance intersection efficiency. Yang and Oguchi [7] proposed a traffic model for predicting total vehicle delay, which affects the observable driving states of HDVs by solving the optimal speed of ICVs to reduce the traffic delay. Although the previous strategies can achieve the improvement of driving efficiency and energy saving of the mixed traffic flow with the given HDVs’ driving state at intersections, due to many unavoidable factors such as sight-line insufficiency and driving habit difference, the driver’s driving behavior is dynamic and random in many cases, which lead to safety accident, traffic jams, even high consumptions at intersection conflicting zone. Nevertheless, the negative impacts of random driving behavior of HDVs on improving driving efficiency and energy saving for mixed traffic flows have not been considered in the previous studies. Therefore, higher requirements need to be put forward for cooperative driving between ICVs and HDVs with random driving behavior [8].
Various research studies have been developed to improve the traffic efficiency for ICVs and HDVs with random driving behavior at unsignalized intersections, and the existing methods can be classified into three categories: (1) learning-based methods [9–11], which leverage machine learning frameworks, such as deep reinforcement learning, to train the cooperative control strategy for ICVs. For example, the reinforcement learning agent learned a policy for IM to let ICVs at unsignalized intersections give up their right of way and yield to other HDVs to optimize traffic flow [10]. (2) Model-based methods [12, 13], which adopt the perspective of rigorous control theory based on the controlled model and offer certain insights for the ICV control problem in mixed traffic. Such as, the uncertain maneuver of the HDVs based on the driver behavior model was regarded as disturbance, and a receding horizon merging control strategy for ICVs to address the problems of safety and traffic efficiency of the mixed traffic merging was proposed [12]. (3) Other methods, such as, an intersection integrated management system was proposed, which used the partially observable Markov decision process (POMDP) modeling method to estimate the driver intention of HDVs, thereby decreasing the uncertainties in decision-making and planning for ICVs, and then, the traffic efficiency was enhanced [14]; in addition, a game theory-based decision-making dynamic was developed to achieve more realistic models of human behavior when making conflicting maneuvers at intersections, and incorporate it into ICVs’ motion planning algorithms and further to improve the traffic efficiency [15]. However, the previous studies mainly focus on improving traffic efficiency under mixed traffic flows but have not yet considered the comprehensive improvement of traffic efficiency and energy-saving for ICVs and HDVs with time-varying speed characteristics under different MPRs and traffic volumes. In addition, for the learning-based methods, the shortages include that the training process is usually computationally demanding, and the resulting strategies might rely on historical information of the traffic environment and vehicles; for the model-based methods, the precise model information requirement for HDVs driving behavior of the entire mixed traffic flow might restrict its practical applications.
In summary, to improve the driving efficiency and energy-saving for mixed traffic flows under different MPRs and traffic volumes at unsignalized intersections, considering the cooperative control performance of ICVs formation and HDVs with time-varying speed characteristics, the hierarchical and distributed cooperative eco-driving scheme is established in this paper. The main contributions of this paper are as follows: a hierarchical and distributed cooperative eco-driving architecture, which contains two layers of optimization objectives: cloud decision layer and vehicle control layer, can achieve the global comprehensive optimization of traffic efficiency and energy saving for large-scale mixed traffic flows under different MPRs and traffic volumes at unsignalized intersections. Especially, in the cloud decision layer, a multivehicle MFAPCD approach of nonlinear multivehicle systems is proposed to achieve the prediction of the time-varying driving speed for HDVs and the anticipated driving speed for ICVs formation to improve the traffic efficiency. The control method designed in this study only used the online I/O data of mixed vehicles during driving based on the CFDL technology to handle the complex, nonlinear, and uncertain issues of multivehicle cooperative driving affected by the random driving speed of the mixed traffic flow.
The rest of this paper is organized as follows: Section 2 presents the system architecture. Section 3 presents the multivehicle MFAPCD scheme to realize the improvement of the traffic efficiency for mixed traffic flows. Section 4 presents the NDMPC method to realize the optimization of energy saving for ICV formation. Numerical experiments are given in Section 5, and we conclude the paper in Section 6.
1.1. Abbreviation
The abbreviation in Table 1 is used throughout this paper.
2. Hierarchical and Distributed Eco-Driving Architecture
As shown in Figure 1, a hierarchical and distributed eco-driving architecture is developed by considering two layers: the cloud decision layer and the vehicle control layer. With this architecture, the anticipated safety driving speed of mixed traffic flow (cloud decision layer) and the multivehicle optimal speed control of ICVs formation (vehicle control layer) can be organically combined, which makes it possible to achieve the global comprehensive optimization of traffic efficiency and energy-saving for mixed vehicles at unsignalized intersections.
For the cloud decision layer, there is an edging computing (EC) control system at intersections, which can collect the global status information (position and speed) of mixed vehicles entering the intersection zone through V2I communication technology, in which the time-varying driving speed of HDVs is observed and predicted by the multivehicle MFAPCD method (that is reconstructed HDVs status information in EC controller). On this basis, the conflict-free order and anticipated safety driving speed for mixed vehicles are calculated, and the anticipated safety driving speed of the corresponding ICV formation to cross the intersection zone without collision is distributed and guided.
For the vehicle control layer, we designed the distributed controller that focuses on the optimization and cooperative control for multivehicle formation based on the NDMPC method according to the anticipated driving speed information obtained from the upper level. With this method, the large-scale systems with multivehicle groups are decoupled into several vehicle subsystems that can interact with each other. On this basis, the fuel consumption, driving safety, and passenger comfort of each vehicle subsystem are comprehensively considered.
3. Multivehicle MFAPCD Scheme for Improving Traffic Efficiency in Cloud Decision Layer
Motivated by the concept of the model-free adaptive control (MFAC), which does not need a precise model and identification process, and has the advantages of small calculation burden, convenient implementation, and simple controller parameter on-line tuning algorithm [16–18], the multivehicle MFAPCD scheme is proposed in this study. The main idea of this method is that build an equivalent CFDL data model at each operation point of the closed-loop nonlinear system based on the novel concept of pseudopartial-derivative (PPD). Then, the system’s PPD is online estimated by using system online I/O data, and the controller is further designed using the CFDL-ITSMPC and CFDL-PC according to the equivalent CFDL data model.
3.1. Observation and Prediction for HDVs’ Time-Varying Driving Speed Based on CFDL-ITSMPC
In the EC controller, the HDVs entering the intersection area are first considered as a class of multiple-input and multiple-output (MIMO) discrete-time nonlinear systems:where represents the system input at the time ; represents the system output at the time ; is the unknown perturbation and is bounded; , , and are the unknown integers; stands for the discrete nonlinear system, and the partial derivative of each component of variable is continuous. Moreover, equation (1) satisfies the generalized Lipschitz continuous condition. For any , and , we havewhere .
For all , when , there is a time-varying parameter based on PPD, so that the equation is transformed into the CFDL data model by the following equation:where ; represents the positions of HDVs; is the speed increment control input of the HDVs’ the state information reconstruction system in the EC controller. In addition, due to the dynamic and random nature of manual driving behavior, road-side unit (RSUs) sensors cannot accurately observe changing speeds [19, 20]. Similar to the practice in reference [12], the uncertain maneuver of the HDVs is regarded as a disturbance in this study, and is an unknown additional disturbance. In equation (3), since is unknown and under the action of is also unknown, thereby reducing the cooperative driving control performance through EC controller to mixed vehicles with conflicting driving directions. To calculate the time-varying velocity of HDVs, the CFDL-ITSMPC approach is proposed, which mainly includes two parts:
3.1.1. Time-Varying Velocity Observation of HDVs
For equation (1), let , where is the estimation error of , and then equation (3) can be rewritten as , where representing the total disturbance. The disturbance observer [21] shown in the following equation is designed to estimate the driving speed and disturbance information of HDVs entering the intersection, respectively:where and are the estimated values of and , respectively; and represent the disturbance observer parameters to be designed, which satisfy the conditions and ; is the observer parameter and satisfies ; is the time step; , ; is the correction term of the observer, satisfying the following equation:where is a symbolic function; among them, for the unknown PPD parameters of , it is necessary to design the PPD parameter estimation algorithm to obtain the following equation:where is an estimated value of in the following equation:where ; if or or , then ; if or , then ; ; ; ; .
3.1.2. Time-Varying Speed Prediction of HDVs Based on Integral Terminal Sliding Mode and Moving Horizon Prediction
We define the output tracking error about the HDVs’ state information reconstruction system in the EC controller as follows:where is the expected position of HDVs, and it is calculated by the intelligent driver model (IDM) [14].
We define the PI-type discrete terminal sliding function to make the systematic error converge quickly as follows [21]:where , , and the integral error item is as follows:where is the ratio of two odd numbers, and .
The control strategy can be derived from the discrete reaching law as follows:
From equation (11), the following equation can be obtained:where is the one-step forward output prediction equation based on the CFDL model, which is shown as follows:where represents the HDVs’ position, is the equivalent control input speed increment, and .
Substituting equation (13) into equation (12), the equivalent control can be obtained as follows:
Furthermore, to improve the control system’s tracking accuracy, a control action is generated by the model predictive control (MPC) to drive the output of the system to the sliding surface. Given equation (14), the total control action of the reconstructed HDVs’ state information system in the EC controller is as follows:
Let , and substituting the control algorithm equations (14) and (15) into equation (11), we get the following equation:
Furthermore, we can obtain the N-step forward prediction sliding mode function as follows:
If , then, prediction equation (17) becomes as follows:where represents the identity matrix, is lower triangular matrices consisting of , , , , , is the system input control horizon. can be determined by the following formula:where ; is the coefficient, . Let , , , and it can be determined by the following equation:
We can further obtain the function as follows:where .
We define the performance function as follows:where the value of determines the weighting of the MPC control action.
Substituting equation (18) into equation (22), under the optimization condition: , the MPC control action for k times is obtained as follows:where .
Then, equation (14) can be expressed as follows:where is the prediction input of the reconstructed HDVs’ state information system in the EC controller. On this basis, the anticipated driving velocity of vehicle formation is designed.
3.2. Prediction of ICVs’ Anticipated Driving Velocity Based on CFDL-PC
The CFDL-PC method for a class of unknown nonlinear nonaffine MIMO systems is combined MFAC with MPC and only dynamic linearization prediction scheme and moving horizon predictive control technology are used to realize system control [15]. In EC controller, the ICVs formations entering the intersection area are also considered as a class of MIMO discrete-time nonlinear systems:where represents the system input at the time ; represents the system output at the time . Moreover, for any , , and , equation (25) satisfies the generalized Lipschitz continuous condition, that is,
For the prediction of ICVs formations’ anticipated driving velocity, the one-step forward output prediction equation based on the CFDL model is as follows:where is the set of positions of the leader ICVs of all formations, and is the estimated value of the PPD parameter .
Then, the N-step forward prediction equation is given as follows:where ; ; if or or , then ; if or , then ; ; .
Since contains unknown PPD parameters , need to be obtained by the design of the PPD parameter estimation algorithm:where ;
Let , , and the predictive control criterion function of driving efficiency is as follows:where is the weighting factor; represents the expected speed increment of the system, and ; represents the predicted speed increment of the system, and ; represents the expected output of the system; represents the predicted output of the system; a set of anticipated safety distances within the prediction horizon for ICV formation is calculated by the following equation:where is the position set of the th HDVs in front of the th ICVs formation; is the position set of th ICVs formation; is the position set of th ICVs formation; is the control input speed increment of the ICVs formation; and is the expected following distance, .
Let , the optimal control variables are obtained as follows:where .
The control variable at the current moment is as follows:where .
Therefore, the speed control of each ICV formation is carried out according to equation (33), to realize the safe and efficient driving of the ICVs formation and HDVs.
4. Multivehicle NDMPC Scheme for Improving Energy-Saving in the Vehicle Control Layer
The NDMPC scheme can fully consider the complexity of vehicle marshalling coupling system with distributed structure, and decompose vehicle marshalling system into several vehicle node subsystems that can interact. On this basis, the local open-loop optimal control problem is allocated to each vehicle node based on the NDMPC algorithm, which is used for distributed multiobjective optimization based on adjacent nodes and cloud decision-making layer information.
We further consider the vehicle nonlinear characteristics such as drivetrain, braking system, and rolling resistance on approaching ICVs. Therefore, we use a nonlinear vehicle longitudinal dynamics model [22, 23] as a predictive model. The equations are discretely as follows:where and represent the velocity and displacement, respectively; is the actual vehicle driving torque; represents the delay coefficient; is the mechanical efficiency of the transmission system; represents the air drag coefficient; is the air density; represents the road slope; represents the rolling resistance coefficient; represents the frontal area; represents the mechanical transmission ratio; is the wheel rolling radius; represents the acceleration of gravity. The key parameters of the vehicle model settings are as shown in Table 2.
In addition, taking fuel vehicles as an example, we use the model in reference [25] to calculate the fuel consumption of all vehicles, and it is discretely as follows:where , , and are the rolling resistance term and the wind resistance coefficient of the tire; and are the fuel consumption model coefficients; represents the vehicle acceleration; represents the engine idle fuel consumption rate. The fuel consumption model key parameters settings are as shown in Table 3.
In addition, vehicle platoon controllers need to be designed separately for the pilot ICVs and following ICVs [23]. We assume that driving state of the pilot vehicle is , . The expected state of pilot vehicle is , where is the anticipated optimal velocity from the EC controller (that is of the th ICVs formation), and is the corresponding desired location. The expected status for ego vehicle and the pilot vehicle is , where . The expected status for the ego vehicle and preceding vehicle is , , where .
4.1. Control Scheme of the Pilot Vehicle
Based on expected travel velocity sent by EC controller, the most economical vehicle torque is calculated and transmitted to the following ICVs. The cost function can be divided into three parts: the tracking error, the energy-saving performance, and the passenger comfort performance. Specifically, we define a function to maintain the tracking accuracy between the cloud decision layer and the pilot ICVs, which minimizes the tracking error between the desired state of the optimal speed from the EC controller and driving speed of the pilot ICVs. In addition, tracking accuracy between the desired conflict-free position and the actual driving location needs to be optimized. With EC controller, the required collision-free position can be easily calculated based on the minimum safe head-to-head distance from the vehicle before the collision [26].
The control scheme is described as follows:where is the vehicle tracking error cost functions; is a ride comfort performance function that minimizes the change rates in input torque between the vehicle’s predictive control variable and the expected control variable, wherein the expected control variable is obtained from the reference velocity of the EC controller; represents the energy-saving function that minimize vehicle fuel consumption in the predicted time-domain, which is obtained by calculating the minimum vehicle fuel consumption accumulated in steps; , , and are the weighting coefficient, respectively; is the fuel consumption of pilot vehicle; is the desired torque while the vehicle driving at the desired reference velocity, and it can be calculated by the following equation:
4.2. Control Scheme of the following Vehicle
The following vehicle controller is designed to ensure that its own vehicle can operate at the optimal economical velocity, while ensuring that the vehicle is in a stable following state with the pilot vehicle and the preceding vehicle, and establishing constraints to ensure stability throughout the vehicle’s formation. Specifically, we design the tracking error function, comfort function, and energy saving function to define the cost function. The control issues are described as follows:where represents the tracking error between the ego vehicle and the pilot vehicle; is tracking error between the ego vehicle and the adjacent ICVs; and are the position and velocity of the adjacent ICVs; is the ride comfort function; is the energy-saving performance; , , , and is the weighting coefficient, respectively; represents the vehicle fuel consumption; represents the vehicle torque of the pilot vehicle, and it can be calculated by the following formula:
5. Simulation Results and Analysis
To verify the feasibility of the algorithm, the joint test platform is created by SUMO and MATLAB in Figure 2. The solution process of the approach is simulated in MATLAB server, and the two-way typical unsignalized intersection scenario is the built-in SUMO traffic simulation environment. The V2I communication signal in this study can completely cover the intersection area, and the communication radius range is set to 200 m. In particular, to resolve the trajectories of conflict with approaching mixed vehicles, such as merging conflicts and crossing conflicts of mixed traffic flow in different lanes at intersections, as shown in Figure 2, we projected the approaching mixed vehicles from different entrance lanes into virtual lanes according to their locations about the intersection origin and constructed a virtual platoon. Furthermore, the conflicting mixed vehicles can coordinate the movements of themselves through EC controller to pass through the intersection conflicts in an orderly manner (such as numbers 1 and 4 in different levels), while vehicles can realize conflict-free movements (such as numbers 3, 4, and 5 in the same level) [26, 27]. In addition, existing studies show that the improvement effect of vehicle travel safety through nonsignal-controlled intersections is limited at low MPRs, but with MPRs exceeding 30% or even higher, the improvement of vehicle safety and traffic efficiency through intersections can be achieved [28, 29]. Therefore, the manuscript is oriented to the multi-intersection scenario with high MPRs (i.e., MPRs not less than 30%), and carries out the cloud-based decision making and cooperative control of multivehicles at multi-intersections with different MPRs. Furthermore, in order to avoid the long convergence time of multivehicle consistency control and the reduction of traffic efficiency due to the excessive number of vehicles in the mixed vehicle queue, this paper limits the number of vehicles in the mixed vehicle queue to no more than 3 [30, 31].
We construct the baseline scenario with signal time assignment (STA) by considering all vehicles driving at a safe distance from the vehicle in front. The green time and unit extension time are set as 15 s and 3 s, respectively. The time-varying speed perturbation of HDVs satisfy . Each working condition is simulated 5 times. The performance indicators of the average speed and average fuel consumption are, respectively, calculated by 100 vehicles, and each vehicle length is 5 m. The driving direction of vehicles is 15% left-turning and 10% right-turning, and the relative space and a relative number of vehicles entering each lane are random [32–34]. The weighting factor of the proposed method is as follows: , , , , , , , , , and . The system key parameters setting is shown in Table 4.
In addition, we provide two experimental scenarios to verify and evaluate the feasibility and effectiveness of the developed algorithm, and the details are as follows:(a)The traffic flow range is set from 500 veh/h to 2,000 veh/h and the MPRs range is set from 30% to 90% in each entrance. We compare the performances of two methods, including the proposed method and the STA method. In addition, the data of vehicles at every sampling step is collected and the improvement effect of the average speed and average fuel consumption is calculated by the following equations:where represents the vehicle number; represents the simulation time (s); is the average road speed (m/s); is calculated by equation (38).(b)The traffic flow is set as 1,000 veh/h in each entrance and the MPRs are set as 70%. In this scenario, we analyze the trajectory of ICVs and HDVs by taking the directions of potential collision conflicts near the intersection conflicting zone as an example.
5.1. Simulation Results under Different MPRs and Traffic Flows
In this section, we verify the control performance of the approach in various MPRs and traffic volumes. The random traffic flow is set from 500 veh/h to 2000 veh/h, and the MPRs are set from 30% to 90%. The performance results of 5 simulations of each working condition are statistically analyzed, as shown in Figures 3 and 4.
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As shown in Figure 3, the average speed of the proposed method under different MPRs and traffic volumes is generally higher than that of the comparison method. The highest average speed occurs around 90% MPRs with a traffic flow of 500 veh/h, and the lowest average speed occurs around 30%–40% and 60% MPRs with a traffic flow of 2000 veh/h; additionally, as shown in Figure 4, the average fuel consumption of the proposed method under different MPRs and traffic flows is generally lower than that of the comparison method. The lowest fuel consumption is close to 80%–90% MPRs with a traffic flow of 500 veh/h, and the highest fuel consumption is close to 30% MPRs with a traffic flow of 2000 veh/h. The results show that the lower traffic volume and the higher MPRs of ICVs, the better the improvement effect of spatiotemporal resource utilization and energy-saving performance.
Overall, through statistics, compared with the benchmark method, the proposed strategy improves the average velocity by about 15.22% as well as reduces the fuel consumption by about 36.43% on average under different traffic conditions. The simulation results illustrate that the proposed method realizes evident positive improvement in all traffic conditions and confirms the great benefits of the algorithm in the mixed traffic intersection.
5.1.1. Simulation Results under Various MPRs and the Same Traffic Flow
Figure 5 depicts the variation of the average speed and average fuel consumption for mixed traffic flows with 30%–70% MPRs under the conditions of the randomly selected speed of 1,000 veh/h in each lane, respectively.
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It can be seen from Figure 5(a) that the average speed of the proposed method is significantly higher than that of the comparison method and increases with MPRs, while the average fuel consumption is significantly lower than that of the comparison method, and decreases with MPRs. The statistical results show that compared with the STA method, the proposed strategy can improve the average velocity by about 14.64% as well as reduce the average fuel consumption by about 20.8% on average under various MPRs. In Figure 5(b), under the conditions of various MPRs, the method proposed in this paper can effectively improve the multivehicle cooperative driving ability of mixed traffic flows and induce ICV formation through EC controller to pass through the intersection without stopping, reducing the idling time of multiple vehicles at the intersection, thereby improving the traffic efficiency. In addition, multiobjective optimization is further carried out for ICV queues to reduce fuel consumption. However, for the comparison method, the average speed is greatly affected by the phase timing of the traffic lights and the spatiotemporal position distribution of the vehicle, and there is no optimization for multivehicle, which leads to the lower traffic velocity and higher fuel consumption. Therefore, the simulation results illustrate that the proposed method can improve both the traffic efficiency and energy-saving performance of the mixed traffic flow at the intersections, and the optimization effect is better with higher MPRs.
5.1.2. Simulation Results under the Same MPRs and Various Traffic Flows
In this scenario, we focus on the variation of average speed and average fuel consumption and set the traffic flow from 500 veh/h to 2,000 veh/h per lane at 70% MPRs. The specific statistical results are shown in Figure 6.
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As shown in Figure 6(a), the average speed of the proposed method is significantly higher than that of the comparison method, while the average fuel consumption is significantly lower than that of the comparison method in Figure 6(b). The statistical results show that, compared with the STA method, the proposed strategy can improve the average velocity by about 14.64% and reduce the average fuel consumption by about 34.11% on average under different traffic flows, respectively. In the proposed method, when the traffic volume continues to increase in high-density traffic conditions, the optimization space for the average speed of mixed traffic flow is smaller, and the optimization effect of traffic efficiency shows a gradual decrease. In the benchmark method, as the traffic volume increases, the variation of the average speed decreases slightly due to the influence of the control period of the traffic light signal, and the fuel consumption increases significantly due to the phenomenon of queuing accumulation near the intersection. In general, our proposed method can improve both traffic efficiency and energy-saving effects for mixed traffic flows at intersections with different traffic volumes.
5.2. A Case Study Analysis
One of the typical cooperative driving cases at the intersection zone for mixed vehicles under the conditions of randomly selected seeds of 1,000 veh/h and 70% MPR in each entrance is illustrated. Figure 7 depicts the intercepted spatiotemporal trajectories of vehicles from two conflicting directions, namely, the driving orientation of vehicles is from the Western entrance to the Eastern exit (W-E) as well as from the Northern entrance to the Southern exit (N-S). The red coverage area represents the conflict points at the intersection. The instantaneous values of the average speed and fuel consumption are demonstrated in Figures 8 and 9, respectively.
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As shown in Figure 7(a), at a distance of about 100 m near the intersection conflict points, the ICVs formation can dynamically adjust the vehicle motion according to the anticipated safety driving speed assigned by the EC controller to achieve collision avoidance with conflicting HDVs in different directions and maintain a safe driving distance without stopping as well as higher cruising speed through the conflict points. In Figure 7(b), the mixed traffic flows near the intersection area are queuing accumulation because of the traffic light control, which causes vehicles’ idling and curves to fluctuate violently. Therefore, the method in this paper can significantly reduce traffic disturbance and weaken the traffic shock wave based on ensuring the safety of multivehicle driving in mixed traffic flow.
In addition, multiobjective optimization is carried out for ICV formation to reduce fuel consumption based on improving traffic efficiency and safety. Thus, combined with Figure 8, the performance indicator of the average road speed is significantly higher than that of the benchmark method, as well as the energy-saving performance of the proposed method is also higher than that of the benchmark method in Figure 9, which realizes the improvement of the crossing capacity and energy-saving performance of the nonsignal-controlled intersection under the mixed traffic flows.
6. Conclusions
In this paper, a hierarchical and distributed eco-driving approach has been developed by considering two layers of optimization objectives: cloud decision layer and vehicle control layer, which has been achieved the comprehensive optimization of the traffic efficiency and energy saving for randomly mixed traffic flows under different MPRs and traffic volumes at unsignalized intersections. The multivehicle MFAPCD has been proposed to improve the traffic efficiency, which takes into account the prediction of the time-varying driving speed for HDVs and the anticipated driving speed for ICVs, and the method has been achieved using only the online I/O data of the mixed vehicles during driving based on a CFDL technology. Simulation results show that compared with the STA strategy, the method can increase the average velocity by about 15.22% on average and decrease the average fuel consumption by about 36.43% on average under different MPRs and traffic volumes, which outperforms the baseline method in both traffic efficiency and energy saving.
The proposed strategy can pave the way for traffic organizers to schedule the movement of large-scale mixed traffic flows at multiunsignalized intersections in real-time, to reduce congestion and improve traffic efficiency, especially ICVs can eventually reduce fuel consumption by tracking speed advisory strategies. On this basis, our future research will extend it to multi-intersection road networks to provide an optimal driving speed profile for each traveling vehicle based on improving traffic efficiency, reducing fuel consumption, and increasing vehicle cruising mileage.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grant 51975310 and Grant 52002209.