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Hierarchical and Distributed Eco-Driving Approach for Mixed Vehicle Clusters at Unsignalized Intersections

Hierarchical and Distributed Eco-Driving Approach for Mixed Vehicle Clusters at Unsignalized... Hindawi Journal of Advanced Transportation Volume 2023, Article ID 7114792, 16 pages https://doi.org/10.1155/2023/7114792 Research Article Hierarchical and Distributed Eco-Driving Approach for Mixed Vehicle Clusters at Unsignalized Intersections 1,2 2 1 1 Jie Yu , Yugong Luo , Weiwei Kong , and Fachao Jiang College of Engineering, China Agricultural University, Beijing 100083, China State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China Correspondence should be addressed to Weiwei Kong; kongwei_1987@hotmail.com Received 13 March 2022; Revised 23 October 2022; Accepted 24 March 2023; Published 22 April 2023 Academic Editor: Arkatkar Shriniwas Copyright © 2023 Jie Yu et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. To improve the driving efciency and energy-saving characteristics for large-scale mixed trafc fows under diferent 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 hi- erarchical and distributed cooperative eco-driving architecture is frst 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 trafc efciency. 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 diferent MPRs and trafc volumes. MPRs and trafc volumes oriented to signal-controlled 1. Introduction intersections, such as the timing and optimization of traf- Te ICVs enabled by the new generation of information and fc signals for cooperative driving of hybrid vehicles [2–4]. communication technology can provide new ideas for However, with the continuous improvement of the com- solving problems such as high time consuming and poor munication network infrastructure and the intelligent level energy saving for vehicles to pass through intersections [1]. of ICVs, the transportation system will be more intelligent, Given the current trafc situation, the transition from to- and the trafc lights will be replaced by the infrastructure called intersection manager. Moreover, there are also several day’s largely human-driven trafc to purely automated trafc will be a gradual process, with the fact that we may scholars focused on a multivehicle cooperative driving experience mixed trafc shortly. Terefore, in such a tran- method to improve the driving efciency or energy-saving sitional period, it is necessary to design a driving scheme to for mixed trafc fows at such nonsignal-controlled in- coordinate the mixed trafc fows of ICVs and HDVs, which tersections. Zohdy and Rakha [5] proposed an improved is of great signifcance for improving trafc efciency and cooperative adaptive cruise control (iCACC) system, and the reducing fuel consumption. trafc efciency and fuel consumption of intersections under At present, several driving efciencies and energy-saving diferent MPRs were discussed, in which HDVs with given improvement methods have been proposed under diferent driving states can maintain a safe driving distance from 2 Journal of Advanced Transportation environment and vehicles; for the model-based methods, the ICVs. Qian et al. [6] proposed a priority-based coordination system with the hypothesis that the driving state of HDVs is precise model information requirement for HDVs driving behavior of the entire mixed trafc fow might restrict its accurately known and can maintain a safe distance from their leading ICVs to enhance intersection efciency. Yang practical applications. and Oguchi [7] proposed a trafc model for predicting total In summary, to improve the driving efciency and vehicle delay, which afects the observable driving states of energy-saving for mixed trafc fows under diferent MPRs HDVs by solving the optimal speed of ICVs to reduce the and trafc volumes at unsignalized intersections, consid- trafc delay. Although the previous strategies can achieve the ering the cooperative control performance of ICVs forma- improvement of driving efciency and energy saving of the tion and HDVs with time-varying speed characteristics, the hierarchical and distributed cooperative eco-driving scheme mixed trafc fow with the given HDVs’ driving state at intersections, due to many unavoidable factors such as sight- is established in this paper. Te main contributions of this paper are as follows: a hierarchical and distributed co- line insufciency and driving habit diference, the driver’s driving behavior is dynamic and random in many cases, operative eco-driving architecture, which contains two layers of optimization objectives: cloud decision layer and which lead to safety accident, trafc jams, even high con- sumptions at intersection conficting zone. Nevertheless, the vehicle control layer, can achieve the global comprehensive negative impacts of random driving behavior of HDVs on optimization of trafc efciency and energy saving for large- improving driving efciency and energy saving for mixed scale mixed trafc fows under diferent MPRs and trafc trafc fows have not been considered in the previous volumes at unsignalized intersections. Especially, in the studies. Terefore, higher requirements need to be put cloud decision layer, a multivehicle MFAPCD approach of forward for cooperative driving between ICVs and HDVs nonlinear multivehicle systems is proposed to achieve the prediction of the time-varying driving speed for HDVs and with random driving behavior [8]. Various research studies have been developed to im- the anticipated driving speed for ICVs formation to improve the trafc efciency. Te control method designed in this prove the trafc efciency for ICVs and HDVs with random driving behavior at unsignalized intersections, and the study only used the online I/O data of mixed vehicles during driving based on the CFDL technology to handle the existing methods can be classifed into three categories: (1) learning-based methods [9–11], which leverage machine complex, nonlinear, and uncertain issues of multivehicle learning frameworks, such as deep reinforcement learning, cooperative driving afected by the random driving speed of to train the cooperative control strategy for ICVs. For ex- the mixed trafc fow. ample, the reinforcement learning agent learned a policy for Te rest of this paper is organized as follows: Section 2 IM to let ICVs at unsignalized intersections give up their presents the system architecture. Section 3 presents the right of way and yield to other HDVs to optimize trafc fow multivehicle MFAPCD scheme to realize the improvement of the trafc efciency for mixed trafc fows. Section 4 [10]. (2) Model-based methods [12, 13], which adopt the perspective of rigorous control theory based on the con- presents the NDMPC method to realize the optimization of energy saving for ICV formation. Numerical experiments trolled model and ofer certain insights for the ICV control problem in mixed trafc. Such as, the uncertain maneuver of are given in Section 5, and we conclude the paper in the HDVs based on the driver behavior model was regarded Section 6. as disturbance, and a receding horizon merging control strategy for ICVs to address the problems of safety and trafc 1.1. Abbreviation. Te abbreviation in Table 1 is used efciency of the mixed trafc merging was proposed [12]. (3) throughout this paper. Other methods, such as, an intersection integrated man- agement system was proposed, which used the partially observable Markov decision process (POMDP) modeling 2. Hierarchical and Distributed Eco- method to estimate the driver intention of HDVs, thereby Driving Architecture decreasing the uncertainties in decision-making and plan- ning for ICVs, and then, the trafc efciency was enhanced As shown in Figure 1, a hierarchical and distributed eco- [14]; in addition, a game theory-based decision-making driving architecture is developed by considering two layers: dynamic was developed to achieve more realistic models the cloud decision layer and the vehicle control layer. With of human behavior when making conficting maneuvers at this architecture, the anticipated safety driving speed of intersections, and incorporate it into ICVs’ motion planning mixed trafc fow (cloud decision layer) and the multivehicle algorithms and further to improve the trafc efciency [15]. optimal speed control of ICVs formation (vehicle control However, the previous studies mainly focus on improving layer) can be organically combined, which makes it possible trafc efciency under mixed trafc fows but have not yet to achieve the global comprehensive optimization of trafc considered the comprehensive improvement of trafc ef- efciency and energy-saving for mixed vehicles at unsign- ciency and energy-saving for ICVs and HDVs with time- alized intersections. varying speed characteristics under diferent MPRs and For the cloud decision layer, there is an edging com- trafc volumes. In addition, for the learning-based methods, puting (EC) control system at intersections, which can the shortages include that the training process is usually collect the global status information (position and speed) of computationally demanding, and the resulting strategies mixed vehicles entering the intersection zone through V2I might rely on historical information of the trafc communication technology, in which the time-varying Journal of Advanced Transportation 3 Table 1: Te major acronyms used in this paper. Abbreviations Descriptions MPRs Market penetration rates ICVs Intelligent and connected vehicles HDVs Human-driven vehicles MFAPCD Model-free adaptive predictive cooperative driving CFDL Compact form dynamic linearization CFDL-ITSMPC CFDL integral terminal sliding mode predictive control CFDL-PC CFDL predictive control NDMPC Nonlinear distributed model predictive control iCACC Improved cooperative adaptive cruise control EC Edging computing MFAC Model-free adaptive control PPD Pseudopartial-derivative RSUs Road-side unit IDM Intelligent driver model MPC Model predictive control STA Signal time assignment W-E Western entrance to the eastern exit N-S Northern entrance to the southern exit Time-varying Driving states Cloud Decision Layer driving states of information of HDVs ICVs Decision information Status information Multi-vehicle MFAPCD scheme for mixed multi-vehicle systems • Observation and prediction for HDVsĎ driving speed • Anticipated driving speed planning for ICVs formations Control command issuance Anticipated driving speed Position and speed Vehicle Control Layer Optimal and cooperative control of formation driving vehicle vehicle vehicle ······ controller 1 controller 2 controller N Energy-saving of each ······ vehicle-subsystems Figure 1: Hierarchical and distributed cooperative control architecture. driving speed of HDVs is observed and predicted by the the intersection zone without collision is distributed and multivehicle MFAPCD method (that is reconstructed HDVs guided. status information in EC controller). On this basis, the For the vehicle control layer, we designed the distributed confict-free order and anticipated safety driving speed for controller that focuses on the optimization and cooperative mixed vehicles are calculated, and the anticipated safety control for multivehicle formation based on the NDMPC driving speed of the corresponding ICV formation to cross method according to the anticipated driving speed 4 Journal of Advanced Transportation information obtained from the upper level. With this discrete nonlinear system, and the partial derivative of each method, the large-scale systems with multivehicle groups are component of (n + 2) variable is continuous. Moreover, decoupled into several vehicle subsystems that can interact equation (1) satisfes the generalized Lipschitz continuous with each other. On this basis, the fuel consumption, driving condition. For any k ≠ k , k , k ≥ 0 and ∆u (k), we have 1 2 1 2 h � � � � safety, and passenger comfort of each vehicle subsystem are � � � � � � � � �y (k + 1) − y (k)� ≤ b�u (k + 1) − u (k)�, (2) h h h h comprehensively considered. where b > 0. 3. MultivehicleMFAPCDSchemeforImproving For all k, when u (k) ≠ 0, there is a time-varying pa- Traffic Efficiency in Cloud Decision Layer rameter Φ based on PPD, so that the equation is trans- c,h formed into the CFDL data model by the following equation: Motivated by the concept of the model-free adaptive control (3) (MFAC), which does not need a precise model and iden- ∆y (k + 1) � Φ (k)∆u (k) + d (k)T , h,i c,h h 0 tifcation process, and has the advantages of small calcula- where ∆y (k + 1) � y (k + 1) − y (k); y represents the h h h h tion burden, convenient implementation, and simple positions of HDVs;∆u is the speed increment control input controller parameter on-line tuning algorithm [16–18], the h of the HDVs’ the state information reconstruction system in multivehicle MFAPCD scheme is proposed in this study. Te the EC controller. In addition, due to the dynamic and main idea of this method is that build an equivalent CFDL random nature of manual driving behavior, road-side unit data model at each operation point of the closed-loop (RSUs) sensors cannot accurately observe changing speeds nonlinear system based on the novel concept of [19, 20]. Similar to the practice in reference [12], the un- pseudopartial-derivative (PPD). Ten, the system’s PPD is certain maneuver of the HDVs is regarded as a disturbance online estimated by using system online I/O data, and the in this study, and d is an unknown additional disturbance. controller is further designed using the CFDL-ITSMPC and 0 In equation (3), since d (k) is unknown and ∆y (k + 1) CFDL-PC according to the equivalent CFDL data model. 0 h under the action of ∆u (k) is also unknown, thereby re- ducing the cooperative driving control performance through 3.1. Observation and Prediction for HDVs’ Time-Varying EC controller to mixed vehicles with conficting driving Driving Speed Based on CFDL-ITSMPC. In the EC con- directions. To calculate the time-varying velocity of HDVs, troller, the HDVs (1, ..., n) entering the intersection area are the CFDL-ITSMPC approach is proposed, which mainly frst considered as a class of multiple-input and multiple- includes two parts: output (MIMO) discrete-time nonlinear systems: y (k + 1) � f y (k), . . . , y k − n , u (k), . . . , u k − n , 􏼐 􏼐 􏼑 􏼁 h h h y h h u 3.1.1. Time-Varying Velocity Observation of HDVs. For 􏽢 􏽥 􏽥 d(k), d(k − 1), . . . , d k − n , equation (1), let Φ � Φ (k) + Φ (k), where Φ is the 􏼁􏼁 c,h c,h c,h c,h estimation error of Φ , and then equation (3) can be re- c,h (1) written as ∆y (k + 1) � Φ (k)∆u (k) + d(k), where h c,h h where u (k) ∈ R represents the system input at the time k; d(k) � Φ (k)∆u (k) + d (k) representing the total dis- h c,h h 0 y (k + 1) ∈ R represents the system output at the time turbance. Te disturbance observer [21] shown in the fol- k + 1; d(k) is the unknown perturbation and d(k) is lowing equation is designed to estimate the driving speed bounded; n , n , and n are the unknown integers; f(·) � and disturbance information of HDVs entering the in- y u d (f (. . .) . . . f (. . .)) ∈ 􏽑 R ↦R stands for the tersection, respectively: 1 n n +n +2 n n y u − 1 􏽢 􏽢 􏽢 􏽢 ⎧ ⎨ z (k + 1) � z (k) + θk υ y (k) − z (k), α, β􏼁 + Φ (k)∆u (k)T + Tz (k), 1 1 1 h 1 c,h h 2 (4) 􏽢 􏽢 􏽢 z (k + 1) � z (k) + θ k υ d(k) − z (k), α, β􏼁, 2 2 2 2 where 􏽢z (k) and 􏽢z (k) are the estimated values of y (k) and where sign(·) is a symbolic function; among them, for the 1 2 h d(k), respectively; k and k represent the disturbance unknown PPD parameters of Φ (k), it is necessary to 1 2 c,h observer parameters to be designed, which satisfy the design the PPD parameter estimation algorithm to obtain 􏽰�� conditions k , k > 0 and k > 2 k ; θ is the observer pa- the following equation: 1 2 1 2 rameter and satisfes θ ≥ 0; T is the time step; α ∈ (0.5, 1), � � � 2� 􏽢 � � J􏼐Φ 􏼑 � ∆􏽢z (k) − Φ (k − 1)∆u (k − 1) − 􏽢z (k)T � � β ∈ (1, 1.5); υ(·) is the correction term of the observer, c,h 1 c,h h 2 � � satisfying the following equation: � � � 􏽢 � + μ Φ (k) − Φ (k − 1) , � � c,h c,h |x| sign(x), |x| < 1, ⎧ ⎨ (6) υ(x, α, β) � (5) ⎩ β |x| sign(x), |x| ≥ 1, where Φ is an estimated value of Φ in the following c,h c,h equation: Journal of Advanced Transportation 5 􏼌 􏼌 􏼌 􏼌2 We defne the PI-type discrete terminal sliding function 􏼌 􏼌 η􏼌∆u (k − 1)􏼌 􏽢 􏽢 Φ (k) � Φ (k − 1) + to make the systematic error converge quickly as follows 􏼌 􏼌 c,h c,h 􏼌 􏼌 􏼌 􏼌 μ + 􏼌∆u (k − 1)􏼌 [21]: s(k) � λ e(k) + λ E(k − 1), (9) 􏽢 1 2 􏽨∆􏽢z (k) − Φ (k − 1)∆u (k − 1) − 􏽢z (k)T 􏽩, 1 c,h h 2 (7) where λ > 0, λ > 0, and the integral error item is as follows: 1 2 􏽢 􏽢 􏽢 ϕ (k) ϕ (k) · · · ϕ (k) z z ch,11 ch,12 ch,1n e � E(k − 1) + e , (10) ⎡ ⎢ ⎤ ⎥ E(k) � 􏽘 ⎢ ⎥ ⎢ ⎥ i k ⎢ ⎥ ⎢ 􏽢 􏽢 􏽢 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ϕ (k) ϕ (k) · · · ϕ (k) ⎥ ⎢ ⎥ n×n 􏽢 ⎢ ch,21 ch,22 ch,2n ⎥ ⎢ ⎥ i�0 ⎢ ⎥ where Φ (k) � ⎢ ⎥ ∈ R ; ⎢ ⎥ c,h ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⋮ ⋮ ⋮ 􏽢 􏽢 􏽢 where z is the ratio of two odd numbers, and 0 < z < 1. ϕ (k) ϕ (k) · · · ϕ (k) ch,n1 ch,n2 ch,nn Te control strategy can be derived from the discrete 􏽢 􏽢 if |ϕ (k)| ≤ ε or |ϕ (k)| > εb or ch,ii ch,ii 2 reaching law as follows: 􏽢 􏽢 􏽢 􏽢 sign(ϕ (k)) ≠ sign(ϕ (1)), then ϕ (k) � ϕ (1); if ch,ii ch,ii ch,ii ch,ii ∆s(k) � s(k + 1) − s(k) � 0. (11) 􏽢 􏽢 􏽢 |ϕ (k)| > b or sign(ϕ (k)) ≠ sign(ϕ (1)), then ch,ij ch,ij ch,ij 􏽢 􏽢 ϕ (k) � ϕ (1); i, j � 1, . . . , n; i ≠ j; η ∈ (0, 1]; μ > 0; ch,ij ch,ij From equation (11), the following equation can be b , b > 0. obtained: 1 2 λ y (k + 1) − y (k + 1)􏼁 + λ E(k) � s(k), (12) 1 h h 2 3.1.2. Time-Varying Speed Prediction of HDVs Based on where y (k + 1) is the one-step forward output prediction Integral Terminal Sliding Mode and Moving Horizon equation based on the CFDL model, which is shown as Prediction. We defne the output tracking error about the follows: HDVs’ state information reconstruction system in the EC controller as follows: 􏽢 􏽢 y (k + 1) � y (k) + Φ (k)∆u (k) + Z (k), (13) h h c,h h 2 e(k) � y (k) − y (k), (8) h h where y represents the HDVs’ position, ∆u is the equiv- h h ∗ 􏽢 alent control input speed increment, and Z � z (k)T . where y is the expected position of HDVs, and it is cal- 2 2 Substituting equation (13) into equation (12), the culated by the intelligent driver model (IDM) [14]. equivalent control ∆u (k) can be obtained as follows: − 1 − 1 ∗ ∆u (k) � 􏼐λ s(k) − λ λ E(k) − Z (k) + y (k + 1) − y (k)􏼑. (14) h 1 1 2 2 h h Φ (k) c,h ∆u (k) � ∆u (k) +∆u (k). (15) hv h mpc Furthermore, to improve the control system’s tracking 􏽥 􏽢 accuracy, a control action ∆u is generated by the model Let ∆Z � Z − Z , and substituting the control algo- 2 2 2 predictive control (MPC) to drive the output of the system to rithm equations (14) and (15) into equation (11), we get the the sliding surface. Given equation (14), the total control following equation: action of the reconstructed HDVs’ state information system in the EC controller is as follows: s(k + 1) � λ y (k + 1) − y (k + 1)􏼁 + λ E(k) 1 h 2 � λ 􏼐y (k) + Φ (k)∆u (k) + Z (k) − y (k + 1)􏼑 + λ E(k) (16) 1 h c,h hv 2 2 􏽢 􏽥 � s(k) + λ Φ (k)∆u (k) − λ ∆Z (k). 1 c,h mpc 1 2 Furthermore, we can obtain the N-step forward pre- diction sliding mode function as follows: 􏽢 􏽢 􏽢 s(k + N) � s(k) + λ 􏽨Φ (k)∆u (k) + Φ (k + 1)∆u (k + 1), . . . , Φ (k + N − 1)∆u (k + N − 1)􏽩 1 c,h mpc c,h mpc c,h mpc (17) 􏽥 􏽥 􏽥 − λ 􏽨∆Z (k) +∆Z (k + 1)+, . . . , +∆Z (k + N − 1)􏽩. 1 2 2 2 6 Journal of Advanced Transportation If ∆u (k + j − 1) � 0, j > N , then, prediction equa- (k + 1), . . . ,∆Z (k + N − 1)] , mpc u 2 u tion (17) becomes as follows: Φ (k) 0 · · · 0 c,h ⎢ ⎥ ⎡ ⎢ ⎤ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 􏽢 􏽢 ⎥ ⎢ Φ (k) Φ (k + 1) · · · 0 ⎥ ⎢ ⎥ S(k) � Λs(k) + A (k)U(k − 1) − ΓF(k − 1), (18) ⎢ c,h c,h ⎥ ⎢ ⎥ 1 ⎢ ⎥ A (k) � ⎢ ⎥ , ⎢ ⎥ ⎢ ⎥ 1 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⋮ ⋮ ⋮ ⎦ where Λ represents the identity matrix, Γ is lower triangular 􏽢 􏽢 􏽢 Φ (k) Φ (k + 1) · · · Φ (k + N + 1) c,h c,h c,h u N ∗ N matrices consisting of λ , S(k) � [s(k + 1), N is the system input control horizon. Φ can be de- T u c,h s(k + 2), . . . , s(k + N )] , U(k − 1) � [∆u (k),∆u u mpc mpc termined by the following formula: 􏽥 􏽥 (k), . . . ,∆u (k + N − 1)] , F(k − 1) � [∆Z (k),∆Z mpc u 2 2 􏽢 􏽢 􏽢 􏽢 Φ (k + j) � θ (k)Φ (k + j − 1) + θ (k)Φ (k + j − 2)+, . . . , +θ (k)Φ k + j − n , 􏼐 􏼑 (19) c,h 1 c,h 2 c,h n c,h p T T 􏽢 􏽢 where j � 1, . . . , N − 1; θ is the coefcient, i � 1, . . . , n . (k − 1), . . . , Φ (k − n )] , Φ (k) � θ (k)φ 􏽢 (k − 1), and u i p c,h p c,h c,h Let θ(k) � [θ (k), . . . , θ (k)] , φ (k − 1) � [Φ it can be determined by the following equation: 1 n c,h c,h � � � T � T 2 � � 􏽢 􏽢 (20) � 􏽢 � min J(θ(k)) � Φ (k) − φ (k − 1)θ(k) + δ‖θ(k) − θ(k − 1)‖ . � c,h c,h � We can further obtain the function as follows: 􏽢 􏽢 φ (k − 1)􏼒Φ (k) − φ (k − 1)θ(k − 1)􏼓 c,h c,h c,h (21) θ(k) � θ(k − 1) + � � , � �2 � � δ + �φ (k − 1)� c,h − 1 T T 􏽢 􏽢 􏽢 􏽢 ∆u (k) � − Χ􏼒A A + ωI􏼓 A (Λs(k) − ΓF(k − 1)), mpc 1 1 1 where δ ∈ (0, 1]. We defne the performance function as follows: (23) T T (22) J � S (k)S(k) + ωU (k − 1)U(k − 1), − 1 where Χ � [λ 0, . . . , 0]. Ten, equation (14) can be expressed as follows: where the value of ω determines the weighting of the MPC control action. Substituting equation (18) into equation (22), under the optimization condition: zJ/zU(k − 1) � 0, the MPC control action for k times is obtained as follows: − 1 − 1 − 1 ∗ ∆u (k) � Φ (k)􏼐λ s(k) − λ λ E(k) − ∆Z (k) + y (k + 1) − y (k)􏼑 hv 2 2 h c,h 1 1 h (24) − 1 T T 􏽢 􏽢 􏽢 􏽢 − Χ􏼒A A + ωI􏼓 A (Λs(k) − ΓF(k − 1)), 1 1 1 where ∆u is the prediction input of the reconstructed are used to realize system control [15]. In EC controller, the hv ICVs formations (1, . . . , n) entering the intersection area are HDVs’ state information system in the EC controller. On this basis, the anticipated driving velocity of vehicle for- also considered as a class of MIMO discrete-time nonlinear mation is designed. systems: y (k + 1) � f􏼐y (k), . . . , y 􏼐k − n 􏼑, u (k), . . . , u k − n 􏼁 􏼑, c c c y c c u 3.2. Prediction of ICVs’ Anticipated Driving Velocity Based on CFDL-PC. Te CFDL-PC method for a class of unknown (25) nonlinear nonafne MIMO systems is combined MFAC where u (k) ∈ R represents the system input at the time k; with MPC and only dynamic linearization prediction scheme and moving horizon predictive control technology y (k + 1) ∈ R represents the system output at the time c Journal of Advanced Transportation 7 k + 1. Moreover, for any k ≠ k , k , k ≥ 0, and ∆u (k), where 1 2 1 2 c equation (25) satisfes the generalized Lipschitz continuous Φ (k) 0 · · · 0 ⎡ ⎢ ⎤ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 􏽢 􏽢 ⎥ condition, that is, ⎢ ⎥ ⎢ ⎥ ⎢ Φ (k) Φ (k + 1) · · · 0 ⎥ ⎢ ⎥ ⎢ c c ⎥ ⎢ ⎥ ⎢ ⎥ A (k) � ⎢ ⎥ ; ⎢ ⎥ � � � � 1c ⎢ ⎥ ⎢ ⎥ � � � � ⎢ ⎣ ⋮ ⋮ ⋮ ⎦ � � � � y (k + 1) − y (k) ≤ b u (k + 1) − u (k) . (26) � � � � c c c c 􏽢 􏽢 􏽢 Φ (k) Φ (k + 1) · · · Φ (k + N + 1) c c c u N ∗ N For the prediction of ICVs formations’ anticipated 􏽢 􏽢 􏽢 ϕ (k) ϕ (k) · · · ϕ (k) c,11 c,12 c,1n ⎢ ⎥ ⎡ ⎢ ⎤ ⎥ driving velocity, the one-step forward output prediction ⎢ ⎥ ⎢ ⎥ ⎢ 􏽢 􏽢 􏽢 ⎥ ⎢ ⎥ ⎢ ϕ (k) ϕ (k) · · · ϕ (k) ⎥ ⎢ ⎥ ⎢ ⎥ n×n 􏽢 ⎢ c,21 c,22 c,2n ⎥ ⎢ ⎥ Φ (k) � ⎢ ⎥ ∈ R ; if ⎢ ⎥ ⎢ ⎥ equation based on the CFDL model is as follows: c ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⋮ ⋮ ⋮ ⎦ 􏽢 􏽢 􏽢 ϕ (k) ϕ (k) · · · ϕ (k) y (k + 1) � y (k) + Φ (k)∆u (k), (27) c,n1 c,n2 c,nn c c c c 􏽢 􏽢 􏽢 |ϕ (k)| ≤ ε or |ϕ (k)| > εb or sign(ϕ (k)) ≠ sign c,ii c,ii 2 c,ii where y is the set of positions of the leader ICVs of all 􏽢 􏽢 􏽢 􏽢 (ϕ (1)), then ϕ (k) � ϕ (1); if |ϕ (k)| > b or c,ii c,ii c,ii c,ij 1 formations, and Φ is the estimated value of the PPD pa- 􏽢 􏽢 􏽢 􏽢 sign(ϕ (k)) ≠ sign(ϕ (1)), then ϕ (k) � ϕ (1); rameter Φ . c,ij c,ij c,ij c,ij Ten, the N-step forward prediction equation is given as i, j � 1, . . . , n; i ≠ j; ∆U (k) � [∆u (k), . . . ,∆u (k+ N c c follows: N − 1)] . Since A (k) contains unknown PPD parameters Φ (k), 1c c Y (k + 1) � Y (k) + A (k)∆U (k), (28) c c 1c N 􏽢 􏽢 􏽢 Φ (k), Φ (k + 1), . . . , Φ (k + N + 1) need to be obtained c c c u by the design of the PPD parameter estimation algorithm: 􏽢 􏽢 􏽢 􏽢 Φ (k + j) � θ (k)Φ (k + j − 1) + θ (k)Φ (k + j − 2)+, . . . , +θ (k)Φ k + j − n , 􏼐 􏼑 (29) c 1 c 2 c n c p ∗ ∗ ∗ T where j � 1, . . . , N − 1; Let Y (k + i) � [y (k + i), ..., y (k + N)] , c c c Y (k + i) � [y (k + i), ..., y (k + N)] , and the predictive c c c control criterion function of driving efciency is as follows: ∗ ∗ T min J ∆U (k) � ∆V (k + 1) − ∆V (k + 1) ∆V (k + 1) − ∆V (k + 1) + λ∆U (k)∆U (k), (30) 􏼁 􏼂 􏼃 􏼂 􏼃 Nu c c c c Nu Nu where λ > 0 is the weighting factor; ∆V represents the expected output of the system; Y represents the predicted c c expected speed increment of the system, and output of the system; a set of anticipated safety distances ∗ ∗ ∗ ∆V (k + 1) � (Y (k + 1) − Y (k))/T; ∆V represents the within the prediction horizon for ICV formation is calcu- c c c lated by the following equation: predicted speed increment of the system, and ∆V (k + 1) � (Y (k + 1) − Y (k))/T; Y represents the c c c 􏼌 􏼌 􏼌 􏼌 􏽢 􏼌 􏼌 Y (k) + A (k)∆u (k) + d , if Y − Y ≤ d , n ≠ 1, ⎧ ⎪ 􏼌 􏼌 h,n− 1 1 hv safe h,n− 1 c,n safe ⎨ 􏼌 􏼌 ∗ 􏼌 􏼌 􏽢 􏼌 􏼌 Y (k + 1) � Y (k) + A (k)∆u (k) + d , if Y − Y ≤ d , n ≠ 1, (31) 􏼌 􏼌 c ⎪ c,n 1c c safe c,n− 1 c,n safe 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 Y (k) + A (k)∆u (k), if 􏼌Y − Y 􏼌 > d , n ≠ 1; or 􏼌Y − Y 􏼌 > d , n ≠ 1; or n � 1, c,n 1c c h,n− 1 c,n safe c,n− 1 c,n safe where Y is the position set of the n − 1th HDVs in front formation; and d is the expected following distance, h,n− 1 safe of the nth ICVs formation; Y is the position set of nth ICVs d � d + τ u . c,n safe min h c formation; Y is the position set of n − 1th ICVs for- Let zJ/zU (k) � 0, the optimal control variables are c,n− 1 Nu mation;∆u is the control input speed increment of the ICVs obtained as follows: − 1 T T 􏽢 􏽢 􏽢 (32) ∆U (k) � λI + A (k)A (k) A (k) Y (k + 1) − Y (k) , 􏼒 􏼓 􏼁 Nu 1 1 1 c c 8 Journal of Advanced Transportation where λ > 0. structure, and decompose vehicle marshalling system into Te control variable at the current moment is as follows: several vehicle node subsystems that can interact. On this basis, the local open-loop optimal control problem is allo- (33) u (k) � u (k − 1) + g ∆U (k), c c Nu cated to each vehicle node based on the NDMPC algorithm, which is used for distributed multiobjective optimization where g � [1, 0, . . . , 0] . N∗1 based on adjacent nodes and cloud decision-making layer Terefore, the speed control of each ICV formation is information. carried out according to equation (33), to realize the safe and We further consider the vehicle nonlinear characteristics efcient driving of the ICVs formation and HDVs. such as drivetrain, braking system, and rolling resistance on approaching ICVs. Terefore, we use a nonlinear vehicle 4. Multivehicle NDMPC Scheme for Improving longitudinal dynamics model [22, 23] as a predictive model. Energy-Saving in the Vehicle Control Layer Te equations are discretely as follows: Te NDMPC scheme can fully consider the complexity of vehicle marshalling coupling system with distributed s(t + 1) � s(t) + v(t)∆T, ⎧ ⎪ 4T (t)i η C Aρ ⎪ q 0 v(t + 1) � v(t) + 􏼠 − v(t) − g sin α − fg cos α􏼡∆T, (34) mr 2m 1 1 T (t + 1) � T (t) + u(t)∆T − T (t)∆T, q q q τ τ where v and s represent the velocity and displacement, r is the wheel rolling radius; g represents the acceleration of respectively; T is the actual vehicle driving torque; τ rep- gravity. Te key parameters of the vehicle model settings are resents the delay coefcient; η is the mechanical efciency of as shown in Table 2. the transmission system; C represents the air drag co- In addition, taking fuel vehicles as an example, we use efcient; ρ is the air density; α represents the road slope; f the model in reference [25] to calculate the fuel consumption represents the rolling resistance coefcient; A represents the of all vehicles, and it is discretely as follows: frontal area; i represents the mechanical transmission ratio; 2 2 F(t + 1) � F(t) + α + δ v(t) b + b v(t) + b v(t) + αmv(t) + δ ma(t) v(t) ∆T, (35) 􏼐 􏼑 􏼐 􏼑 1 1 2 3 2 a>0 where b , b , and b are the rolling resistance term and the 4.1. Control Scheme of the Pilot Vehicle. Based on expected 1 2 3 wind resistance coefcient of the tire; δ and δ are the fuel travel velocity sent by EC controller, the most eco- 1 2 consumption model coefcients; a represents the vehicle nomical vehicle torque is calculated and transmitted to acceleration; α represents the engine idle fuel consumption the following ICVs. Te cost function can be divided into rate. Te fuel consumption model key parameters settings three parts: the tracking error, the energy-saving per- are as shown in Table 3. formance, and the passenger comfort performance. In addition, vehicle platoon controllers need to be Specifcally, we defne a function to maintain the tracking designed separately for the pilot ICVs and following ICVs accuracy between the cloud decision layer and the pilot [23]. We assume that driving state of the pilot vehicle is ICVs, which minimizes the tracking error between the p p p p T y � [S , v , T ] , s ∈ {1, 2, . . . , n}. Te expected state of desired state of the optimal speed from the EC controller s s s q,s ∗ ∗ ∗ ∗ pilot vehicle is y � [S , v ] , where v is the anticipated and driving speed of the pilot ICVs. In addition, tracking ec ec ec ec optimal velocity from the EC controller (that is u of the nth accuracy between the desired confict-free position and ICVs formation), and S is the corresponding desired lo- the actual driving location needs to be optimized. With ec cation. Te expected status for ego vehicle and the pilot EC controller, the required collision-free position can be a a T vehicle is y � [S − (s − 1)d , v , T ] , where easily calculated based on the minimum safe head- sdes 1 des 1 q,1 d � d + τ v . Te expected status for the ego vehicle to-head distance from the vehicle before the des min h 1 a a T and preceding vehicle is y � [S − d, v , T ] , collision [26]. js js js q,js js ∈ {1, 2, . . . , n}, where d � d + τ v . Te control scheme is described as follows: min h js Journal of Advanced Transportation 9 Table 2: Vehicle model parameters [22, 24]. Parameters m r C g f η τ w D Numerical value (unit) 1,230 kg 0.38 m 0.39 9.8 m/s 0.012 0.96 0.3 s Table 3: Fuel consumption model parameters [3]. Parameters a β β b b b 1 2 1 2 3 Numerical value (unit) 0.67 ml/s 0.07 0.03 0.27 0.02 0.67E − 03 N − 1 min J (t) � 􏽘 􏼐J (k|t) + J (k|t) + J (k|t)􏼑 1 1,s 2,s 3,s k�0 � � � � � � � � � � � � ∗ p p ∗ � � � � � � w y (k|t) − y (k|t) + w u (k|t) − u v (k|t) + w f (k|t) � 􏼁� � 􏼁 􏼁� � 􏼁 � l1 ec s l2 s 0 ec l3 s 2 2 2 s.t. v ≤ v (k|t) ≤ v min s max a ≤∆v (k|t) ≤ a min s max (36) T ≤ u (k|t) ≤ T min s max 􏼌 􏼌 􏼌 􏼌 p 􏼌 ∗ 􏼌 􏼌 􏼌 v N t � v N t 􏼒 􏼓 􏼒 􏼓 􏼌 􏼌 s p ec p 􏼌 􏼌 􏼌 􏼌 p ∗ 􏼌 􏼌 􏼌 􏼌 S 􏼒N t􏼓 � s 􏼒N t􏼓 s p􏼌 p􏼌 ec 􏼌 􏼌 􏼌 􏼌 p ∗ 􏼌 􏼌 􏼌 􏼌 T 􏼒N t􏼓 � h 􏼒v 􏼒N t􏼓􏼓, p􏼌 s p􏼌 q,s ec where J (k|t) is the vehicle tracking error cost functions; consumption in the predicted time-domain, which is ob- 1,s J (k|t) is a ride comfort performance function that min- tained by calculating the minimum vehicle fuel consumption 2,s imizes the change rates in input torque between the vehicle’s accumulated in N steps; w , w , and w are the weighting p l1 l2 l3 predictive control variable and the expected control variable, coefcient, respectively; f (k|t) is the fuel consumption of wherein the expected control variable is obtained from the pilot vehicle; u (v (k|t)) is the desired torque while the 0 ec reference velocity of the EC controller; J (k|t) represents vehicle driving at the desired reference velocity, and it can be 3,s the energy-saving function that minimize vehicle fuel calculated by the following equation: r 1 2 ∗ ∗ u 􏼐v 􏼐N t􏼑􏼑 � 􏼒 C Aρ􏼒v 􏼐N t􏼑 􏼓 + mgf cos α + mg sin α􏼓. (37) 0 ec p D ec p 4i η 2 4.2. Control Scheme of the following Vehicle. Te following establishing constraints to ensure stability throughout the vehicle controller is designed to ensure that its own ve- vehicle’s formation. Specifcally, we design the tracking hicle can operate at the optimal economical velocity, while error function, comfort function, and energy saving ensuring that the vehicle is in a stable following state with function to defne the cost function. Te control issues are the pilot vehicle and the preceding vehicle, and described as follows: 10 Journal of Advanced Transportation N − 1 min J (t) � 􏽘 J (k|t) + J (k|t) + J (k|t) + J (k|t) 􏼐 􏼑 2 1,s 2,s 3,s 4,s k�0 � � � � � � � � � � � � � � � � p p p a � � � � � � � � � � � �w y (k|t) − y (k|t)􏼁� + w 􏼐y (k|t) − y (k|t)􏼑 + �w u (k|t) − u v (k|t)􏼁 􏼁� + �w f (k|t)􏼁 � 1 sdes � 2 js � 3 s 0 4 s s 2 s 1 2 2 s.t. v ≤ v (k|t) ≤ v min max a ≤∆v (k|t) ≤ a min s max T ≤ u (k|t) ≤ T min s max 􏼌 􏼌 􏼌 􏼌 p a 􏼌 􏼌 􏼌 􏼌 v 􏼒N t􏼓 � v 􏼒N t􏼓 s p􏼌 js p􏼌 􏼌 􏼌 􏼌 􏼌 p 􏼌 a a 􏼌 􏼌 􏼌 S N t � S v N t − d 􏼒 􏼓 􏼒 􏼒 􏼓􏼓 􏼌 􏼌 s p 1 1 p 􏼌 􏼌 􏼌 􏼌 p a 􏼌 􏼌 􏼌 􏼌 S 􏼒N t􏼓 � S 􏼒N t􏼓 − (s − 1)d 􏼌 􏼌 s p js p des 􏼌 􏼌 􏼌 􏼌 p a 􏼌 􏼌 􏼌 􏼌 T 􏼒N t􏼓 � h 􏼒v 􏼒N t􏼓􏼓, p􏼌 s p􏼌 q,s js (38) where J (k|t) represents the tracking error between the ego saving performance; w , w , w , and w is the weighting 1,s 1 2 3 4 vehicle and the pilot vehicle; J (k|t) is tracking error be- coefcient, respectively; f (k|t) represents the vehicle fuel 2,s s tween the ego vehicle and the adjacent ICVs; S (k|t) and consumption; u (v (k|t)) represents the vehicle torque of js 0 1 v (k|t) are the position and velocity of the adjacent ICVs; the pilot vehicle, and it can be calculated by the following js J (k|t) is the ride comfort function; J (k|t) is the energy- formula: 3,s 4,s 􏼌 􏼌 􏼌 r 1 􏼌 􏼌 􏼌 􏼌 􏼌 u 􏼒v 􏼒N t􏼓􏼓 � 􏼒 C Aρv 􏼒N t􏼓 + mgf cos α + mg sin α􏼡. (39) 􏼌 􏼌 0 1 p D 1 p 4i η 2 higher, the improvement of vehicle safety and trafc ef- 5. Simulation Results and Analysis ciency through intersections can be achieved [28, 29]. To verify the feasibility of the algorithm, the joint test Terefore, the manuscript is oriented to the multi- platform is created by SUMO and MATLAB in Figure 2. Te intersection scenario with high MPRs (i.e., MPRs not less solution process of the approach is simulated in MATLAB than 30%), and carries out the cloud-based decision making server, and the two-way typical unsignalized intersection and cooperative control of multivehicles at multi- scenario is the built-in SUMO trafc simulation environ- intersections with diferent MPRs. Furthermore, in order ment. Te V2I communication signal in this study can to avoid the long convergence time of multivehicle con- completely cover the intersection area, and the communi- sistency control and the reduction of trafc efciency due to cation radius range is set to 200 m. In particular, to resolve the excessive number of vehicles in the mixed vehicle queue, the trajectories of confict with approaching mixed vehicles, this paper limits the number of vehicles in the mixed vehicle such as merging conficts and crossing conficts of mixed queue to no more than 3 [30, 31]. trafc fow in diferent lanes at intersections, as shown in We construct the baseline scenario with signal time Figure 2, we projected the approaching mixed vehicles from assignment (STA) by considering all vehicles driving at a safe diferent entrance lanes into virtual lanes according to their distance from the vehicle in front. Te green time and unit locations about the intersection origin and constructed extension time are set as 15 s and 3 s, respectively. Te time- a virtual platoon. Furthermore, the conficting mixed ve- varying speed perturbation of HDVs satisfy N(5, 0.5). Each hicles can coordinate the movements of themselves through working condition is simulated 5 times. Te performance EC controller to pass through the intersection conficts in an indicators of the average speed and average fuel con- orderly manner (such as numbers 1 and 4 in diferent levels), sumption are, respectively, calculated by 100 vehicles, and while vehicles can realize confict-free movements (such as each vehicle length is 5 m. Te driving direction of vehicles is numbers 3, 4, and 5 in the same level) [26, 27]. In addition, 15% left-turning and 10% right-turning, and the relative existing studies show that the improvement efect of vehicle space and a relative number of vehicles entering each lane travel safety through nonsignal-controlled intersections is are random [32–34]. Te weighting factor of the proposed limited at low MPRs, but with MPRs exceeding 30% or even method is as follows: ω � 0.3, ω � 0.3, ω � 0.4, λ � 600, 1 2 3 Journal of Advanced Transportation 11 Matlab solution server SUMO trafc simulation environment HDV ICVs formation Speed Input North • Driving states of HDVs and ICVs entrance trafc fow control EC Input • Environmental information WBL WBT WBR SBL SBT SBR controller command 45 6 78 9 Observation and prediction for HDVs’ time- varying driving speed module Input Matlab EC trafc fow controller function 9 7 East Multi-vehicle optimization cooperative driving entrance TraCI control module West Mixed virtual interface entrance queue Communication radius Input Level Vehicle control information distribution module 4 trafc fow Car-following EBL EBT EBR 1 NBL NBT NBR Vehicle status acquisition module 10 11 12 Vehicle 12 3 3 running status and • Data for visualization 100 South scenario Input entrance 5 7 Output trafc fow information E-W Typical unsignalized intersection S-N -100 15 20 25 30 35 40 45 Figure 2: Joint simulation platform architecture. (b) Te trafc fow is set as 1,000 veh/h in each entrance Table 4: System key parameters setting [24, 26]. and the MPRs are set as 70%. In this scenario, we Numerical analyze the trajectory of ICVs and HDVs by taking Physical meanings Variables values (unit) the directions of potential collision conficts near the Initial speed v , v 10 m/s s js intersection conficting zone as an example. Minimum car-following distance d 5 m min Time-step ∆T 0.1 Headway τ 0.65 2 5.1. Simulation Results under Diferent MPRs and Trafc Maximum acceleration a 2 m/s max 2 Flows. In this section, we verify the control performance of Minimum acceleration a − 2 m/s min the approach in various MPRs and trafc volumes. Te Prediction time-domain N 10 random trafc fow is set from 500 veh/h to 2000 veh/h, and Control time-domain N 3 the MPRs are set from 30% to 90%. Te performance results Order of parameter prediction n 3 of 5 simulations of each working condition are statistically analyzed, as shown in Figures 3 and 4. λ � 0.3, λ � 0.2, μ � 0.015, η � 1, δ � 0.6, and ϕ (1) � 10. 1 2 c As shown in Figure 3, the average speed of the proposed Te system key parameters setting is shown in Table 4. method under diferent MPRs and trafc volumes is gen- In addition, we provide two experimental scenarios to erally higher than that of the comparison method. Te verify and evaluate the feasibility and efectiveness of the highest average speed occurs around 90% MPRs with developed algorithm, and the details are as follows: a trafc fow of 500 veh/h, and the lowest average speed occurs around 30%–40% and 60% MPRs with a trafc fow (a) Te trafc fow range is set from 500 veh/h to of 2000 veh/h; additionally, as shown in Figure 4, the average 2,000 veh/h and the MPRs range is set from 30% to fuel consumption of the proposed method under diferent 90% in each entrance. We compare the performances MPRs and trafc fows is generally lower than that of the of two methods, including the proposed method and comparison method. Te lowest fuel consumption is close to the STA method. In addition, the data of vehicles at 80%–90% MPRs with a trafc fow of 500 veh/h, and the every sampling step is collected and the improvement highest fuel consumption is close to 30% MPRs with a trafc efect of the average speed and average fuel con- fow of 2000 veh/h. Te results show that the lower trafc sumption is calculated by the following equations: volume and the higher MPRs of ICVs, the better the im- v􏼁 provement efect of spatiotemporal resource utilization and V � 􏽘 , (40) energy-saving performance. i�1 Overall, through statistics, compared with the m benchmark method, the proposed strategy improves the 􏼐􏽐 􏼐F 􏼑/m􏼑 j�1 i,j average velocity by about 15.22% as well as reduces the (41) F � 􏽘 . fuel consumption by about 36.43% on average under i�1 diferent trafc conditions. Te simulation results illus- where j � 1, . . . , m represents the vehicle number; trate that the proposed method realizes evident positive i � 1, . . . , n represents the simulation time (s); v is improvement in all trafc conditions and confrms the great benefts of the algorithm in the mixed trafc the average road speed (m/s); F is calculated by equation (38). intersection. Position (m) 8.5 Flow (veh/h) Flow (veh/h) 12 Journal of Advanced Transportation 2000 10.5 10.5 9.5 9.5 8 9 8.5 8.5 90 8 30 40 50 60 70 80 90 MPRs (a) (b) 2000 8.4 8.4 8.2 8.2 7.8 7.8 7.6 7.6 7.4 7.4 7.2 7.2 50 7 30 40 50 60 70 80 90 MPRs (c) (d) Figure 3: Comparison results of average velocity under diferent volumes and MPRs. (a) Average velocity of the proposed method in 3D. (b) Average velocity of the proposed method in 2D. (c) Average velocity of the benchmark method in 3D. (d) Average velocity of the benchmark method in 2D. 5.1.1. Simulation Results under Various MPRs and the Same the vehicle, and there is no optimization for multivehicle, Trafc Flow. Figure 5 depicts the variation of the average which leads to the lower trafc velocity and higher fuel speed and average fuel consumption for mixed trafc fows consumption. Terefore, the simulation results illustrate that with 30%–70% MPRs under the conditions of the randomly the proposed method can improve both the trafc efciency selected speed of 1,000 veh/h in each lane, respectively. and energy-saving performance of the mixed trafc fow at It can be seen from Figure 5(a) that the average speed of the intersections, and the optimization efect is better with higher MPRs. the proposed method is signifcantly higher than that of the comparison method and increases with MPRs, while the average fuel consumption is signifcantly lower than that of the comparison method, and decreases with MPRs. Te 5.1.2. Simulation Results under the Same MPRs and Various statistical results show that compared with the STA method, Trafc Flows. In this scenario, we focus on the variation of the proposed strategy can improve the average velocity by average speed and average fuel consumption and set the about 14.64% as well as reduce the average fuel consumption trafc fow from 500 veh/h to 2,000 veh/h per lane at 70% by about 20.8% on average under various MPRs. In MPRs. Te specifc statistical results are shown in Figure 6. Figure 5(b), under the conditions of various MPRs, the As shown in Figure 6(a), the average speed of the method proposed in this paper can efectively improve the proposed method is signifcantly higher than that of the multivehicle cooperative driving ability of mixed trafc fows comparison method, while the average fuel consumption is and induce ICV formation through EC controller to pass signifcantly lower than that of the comparison method in through the intersection without stopping, reducing the Figure 6(b). Te statistical results show that, compared with idling time of multiple vehicles at the intersection, thereby the STA method, the proposed strategy can improve the improving the trafc efciency. In addition, multiobjective average velocity by about 14.64% and reduce the average fuel optimization is further carried out for ICV queues to reduce consumption by about 34.11% on average under diferent fuel consumption. However, for the comparison method, the trafc fows, respectively. In the proposed method, when the average speed is greatly afected by the phase timing of the trafc volume continues to increase in high-density trafc trafc lights and the spatiotemporal position distribution of conditions, the optimization space for the average speed of 7.2 MPRs MPRs 7.4 7.6 7.4 8.5 7.8 7.6 9.5 7.8 9.5 7.6 7.8 8.5 8.2 Average Velocity (m/s) Average Velocity (m/s) Flow (veh/h) Flow (veh/h) 35 Flow (veh/h) Flow (veh/h) Journal of Advanced Transportation 13 2000 24 24 23.5 22.5 21.5 20.5 19.5 18.5 30 40 50 60 70 80 90 MPRs (a) (b) 55 2000 55 60 50 50 1000 60 500 500 30 40 50 60 70 80 90 MPRs (c) (d) Figure 4: Comparison results of average fuel consumption under diferent volumes and MPRs. (a) Average fuel consumption of the proposed method in 3D. (b) Average fuel consumption of the proposed method in 2D. (c) Average fuel consumption of the benchmark method in 3D. (d) Average fuel consumption of the benchmark method in 2D. 20 30 40 50 60 70 80 90 100 30 50 70 90 MPRs MPRs Te Proposed Method Te Proposed Method STA Method STA Method (a) (b) Figure 5: Comparison results of two methods. (a) Comparison results of average velocity. (b) Comparison results of average fuel consumption. mixed trafc fow is smaller, and the optimization efect of proposed method can improve both trafc efciency and trafc efciency shows a gradual decrease. In the benchmark energy-saving efects for mixed trafc fows at intersections method, as the trafc volume increases, the variation of the with diferent trafc volumes. average speed decreases slightly due to the infuence of the control period of the trafc light signal, and the fuel con- 5.2. A Case Study Analysis. One of the typical cooperative sumption increases signifcantly due to the phenomenon of driving cases at the intersection zone for mixed vehicles queuing accumulation near the intersection. In general, our under the conditions of randomly selected seeds of MPRs MPRs Average Velocity (m/s) Average Fuel Average Fuel Consumption (L) Consumption (L) Average Fuel Consumption (L) Flow (veh/h) Flow (veh/h) 14 Journal of Advanced Transportation 12 50 0 0 500 1000 1500 2000 500 1000 1500 2000 Flow (veh/h) Flow (veh/h) Te Proposed Method Te Proposed Method STA Method STA Method (a) (b) Figure 6: Comparison results of two methods. (a) Comparison results of average velocity. (b) Comparison results of average fuel consumption. 100 100 90 90 80 80 70 70 60 60 50 50 30 30 20 20 Conflict Conflict 0 0 points points 90 95 100 105 110 90 95 100 105 110 Time (s) Time (s) W-E/ICV N-S/ICV W-E/ICV N-S/ICV W-E/HDV N-S/HDV W-E/HDV N-S/HDV (a) (b) Figure 7: Position-time curve of mixed vehicle cooperative driving. (a) Trajectories of the proposed method. (b) Trajectories of the benchmark method. 1,000 veh/h and 70% MPR in each entrance is illustrated. 80 Figure 7 depicts the intercepted spatiotemporal trajectories of vehicles from two conficting 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). Te red coverage area 90 95 100 105 110 represents the confict points at the intersection. Te in- Time (s) stantaneous values of the average speed and fuel con- sumption are demonstrated in Figures 8 and 9, respectively. Te Proposed Method As shown in Figure 7(a), at a distance of about 100 m Actuated STA near the intersection confict points, the ICVs formation can Figure 8: Test results of fuel consumption with two methods. dynamically adjust the vehicle motion according to the anticipated safety driving speed assigned by the EC con- troller to achieve collision avoidance with conficting HDVs near the intersection area are queuing accumulation because in diferent directions and maintain a safe driving distance of the trafc light control, which causes vehicles’ idling and without stopping as well as higher cruising speed through curves to fuctuate violently. Terefore, the method in this the confict points. In Figure 7(b), the mixed trafc fows paper can signifcantly reduce trafc disturbance and Location (m) Average Velocity (m/s) Average Fuel Location (m) Consumption (L) Average Fuel Consumption (L) Journal of Advanced Transportation 15 Data Availability Te data used to support the fndings of this study are available from the corresponding author upon request. 0 Conflicts of Interest 90 95 100 105 110 Time (s) Te authors declare that they have no conficts of interest. Te Proposed Method Actuated STA Acknowledgments Figure 9: Test results of average velocity with two methods. Tis work was supported by the National Natural Science Foundation of China under Grant 51975310 and Grant weaken the trafc shock wave based on ensuring the safety of multivehicle driving in mixed trafc fow. In addition, multiobjective optimization is carried out References for ICV formation to reduce fuel consumption based on [1] M. Yang, H. Yu, and L. 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Hierarchical and Distributed Eco-Driving Approach for Mixed Vehicle Clusters at Unsignalized Intersections

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0197-6729
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DOI
10.1155/2023/7114792
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Hindawi Journal of Advanced Transportation Volume 2023, Article ID 7114792, 16 pages https://doi.org/10.1155/2023/7114792 Research Article Hierarchical and Distributed Eco-Driving Approach for Mixed Vehicle Clusters at Unsignalized Intersections 1,2 2 1 1 Jie Yu , Yugong Luo , Weiwei Kong , and Fachao Jiang College of Engineering, China Agricultural University, Beijing 100083, China State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China Correspondence should be addressed to Weiwei Kong; kongwei_1987@hotmail.com Received 13 March 2022; Revised 23 October 2022; Accepted 24 March 2023; Published 22 April 2023 Academic Editor: Arkatkar Shriniwas Copyright © 2023 Jie Yu et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. To improve the driving efciency and energy-saving characteristics for large-scale mixed trafc fows under diferent 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 hi- erarchical and distributed cooperative eco-driving architecture is frst 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 trafc efciency. 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 diferent MPRs and trafc volumes. MPRs and trafc volumes oriented to signal-controlled 1. Introduction intersections, such as the timing and optimization of traf- Te ICVs enabled by the new generation of information and fc signals for cooperative driving of hybrid vehicles [2–4]. communication technology can provide new ideas for However, with the continuous improvement of the com- solving problems such as high time consuming and poor munication network infrastructure and the intelligent level energy saving for vehicles to pass through intersections [1]. of ICVs, the transportation system will be more intelligent, Given the current trafc situation, the transition from to- and the trafc lights will be replaced by the infrastructure called intersection manager. Moreover, there are also several day’s largely human-driven trafc to purely automated trafc will be a gradual process, with the fact that we may scholars focused on a multivehicle cooperative driving experience mixed trafc shortly. Terefore, in such a tran- method to improve the driving efciency or energy-saving sitional period, it is necessary to design a driving scheme to for mixed trafc fows at such nonsignal-controlled in- coordinate the mixed trafc fows of ICVs and HDVs, which tersections. Zohdy and Rakha [5] proposed an improved is of great signifcance for improving trafc efciency and cooperative adaptive cruise control (iCACC) system, and the reducing fuel consumption. trafc efciency and fuel consumption of intersections under At present, several driving efciencies and energy-saving diferent MPRs were discussed, in which HDVs with given improvement methods have been proposed under diferent driving states can maintain a safe driving distance from 2 Journal of Advanced Transportation environment and vehicles; for the model-based methods, the ICVs. Qian et al. [6] proposed a priority-based coordination system with the hypothesis that the driving state of HDVs is precise model information requirement for HDVs driving behavior of the entire mixed trafc fow might restrict its accurately known and can maintain a safe distance from their leading ICVs to enhance intersection efciency. Yang practical applications. and Oguchi [7] proposed a trafc model for predicting total In summary, to improve the driving efciency and vehicle delay, which afects the observable driving states of energy-saving for mixed trafc fows under diferent MPRs HDVs by solving the optimal speed of ICVs to reduce the and trafc volumes at unsignalized intersections, consid- trafc delay. Although the previous strategies can achieve the ering the cooperative control performance of ICVs forma- improvement of driving efciency and energy saving of the tion and HDVs with time-varying speed characteristics, the hierarchical and distributed cooperative eco-driving scheme mixed trafc fow with the given HDVs’ driving state at intersections, due to many unavoidable factors such as sight- is established in this paper. Te main contributions of this paper are as follows: a hierarchical and distributed co- line insufciency and driving habit diference, the driver’s driving behavior is dynamic and random in many cases, operative eco-driving architecture, which contains two layers of optimization objectives: cloud decision layer and which lead to safety accident, trafc jams, even high con- sumptions at intersection conficting zone. Nevertheless, the vehicle control layer, can achieve the global comprehensive negative impacts of random driving behavior of HDVs on optimization of trafc efciency and energy saving for large- improving driving efciency and energy saving for mixed scale mixed trafc fows under diferent MPRs and trafc trafc fows have not been considered in the previous volumes at unsignalized intersections. Especially, in the studies. Terefore, higher requirements need to be put cloud decision layer, a multivehicle MFAPCD approach of forward for cooperative driving between ICVs and HDVs nonlinear multivehicle systems is proposed to achieve the prediction of the time-varying driving speed for HDVs and with random driving behavior [8]. Various research studies have been developed to im- the anticipated driving speed for ICVs formation to improve the trafc efciency. Te control method designed in this prove the trafc efciency for ICVs and HDVs with random driving behavior at unsignalized intersections, and the study only used the online I/O data of mixed vehicles during driving based on the CFDL technology to handle the existing methods can be classifed into three categories: (1) learning-based methods [9–11], which leverage machine complex, nonlinear, and uncertain issues of multivehicle learning frameworks, such as deep reinforcement learning, cooperative driving afected by the random driving speed of to train the cooperative control strategy for ICVs. For ex- the mixed trafc fow. ample, the reinforcement learning agent learned a policy for Te rest of this paper is organized as follows: Section 2 IM to let ICVs at unsignalized intersections give up their presents the system architecture. Section 3 presents the right of way and yield to other HDVs to optimize trafc fow multivehicle MFAPCD scheme to realize the improvement of the trafc efciency for mixed trafc fows. Section 4 [10]. (2) Model-based methods [12, 13], which adopt the perspective of rigorous control theory based on the con- presents the NDMPC method to realize the optimization of energy saving for ICV formation. Numerical experiments trolled model and ofer certain insights for the ICV control problem in mixed trafc. Such as, the uncertain maneuver of are given in Section 5, and we conclude the paper in the HDVs based on the driver behavior model was regarded Section 6. as disturbance, and a receding horizon merging control strategy for ICVs to address the problems of safety and trafc 1.1. Abbreviation. Te abbreviation in Table 1 is used efciency of the mixed trafc merging was proposed [12]. (3) throughout this paper. Other methods, such as, an intersection integrated man- agement system was proposed, which used the partially observable Markov decision process (POMDP) modeling 2. Hierarchical and Distributed Eco- method to estimate the driver intention of HDVs, thereby Driving Architecture decreasing the uncertainties in decision-making and plan- ning for ICVs, and then, the trafc efciency was enhanced As shown in Figure 1, a hierarchical and distributed eco- [14]; in addition, a game theory-based decision-making driving architecture is developed by considering two layers: dynamic was developed to achieve more realistic models the cloud decision layer and the vehicle control layer. With of human behavior when making conficting maneuvers at this architecture, the anticipated safety driving speed of intersections, and incorporate it into ICVs’ motion planning mixed trafc fow (cloud decision layer) and the multivehicle algorithms and further to improve the trafc efciency [15]. optimal speed control of ICVs formation (vehicle control However, the previous studies mainly focus on improving layer) can be organically combined, which makes it possible trafc efciency under mixed trafc fows but have not yet to achieve the global comprehensive optimization of trafc considered the comprehensive improvement of trafc ef- efciency and energy-saving for mixed vehicles at unsign- ciency and energy-saving for ICVs and HDVs with time- alized intersections. varying speed characteristics under diferent MPRs and For the cloud decision layer, there is an edging com- trafc volumes. In addition, for the learning-based methods, puting (EC) control system at intersections, which can the shortages include that the training process is usually collect the global status information (position and speed) of computationally demanding, and the resulting strategies mixed vehicles entering the intersection zone through V2I might rely on historical information of the trafc communication technology, in which the time-varying Journal of Advanced Transportation 3 Table 1: Te major acronyms used in this paper. Abbreviations Descriptions MPRs Market penetration rates ICVs Intelligent and connected vehicles HDVs Human-driven vehicles MFAPCD Model-free adaptive predictive cooperative driving CFDL Compact form dynamic linearization CFDL-ITSMPC CFDL integral terminal sliding mode predictive control CFDL-PC CFDL predictive control NDMPC Nonlinear distributed model predictive control iCACC Improved cooperative adaptive cruise control EC Edging computing MFAC Model-free adaptive control PPD Pseudopartial-derivative RSUs Road-side unit IDM Intelligent driver model MPC Model predictive control STA Signal time assignment W-E Western entrance to the eastern exit N-S Northern entrance to the southern exit Time-varying Driving states Cloud Decision Layer driving states of information of HDVs ICVs Decision information Status information Multi-vehicle MFAPCD scheme for mixed multi-vehicle systems • Observation and prediction for HDVsĎ driving speed • Anticipated driving speed planning for ICVs formations Control command issuance Anticipated driving speed Position and speed Vehicle Control Layer Optimal and cooperative control of formation driving vehicle vehicle vehicle ······ controller 1 controller 2 controller N Energy-saving of each ······ vehicle-subsystems Figure 1: Hierarchical and distributed cooperative control architecture. driving speed of HDVs is observed and predicted by the the intersection zone without collision is distributed and multivehicle MFAPCD method (that is reconstructed HDVs guided. status information in EC controller). On this basis, the For the vehicle control layer, we designed the distributed confict-free order and anticipated safety driving speed for controller that focuses on the optimization and cooperative mixed vehicles are calculated, and the anticipated safety control for multivehicle formation based on the NDMPC driving speed of the corresponding ICV formation to cross method according to the anticipated driving speed 4 Journal of Advanced Transportation information obtained from the upper level. With this discrete nonlinear system, and the partial derivative of each method, the large-scale systems with multivehicle groups are component of (n + 2) variable is continuous. Moreover, decoupled into several vehicle subsystems that can interact equation (1) satisfes the generalized Lipschitz continuous with each other. On this basis, the fuel consumption, driving condition. For any k ≠ k , k , k ≥ 0 and ∆u (k), we have 1 2 1 2 h � � � � safety, and passenger comfort of each vehicle subsystem are � � � � � � � � �y (k + 1) − y (k)� ≤ b�u (k + 1) − u (k)�, (2) h h h h comprehensively considered. where b > 0. 3. MultivehicleMFAPCDSchemeforImproving For all k, when u (k) ≠ 0, there is a time-varying pa- Traffic Efficiency in Cloud Decision Layer rameter Φ based on PPD, so that the equation is trans- c,h formed into the CFDL data model by the following equation: Motivated by the concept of the model-free adaptive control (3) (MFAC), which does not need a precise model and iden- ∆y (k + 1) � Φ (k)∆u (k) + d (k)T , h,i c,h h 0 tifcation process, and has the advantages of small calcula- where ∆y (k + 1) � y (k + 1) − y (k); y represents the h h h h tion burden, convenient implementation, and simple positions of HDVs;∆u is the speed increment control input controller parameter on-line tuning algorithm [16–18], the h of the HDVs’ the state information reconstruction system in multivehicle MFAPCD scheme is proposed in this study. Te the EC controller. In addition, due to the dynamic and main idea of this method is that build an equivalent CFDL random nature of manual driving behavior, road-side unit data model at each operation point of the closed-loop (RSUs) sensors cannot accurately observe changing speeds nonlinear system based on the novel concept of [19, 20]. Similar to the practice in reference [12], the un- pseudopartial-derivative (PPD). Ten, the system’s PPD is certain maneuver of the HDVs is regarded as a disturbance online estimated by using system online I/O data, and the in this study, and d is an unknown additional disturbance. controller is further designed using the CFDL-ITSMPC and 0 In equation (3), since d (k) is unknown and ∆y (k + 1) CFDL-PC according to the equivalent CFDL data model. 0 h under the action of ∆u (k) is also unknown, thereby re- ducing the cooperative driving control performance through 3.1. Observation and Prediction for HDVs’ Time-Varying EC controller to mixed vehicles with conficting driving Driving Speed Based on CFDL-ITSMPC. In the EC con- directions. To calculate the time-varying velocity of HDVs, troller, the HDVs (1, ..., n) entering the intersection area are the CFDL-ITSMPC approach is proposed, which mainly frst considered as a class of multiple-input and multiple- includes two parts: output (MIMO) discrete-time nonlinear systems: y (k + 1) � f y (k), . . . , y k − n , u (k), . . . , u k − n , 􏼐 􏼐 􏼑 􏼁 h h h y h h u 3.1.1. Time-Varying Velocity Observation of HDVs. For 􏽢 􏽥 􏽥 d(k), d(k − 1), . . . , d k − n , equation (1), let Φ � Φ (k) + Φ (k), where Φ is the 􏼁􏼁 c,h c,h c,h c,h estimation error of Φ , and then equation (3) can be re- c,h (1) written as ∆y (k + 1) � Φ (k)∆u (k) + d(k), where h c,h h where u (k) ∈ R represents the system input at the time k; d(k) � Φ (k)∆u (k) + d (k) representing the total dis- h c,h h 0 y (k + 1) ∈ R represents the system output at the time turbance. Te disturbance observer [21] shown in the fol- k + 1; d(k) is the unknown perturbation and d(k) is lowing equation is designed to estimate the driving speed bounded; n , n , and n are the unknown integers; f(·) � and disturbance information of HDVs entering the in- y u d (f (. . .) . . . f (. . .)) ∈ 􏽑 R ↦R stands for the tersection, respectively: 1 n n +n +2 n n y u − 1 􏽢 􏽢 􏽢 􏽢 ⎧ ⎨ z (k + 1) � z (k) + θk υ y (k) − z (k), α, β􏼁 + Φ (k)∆u (k)T + Tz (k), 1 1 1 h 1 c,h h 2 (4) 􏽢 􏽢 􏽢 z (k + 1) � z (k) + θ k υ d(k) − z (k), α, β􏼁, 2 2 2 2 where 􏽢z (k) and 􏽢z (k) are the estimated values of y (k) and where sign(·) is a symbolic function; among them, for the 1 2 h d(k), respectively; k and k represent the disturbance unknown PPD parameters of Φ (k), it is necessary to 1 2 c,h observer parameters to be designed, which satisfy the design the PPD parameter estimation algorithm to obtain 􏽰�� conditions k , k > 0 and k > 2 k ; θ is the observer pa- the following equation: 1 2 1 2 rameter and satisfes θ ≥ 0; T is the time step; α ∈ (0.5, 1), � � � 2� 􏽢 � � J􏼐Φ 􏼑 � ∆􏽢z (k) − Φ (k − 1)∆u (k − 1) − 􏽢z (k)T � � β ∈ (1, 1.5); υ(·) is the correction term of the observer, c,h 1 c,h h 2 � � satisfying the following equation: � � � 􏽢 � + μ Φ (k) − Φ (k − 1) , � � c,h c,h |x| sign(x), |x| < 1, ⎧ ⎨ (6) υ(x, α, β) � (5) ⎩ β |x| sign(x), |x| ≥ 1, where Φ is an estimated value of Φ in the following c,h c,h equation: Journal of Advanced Transportation 5 􏼌 􏼌 􏼌 􏼌2 We defne the PI-type discrete terminal sliding function 􏼌 􏼌 η􏼌∆u (k − 1)􏼌 􏽢 􏽢 Φ (k) � Φ (k − 1) + to make the systematic error converge quickly as follows 􏼌 􏼌 c,h c,h 􏼌 􏼌 􏼌 􏼌 μ + 􏼌∆u (k − 1)􏼌 [21]: s(k) � λ e(k) + λ E(k − 1), (9) 􏽢 1 2 􏽨∆􏽢z (k) − Φ (k − 1)∆u (k − 1) − 􏽢z (k)T 􏽩, 1 c,h h 2 (7) where λ > 0, λ > 0, and the integral error item is as follows: 1 2 􏽢 􏽢 􏽢 ϕ (k) ϕ (k) · · · ϕ (k) z z ch,11 ch,12 ch,1n e � E(k − 1) + e , (10) ⎡ ⎢ ⎤ ⎥ E(k) � 􏽘 ⎢ ⎥ ⎢ ⎥ i k ⎢ ⎥ ⎢ 􏽢 􏽢 􏽢 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ϕ (k) ϕ (k) · · · ϕ (k) ⎥ ⎢ ⎥ n×n 􏽢 ⎢ ch,21 ch,22 ch,2n ⎥ ⎢ ⎥ i�0 ⎢ ⎥ where Φ (k) � ⎢ ⎥ ∈ R ; ⎢ ⎥ c,h ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⋮ ⋮ ⋮ 􏽢 􏽢 􏽢 where z is the ratio of two odd numbers, and 0 < z < 1. ϕ (k) ϕ (k) · · · ϕ (k) ch,n1 ch,n2 ch,nn Te control strategy can be derived from the discrete 􏽢 􏽢 if |ϕ (k)| ≤ ε or |ϕ (k)| > εb or ch,ii ch,ii 2 reaching law as follows: 􏽢 􏽢 􏽢 􏽢 sign(ϕ (k)) ≠ sign(ϕ (1)), then ϕ (k) � ϕ (1); if ch,ii ch,ii ch,ii ch,ii ∆s(k) � s(k + 1) − s(k) � 0. (11) 􏽢 􏽢 􏽢 |ϕ (k)| > b or sign(ϕ (k)) ≠ sign(ϕ (1)), then ch,ij ch,ij ch,ij 􏽢 􏽢 ϕ (k) � ϕ (1); i, j � 1, . . . , n; i ≠ j; η ∈ (0, 1]; μ > 0; ch,ij ch,ij From equation (11), the following equation can be b , b > 0. obtained: 1 2 λ y (k + 1) − y (k + 1)􏼁 + λ E(k) � s(k), (12) 1 h h 2 3.1.2. Time-Varying Speed Prediction of HDVs Based on where y (k + 1) is the one-step forward output prediction Integral Terminal Sliding Mode and Moving Horizon equation based on the CFDL model, which is shown as Prediction. We defne the output tracking error about the follows: HDVs’ state information reconstruction system in the EC controller as follows: 􏽢 􏽢 y (k + 1) � y (k) + Φ (k)∆u (k) + Z (k), (13) h h c,h h 2 e(k) � y (k) − y (k), (8) h h where y represents the HDVs’ position, ∆u is the equiv- h h ∗ 􏽢 alent control input speed increment, and Z � z (k)T . where y is the expected position of HDVs, and it is cal- 2 2 Substituting equation (13) into equation (12), the culated by the intelligent driver model (IDM) [14]. equivalent control ∆u (k) can be obtained as follows: − 1 − 1 ∗ ∆u (k) � 􏼐λ s(k) − λ λ E(k) − Z (k) + y (k + 1) − y (k)􏼑. (14) h 1 1 2 2 h h Φ (k) c,h ∆u (k) � ∆u (k) +∆u (k). (15) hv h mpc Furthermore, to improve the control system’s tracking 􏽥 􏽢 accuracy, a control action ∆u is generated by the model Let ∆Z � Z − Z , and substituting the control algo- 2 2 2 predictive control (MPC) to drive the output of the system to rithm equations (14) and (15) into equation (11), we get the the sliding surface. Given equation (14), the total control following equation: action of the reconstructed HDVs’ state information system in the EC controller is as follows: s(k + 1) � λ y (k + 1) − y (k + 1)􏼁 + λ E(k) 1 h 2 � λ 􏼐y (k) + Φ (k)∆u (k) + Z (k) − y (k + 1)􏼑 + λ E(k) (16) 1 h c,h hv 2 2 􏽢 􏽥 � s(k) + λ Φ (k)∆u (k) − λ ∆Z (k). 1 c,h mpc 1 2 Furthermore, we can obtain the N-step forward pre- diction sliding mode function as follows: 􏽢 􏽢 􏽢 s(k + N) � s(k) + λ 􏽨Φ (k)∆u (k) + Φ (k + 1)∆u (k + 1), . . . , Φ (k + N − 1)∆u (k + N − 1)􏽩 1 c,h mpc c,h mpc c,h mpc (17) 􏽥 􏽥 􏽥 − λ 􏽨∆Z (k) +∆Z (k + 1)+, . . . , +∆Z (k + N − 1)􏽩. 1 2 2 2 6 Journal of Advanced Transportation If ∆u (k + j − 1) � 0, j > N , then, prediction equa- (k + 1), . . . ,∆Z (k + N − 1)] , mpc u 2 u tion (17) becomes as follows: Φ (k) 0 · · · 0 c,h ⎢ ⎥ ⎡ ⎢ ⎤ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 􏽢 􏽢 ⎥ ⎢ Φ (k) Φ (k + 1) · · · 0 ⎥ ⎢ ⎥ S(k) � Λs(k) + A (k)U(k − 1) − ΓF(k − 1), (18) ⎢ c,h c,h ⎥ ⎢ ⎥ 1 ⎢ ⎥ A (k) � ⎢ ⎥ , ⎢ ⎥ ⎢ ⎥ 1 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⋮ ⋮ ⋮ ⎦ where Λ represents the identity matrix, Γ is lower triangular 􏽢 􏽢 􏽢 Φ (k) Φ (k + 1) · · · Φ (k + N + 1) c,h c,h c,h u N ∗ N matrices consisting of λ , S(k) � [s(k + 1), N is the system input control horizon. Φ can be de- T u c,h s(k + 2), . . . , s(k + N )] , U(k − 1) � [∆u (k),∆u u mpc mpc termined by the following formula: 􏽥 􏽥 (k), . . . ,∆u (k + N − 1)] , F(k − 1) � [∆Z (k),∆Z mpc u 2 2 􏽢 􏽢 􏽢 􏽢 Φ (k + j) � θ (k)Φ (k + j − 1) + θ (k)Φ (k + j − 2)+, . . . , +θ (k)Φ k + j − n , 􏼐 􏼑 (19) c,h 1 c,h 2 c,h n c,h p T T 􏽢 􏽢 where j � 1, . . . , N − 1; θ is the coefcient, i � 1, . . . , n . (k − 1), . . . , Φ (k − n )] , Φ (k) � θ (k)φ 􏽢 (k − 1), and u i p c,h p c,h c,h Let θ(k) � [θ (k), . . . , θ (k)] , φ (k − 1) � [Φ it can be determined by the following equation: 1 n c,h c,h � � � T � T 2 � � 􏽢 􏽢 (20) � 􏽢 � min J(θ(k)) � Φ (k) − φ (k − 1)θ(k) + δ‖θ(k) − θ(k − 1)‖ . � c,h c,h � We can further obtain the function as follows: 􏽢 􏽢 φ (k − 1)􏼒Φ (k) − φ (k − 1)θ(k − 1)􏼓 c,h c,h c,h (21) θ(k) � θ(k − 1) + � � , � �2 � � δ + �φ (k − 1)� c,h − 1 T T 􏽢 􏽢 􏽢 􏽢 ∆u (k) � − Χ􏼒A A + ωI􏼓 A (Λs(k) − ΓF(k − 1)), mpc 1 1 1 where δ ∈ (0, 1]. We defne the performance function as follows: (23) T T (22) J � S (k)S(k) + ωU (k − 1)U(k − 1), − 1 where Χ � [λ 0, . . . , 0]. Ten, equation (14) can be expressed as follows: where the value of ω determines the weighting of the MPC control action. Substituting equation (18) into equation (22), under the optimization condition: zJ/zU(k − 1) � 0, the MPC control action for k times is obtained as follows: − 1 − 1 − 1 ∗ ∆u (k) � Φ (k)􏼐λ s(k) − λ λ E(k) − ∆Z (k) + y (k + 1) − y (k)􏼑 hv 2 2 h c,h 1 1 h (24) − 1 T T 􏽢 􏽢 􏽢 􏽢 − Χ􏼒A A + ωI􏼓 A (Λs(k) − ΓF(k − 1)), 1 1 1 where ∆u is the prediction input of the reconstructed are used to realize system control [15]. In EC controller, the hv ICVs formations (1, . . . , n) entering the intersection area are HDVs’ state information system in the EC controller. On this basis, the anticipated driving velocity of vehicle for- also considered as a class of MIMO discrete-time nonlinear mation is designed. systems: y (k + 1) � f􏼐y (k), . . . , y 􏼐k − n 􏼑, u (k), . . . , u k − n 􏼁 􏼑, c c c y c c u 3.2. Prediction of ICVs’ Anticipated Driving Velocity Based on CFDL-PC. Te CFDL-PC method for a class of unknown (25) nonlinear nonafne MIMO systems is combined MFAC where u (k) ∈ R represents the system input at the time k; with MPC and only dynamic linearization prediction scheme and moving horizon predictive control technology y (k + 1) ∈ R represents the system output at the time c Journal of Advanced Transportation 7 k + 1. Moreover, for any k ≠ k , k , k ≥ 0, and ∆u (k), where 1 2 1 2 c equation (25) satisfes the generalized Lipschitz continuous Φ (k) 0 · · · 0 ⎡ ⎢ ⎤ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 􏽢 􏽢 ⎥ condition, that is, ⎢ ⎥ ⎢ ⎥ ⎢ Φ (k) Φ (k + 1) · · · 0 ⎥ ⎢ ⎥ ⎢ c c ⎥ ⎢ ⎥ ⎢ ⎥ A (k) � ⎢ ⎥ ; ⎢ ⎥ � � � � 1c ⎢ ⎥ ⎢ ⎥ � � � � ⎢ ⎣ ⋮ ⋮ ⋮ ⎦ � � � � y (k + 1) − y (k) ≤ b u (k + 1) − u (k) . (26) � � � � c c c c 􏽢 􏽢 􏽢 Φ (k) Φ (k + 1) · · · Φ (k + N + 1) c c c u N ∗ N For the prediction of ICVs formations’ anticipated 􏽢 􏽢 􏽢 ϕ (k) ϕ (k) · · · ϕ (k) c,11 c,12 c,1n ⎢ ⎥ ⎡ ⎢ ⎤ ⎥ driving velocity, the one-step forward output prediction ⎢ ⎥ ⎢ ⎥ ⎢ 􏽢 􏽢 􏽢 ⎥ ⎢ ⎥ ⎢ ϕ (k) ϕ (k) · · · ϕ (k) ⎥ ⎢ ⎥ ⎢ ⎥ n×n 􏽢 ⎢ c,21 c,22 c,2n ⎥ ⎢ ⎥ Φ (k) � ⎢ ⎥ ∈ R ; if ⎢ ⎥ ⎢ ⎥ equation based on the CFDL model is as follows: c ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⋮ ⋮ ⋮ ⎦ 􏽢 􏽢 􏽢 ϕ (k) ϕ (k) · · · ϕ (k) y (k + 1) � y (k) + Φ (k)∆u (k), (27) c,n1 c,n2 c,nn c c c c 􏽢 􏽢 􏽢 |ϕ (k)| ≤ ε or |ϕ (k)| > εb or sign(ϕ (k)) ≠ sign c,ii c,ii 2 c,ii where y is the set of positions of the leader ICVs of all 􏽢 􏽢 􏽢 􏽢 (ϕ (1)), then ϕ (k) � ϕ (1); if |ϕ (k)| > b or c,ii c,ii c,ii c,ij 1 formations, and Φ is the estimated value of the PPD pa- 􏽢 􏽢 􏽢 􏽢 sign(ϕ (k)) ≠ sign(ϕ (1)), then ϕ (k) � ϕ (1); rameter Φ . c,ij c,ij c,ij c,ij Ten, the N-step forward prediction equation is given as i, j � 1, . . . , n; i ≠ j; ∆U (k) � [∆u (k), . . . ,∆u (k+ N c c follows: N − 1)] . Since A (k) contains unknown PPD parameters Φ (k), 1c c Y (k + 1) � Y (k) + A (k)∆U (k), (28) c c 1c N 􏽢 􏽢 􏽢 Φ (k), Φ (k + 1), . . . , Φ (k + N + 1) need to be obtained c c c u by the design of the PPD parameter estimation algorithm: 􏽢 􏽢 􏽢 􏽢 Φ (k + j) � θ (k)Φ (k + j − 1) + θ (k)Φ (k + j − 2)+, . . . , +θ (k)Φ k + j − n , 􏼐 􏼑 (29) c 1 c 2 c n c p ∗ ∗ ∗ T where j � 1, . . . , N − 1; Let Y (k + i) � [y (k + i), ..., y (k + N)] , c c c Y (k + i) � [y (k + i), ..., y (k + N)] , and the predictive c c c control criterion function of driving efciency is as follows: ∗ ∗ T min J ∆U (k) � ∆V (k + 1) − ∆V (k + 1) ∆V (k + 1) − ∆V (k + 1) + λ∆U (k)∆U (k), (30) 􏼁 􏼂 􏼃 􏼂 􏼃 Nu c c c c Nu Nu where λ > 0 is the weighting factor; ∆V represents the expected output of the system; Y represents the predicted c c expected speed increment of the system, and output of the system; a set of anticipated safety distances ∗ ∗ ∗ ∆V (k + 1) � (Y (k + 1) − Y (k))/T; ∆V represents the within the prediction horizon for ICV formation is calcu- c c c lated by the following equation: predicted speed increment of the system, and ∆V (k + 1) � (Y (k + 1) − Y (k))/T; Y represents the c c c 􏼌 􏼌 􏼌 􏼌 􏽢 􏼌 􏼌 Y (k) + A (k)∆u (k) + d , if Y − Y ≤ d , n ≠ 1, ⎧ ⎪ 􏼌 􏼌 h,n− 1 1 hv safe h,n− 1 c,n safe ⎨ 􏼌 􏼌 ∗ 􏼌 􏼌 􏽢 􏼌 􏼌 Y (k + 1) � Y (k) + A (k)∆u (k) + d , if Y − Y ≤ d , n ≠ 1, (31) 􏼌 􏼌 c ⎪ c,n 1c c safe c,n− 1 c,n safe 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 Y (k) + A (k)∆u (k), if 􏼌Y − Y 􏼌 > d , n ≠ 1; or 􏼌Y − Y 􏼌 > d , n ≠ 1; or n � 1, c,n 1c c h,n− 1 c,n safe c,n− 1 c,n safe where Y is the position set of the n − 1th HDVs in front formation; and d is the expected following distance, h,n− 1 safe of the nth ICVs formation; Y is the position set of nth ICVs d � d + τ u . c,n safe min h c formation; Y is the position set of n − 1th ICVs for- Let zJ/zU (k) � 0, the optimal control variables are c,n− 1 Nu mation;∆u is the control input speed increment of the ICVs obtained as follows: − 1 T T 􏽢 􏽢 􏽢 (32) ∆U (k) � λI + A (k)A (k) A (k) Y (k + 1) − Y (k) , 􏼒 􏼓 􏼁 Nu 1 1 1 c c 8 Journal of Advanced Transportation where λ > 0. structure, and decompose vehicle marshalling system into Te control variable at the current moment is as follows: several vehicle node subsystems that can interact. On this basis, the local open-loop optimal control problem is allo- (33) u (k) � u (k − 1) + g ∆U (k), c c Nu cated to each vehicle node based on the NDMPC algorithm, which is used for distributed multiobjective optimization where g � [1, 0, . . . , 0] . N∗1 based on adjacent nodes and cloud decision-making layer Terefore, the speed control of each ICV formation is information. carried out according to equation (33), to realize the safe and We further consider the vehicle nonlinear characteristics efcient driving of the ICVs formation and HDVs. such as drivetrain, braking system, and rolling resistance on approaching ICVs. Terefore, we use a nonlinear vehicle 4. Multivehicle NDMPC Scheme for Improving longitudinal dynamics model [22, 23] as a predictive model. Energy-Saving in the Vehicle Control Layer Te equations are discretely as follows: Te NDMPC scheme can fully consider the complexity of vehicle marshalling coupling system with distributed s(t + 1) � s(t) + v(t)∆T, ⎧ ⎪ 4T (t)i η C Aρ ⎪ q 0 v(t + 1) � v(t) + 􏼠 − v(t) − g sin α − fg cos α􏼡∆T, (34) mr 2m 1 1 T (t + 1) � T (t) + u(t)∆T − T (t)∆T, q q q τ τ where v and s represent the velocity and displacement, r is the wheel rolling radius; g represents the acceleration of respectively; T is the actual vehicle driving torque; τ rep- gravity. Te key parameters of the vehicle model settings are resents the delay coefcient; η is the mechanical efciency of as shown in Table 2. the transmission system; C represents the air drag co- In addition, taking fuel vehicles as an example, we use efcient; ρ is the air density; α represents the road slope; f the model in reference [25] to calculate the fuel consumption represents the rolling resistance coefcient; A represents the of all vehicles, and it is discretely as follows: frontal area; i represents the mechanical transmission ratio; 2 2 F(t + 1) � F(t) + α + δ v(t) b + b v(t) + b v(t) + αmv(t) + δ ma(t) v(t) ∆T, (35) 􏼐 􏼑 􏼐 􏼑 1 1 2 3 2 a>0 where b , b , and b are the rolling resistance term and the 4.1. Control Scheme of the Pilot Vehicle. Based on expected 1 2 3 wind resistance coefcient of the tire; δ and δ are the fuel travel velocity sent by EC controller, the most eco- 1 2 consumption model coefcients; a represents the vehicle nomical vehicle torque is calculated and transmitted to acceleration; α represents the engine idle fuel consumption the following ICVs. Te cost function can be divided into rate. Te fuel consumption model key parameters settings three parts: the tracking error, the energy-saving per- are as shown in Table 3. formance, and the passenger comfort performance. In addition, vehicle platoon controllers need to be Specifcally, we defne a function to maintain the tracking designed separately for the pilot ICVs and following ICVs accuracy between the cloud decision layer and the pilot [23]. We assume that driving state of the pilot vehicle is ICVs, which minimizes the tracking error between the p p p p T y � [S , v , T ] , s ∈ {1, 2, . . . , n}. Te expected state of desired state of the optimal speed from the EC controller s s s q,s ∗ ∗ ∗ ∗ pilot vehicle is y � [S , v ] , where v is the anticipated and driving speed of the pilot ICVs. In addition, tracking ec ec ec ec optimal velocity from the EC controller (that is u of the nth accuracy between the desired confict-free position and ICVs formation), and S is the corresponding desired lo- the actual driving location needs to be optimized. With ec cation. Te expected status for ego vehicle and the pilot EC controller, the required collision-free position can be a a T vehicle is y � [S − (s − 1)d , v , T ] , where easily calculated based on the minimum safe head- sdes 1 des 1 q,1 d � d + τ v . Te expected status for the ego vehicle to-head distance from the vehicle before the des min h 1 a a T and preceding vehicle is y � [S − d, v , T ] , collision [26]. js js js q,js js ∈ {1, 2, . . . , n}, where d � d + τ v . Te control scheme is described as follows: min h js Journal of Advanced Transportation 9 Table 2: Vehicle model parameters [22, 24]. Parameters m r C g f η τ w D Numerical value (unit) 1,230 kg 0.38 m 0.39 9.8 m/s 0.012 0.96 0.3 s Table 3: Fuel consumption model parameters [3]. Parameters a β β b b b 1 2 1 2 3 Numerical value (unit) 0.67 ml/s 0.07 0.03 0.27 0.02 0.67E − 03 N − 1 min J (t) � 􏽘 􏼐J (k|t) + J (k|t) + J (k|t)􏼑 1 1,s 2,s 3,s k�0 � � � � � � � � � � � � ∗ p p ∗ � � � � � � w y (k|t) − y (k|t) + w u (k|t) − u v (k|t) + w f (k|t) � 􏼁� � 􏼁 􏼁� � 􏼁 � l1 ec s l2 s 0 ec l3 s 2 2 2 s.t. v ≤ v (k|t) ≤ v min s max a ≤∆v (k|t) ≤ a min s max (36) T ≤ u (k|t) ≤ T min s max 􏼌 􏼌 􏼌 􏼌 p 􏼌 ∗ 􏼌 􏼌 􏼌 v N t � v N t 􏼒 􏼓 􏼒 􏼓 􏼌 􏼌 s p ec p 􏼌 􏼌 􏼌 􏼌 p ∗ 􏼌 􏼌 􏼌 􏼌 S 􏼒N t􏼓 � s 􏼒N t􏼓 s p􏼌 p􏼌 ec 􏼌 􏼌 􏼌 􏼌 p ∗ 􏼌 􏼌 􏼌 􏼌 T 􏼒N t􏼓 � h 􏼒v 􏼒N t􏼓􏼓, p􏼌 s p􏼌 q,s ec where J (k|t) is the vehicle tracking error cost functions; consumption in the predicted time-domain, which is ob- 1,s J (k|t) is a ride comfort performance function that min- tained by calculating the minimum vehicle fuel consumption 2,s imizes the change rates in input torque between the vehicle’s accumulated in N steps; w , w , and w are the weighting p l1 l2 l3 predictive control variable and the expected control variable, coefcient, respectively; f (k|t) is the fuel consumption of wherein the expected control variable is obtained from the pilot vehicle; u (v (k|t)) is the desired torque while the 0 ec reference velocity of the EC controller; J (k|t) represents vehicle driving at the desired reference velocity, and it can be 3,s the energy-saving function that minimize vehicle fuel calculated by the following equation: r 1 2 ∗ ∗ u 􏼐v 􏼐N t􏼑􏼑 � 􏼒 C Aρ􏼒v 􏼐N t􏼑 􏼓 + mgf cos α + mg sin α􏼓. (37) 0 ec p D ec p 4i η 2 4.2. Control Scheme of the following Vehicle. Te following establishing constraints to ensure stability throughout the vehicle controller is designed to ensure that its own ve- vehicle’s formation. Specifcally, we design the tracking hicle can operate at the optimal economical velocity, while error function, comfort function, and energy saving ensuring that the vehicle is in a stable following state with function to defne the cost function. Te control issues are the pilot vehicle and the preceding vehicle, and described as follows: 10 Journal of Advanced Transportation N − 1 min J (t) � 􏽘 J (k|t) + J (k|t) + J (k|t) + J (k|t) 􏼐 􏼑 2 1,s 2,s 3,s 4,s k�0 � � � � � � � � � � � � � � � � p p p a � � � � � � � � � � � �w y (k|t) − y (k|t)􏼁� + w 􏼐y (k|t) − y (k|t)􏼑 + �w u (k|t) − u v (k|t)􏼁 􏼁� + �w f (k|t)􏼁 � 1 sdes � 2 js � 3 s 0 4 s s 2 s 1 2 2 s.t. v ≤ v (k|t) ≤ v min max a ≤∆v (k|t) ≤ a min s max T ≤ u (k|t) ≤ T min s max 􏼌 􏼌 􏼌 􏼌 p a 􏼌 􏼌 􏼌 􏼌 v 􏼒N t􏼓 � v 􏼒N t􏼓 s p􏼌 js p􏼌 􏼌 􏼌 􏼌 􏼌 p 􏼌 a a 􏼌 􏼌 􏼌 S N t � S v N t − d 􏼒 􏼓 􏼒 􏼒 􏼓􏼓 􏼌 􏼌 s p 1 1 p 􏼌 􏼌 􏼌 􏼌 p a 􏼌 􏼌 􏼌 􏼌 S 􏼒N t􏼓 � S 􏼒N t􏼓 − (s − 1)d 􏼌 􏼌 s p js p des 􏼌 􏼌 􏼌 􏼌 p a 􏼌 􏼌 􏼌 􏼌 T 􏼒N t􏼓 � h 􏼒v 􏼒N t􏼓􏼓, p􏼌 s p􏼌 q,s js (38) where J (k|t) represents the tracking error between the ego saving performance; w , w , w , and w is the weighting 1,s 1 2 3 4 vehicle and the pilot vehicle; J (k|t) is tracking error be- coefcient, respectively; f (k|t) represents the vehicle fuel 2,s s tween the ego vehicle and the adjacent ICVs; S (k|t) and consumption; u (v (k|t)) represents the vehicle torque of js 0 1 v (k|t) are the position and velocity of the adjacent ICVs; the pilot vehicle, and it can be calculated by the following js J (k|t) is the ride comfort function; J (k|t) is the energy- formula: 3,s 4,s 􏼌 􏼌 􏼌 r 1 􏼌 􏼌 􏼌 􏼌 􏼌 u 􏼒v 􏼒N t􏼓􏼓 � 􏼒 C Aρv 􏼒N t􏼓 + mgf cos α + mg sin α􏼡. (39) 􏼌 􏼌 0 1 p D 1 p 4i η 2 higher, the improvement of vehicle safety and trafc ef- 5. Simulation Results and Analysis ciency through intersections can be achieved [28, 29]. To verify the feasibility of the algorithm, the joint test Terefore, the manuscript is oriented to the multi- platform is created by SUMO and MATLAB in Figure 2. Te intersection scenario with high MPRs (i.e., MPRs not less solution process of the approach is simulated in MATLAB than 30%), and carries out the cloud-based decision making server, and the two-way typical unsignalized intersection and cooperative control of multivehicles at multi- scenario is the built-in SUMO trafc simulation environ- intersections with diferent MPRs. Furthermore, in order ment. Te V2I communication signal in this study can to avoid the long convergence time of multivehicle con- completely cover the intersection area, and the communi- sistency control and the reduction of trafc efciency due to cation radius range is set to 200 m. In particular, to resolve the excessive number of vehicles in the mixed vehicle queue, the trajectories of confict with approaching mixed vehicles, this paper limits the number of vehicles in the mixed vehicle such as merging conficts and crossing conficts of mixed queue to no more than 3 [30, 31]. trafc fow in diferent lanes at intersections, as shown in We construct the baseline scenario with signal time Figure 2, we projected the approaching mixed vehicles from assignment (STA) by considering all vehicles driving at a safe diferent entrance lanes into virtual lanes according to their distance from the vehicle in front. Te green time and unit locations about the intersection origin and constructed extension time are set as 15 s and 3 s, respectively. Te time- a virtual platoon. Furthermore, the conficting mixed ve- varying speed perturbation of HDVs satisfy N(5, 0.5). Each hicles can coordinate the movements of themselves through working condition is simulated 5 times. Te performance EC controller to pass through the intersection conficts in an indicators of the average speed and average fuel con- orderly manner (such as numbers 1 and 4 in diferent levels), sumption are, respectively, calculated by 100 vehicles, and while vehicles can realize confict-free movements (such as each vehicle length is 5 m. Te driving direction of vehicles is numbers 3, 4, and 5 in the same level) [26, 27]. In addition, 15% left-turning and 10% right-turning, and the relative existing studies show that the improvement efect of vehicle space and a relative number of vehicles entering each lane travel safety through nonsignal-controlled intersections is are random [32–34]. Te weighting factor of the proposed limited at low MPRs, but with MPRs exceeding 30% or even method is as follows: ω � 0.3, ω � 0.3, ω � 0.4, λ � 600, 1 2 3 Journal of Advanced Transportation 11 Matlab solution server SUMO trafc simulation environment HDV ICVs formation Speed Input North • Driving states of HDVs and ICVs entrance trafc fow control EC Input • Environmental information WBL WBT WBR SBL SBT SBR controller command 45 6 78 9 Observation and prediction for HDVs’ time- varying driving speed module Input Matlab EC trafc fow controller function 9 7 East Multi-vehicle optimization cooperative driving entrance TraCI control module West Mixed virtual interface entrance queue Communication radius Input Level Vehicle control information distribution module 4 trafc fow Car-following EBL EBT EBR 1 NBL NBT NBR Vehicle status acquisition module 10 11 12 Vehicle 12 3 3 running status and • Data for visualization 100 South scenario Input entrance 5 7 Output trafc fow information E-W Typical unsignalized intersection S-N -100 15 20 25 30 35 40 45 Figure 2: Joint simulation platform architecture. (b) Te trafc fow is set as 1,000 veh/h in each entrance Table 4: System key parameters setting [24, 26]. and the MPRs are set as 70%. In this scenario, we Numerical analyze the trajectory of ICVs and HDVs by taking Physical meanings Variables values (unit) the directions of potential collision conficts near the Initial speed v , v 10 m/s s js intersection conficting zone as an example. Minimum car-following distance d 5 m min Time-step ∆T 0.1 Headway τ 0.65 2 5.1. Simulation Results under Diferent MPRs and Trafc Maximum acceleration a 2 m/s max 2 Flows. In this section, we verify the control performance of Minimum acceleration a − 2 m/s min the approach in various MPRs and trafc volumes. Te Prediction time-domain N 10 random trafc fow is set from 500 veh/h to 2000 veh/h, and Control time-domain N 3 the MPRs are set from 30% to 90%. Te performance results Order of parameter prediction n 3 of 5 simulations of each working condition are statistically analyzed, as shown in Figures 3 and 4. λ � 0.3, λ � 0.2, μ � 0.015, η � 1, δ � 0.6, and ϕ (1) � 10. 1 2 c As shown in Figure 3, the average speed of the proposed Te system key parameters setting is shown in Table 4. method under diferent MPRs and trafc volumes is gen- In addition, we provide two experimental scenarios to erally higher than that of the comparison method. Te verify and evaluate the feasibility and efectiveness of the highest average speed occurs around 90% MPRs with developed algorithm, and the details are as follows: a trafc fow of 500 veh/h, and the lowest average speed occurs around 30%–40% and 60% MPRs with a trafc fow (a) Te trafc fow range is set from 500 veh/h to of 2000 veh/h; additionally, as shown in Figure 4, the average 2,000 veh/h and the MPRs range is set from 30% to fuel consumption of the proposed method under diferent 90% in each entrance. We compare the performances MPRs and trafc fows is generally lower than that of the of two methods, including the proposed method and comparison method. Te lowest fuel consumption is close to the STA method. In addition, the data of vehicles at 80%–90% MPRs with a trafc fow of 500 veh/h, and the every sampling step is collected and the improvement highest fuel consumption is close to 30% MPRs with a trafc efect of the average speed and average fuel con- fow of 2000 veh/h. Te results show that the lower trafc sumption is calculated by the following equations: volume and the higher MPRs of ICVs, the better the im- v􏼁 provement efect of spatiotemporal resource utilization and V � 􏽘 , (40) energy-saving performance. i�1 Overall, through statistics, compared with the m benchmark method, the proposed strategy improves the 􏼐􏽐 􏼐F 􏼑/m􏼑 j�1 i,j average velocity by about 15.22% as well as reduces the (41) F � 􏽘 . fuel consumption by about 36.43% on average under i�1 diferent trafc conditions. Te simulation results illus- where j � 1, . . . , m represents the vehicle number; trate that the proposed method realizes evident positive i � 1, . . . , n represents the simulation time (s); v is improvement in all trafc conditions and confrms the great benefts of the algorithm in the mixed trafc the average road speed (m/s); F is calculated by equation (38). intersection. Position (m) 8.5 Flow (veh/h) Flow (veh/h) 12 Journal of Advanced Transportation 2000 10.5 10.5 9.5 9.5 8 9 8.5 8.5 90 8 30 40 50 60 70 80 90 MPRs (a) (b) 2000 8.4 8.4 8.2 8.2 7.8 7.8 7.6 7.6 7.4 7.4 7.2 7.2 50 7 30 40 50 60 70 80 90 MPRs (c) (d) Figure 3: Comparison results of average velocity under diferent volumes and MPRs. (a) Average velocity of the proposed method in 3D. (b) Average velocity of the proposed method in 2D. (c) Average velocity of the benchmark method in 3D. (d) Average velocity of the benchmark method in 2D. 5.1.1. Simulation Results under Various MPRs and the Same the vehicle, and there is no optimization for multivehicle, Trafc Flow. Figure 5 depicts the variation of the average which leads to the lower trafc velocity and higher fuel speed and average fuel consumption for mixed trafc fows consumption. Terefore, the simulation results illustrate that with 30%–70% MPRs under the conditions of the randomly the proposed method can improve both the trafc efciency selected speed of 1,000 veh/h in each lane, respectively. and energy-saving performance of the mixed trafc fow at It can be seen from Figure 5(a) that the average speed of the intersections, and the optimization efect is better with higher MPRs. the proposed method is signifcantly higher than that of the comparison method and increases with MPRs, while the average fuel consumption is signifcantly lower than that of the comparison method, and decreases with MPRs. Te 5.1.2. Simulation Results under the Same MPRs and Various statistical results show that compared with the STA method, Trafc Flows. In this scenario, we focus on the variation of the proposed strategy can improve the average velocity by average speed and average fuel consumption and set the about 14.64% as well as reduce the average fuel consumption trafc fow from 500 veh/h to 2,000 veh/h per lane at 70% by about 20.8% on average under various MPRs. In MPRs. Te specifc statistical results are shown in Figure 6. Figure 5(b), under the conditions of various MPRs, the As shown in Figure 6(a), the average speed of the method proposed in this paper can efectively improve the proposed method is signifcantly higher than that of the multivehicle cooperative driving ability of mixed trafc fows comparison method, while the average fuel consumption is and induce ICV formation through EC controller to pass signifcantly lower than that of the comparison method in through the intersection without stopping, reducing the Figure 6(b). Te statistical results show that, compared with idling time of multiple vehicles at the intersection, thereby the STA method, the proposed strategy can improve the improving the trafc efciency. In addition, multiobjective average velocity by about 14.64% and reduce the average fuel optimization is further carried out for ICV queues to reduce consumption by about 34.11% on average under diferent fuel consumption. However, for the comparison method, the trafc fows, respectively. In the proposed method, when the average speed is greatly afected by the phase timing of the trafc volume continues to increase in high-density trafc trafc lights and the spatiotemporal position distribution of conditions, the optimization space for the average speed of 7.2 MPRs MPRs 7.4 7.6 7.4 8.5 7.8 7.6 9.5 7.8 9.5 7.6 7.8 8.5 8.2 Average Velocity (m/s) Average Velocity (m/s) Flow (veh/h) Flow (veh/h) 35 Flow (veh/h) Flow (veh/h) Journal of Advanced Transportation 13 2000 24 24 23.5 22.5 21.5 20.5 19.5 18.5 30 40 50 60 70 80 90 MPRs (a) (b) 55 2000 55 60 50 50 1000 60 500 500 30 40 50 60 70 80 90 MPRs (c) (d) Figure 4: Comparison results of average fuel consumption under diferent volumes and MPRs. (a) Average fuel consumption of the proposed method in 3D. (b) Average fuel consumption of the proposed method in 2D. (c) Average fuel consumption of the benchmark method in 3D. (d) Average fuel consumption of the benchmark method in 2D. 20 30 40 50 60 70 80 90 100 30 50 70 90 MPRs MPRs Te Proposed Method Te Proposed Method STA Method STA Method (a) (b) Figure 5: Comparison results of two methods. (a) Comparison results of average velocity. (b) Comparison results of average fuel consumption. mixed trafc fow is smaller, and the optimization efect of proposed method can improve both trafc efciency and trafc efciency shows a gradual decrease. In the benchmark energy-saving efects for mixed trafc fows at intersections method, as the trafc volume increases, the variation of the with diferent trafc volumes. average speed decreases slightly due to the infuence of the control period of the trafc light signal, and the fuel con- 5.2. A Case Study Analysis. One of the typical cooperative sumption increases signifcantly due to the phenomenon of driving cases at the intersection zone for mixed vehicles queuing accumulation near the intersection. In general, our under the conditions of randomly selected seeds of MPRs MPRs Average Velocity (m/s) Average Fuel Average Fuel Consumption (L) Consumption (L) Average Fuel Consumption (L) Flow (veh/h) Flow (veh/h) 14 Journal of Advanced Transportation 12 50 0 0 500 1000 1500 2000 500 1000 1500 2000 Flow (veh/h) Flow (veh/h) Te Proposed Method Te Proposed Method STA Method STA Method (a) (b) Figure 6: Comparison results of two methods. (a) Comparison results of average velocity. (b) Comparison results of average fuel consumption. 100 100 90 90 80 80 70 70 60 60 50 50 30 30 20 20 Conflict Conflict 0 0 points points 90 95 100 105 110 90 95 100 105 110 Time (s) Time (s) W-E/ICV N-S/ICV W-E/ICV N-S/ICV W-E/HDV N-S/HDV W-E/HDV N-S/HDV (a) (b) Figure 7: Position-time curve of mixed vehicle cooperative driving. (a) Trajectories of the proposed method. (b) Trajectories of the benchmark method. 1,000 veh/h and 70% MPR in each entrance is illustrated. 80 Figure 7 depicts the intercepted spatiotemporal trajectories of vehicles from two conficting 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). Te red coverage area 90 95 100 105 110 represents the confict points at the intersection. Te in- Time (s) stantaneous values of the average speed and fuel con- sumption are demonstrated in Figures 8 and 9, respectively. Te Proposed Method As shown in Figure 7(a), at a distance of about 100 m Actuated STA near the intersection confict points, the ICVs formation can Figure 8: Test results of fuel consumption with two methods. dynamically adjust the vehicle motion according to the anticipated safety driving speed assigned by the EC con- troller to achieve collision avoidance with conficting HDVs near the intersection area are queuing accumulation because in diferent directions and maintain a safe driving distance of the trafc light control, which causes vehicles’ idling and without stopping as well as higher cruising speed through curves to fuctuate violently. Terefore, the method in this the confict points. In Figure 7(b), the mixed trafc fows paper can signifcantly reduce trafc disturbance and Location (m) Average Velocity (m/s) Average Fuel Location (m) Consumption (L) Average Fuel Consumption (L) Journal of Advanced Transportation 15 Data Availability Te data used to support the fndings of this study are available from the corresponding author upon request. 0 Conflicts of Interest 90 95 100 105 110 Time (s) Te authors declare that they have no conficts of interest. Te Proposed Method Actuated STA Acknowledgments Figure 9: Test results of average velocity with two methods. Tis work was supported by the National Natural Science Foundation of China under Grant 51975310 and Grant weaken the trafc shock wave based on ensuring the safety of multivehicle driving in mixed trafc fow. In addition, multiobjective optimization is carried out References for ICV formation to reduce fuel consumption based on [1] M. Yang, H. Yu, and L. 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Journal of Advanced Transportation – Hindawi Publishing Corporation

Published: Apr 22, 2023

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