技术领域Technical Field
本发明涉及交通工程领域，特别是一种无信号交叉口车辆通行顺序决策与轨迹优化方法及系统。The invention relates to the field of traffic engineering, and in particular to a method and system for making decisions on vehicle traffic sequence and optimizing trajectory at an unsignalized intersection.
背景技术Background technique
交叉口通常被认为是交通网络中的瓶颈和事故多发区，不同方向的车流汇集于此产生轨迹冲突。高效的交通信号控制策略，如自适应信号控制等在提高传统的完全由人类驾驶的车辆(HV)交通的交叉口吞吐量方面表现出了卓越的性能。随着通信技术的发展，网联人类驾驶车辆(CV)可以在没有交通信号的情况下被引导做出适当反应并提高交通安全与通行效率，无冲突方向的车辆可以同时占用交叉口。与车辆自动化相结合，智能网联车(CAV)可以进一步在无信号交叉口以协作的方式运行，利用更大的灵活性来缓解拥堵、提高安全性、降低油耗和排放。Intersections are often considered bottlenecks and accident-prone areas in traffic networks, where traffic from different directions converge to create trajectory conflicts. Efficient traffic signal control strategies, such as adaptive signal control, have shown excellent performance in improving intersection throughput for traditional fully human-driven vehicle (HV) traffic. With the development of communication technology, connected human-driven vehicles (CVs) can be guided to respond appropriately and improve traffic safety and efficiency in the absence of traffic signals, and vehicles in non-conflicting directions can occupy intersections simultaneously. Combined with vehicle automation, intelligent connected vehicles (CAVs) can further operate in a collaborative manner at unsignalized intersections, using greater flexibility to alleviate congestion, improve safety, and reduce fuel consumption and emissions.
纯CAV环境下的无信号交叉口被认为是缓解交通瓶颈的有效途径，学者在这一领域进行了大量探索。一般来说，自主交叉路口管理(AIM)包括两项主要任务：(1)规划轨迹以分离运动冲突；(2)根据规划轨迹以一定目标控制车辆。解决冲突的常用方法有两种：基于规则和基于优化的模型。而许多研究强调微观控制层面，并通过一些简化的启发式规则来确定通过顺序。常用的规则包括先到先服务(FCFS)、最长队伍优先(LQF)等。而相比于基于规则的方法，基于优化的方法则在提高系统效率和降低个人旅行成本方面会有更好的表现，常用的方法为混合整数线性规划模型(MILP)，但通常以系统最优为目标，对于车辆公平性的考虑较少。Unsignalized intersections in pure CAV environments are considered to be an effective way to alleviate traffic bottlenecks, and scholars have conducted extensive research in this field. Generally speaking, autonomous intersection management (AIM) includes two main tasks: (1) planning trajectories to separate motion conflicts; (2) controlling vehicles with certain goals based on the planned trajectories. There are two common methods for resolving conflicts: rule-based and optimization-based models. Many studies emphasize the micro-control level and determine the order of passing through through some simplified heuristic rules. Commonly used rules include first-come, first-served (FCFS), longest queue first (LQF), etc. Compared with rule-based methods, optimization-based methods have better performance in improving system efficiency and reducing personal travel costs. The commonly used method is the mixed integer linear programming model (MILP), but it usually takes system optimization as the goal and pays less attention to vehicle fairness.
近年来，V2X技术促进了车辆以车队的形式协作，以提高交叉口吞吐量并减轻计算负担。研究显示，CAV以车队的形式进行协作，可以有效减少行驶时间和燃料消耗。此外，车辆以车队的形式通过交叉口，还可以降低优化模型求解复杂度。但对于车队中车辆的组成数量，应依据交叉口规划区域内车辆的实时状态，作为优化模型的决策变量。In recent years, V2X technology has promoted the cooperation of vehicles in the form of convoys to improve intersection throughput and reduce computational burden. Studies have shown that CAVs working together in the form of convoys can effectively reduce travel time and fuel consumption. In addition, vehicles passing through intersections in the form of convoys can also reduce the complexity of solving optimization models. However, the number of vehicles in the convoy should be based on the real-time status of vehicles in the intersection planning area as the decision variable of the optimization model.
鉴于短期内可能无法实现CAV市场的完全饱和，探索CAV和HV的混合环境在未来将是一个更加复杂但又具有实际意义的挑战。在混合环境下，CAV的行为可以用一系列的控制方法进行描述，HV的行为可以用相应的车辆跟驰模型刻画。而对于车队轨迹的优化，若限制CAV作为头车则在其渗透率较低的情况下难以实现，而在较容易实现的网联环境下，人类驾驶的车辆(HV)可以实现无冲突通行，让驾驶员在提供速度建议的设备的帮助下，在预期时间进入交叉口。Given that full saturation of the CAV market may not be achieved in the short term, exploring the mixed environment of CAVs and HVs will be a more complex but practical challenge in the future. In a mixed environment, the behavior of CAVs can be described by a series of control methods, and the behavior of HVs can be characterized by the corresponding vehicle following model. As for the optimization of the convoy trajectory, if CAV is restricted to be the lead vehicle, it will be difficult to achieve when its penetration rate is low. In a more easily implemented connected environment, human-driven vehicles (HVs) can achieve conflict-free passage, allowing drivers to enter the intersection at the expected time with the help of devices that provide speed recommendations.
因此，提出一种智能网联车(CAV)和网联人类驾驶车辆(CV)的混合环境下基于车辆编队的无信号交叉口车辆通行顺序决策与轨迹优化方法及系统是非常有必要的。Therefore, it is very necessary to propose a method and system for vehicle traffic order decision and trajectory optimization at unsignalized intersections based on vehicle formation in a mixed environment of intelligent connected vehicles (CAV) and connected human-driven vehicles (CV).
发明内容Summary of the invention
本发明的第一目的是提供一种无信号交叉口车辆通行顺序决策与轨迹优化方法，提高无信号交叉口车辆通行效率，为交通拥堵的缓解提供参考。The first purpose of the present invention is to provide a method for deciding the traffic order and optimizing the trajectory of vehicles at an unsignalized intersection, so as to improve the traffic efficiency of vehicles at the unsignalized intersection and provide a reference for alleviating traffic congestion.
为实现本发明第一目的的技术方案如下：The technical solution for achieving the first object of the present invention is as follows:
一种无信号交叉口车辆通行顺序决策与轨迹优化方法，所述方法考虑全网联环境中智能网联车和网联人类驾驶车辆的混合环境，利用车联网技术与自动驾驶技术，确定无信号交叉口各进口道车队构成以及通行顺序，包括步骤：A method for vehicle traffic order decision and trajectory optimization at an unsignalized intersection, the method considering a mixed environment of intelligent networked vehicles and networked human-driven vehicles in a fully networked environment, using vehicle networking technology and autonomous driving technology, to determine the vehicle fleet composition and traffic order of each entrance lane of an unsignalized intersection, including the following steps:
S1、收集无信号交叉口出现区内所有车辆的位置、速度、加速度，车辆类型，以及网联人类驾驶车辆的意图信息；所述无信号交叉口分为出现区、控制区、汇流区，首先在无信号交叉口出现区内进行车辆编队与通行顺序优化，然后在无信号交叉口控制区内实现车队头车轨迹优化或速度建议，最后在无信号交叉口汇流区实现车队的无冲突通行；所述网联人类驾驶车辆的意图信息包括愿意遵从速度建议、不愿意遵从速度建议；S1. Collect the position, speed, acceleration, vehicle type, and intention information of the connected human-driven vehicles in the appearance area of the unsignalized intersection; the unsignalized intersection is divided into an appearance area, a control area, and a confluence area. First, optimize the vehicle formation and passage sequence in the appearance area of the unsignalized intersection, then optimize the trajectory of the leading vehicle of the convoy or speed suggestions in the control area of the unsignalized intersection, and finally achieve conflict-free passage of the convoy in the confluence area of the unsignalized intersection; the intention information of the connected human-driven vehicles includes willingness to comply with speed suggestions or unwillingness to comply with speed suggestions;
S2、将无信号交叉口出现区内所有车辆按照到达次序进行排序，形成虚拟队列；S2, sorting all vehicles in the unsignalized intersection area according to the order of arrival to form a virtual queue;
S3、根据基于车辆编队并考虑公平性和网联人类驾驶车辆意图的无信号交叉口通行顺序优化模型或结合先到先服务模型，确定最优车队组成方案以及无冲突的通行顺序，从而规划出各车队进入无信号交叉口汇流区的时刻以及所分配的无信号交叉口汇流区的占用时间；S3. Determine the optimal fleet composition plan and conflict-free traffic order based on a traffic order optimization model for unsignalized intersections that is based on vehicle platooning and takes into account fairness and the intention of connected human-driven vehicles, or in combination with a first-come, first-served model, so as to plan the time for each fleet to enter the unsignalized intersection merging area and the allocated occupancy time of the unsignalized intersection merging area;
S4、根据当前车辆状态，通过非线性规划模型为智能网联车头车生成最优轨迹，并控制智能网联车头车，使智能网联车头车带领车队按照所规划的各车队进入无信号交叉口汇流区的时刻通过无信号交叉口控制区，以及按照所分配的无信号交叉口汇流区的占用时间通过无信号交叉口汇流区；通过速度建议模型为愿意遵从速度建议的网联人类驾驶车辆头车给出下一时段的速度建议，使愿意遵从速度建议的网联人类驾驶车辆头车带领车队按照所规划的各车队进入无信号交叉口汇流区的时刻通过无信号交叉口控制区，以及按照所分配的无信号交叉口汇流区的占用时间通过无信号交叉口汇流区；所述智能网联车头车是指车队的第一辆车为智能网联车，所述网联人类驾驶车辆头车是指车队的第一辆车为网联人类驾驶车辆。S4. Generate an optimal trajectory for the leading vehicle of the intelligent connected vehicle through a nonlinear programming model according to the current vehicle state, and control the leading vehicle of the intelligent connected vehicle so that the leading vehicle of the intelligent connected vehicle leads the convoy through the unsignalized intersection control area according to the planned time when each convoy enters the unsignalized intersection merging area, and passes through the unsignalized intersection merging area according to the allocated occupancy time of the unsignalized intersection merging area; give a speed recommendation for the next time period to the leading vehicle of the connected human-driven vehicle that is willing to follow the speed recommendation through a speed recommendation model, so that the leading vehicle of the connected human-driven vehicle that is willing to follow the speed recommendation leads the convoy through the unsignalized intersection control area according to the planned time when each convoy enters the unsignalized intersection merging area, and passes through the unsignalized intersection merging area according to the allocated occupancy time of the unsignalized intersection merging area; the leading vehicle of the intelligent connected vehicle refers to the first vehicle in the convoy being an intelligent connected vehicle, and the leading vehicle of the connected human-driven vehicle refers to the first vehicle in the convoy being a connected human-driven vehicle.
进一步地，所述基于车辆编队并考虑公平性和网联人类驾驶车辆意图的无信号交叉口通行顺序优化模型的决策变量是将虚拟队列划分为的N个初集合内的车辆数；根据所述决策变量并结合网联人类驾驶车辆意图信息，确定车队组成方案(这里的车队组成方案不一定是最优车队组成方案，而是由决策变量以及网联人类驾驶车辆意图信息确定的方案，与解空间、车辆情况相关)，具体包括：Furthermore, the decision variable of the traffic order optimization model for unsignalized intersections based on vehicle platooning and considering fairness and the intention of connected human-driven vehicles is the number of vehicles in the N initial sets into which the virtual queue is divided; according to the decision variable and combined with the intention information of connected human-driven vehicles, a fleet composition scheme is determined (the fleet composition scheme here is not necessarily the optimal fleet composition scheme, but a scheme determined by the decision variables and the intention information of connected human-driven vehicles, which is related to the solution space and vehicle conditions), specifically including:
步骤a、将虚拟队列划分为N个集合，并将这N个集合称为初集合；Step a: divide the virtual queue into N sets, and these N sets are called initial sets;
步骤b、位于同一初集合、同一车道的车辆，形成一个准车队；Step b: Vehicles in the same initial assembly and the same lane form a quasi-convoy;
步骤c、判断每个准车队的头车类型；若准车队的头车为智能网联车，则该准车队形成一个车队；若准车队的头车为网联人类驾驶车辆，且愿意遵从速度建议，则该准车队形成一个车队；若准车队的头车为网联人类驾驶车辆，且不愿意遵从速度建议，则该准车队的头车作为单独车辆，形成一个车队，而该准车队的其余车辆作为另一个准车队，重复执行步骤c，直到准车队形成车队；Step c, determining the type of the leading vehicle of each quasi-convoy; if the leading vehicle of the quasi-convoy is an intelligent network-connected vehicle, the quasi-convoy forms a convoy; if the leading vehicle of the quasi-convoy is a network-connected human-driven vehicle and is willing to follow the speed recommendation, the quasi-convoy forms a convoy; if the leading vehicle of the quasi-convoy is a network-connected human-driven vehicle and is unwilling to follow the speed recommendation, the leading vehicle of the quasi-convoy is used as a single vehicle to form a convoy, and the remaining vehicles of the quasi-convoy are used as another quasi-convoy, and step c is repeated until the quasi-convoy forms a convoy;
步骤d、由所形成的车队确定车队组成方案，并且在所确定的车队组成方案中每条车道上的第k个车队属于一个集合，称为第k个终集合；Step d: determining a convoy composition scheme based on the formed convoys, and the k-th convoy on each lane in the determined convoy composition scheme belongs to a set, which is called the k-th final set;
(初集合是由决策变量直接确定，而终集合是由决策变量和网联人类驾驶车辆意图信息共同确定。)(The initial set is directly determined by the decision variables, while the final set is determined by the decision variables and the connected human driving vehicle intention information.)
所述基于车辆编队并考虑公平性和网联人类驾驶车辆意图的无信号交叉口通行顺序优化模型的目标函数为：The objective function of the traffic order optimization model for unsignalized intersections based on vehicle platooning and considering fairness and the intention of connected human-driven vehicles is:
其中，ta(i,j,s)表示第i条车道上第s个终集合内的第j辆车进入无信号交叉口出现区的时刻；te(i,j,s)表示为第i条车道上第s个终集合内的第j辆车规划的进入无信号交叉口汇流区的时刻；表示第i条车道上第s个终集合内的车辆数；I总表示车道总数；S总表示终集合总数；Wherein,ta (i,j,s) represents the time when the jth vehicle in the sth final set on the i-th lane enters the unsignalized intersection appearance area;te (i,j,s) represents the time planned for the jth vehicle in the sth final set on the i-th lane to enter the unsignalized intersection merging area; represents the number of vehicles in the sth final set on the i-th lane;Itotal represents the total number of lanes;Stotal represents the total number of final sets;
所述基于车辆编队并考虑公平性和网联人类驾驶车辆意图的无信号交叉口通行顺序优化模型的约束条件包括：The constraints of the unsignalized intersection traffic order optimization model based on vehicle platooning and considering fairness and the intention of connected human-driven vehicles include:
1)车辆运动学基本约束，即车辆的位置、速度、加速度满足二阶动力学约束：1) Basic vehicle kinematic constraints, that is, the vehicle's position, velocity, and acceleration satisfy the second-order dynamic constraints:
其中，p(t)表示t时刻车辆的位置，v(t)表示t时刻车辆的速度，u(t)表示t时刻车辆的加速度；Among them, p(t) represents the position of the vehicle at time t, v(t) represents the speed of the vehicle at time t, and u(t) represents the acceleration of the vehicle at time t;
2)最早到达时间约束：为车辆规划的进入无信号交叉口汇流区的时刻受到车辆当前状态的限制，不可早于最早到达时间，即：2) Earliest arrival time constraint: The time for a vehicle to enter the merging area of an unsignalized intersection is limited by the current state of the vehicle and cannot be earlier than the earliest arrival time, that is:
其中，t表示当前时间戳，te表示为车辆规划的进入无信号交叉口汇流区的时刻，c表示无信号交叉口出现区内的车辆，Ψs表示所确定的车队组成方案中的终集合；最早到达时间Tm满足：Where t represents the current timestamp,te represents the time when the vehicle is scheduled to enter the merging area of the unsignalized intersection, c represents the vehicle in the unsignalized intersection appearance area,Ψs represents the final set in the determined convoy composition scheme; the earliest arrival timeTm satisfies:
其中，vmax表示车辆的最大速度限制，umax表示车辆的最大加速度限制，d(t)表示t时刻车辆到无信号交叉口汇流区的距离；Where vmax represents the maximum speed limit of the vehicle, umax represents the maximum acceleration limit of the vehicle, and d(t) represents the distance from the vehicle to the merging area of the unsignalized intersection at time t;
3)车队占用时间约束：车队占用无信号交叉口汇流区的时间与车队的车辆数有关，同时考虑车辆启动反应时间，计算车队最大占用时间，车队占用时间则用车队最大占用时间计算，即：3) Team occupancy time constraint: The time that a team occupies the merging area of an unsignalized intersection is related to the number of vehicles in the team. Taking into account the vehicle start reaction time, the maximum team occupancy time is calculated. The team occupancy time is calculated using the team maximum occupancy time, that is:
To＝Ts+(n-1)Tr，(4.1)To = Ts + (n-1) Tr , (4.1)
其中，n表示车队的车辆数，Tr表示车辆启动反应时间；Ts表示车队最后一辆车启动进入无信号交叉口汇流区的时间，满足：Where n is the number of vehicles in the convoy,Tr is the vehicle start reaction time, andTs is the time when the last vehicle in the convoy starts to enter the merging area of the unsignalized intersection, satisfying:
其中，ls表示车队最后一辆车的停车位置距离无信号交叉口汇流区的距离，ls＝L+H+(n-1)(H+s0)，L表示车辆所在车道在无信号交叉口汇流区内的轨迹长度，H表示车辆长度，s0表示最小车辆间距；Where, ls represents the distance between the parking position of the last vehicle in the convoy and the merging area of the unsignalized intersection, ls =L+H+(n-1)(H+s0 ), L represents the trajectory length of the lane where the vehicle is located in the merging area of the unsignalized intersection, H represents the vehicle length, and s0 represents the minimum vehicle spacing;
4)车队无冲突约束：考虑不同车道轨迹的冲突关系，为车队安排无冲突的轨迹，可兼容的车队可以同时占用无信号交叉口汇流区，因此，车队通行顺序决策的规则为每个车队进入无信号交叉口汇流区的时间晚于具有更高优先级且与之不兼容的车队，即：4) Conflict-free constraints for convoys: Considering the conflict relationship between different lane trajectories, conflict-free trajectories are arranged for convoys. Compatible convoys can occupy the unsignalized intersection merging area at the same time. Therefore, the rule for convoy passage order decision is that each convoy enters the unsignalized intersection merging area later than the convoy with higher priority and incompatible with it, that is:
其中，表示为第i条车道上第s个终集合内的车队头车规划的进入无信号交叉口汇流区的时刻，/>表示为第i′条车道上第s′个终集合内的车队头车规划的进入无信号交叉口汇流区的时刻，/>表示第i′条车道上第s′个终集合内的车队头车占用无信号交叉口汇流区的时间，I表示车道编号集合，S表示终集合编号集合；若s>s′或s＝s′，且第i′条车道在同一终集合中具有优先权，则二进制变量ωii′为1，否则二进制变量ωii′为0；二进制变量λii′用于识别两个车队是否兼容(即两个车队在无信号交叉口汇流区内的轨迹是否冲突)，若两个车队兼容，则λii′＝0，否则λii′＝1。in, It represents the time when the leading vehicle in the sth terminal set on the ith lane plans to enter the merging area of the unsignalized intersection, /> It is represented by the time when the leading vehicle in the s′th terminal set on the i′th lane plans to enter the merging area of the unsignalized intersection, /> represents the time that the head vehicle of the convoy in the s′th terminal set on the i′th lane occupies the merging area of the unsignalized intersection, I represents the lane number set, and S represents the terminal set number set; if s>s′ or s＝s′, and the i′th lane has priority in the same terminal set, then the binary variable ωii′ is 1, otherwise the binary variable ωii′ is 0; the binary variable λii′ is used to identify whether the two convoys are compatible (that is, whether the trajectories of the two convoys in the merging area of the unsignalized intersection conflict), if the two convoys are compatible, then λii′ ＝0, otherwise λii′ ＝1.
进一步地，与不愿意遵从速度建议的网联人类驾驶车辆形成的车队，位于同一终集合的各车道上的车队，根据先到先服务模型按照车队头车先到先服务规则决策车辆通行顺序。Furthermore, for convoys formed by connected human-driven vehicles that are unwilling to follow speed recommendations, the order of vehicle passage in convoys located in each lane of the same terminal assembly is determined according to the first-come, first-served model based on the first-come, first-served rule for the head vehicle in the convoy.
进一步地，所述非线性规划模型为智能网联车头车生成最优轨迹；所述非线性规划模型如下：Furthermore, the nonlinear programming model generates an optimal trajectory for the intelligent networked vehicle head vehicle; the nonlinear programming model is as follows:
v1(ts)＝v1， (6.6)v1 (ts )＝v1 , (6.6)
p1(ts)＝0， (6.7)p1 (ts )＝0， (6.7)
p1(te)＝d1，(6.9)p1 (te ) = d1 , (6.9)
其中，t表示当前时间戳，te表示为车辆规划的进入无信号交叉口汇流区的时刻，ts表示车辆轨迹规划时刻，d1表示智能网联车头车当前位置到无信号交叉口汇流区的距离，表示智能网联车头车的期望速度，v1表示智能网联车头车的速度，p1(t)表示t时刻智能网联车头车的位置，v1(t)表示t时刻智能网联车头车的速度，u1(t)表示t时刻智能网联车头车的加速度，/>表示智能网联车头车的最小速度限制，/>表示智能网联车头车的最大速度限制，/>表示智能网联车头车的最小加速度限制，/>表示智能网联车头车的最大加速度限制；式(6.1)表示最小化ts时刻至te时刻内智能网联车头车油耗；式(6.2)表示智能网联车头车的速度限制；式(6.3)表示智能网联车头车的加速度限制；式(6.4)表示智能网联车头车的位置更新规则；式(6.5)表示智能网联车头车的速度更新规则；式(6.6)表示ts时刻智能网联车头车的速度约束，为起始约束；式(6.7)表示ts时刻智能网联车头车的位置约束，为起始约束；式(6.8)表示te时刻智能网联车头车的速度约束，为终端约束；式(6.9)表示te时刻智能网联车头车的位置约束，为终端约束。Wherein, t represents the current timestamp, te represents the time when the vehicle is planned to enter the merging area of the unsignalized intersection, ts represents the time when the vehicle trajectory is planned, d1 represents the distance from the current position of the intelligent connected vehicle to the merging area of the unsignalized intersection, represents the expected speed of the intelligent network leading vehicle, v1 represents the speed of the intelligent network leading vehicle, p1 (t) represents the position of the intelligent network leading vehicle at time t, v1 (t) represents the speed of the intelligent network leading vehicle at time t, u1 (t) represents the acceleration of the intelligent network leading vehicle at time t, /> Indicates the minimum speed limit of the intelligent networked vehicle head vehicle, /> Indicates the maximum speed limit of the intelligent networked vehicle head vehicle, /> Indicates the minimum acceleration limit of the intelligent networked vehicle head vehicle, /> represents the maximum acceleration limit of the intelligent connected vehicle leading vehicle; formula (6.1) represents the minimization of the fuel consumption of the intelligent connected vehicle leading vehicle from timets to timete ; formula (6.2) represents the speed limit of the intelligent connected vehicle leading vehicle; formula (6.3) represents the acceleration limit of the intelligent connected vehicle leading vehicle; formula (6.4) represents the position update rule of the intelligent connected vehicle leading vehicle; formula (6.5) represents the speed update rule of the intelligent connected vehicle leading vehicle; formula (6.6) represents the speed constraint of the intelligent connected vehicle leading vehicle at timets , which is the starting constraint; formula (6.7) represents the position constraint of the intelligent connected vehicle leading vehicle at timets , which is the starting constraint; formula (6.8) represents the speed constraint of the intelligent connected vehicle leading vehicle at timete , which is the terminal constraint; formula (6.9) represents the position constraint of the intelligent connected vehicle leading vehicle at timete , which is the terminal constraint.
进一步地，所述速度建议模型为愿意遵从速度建议的网联人类驾驶车辆头车给出下一时段的速度建议，包括加速、匀速、减速建议；所述速度建议模型如下：Furthermore, the speed suggestion model provides speed suggestions for the next time period for the leading vehicle of the connected human-driven vehicle that is willing to follow the speed suggestions, including acceleration, constant speed, and deceleration suggestions; the speed suggestion model is as follows:
当时，速度建议模型为愿意遵从速度建议的网联人类驾驶车辆头车提供加速建议；when When the speed recommendation model is set to reach the speed of the vehicle, it will provide acceleration recommendations to the leading connected human-driven vehicle that is willing to follow the speed recommendation.
当时，速度建议模型为愿意遵从速度建议的网联人类驾驶车辆头车提供匀速建议；when When , the speed recommendation model provides a uniform speed recommendation to the leading connected human-driven vehicle that is willing to follow the speed recommendation;
当时，速度建议模型为愿意遵从速度建议的网联人类驾驶车辆头车提供减速建议；when When the speed recommendation model is set to reach the speed limit, it will provide a deceleration recommendation to the leading connected human-driven vehicle that is willing to follow the speed recommendation.
其中，t表示当前时间戳，te表示为车辆规划的进入无信号交叉口汇流区的时刻，v2(t)表示t时刻愿意遵从速度建议的网联人类驾驶车辆头车的速度，d2(t)表示愿意遵从速度建议的网联人类驾驶车辆头车当前位置到无信号交叉口汇流区的距离，a(-)表示愿意遵从速度建议的网联人类驾驶车辆头车的最大减速度；η1和η2为参数，调节可控制速度建议保守程度。Wherein, t represents the current timestamp,te represents the time when the vehicle is planned to enter the merging area of the unsignalized intersection, v2 (t) represents the speed of the leading connected human-driven vehicle that is willing to follow the speed recommendation at time t, d2 (t) represents the distance from the current position of the leading connected human-driven vehicle that is willing to follow the speed recommendation to the merging area of the unsignalized intersection, a(-) represents the maximum deceleration of the leading connected human-driven vehicle that is willing to follow the speed recommendation; η1 and η2 are parameters that adjust the conservativeness of the controllable speed recommendation.
进一步地，车队中非头车的智能网联车与其前车的间隙保持规则如下：Furthermore, the rules for maintaining the gap between the non-leading intelligent connected vehicle in the convoy and the vehicle in front of it are as follows:
e＝g(t)-H0-g*， (7.1)e＝g(t)-H0 -g* , (7.1)
其中，t表示当前时间戳，Δta表示时间间隔，g(t)表示t时刻车队中非头车的智能网联车与其前车的间隙，H0表示车队中非头车的智能网联车的车辆长度，g*表示期望间隙，e表示跟踪误差，表示跟踪误差对于时间的一阶导数，θp＝0.45和θd＝0.125为调整间隙的参数，v3(t)表示t时刻车队中非头车的智能网联车的速度，v3(t+Δta)表示t+Δta时刻车队中非头车的智能网联车的速度。Where t represents the current timestamp, Δta represents the time interval, g(t) represents the gap between the non-leading intelligent connected vehicle in the convoy and its preceding vehicle at time t, H0 represents the vehicle length of the non-leading intelligent connected vehicle in the convoy, g* represents the expected gap, e represents the tracking error, represents the first-order derivative of the tracking error with respect to time, θp =0.45 and θd =0.125 are parameters for adjusting the gap, v3 (t) represents the speed of the non-head intelligent connected vehicle in the convoy at time t, and v3 (t+Δta ) represents the speed of the non-head intelligent connected vehicle in the convoy at time t+Δta .
进一步地，车队中非头车的网联人类驾驶车辆和愿意遵从速度建议的网联人类驾驶车辆头车的行为采用考虑随机性的Gipps跟驰模型，其随机性表示为：Furthermore, the behaviors of non-leading connected human-driven vehicles in the convoy and leading connected human-driven vehicles willing to follow speed recommendations adopt the Gipps following model considering randomness, and its randomness is expressed as:
u0(t)＝a(t)+bq(t)r(t)， (8.1)u0 (t) = a(t) + bq(t)r(t), (8.1)
其中，a(t)表示t时刻根据Gipps跟驰模型生成的加速度；b表示不同加速度下的标准差；q(t)是介于0和1之间的均匀分布随机数；r(t)是1或-1，概率分别为50％；u0(t)表示实际执行的加速度。Where a(t) represents the acceleration generated according to the Gipps car-following model at time t; b represents the standard deviation under different accelerations; q(t) is a uniformly distributed random number between 0 and 1; r(t) is 1 or -1, with a probability of 50% respectively; u0 (t) represents the actual acceleration performed.
本发明的第二目的是提供一种无信号交叉口车辆通行顺序决策与轨迹优化系统，提高无信号交叉口车辆通行效率。The second object of the present invention is to provide a vehicle traffic sequence decision and trajectory optimization system for an unsignalized intersection to improve the vehicle traffic efficiency at the unsignalized intersection.
为实现本发明第二目的的技术方案如下：The technical solution for achieving the second object of the present invention is as follows:
一种无信号交叉口车辆通行顺序决策与轨迹优化系统，所述系统是采用前述任一种无信号交叉口车辆通行顺序决策与轨迹优化方法工作的；所述系统包括路侧感知与通信设备、路侧计算单元、车载单元；A vehicle traffic order decision and trajectory optimization system for an unsignalized intersection, the system works by adopting any of the above-mentioned vehicle traffic order decision and trajectory optimization methods for an unsignalized intersection; the system includes a roadside sensing and communication device, a roadside computing unit, and a vehicle-mounted unit;
所述路侧感知与通信设备，收集无信号交叉口出现区内所有车辆的位置、速度、加速度，车辆类型，网联人类驾驶车辆意图信息，并将无信号交叉口出现区内所有车辆信息传输给路侧计算单元；The roadside sensing and communication device collects the position, speed, acceleration, vehicle type, and vehicle intention information of all vehicles in the unsignalized intersection area, and transmits the information of all vehicles in the unsignalized intersection area to the roadside computing unit;
所述路侧计算单元作为无信号交叉口的管理中心，根据接收到的车辆信息，将无信号交叉口出现区内所有车辆按照到达次序进行排序，形成虚拟队列，确定最优车队组成方案以及无冲突的通行顺序，从而规划出各车队进入无信号交叉口汇流区的时刻以及所分配的无信号交叉口汇流区的占用时间，并传输给车载单元；所述路侧计算单元包括基于车辆编队并考虑公平性和网联人类驾驶车辆意图的无信号交叉口通行顺序优化模型、先到先服务模型；The roadside computing unit, as the management center of the unsignalized intersection, sorts all vehicles in the unsignalized intersection appearance area according to the arrival order based on the received vehicle information to form a virtual queue, determines the optimal fleet composition plan and the conflict-free passage order, thereby planning the time for each fleet to enter the unsignalized intersection merging area and the allocated occupancy time of the unsignalized intersection merging area, and transmits them to the vehicle-mounted unit; the roadside computing unit includes an unsignalized intersection passage order optimization model and a first-come-first-served model based on vehicle formation and considering fairness and the intention of networked human driving vehicles;
所述车载单元包括非线性规划模型、速度建议模型；所述非线性规划模型为智能网联车头车生成最优轨迹，并控制智能网联车头车，使智能网联车头车带领车队按照所规划的各车队进入无信号交叉口汇流区的时刻通过无信号交叉口控制区，以及按照所分配的无信号交叉口汇流区的占用时间通过无信号交叉口汇流区；所述速度建议模型为愿意遵从速度建议的网联人类驾驶车辆头车给出下一时段的速度建议，使愿意遵从速度建议的网联人类驾驶车辆头车带领车队按照所规划的各车队进入无信号交叉口汇流区的时刻通过无信号交叉口控制区，以及按照所分配的无信号交叉口汇流区的占用时间通过无信号交叉口汇流区。The on-board unit includes a nonlinear programming model and a speed recommendation model; the nonlinear programming model generates an optimal trajectory for the intelligent connected vehicle lead vehicle, and controls the intelligent connected vehicle lead vehicle so that the intelligent connected vehicle lead vehicle leads the convoy through the unsignalized intersection control area according to the planned time when each convoy enters the unsignalized intersection merging area, and passes through the unsignalized intersection merging area according to the allocated occupancy time of the unsignalized intersection merging area; the speed recommendation model gives a speed recommendation for the next time period to the connected human-driven vehicle lead vehicle that is willing to comply with the speed recommendation, so that the connected human-driven vehicle lead vehicle that is willing to comply with the speed recommendation leads the convoy through the unsignalized intersection control area according to the planned time when each convoy enters the unsignalized intersection merging area, and passes through the unsignalized intersection merging area according to the allocated occupancy time of the unsignalized intersection merging area.
与现有技术相比，本发明具有以下优势：Compared with the prior art, the present invention has the following advantages:
一、本发明组织无信号交叉口内车辆以车队形式通过，并结合简单规则与优化模型，在考虑车辆通行公平性的基础上对车辆通行次序进行决策，提出具有更强适应性，同时能够降低计算复杂度的无信号交叉口自主管理方法与系统，具有实际意义。1. The present invention organizes vehicles in an unsignalized intersection to pass through in the form of a convoy, and combines simple rules with optimization models to make decisions on the order of vehicle passage based on the fairness of vehicle passage, and proposes an unsignalized intersection autonomous management method and system with stronger adaptability and reduced computational complexity, which has practical significance.
二、本发明考虑智能网联车和网联人类驾驶车辆的混合环境相比于纯智能网联车的环境更易实现，也更具实际意义；本发明考虑网联人类驾驶车辆驾驶者的意图，允许网联人类驾驶车辆作为车队头车并为其提供速度建议，而为智能网联车头车设计最优轨迹，可以有效模拟混合环境的特征。2. The present invention considers that the mixed environment of intelligent connected vehicles and connected human-driven vehicles is easier to implement and more practical than the environment of pure intelligent connected vehicles; the present invention considers the intention of the driver of the connected human-driven vehicle, allows the connected human-driven vehicle to be the head vehicle of the fleet and provides speed recommendations for it, and designs the optimal trajectory for the head vehicle of the intelligent connected vehicle, which can effectively simulate the characteristics of the mixed environment.
三、本发明运用无信号交叉口车辆编队方案、车队通过顺序同时进行优化，同时考虑了车辆通行公平性与网联人类驾驶车辆不愿意遵从速度建议的情况，接着基于优化结果为智能网联车头车提供最优轨迹，为愿意遵从速度建议的网联人类驾驶车辆头车提供速度建议，控制或引导车辆以更高的通行效率通过无信号交叉口，从而在降低车辆的平均延误的基础上，控制最大延误并降低燃油消耗。3. The present invention uses the vehicle formation plan and the passing order of the fleet at an unsignalized intersection to optimize at the same time, while taking into account the fairness of vehicle traffic and the situation where networked human-driven vehicles are unwilling to follow speed recommendations. Then, based on the optimization results, the optimal trajectory is provided for the leading vehicle of the intelligent networked vehicle, and speed recommendations are provided for the leading vehicle of the networked human-driven vehicle that is willing to follow the speed recommendations, so as to control or guide the vehicles to pass through the unsignalized intersection with higher traffic efficiency, thereby controlling the maximum delay and reducing fuel consumption on the basis of reducing the average delay of the vehicle.
下面通过具体实施方式及附图对本发明作进一步详细说明，但并不意味着对本发明保护范围的限制。The present invention is further described in detail below through specific implementation modes and drawings, but it is not intended to limit the protection scope of the present invention.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为本发明实施例无信号交叉口车辆通行顺序决策与轨迹优化方法及系统的框架示意图。FIG. 1 is a schematic diagram of the framework of a method and system for vehicle traffic sequence decision and trajectory optimization at an unsignalized intersection according to an embodiment of the present invention.
图2为本发明实施例的无信号交叉口示意图。FIG. 2 is a schematic diagram of an unsignalized intersection according to an embodiment of the present invention.
图3为本发明实施例确定车队组成方案的流程示意图。FIG. 3 is a schematic diagram of a flow chart of determining a fleet composition scheme according to an embodiment of the present invention.
图4为采用本发明实施例所提供的方法与采用其他方法，在CAV渗透率100％，不同交通需求下车辆的平均延误结果对比图。FIG. 4 is a comparison chart of average vehicle delay results under different traffic demands when the CAV penetration rate is 100% using the method provided by an embodiment of the present invention and using other methods.
图5为采用本发明实施例所提供的方法与采用其他方法，在CAV渗透率100％，不同交通需求下车辆的最大延误结果对比图。FIG5 is a comparison diagram of the maximum delay results of vehicles under different traffic demands when the CAV penetration rate is 100% using the method provided by the embodiment of the present invention and using other methods.
图6为采用本发明实施例所提供的方法与采用其他方法，在不同CAV渗透率，交通需求为1200veh/h下车辆的平均延误结果对比图。FIG6 is a comparison chart of average vehicle delay results when the method provided by an embodiment of the present invention is used and other methods are used at different CAV penetration rates and a traffic demand of 1200 veh/h.
图7为采用本发明实施例所提供的方法与采用其他方法，在不同CAV渗透率，交通需求为1200veh/h下车辆的最大延误结果对比图。FIG. 7 is a comparison diagram of the maximum delay results of vehicles using the method provided by an embodiment of the present invention and other methods at different CAV penetration rates and a traffic demand of 1200 veh/h.
图8为采用本发明实施例所提供的方法与采用其他方法的车辆燃油消耗指标展示图。FIG. 8 is a graph showing fuel consumption indicators of vehicles using the method provided by an embodiment of the present invention and other methods.
具体实施方式Detailed ways
实施例Example
本例给出一种无信号交叉口车辆通行顺序决策与轨迹优化方法，所述方法考虑全网联环境中智能网联车和网联人类驾驶车辆的混合环境，利用车联网技术与自动驾驶技术，确定无信号交叉口各进口道车队构成以及通行顺序，包括步骤：This example provides a method for vehicle traffic order decision and trajectory optimization at an unsignalized intersection. The method considers a mixed environment of intelligent connected vehicles and connected human-driven vehicles in a fully connected environment, and uses vehicle networking technology and autonomous driving technology to determine the fleet composition and traffic order of each entrance lane of an unsignalized intersection, including the following steps:
S1、收集无信号交叉口出现区内所有车辆的位置、速度、加速度，车辆类型，以及网联人类驾驶车辆的意图信息；所述无信号交叉口分为出现区、控制区、汇流区，首先在无信号交叉口出现区内进行车辆编队与通行顺序优化，然后在无信号交叉口控制区内实现车队头车轨迹优化或速度建议，最后在无信号交叉口汇流区实现车队的无冲突通行；所述网联人类驾驶车辆的意图信息包括愿意遵从速度建议、不愿意遵从速度建议；S1. Collect the position, speed, acceleration, vehicle type, and intention information of the connected human-driven vehicles in the appearance area of the unsignalized intersection; the unsignalized intersection is divided into an appearance area, a control area, and a confluence area. First, optimize the vehicle formation and passage sequence in the appearance area of the unsignalized intersection, then optimize the trajectory of the leading vehicle of the convoy or speed suggestions in the control area of the unsignalized intersection, and finally achieve conflict-free passage of the convoy in the confluence area of the unsignalized intersection; the intention information of the connected human-driven vehicles includes willingness to comply with speed suggestions or unwillingness to comply with speed suggestions;
S2、将无信号交叉口出现区内所有车辆按照到达次序进行排序，形成虚拟队列；S2, sorting all vehicles in the unsignalized intersection area according to the order of arrival to form a virtual queue;
S3、根据基于车辆编队并考虑公平性和网联人类驾驶车辆意图的无信号交叉口通行顺序优化模型或结合先到先服务模型，确定最优车队组成方案以及无冲突的通行顺序，从而规划出各车队进入无信号交叉口汇流区的时刻以及所分配的无信号交叉口汇流区的占用时间；S3. Determine the optimal fleet composition plan and conflict-free traffic order based on a traffic order optimization model for unsignalized intersections that is based on vehicle platooning and takes into account fairness and the intention of connected human-driven vehicles, or in combination with a first-come, first-served model, so as to plan the time for each fleet to enter the unsignalized intersection merging area and the allocated occupancy time of the unsignalized intersection merging area;
S4、根据当前车辆状态，通过非线性规划模型为智能网联车头车生成最优轨迹，并控制智能网联车头车，使智能网联车头车带领车队按照所规划的各车队进入无信号交叉口汇流区的时刻通过无信号交叉口控制区，以及按照所分配的无信号交叉口汇流区的占用时间通过无信号交叉口汇流区；通过速度建议模型为愿意遵从速度建议的网联人类驾驶车辆头车给出下一时段的速度建议，使愿意遵从速度建议的网联人类驾驶车辆头车带领车队按照所规划的各车队进入无信号交叉口汇流区的时刻通过无信号交叉口控制区，以及按照所分配的无信号交叉口汇流区的占用时间通过无信号交叉口汇流区；所述智能网联车头车是指车队的第一辆车为智能网联车，所述网联人类驾驶车辆头车是指车队的第一辆车为网联人类驾驶车辆。S4. Generate an optimal trajectory for the leading vehicle of the intelligent connected vehicle through a nonlinear programming model according to the current vehicle state, and control the leading vehicle of the intelligent connected vehicle so that the leading vehicle of the intelligent connected vehicle leads the convoy through the unsignalized intersection control area according to the planned time when each convoy enters the unsignalized intersection merging area, and passes through the unsignalized intersection merging area according to the allocated occupancy time of the unsignalized intersection merging area; give a speed recommendation for the next time period to the leading vehicle of the connected human-driven vehicle that is willing to follow the speed recommendation through a speed recommendation model, so that the leading vehicle of the connected human-driven vehicle that is willing to follow the speed recommendation leads the convoy through the unsignalized intersection control area according to the planned time when each convoy enters the unsignalized intersection merging area, and passes through the unsignalized intersection merging area according to the allocated occupancy time of the unsignalized intersection merging area; the leading vehicle of the intelligent connected vehicle refers to the first vehicle in the convoy being an intelligent connected vehicle, and the leading vehicle of the connected human-driven vehicle refers to the first vehicle in the convoy being a connected human-driven vehicle.
本例所述基于车辆编队并考虑公平性和网联人类驾驶车辆意图的无信号交叉口通行顺序优化模型的决策变量是将虚拟队列划分为的N个初集合内的车辆数；根据所述决策变量并结合网联人类驾驶车辆意图信息，确定车队组成方案，具体包括：The decision variable of the traffic order optimization model for unsignalized intersections based on vehicle platooning and considering fairness and the intention of connected human-driven vehicles in this example is the number of vehicles in the N initial sets into which the virtual queue is divided; according to the decision variable and combined with the intention information of connected human-driven vehicles, the platoon composition plan is determined, which specifically includes:
步骤a、将虚拟队列划分为N个集合，并将这N个集合称为初集合；Step a: divide the virtual queue into N sets, and these N sets are called initial sets;
步骤b、位于同一初集合、同一车道的车辆，形成一个准车队；Step b: Vehicles in the same initial assembly and the same lane form a quasi-convoy;
步骤c、判断每个准车队的头车类型；若准车队的头车为智能网联车，则该准车队形成一个车队；若准车队的头车为网联人类驾驶车辆，且愿意遵从速度建议，则该准车队形成一个车队；若准车队的头车为网联人类驾驶车辆，且不愿意遵从速度建议，则该准车队的头车作为单独车辆，形成一个车队，而该准车队的其余车辆作为另一个准车队，重复执行步骤c，直到准车队形成车队；Step c, determining the type of the leading vehicle of each quasi-convoy; if the leading vehicle of the quasi-convoy is an intelligent network-connected vehicle, the quasi-convoy forms a convoy; if the leading vehicle of the quasi-convoy is a network-connected human-driven vehicle and is willing to follow the speed recommendation, the quasi-convoy forms a convoy; if the leading vehicle of the quasi-convoy is a network-connected human-driven vehicle and is unwilling to follow the speed recommendation, the leading vehicle of the quasi-convoy is used as a single vehicle to form a convoy, and the remaining vehicles of the quasi-convoy are used as another quasi-convoy, and step c is repeated until the quasi-convoy forms a convoy;
步骤d、由所形成的车队确定车队组成方案，并且在所确定的车队组成方案中每条车道上的第k个车队属于一个集合，称为第k个终集合；Step d: determining a convoy composition scheme based on the formed convoys, and the k-th convoy on each lane in the determined convoy composition scheme belongs to a set, which is called the k-th final set;
所述基于车辆编队并考虑公平性和网联人类驾驶车辆意图的无信号交叉口通行顺序优化模型的目标函数为：The objective function of the traffic order optimization model for unsignalized intersections based on vehicle platooning and considering fairness and the intention of connected human-driven vehicles is:
其中，ta(i,j,s)表示第i条车道上第s个终集合内的第j辆车进入无信号交叉口出现区的时刻；te(i,j,s)表示为第i条车道上第s个终集合内的第j辆车规划的进入无信号交叉口汇流区的时刻；表示第i条车道上第s个终集合内的车辆数；I总表示车道总数；S总表示终集合总数；Wherein,ta (i,j,s) represents the time when the jth vehicle in the sth final set on the i-th lane enters the unsignalized intersection appearance area;te (i,j,s) represents the time planned for the jth vehicle in the sth final set on the i-th lane to enter the unsignalized intersection merging area; represents the number of vehicles in the sth final set on the i-th lane;Itotal represents the total number of lanes;Stotal represents the total number of final sets;
所述基于车辆编队并考虑公平性和网联人类驾驶车辆意图的无信号交叉口通行顺序优化模型的约束条件包括：The constraints of the unsignalized intersection traffic order optimization model based on vehicle platooning and considering fairness and the intention of connected human-driven vehicles include:
1)车辆运动学基本约束，即车辆的位置、速度、加速度满足二阶动力学约束：1) Basic vehicle kinematic constraints, that is, the vehicle's position, velocity, and acceleration satisfy the second-order dynamic constraints:
其中，p(t)表示t时刻车辆的位置，v(t)表示t时刻车辆的速度，u(t)表示t时刻车辆的加速度；Among them, p(t) represents the position of the vehicle at time t, v(t) represents the speed of the vehicle at time t, and u(t) represents the acceleration of the vehicle at time t;
2)最早到达时间约束：为车辆规划的进入无信号交叉口汇流区的时刻受到车辆当前状态的限制，不可早于最早到达时间，即：2) Earliest arrival time constraint: The time for a vehicle to enter the merging area of an unsignalized intersection is limited by the current state of the vehicle and cannot be earlier than the earliest arrival time, that is:
其中，t表示当前时间戳，te表示为车辆规划的进入无信号交叉口汇流区的时刻，c表示无信号交叉口出现区内的车辆，Ψs表示所确定的车队组成方案中的终集合；最早到达时间Tm满足：Where t represents the current timestamp,te represents the time when the vehicle is scheduled to enter the merging area of the unsignalized intersection, c represents the vehicle in the unsignalized intersection appearance area,Ψs represents the final set in the determined convoy composition scheme; the earliest arrival timeTm satisfies:
其中，vmax表示车辆的最大速度限制，umax表示车辆的最大加速度限制，d(t)表示t时刻车辆到无信号交叉口汇流区的距离；Where vmax represents the maximum speed limit of the vehicle, umax represents the maximum acceleration limit of the vehicle, and d(t) represents the distance from the vehicle to the merging area of the unsignalized intersection at time t;
3)车队占用时间约束：车队占用无信号交叉口汇流区的时间与车队的车辆数有关，同时考虑车辆启动反应时间，计算车队最大占用时间，车队占用时间则用车队最大占用时间计算，即：3) Team occupancy time constraint: The time that a team occupies the merging area of an unsignalized intersection is related to the number of vehicles in the team. Taking into account the vehicle start reaction time, the maximum team occupancy time is calculated. The team occupancy time is calculated using the team maximum occupancy time, that is:
To＝Ts+(n-1)Tr，(4.1)To = Ts + (n-1) Tr , (4.1)
其中，n表示车队的车辆数，Tr表示车辆启动反应时间；Ts表示车队最后一辆车启动进入无信号交叉口汇流区的时间，满足：Where n is the number of vehicles in the convoy,Tr is the vehicle start reaction time, andTs is the time when the last vehicle in the convoy starts to enter the merging area of the unsignalized intersection, satisfying:
其中，ls表示车队最后一辆车的停车位置距离无信号交叉口汇流区的距离，ls＝L+H+(n-1)(H+s0)，L表示车辆所在车道在无信号交叉口汇流区内的轨迹长度，H表示车辆长度，s0表示最小车辆间距；Where, ls represents the distance between the parking position of the last vehicle in the convoy and the merging area of the unsignalized intersection, ls =L+H+(n-1)(H+s0 ), L represents the trajectory length of the lane where the vehicle is located in the merging area of the unsignalized intersection, H represents the vehicle length, and s0 represents the minimum vehicle spacing;
4)车队无冲突约束：考虑不同车道轨迹的冲突关系，为车队安排无冲突的轨迹，可兼容的车队可以同时占用无信号交叉口汇流区，因此，车队通行顺序决策的规则为每个车队进入无信号交叉口汇流区的时间晚于具有更高优先级且与之不兼容的车队，即：4) Conflict-free constraints for convoys: Considering the conflict relationship between different lane trajectories, conflict-free trajectories are arranged for convoys. Compatible convoys can occupy the unsignalized intersection merging area at the same time. Therefore, the rule for convoy passage order decision is that each convoy enters the unsignalized intersection merging area later than the convoy with higher priority and incompatible with it, that is:
其中，表示为第i条车道上第s个终集合内的车队头车规划的进入无信号交叉口汇流区的时刻，/>表示为第i′条车道上第s′个终集合内的车队头车规划的进入无信号交叉口汇流区的时刻，/>表示第i′条车道上第s′个终集合内的车队头车占用无信号交叉口汇流区的时间，I表示车道编号集合，S表示终集合编号集合；若s>s′或s＝s′，且第i′条车道在同一终集合中具有优先权，则二进制变量ωii′为1，否则二进制变量ωii′为0；二进制变量λii′用于识别两个车队是否兼容，若两个车队兼容，则λii′＝0，否则λii′＝1。in, It represents the time when the leading vehicle in the sth terminal set on the ith lane plans to enter the merging area of the unsignalized intersection, /> It is represented by the time when the leading vehicle in the s′th terminal set on the i′th lane plans to enter the merging area of the unsignalized intersection, /> represents the time that the head vehicle of the convoy in the s′th terminal set on the i′th lane occupies the merging area of the unsignalized intersection, I represents the lane number set, and S represents the terminal set number set; if s>s′ or s＝s′, and the i′th lane has priority in the same terminal set, then the binary variable ωii′ is 1, otherwise the binary variable ωii′ is 0; the binary variable λii′ is used to identify whether the two convoys are compatible, if the two convoys are compatible, then λii′ ＝0, otherwise λii′ ＝1.
本例中与不愿意遵从速度建议的网联人类驾驶车辆形成的车队，位于同一终集合的各车道上的车队，根据先到先服务模型按照车队头车先到先服务规则决策车辆通行顺序。In this example, the convoy formed by connected human-driven vehicles that are unwilling to follow speed recommendations is located in the same terminal assembly lanes. The order of vehicle passage is determined according to the first-come, first-served model and the first-come, first-served rule for the head vehicle in the convoy.
本例所述非线性规划模型为智能网联车头车生成最优轨迹；所述非线性规划模型如下：The nonlinear programming model in this example generates the optimal trajectory for the intelligent connected vehicle head vehicle; the nonlinear programming model is as follows:
v1(ts)＝v1， (6.6)v1 (ts )＝v1 , (6.6)
p1(ts)＝0， (6.7)p1 (ts )＝0， (6.7)
p1(te)＝d1，(6.9)p1 (te ) = d1 , (6.9)
其中，t表示当前时间戳，te表示为车辆规划的进入无信号交叉口汇流区的时刻，ts表示车辆轨迹规划时刻，d1表示智能网联车头车当前位置到无信号交叉口汇流区的距离，表示智能网联车头车的期望速度，v1表示智能网联车头车的速度，p1(t)表示t时刻智能网联车头车的位置，v1(t)表示t时刻智能网联车头车的速度，u1(t)表示t时刻智能网联车头车的加速度，/>表示智能网联车头车的最小速度限制，/>表示智能网联车头车的最大速度限制，/>表示智能网联车头车的最小加速度限制，/>表示智能网联车头车的最大加速度限制；式(6.1)表示最小化ts时刻至te时刻内智能网联车头车油耗；式(6.2)表示智能网联车头车的速度限制；式(6.3)表示智能网联车头车的加速度限制；式(6.4)表示智能网联车头车的位置更新规则；式(6.5)表示智能网联车头车的速度更新规则；式(6.6)表示ts时刻智能网联车头车的速度约束，为起始约束；式(6.7)表示ts时刻智能网联车头车的位置约束，为起始约束；式(6.8)表示te时刻智能网联车头车的速度约束，为终端约束；式(6.9)表示te时刻智能网联车头车的位置约束，为终端约束。Wherein, t represents the current timestamp, te represents the time when the vehicle is planned to enter the merging area of the unsignalized intersection, ts represents the time when the vehicle trajectory is planned, d1 represents the distance from the current position of the intelligent connected vehicle to the merging area of the unsignalized intersection, represents the expected speed of the intelligent connected vehicle, v1 represents the speed of the intelligent connected vehicle, p1 (t) represents the position of the intelligent connected vehicle at time t, v1 (t) represents the speed of the intelligent connected vehicle at time t, u1 (t) represents the acceleration of the intelligent connected vehicle at time t, /> Indicates the minimum speed limit of the intelligent networked vehicle head vehicle, /> Indicates the maximum speed limit of the intelligent networked vehicle head vehicle, /> Indicates the minimum acceleration limit of the intelligent networked vehicle head vehicle, /> represents the maximum acceleration limit of the intelligent connected vehicle leading vehicle; formula (6.1) represents the minimization of the fuel consumption of the intelligent connected vehicle leading vehicle from timets to timete ; formula (6.2) represents the speed limit of the intelligent connected vehicle leading vehicle; formula (6.3) represents the acceleration limit of the intelligent connected vehicle leading vehicle; formula (6.4) represents the position update rule of the intelligent connected vehicle leading vehicle; formula (6.5) represents the speed update rule of the intelligent connected vehicle leading vehicle; formula (6.6) represents the speed constraint of the intelligent connected vehicle leading vehicle at timets , which is the starting constraint; formula (6.7) represents the position constraint of the intelligent connected vehicle leading vehicle at timets , which is the starting constraint; formula (6.8) represents the speed constraint of the intelligent connected vehicle leading vehicle at timete , which is the terminal constraint; formula (6.9) represents the position constraint of the intelligent connected vehicle leading vehicle at timete , which is the terminal constraint.
本例所述速度建议模型为愿意遵从速度建议的网联人类驾驶车辆头车给出下一时段的速度建议，包括加速、匀速、减速建议；所述速度建议模型如下：The speed recommendation model in this example provides speed recommendations for the next period for the leading vehicle of the connected human-driven vehicle that is willing to follow the speed recommendations, including acceleration, constant speed, and deceleration recommendations; the speed recommendation model is as follows:
当时，速度建议模型为愿意遵从速度建议的网联人类驾驶车辆头车提供加速建议；when When the speed recommendation model is set to reach the speed of the vehicle, it will provide acceleration recommendations to the leading connected human-driven vehicle that is willing to follow the speed recommendation.
当时，速度建议模型为愿意遵从速度建议的网联人类驾驶车辆头车提供匀速建议；when When , the speed recommendation model provides a uniform speed recommendation to the leading connected human-driven vehicle that is willing to follow the speed recommendation;
当时，速度建议模型为愿意遵从速度建议的网联人类驾驶车辆头车提供减速建议；when When the speed recommendation model is set to reach the speed limit, it will provide a deceleration recommendation to the leading connected human-driven vehicle that is willing to follow the speed recommendation.
其中，t表示当前时间戳，te表示为车辆规划的进入无信号交叉口汇流区的时刻，v2(t)表示t时刻愿意遵从速度建议的网联人类驾驶车辆头车的速度，d2(t)表示愿意遵从速度建议的网联人类驾驶车辆头车当前位置到无信号交叉口汇流区的距离，a(-)表示愿意遵从速度建议的网联人类驾驶车辆头车的最大减速度；η1和η2为参数，调节可控制速度建议保守程度。Wherein, t represents the current timestamp,te represents the time when the vehicle is planned to enter the merging area of the unsignalized intersection, v2 (t) represents the speed of the leading connected human-driven vehicle that is willing to follow the speed recommendation at time t, d2 (t) represents the distance from the current position of the leading connected human-driven vehicle that is willing to follow the speed recommendation to the merging area of the unsignalized intersection, a(-) represents the maximum deceleration of the leading connected human-driven vehicle that is willing to follow the speed recommendation; η1 and η2 are parameters that adjust the conservativeness of the controllable speed recommendation.
本例车队中非头车的智能网联车与其前车的间隙保持规则如下：In this example, the rules for maintaining a gap between the non-leading smart connected vehicle and the vehicle in front of it are as follows:
e＝g(t)-H0-g*， (7.1)e＝g(t)-H0 -g* , (7.1)
其中，t表示当前时间戳，Δta表示时间间隔，g(t)表示t时刻车队中非头车的智能网联车与其前车的间隙，H0表示车队中非头车的智能网联车的车辆长度，g*表示期望间隙，e表示跟踪误差，表示跟踪误差对于时间的一阶导数，θp＝0.45和θd＝0.125为调整间隙的参数，v3(t)表示t时刻车队中非头车的智能网联车的速度，v3(t+Δta)表示t+Δta时刻车队中非头车的智能网联车的速度。Where t represents the current timestamp, Δta represents the time interval, g(t) represents the gap between the non-leading intelligent connected vehicle in the convoy and its preceding vehicle at time t, H0 represents the vehicle length of the non-leading intelligent connected vehicle in the convoy, g* represents the expected gap, e represents the tracking error, represents the first-order derivative of the tracking error with respect to time, θp =0.45 and θd =0.125 are parameters for adjusting the gap, v3 (t) represents the speed of the non-head intelligent connected vehicle in the convoy at time t, and v3 (t+Δta ) represents the speed of the non-head intelligent connected vehicle in the convoy at time t+Δta .
本例车队中非头车的网联人类驾驶车辆和愿意遵从速度建议的网联人类驾驶车辆头车的行为采用考虑随机性的Gipps跟驰模型，其随机性表示为：The behaviors of the non-leading connected human-driven vehicles and the leading connected human-driven vehicles willing to follow speed recommendations in this convoy adopt the Gipps following model with randomness, and its randomness is expressed as:
uo(t)＝a(t)+bq(t)r(t)， (8.1)uo (t) = a (t) + bq (t) r (t), (8.1)
其中，a(t)表示t时刻根据Gipps跟驰模型生成的加速度；b表示不同加速度下的标准差；q(t)是介于0和1之间的均匀分布随机数；r(t)是1或-1，概率分别为50％；u0(t)表示实际执行的加速度。Where a(t) represents the acceleration generated according to the Gipps car-following model at time t; b represents the standard deviation under different accelerations; q(t) is a uniformly distributed random number between 0 and 1; r(t) is 1 or -1, with a probability of 50% respectively; u0 (t) represents the actual acceleration performed.
本例还给出一种无信号交叉口车辆通行顺序决策与轨迹优化系统，所述系统是采用本例给出一种无信号交叉口车辆通行顺序决策与轨迹优化方法工作的；所述系统包括路侧感知与通信设备、路侧计算单元、车载单元；This example also provides a vehicle traffic sequence decision and trajectory optimization system for an unsignalized intersection, the system works by using a vehicle traffic sequence decision and trajectory optimization method for an unsignalized intersection provided in this example; the system includes a roadside sensing and communication device, a roadside computing unit, and a vehicle-mounted unit;
所述路侧感知与通信设备，收集无信号交叉口出现区内所有车辆的位置、速度、加速度，车辆类型，网联人类驾驶车辆意图信息，并将无信号交叉口出现区内所有车辆信息传输给路侧计算单元；The roadside sensing and communication device collects the position, speed, acceleration, vehicle type, and vehicle intention information of all vehicles in the unsignalized intersection area, and transmits the information of all vehicles in the unsignalized intersection area to the roadside computing unit;
所述路侧计算单元作为无信号交叉口的管理中心，根据接收到的车辆信息，将无信号交叉口出现区内所有车辆按照到达次序进行排序，形成虚拟队列，确定最优车队组成方案以及无冲突的通行顺序，从而规划出各车队进入无信号交叉口汇流区的时刻以及所分配的无信号交叉口汇流区的占用时间，并传输给车载单元；所述路侧计算单元包括基于车辆编队并考虑公平性和网联人类驾驶车辆意图的无信号交叉口通行顺序优化模型、先到先服务模型；The roadside computing unit, as the management center of the unsignalized intersection, sorts all vehicles in the unsignalized intersection appearance area according to the arrival order based on the received vehicle information to form a virtual queue, determines the optimal fleet composition plan and the conflict-free passage order, thereby planning the time for each fleet to enter the unsignalized intersection merging area and the allocated occupancy time of the unsignalized intersection merging area, and transmits them to the vehicle-mounted unit; the roadside computing unit includes an unsignalized intersection passage order optimization model and a first-come-first-served model based on vehicle formation and considering fairness and the intention of networked human driving vehicles;
所述车载单元包括非线性规划模型、速度建议模型；所述非线性规划模型为智能网联车头车生成最优轨迹，并控制智能网联车头车，使智能网联车头车带领车队按照所规划的各车队进入无信号交叉口汇流区的时刻通过无信号交叉口控制区，以及按照所分配的无信号交叉口汇流区的占用时间通过无信号交叉口汇流区；所述速度建议模型为愿意遵从速度建议的网联人类驾驶车辆头车给出下一时段的速度建议，使愿意遵从速度建议的网联人类驾驶车辆头车带领车队按照所规划的各车队进入无信号交叉口汇流区的时刻通过无信号交叉口控制区，以及按照所分配的无信号交叉口汇流区的占用时间通过无信号交叉口汇流区。The on-board unit includes a nonlinear programming model and a speed recommendation model; the nonlinear programming model generates an optimal trajectory for the intelligent connected vehicle lead vehicle, and controls the intelligent connected vehicle lead vehicle so that the intelligent connected vehicle lead vehicle leads the convoy through the unsignalized intersection control area according to the planned time when each convoy enters the unsignalized intersection merging area, and passes through the unsignalized intersection merging area according to the allocated occupancy time of the unsignalized intersection merging area; the speed recommendation model gives a speed recommendation for the next time period to the connected human-driven vehicle lead vehicle that is willing to comply with the speed recommendation, so that the connected human-driven vehicle lead vehicle that is willing to comply with the speed recommendation leads the convoy through the unsignalized intersection control area according to the planned time when each convoy enters the unsignalized intersection merging area, and passes through the unsignalized intersection merging area according to the allocated occupancy time of the unsignalized intersection merging area.
现基于Matlab开展数值仿真实验以验证本例所提出方法(记为AIM_O)的有效性，具体包括：Now we conduct numerical simulation experiments based on Matlab to verify the effectiveness of the method proposed in this example (denoted as AIM_O), including:
图1为本例无信号交叉口车辆通行顺序决策与轨迹优化方法及系统的框架示意图。FIG1 is a schematic diagram of the framework of the vehicle traffic sequence decision and trajectory optimization method and system at an unsignalized intersection in this example.
图2为本例的无信号交叉口示意图。无信号交叉口分为三个区，分别为出现区(Staging Zong,SZ)、控制区(Control Zone,CZ)、汇流区(Merging Zone,MZ)，其对应长度分别为160m、40m、35m，在三个区内的车辆分别属于集合ψs(终集合)、ψC、ψM。无信号交叉口包括8条车道，车道编号i∈I＝{1,2,…,8}，包括直行和左转车道，每条车道在无信号交叉口汇流区具有确定的轨迹长度Li。无信号交叉口考虑的混合环境包括智能网联车(CAV)和网联人驾车辆(CV)。各车道车辆到达无信号交叉口出现区服从泊松分布，且不考虑车辆换道行为。Figure 2 is a schematic diagram of the unsignalized intersection in this example. The unsignalized intersection is divided into three zones, namely the Staging Zone (SZ), Control Zone (CZ), and Merging Zone (MZ), with corresponding lengths of 160m, 40m, and 35m, respectively. The vehicles in the three zones belong to the sets ψs (final set), ψC , and ψM , respectively. The unsignalized intersection includes 8 lanes, with lane numbers i∈I＝{1,2,…,8}, including straight and left turn lanes. Each lane has a certain trajectory lengthLi in the merging zone of the unsignalized intersection. The mixed environment considered in the unsignalized intersection includes intelligent connected vehicles (CAV) and connected human vehicles (CV). The vehicles in each lane arrive at the staging zone of the unsignalized intersection according to the Poisson distribution, and the lane changing behavior of the vehicle is not considered.
在无信号交叉口出现区(SZ)内：路侧感知与通信设备收集无信号交叉口出现区内所有车辆的位置、速度、加速度，车辆类型(CV用α＝0表示，CAV用α＝1表示)，网联人类驾驶车辆意图信息(β＝0表示不愿意遵从速度建议的CV，β＝1表示愿意遵从速度建议的CV)，并将车辆信息传输给路侧计算单元。路侧计算单元接收到车辆信息，将无信号交叉口出现区内所有车辆按照到达次序进行排序，形成虚拟队列，基于车辆编队并考虑公平性和网联人类驾驶车辆意图的无信号交叉口通行顺序优化模型(简称为优化模型)的决策变量并结合网联人类驾驶车辆意图信息，确定车队组成方案；求解得到基于优化模型的最优车队组成方案以及无冲突的通行顺序，从而规划出各车队进入无信号交叉口汇流区的时刻以及所分配的无信号交叉口汇流区的占用时间，并传输给车载单元。In the unsignalized intersection zone (SZ): the roadside sensing and communication equipment collects the position, speed, acceleration, vehicle type (CV is represented by α=0, CAV is represented by α=1), and the intention information of the connected human driving vehicle (β=0 represents CV that is unwilling to follow the speed recommendation, and β=1 represents CV that is willing to follow the speed recommendation) of all vehicles in the unsignalized intersection zone, and transmits the vehicle information to the roadside computing unit. The roadside computing unit receives the vehicle information, sorts all vehicles in the unsignalized intersection zone according to the arrival order, forms a virtual queue, and determines the fleet composition scheme based on the decision variables of the unsignalized intersection traffic sequence optimization model (hereinafter referred to as the optimization model) that considers fairness and the intention of the connected human driving vehicle and combines the intention information of the connected human driving vehicle; solves the optimal fleet composition scheme based on the optimization model and the conflict-free traffic sequence, so as to plan the time for each fleet to enter the unsignalized intersection confluence area and the allocated occupancy time of the unsignalized intersection confluence area, and transmits it to the vehicle-mounted unit.
在无信号交叉口控制区(CZ)内：车载单元接收到路侧计算单元传输的信息，通过非线性规划模型为智能网联车头车生成最优轨迹，并控制智能网联车头车，使智能网联车头车带领车队按照所规划的各车队进入无信号交叉口汇流区的时刻通过无信号交叉口控制区；通过速度建议模型为愿意遵从速度建议的网联人类驾驶车辆头车给出下一时段的速度建议，使愿意遵从速度建议的网联人类驾驶车辆头车带领车队按照所规划的各车队进入无信号交叉口汇流区的时刻通过无信号交叉口控制区。In the unsignalized intersection control zone (CZ): the on-board unit receives the information transmitted by the roadside computing unit, generates the optimal trajectory for the intelligent connected vehicle lead vehicle through the nonlinear programming model, and controls the intelligent connected vehicle lead vehicle so that the intelligent connected vehicle lead vehicle leads the convoy through the unsignalized intersection control zone according to the planned time when each convoy enters the unsignalized intersection merging area; through the speed recommendation model, a speed recommendation for the next time period is given to the connected human-driven vehicle lead vehicle that is willing to follow the speed recommendation, so that the connected human-driven vehicle lead vehicle that is willing to follow the speed recommendation leads the convoy through the unsignalized intersection control zone according to the planned time when each convoy enters the unsignalized intersection merging area.
在无信号交叉口汇流区(MZ)内：各车队按照所分配的无信号交叉口汇流区的占用时间通过无信号交叉口汇流区。In the unsignalized intersection merging zone (MZ): Each convoy passes through the unsignalized intersection merging zone according to the allocated unsignalized intersection merging zone occupancy time.
图3为本例的确定车队组成方案的流程示意图。假设仅有图2所示的1号车道和3号车道有车辆，图3中的方框表示与图2对应的1号车道的车辆，图3中的圆圈表示与图2对应的3号车道的车辆，方框和圆圈内的数字表示车辆到达无信号交叉口出现区的顺序(如1表示最先到达无信号交叉口出现区的车辆)。假设1号车辆为智能网联车头车，3号车辆为愿意遵从速度建议的网联人类驾驶车辆头车，7号车辆为不愿意遵从速度建议的网联人类驾驶车辆，8号车辆为愿意遵从速度建议的网联人类驾驶车辆。首先考虑将无信号交叉口出现区内的车辆划分为2个初集合，表示直接由决策变量/>确定的车辆初集合，然后根据CV意图进行动态调整，最终形成稳定车队，确定的车辆终集合为/>具体如下：将虚拟队列划分为2个初集合，即划分无信号交叉口出现区内的所有车辆为2个初集合，决策变量为5和4，即2个初集合内的车辆数分别为5辆和4辆。其中，1、2、4、6号车辆位于同一车道，而3、5、7、8、9号车辆位于同一车道。因此，根据“位于同一初集合、同一车道的车辆，形成一个准车队”，这里的准车队有4个(1、2、4号车辆为一个准车队，6号车辆为一个准车队，3、5号车辆为一个准车队，7、8、9号车辆为一个准车队)。由于准车队的头车中7号车辆为不愿意遵从速度建议的网联人类驾驶车辆，则将7号车辆作为单独车辆，形成一个车队；而该准车队中的其余车辆即8号车辆和9号车辆作为另一个准车队，此时因为8号车辆为愿意遵从速度建议的网联人类驾驶车辆，所以8号车辆和9号车辆形成一个车队(若8号车辆为不愿意遵从速度建议的网联人类驾驶车辆，同理作为单独车辆，形成一个车队；以此类推)。由所形成的车队确定车队组成方案(1、2、4号车辆为一个车队，3、5号车辆为一个车队，6号车辆为一个车队，7号车辆为一个车队，8、9号车辆为一个车队)，其中位于第一个终集合/>内的车队头车1号车辆(智能网联车头车)遵从非线性规划模型给出的最优轨迹，车队头车3号车辆(网联人类驾驶车辆头车)遵从速度建议模型给出的下一时段的速度建议，可优化车队的通行次序；位于第二个终集合/>内的车队由于7号车辆不愿意遵从速度建议，则按照先到先服务模型提供的头车先到先服务的规则确定该终集合内车队的通行顺序；结合第三个终集合内车队进入无信号交叉口的时间，确定该决策变量下的最优通行方案，计算总车辆延误。Figure 3 is a flowchart of determining the fleet composition plan in this example. Assuming that there are only vehicles in lane 1 and lane 3 shown in Figure 2, the boxes in Figure 3 represent vehicles in lane 1 corresponding to Figure 2, and the circles in Figure 3 represent vehicles in lane 3 corresponding to Figure 2. The numbers in the boxes and circles represent the order in which the vehicles arrive at the unsignalized intersection area (such as 1 represents the first vehicle to arrive at the unsignalized intersection area). Assume that vehicle No. 1 is the leading intelligent connected vehicle, vehicle No. 3 is the leading connected human-driven vehicle that is willing to follow speed recommendations, vehicle No. 7 is a connected human-driven vehicle that is unwilling to follow speed recommendations, and vehicle No. 8 is a connected human-driven vehicle that is willing to follow speed recommendations. First, consider dividing the vehicles in the unsignalized intersection area into two initial sets. Indicates that the decision variables are directly The initial set of vehicles is determined, and then dynamically adjusted according to CV intentions to eventually form a stable fleet. The final set of vehicles is determined as/> The details are as follows: the virtual queue is divided into 2 initial sets, that is, all vehicles in the area where the unsignalized intersection appears are divided into 2 initial sets, and the decision variables are 5 and 4, that is, the number of vehicles in the 2 initial sets is 5 and 4 respectively. Among them, vehicles 1, 2, 4, and 6 are in the same lane, and vehicles 3, 5, 7, 8, and 9 are in the same lane. Therefore, according to "vehicles in the same initial set and the same lane form a quasi-convoy", there are 4 quasi-convoys here (vehicles 1, 2, and 4 are a quasi-convoy, vehicle 6 is a quasi-convoy, vehicles 3 and 5 are a quasi-convoy, and vehicles 7, 8, and 9 are a quasi-convoy). Since vehicle No. 7 in the lead vehicle of the quasi-convoy is a connected human-driven vehicle that is unwilling to comply with speed recommendations, vehicle No. 7 is treated as a single vehicle to form a convoy; and the remaining vehicles in the quasi-convoy, namely vehicles No. 8 and No. 9, are treated as another quasi-convoy. At this time, since vehicle No. 8 is a connected human-driven vehicle that is willing to comply with speed recommendations, vehicles No. 8 and No. 9 form a convoy (if vehicle No. 8 is a connected human-driven vehicle that is unwilling to comply with speed recommendations, it is treated as a single vehicle to form a convoy; and so on). The convoy formation plan is determined by the formed convoy (vehicles No. 1, 2, and 4 form a convoy, vehicles No. 3 and 5 form a convoy, vehicle No. 6 forms a convoy, vehicle No. 7 forms a convoy, and vehicles No. 8 and 9 form a convoy), among which the first terminal group/> The first vehicle No. 1 in the convoy (the first vehicle of the intelligent networked vehicle) follows the optimal trajectory given by the nonlinear programming model, and the first vehicle No. 3 in the convoy (the first vehicle of the networked human-driven vehicle) follows the speed recommendation for the next period given by the speed recommendation model, which can optimize the traffic order of the convoy; the second terminal set/> Since vehicle No. 7 is unwilling to follow the speed recommendation, the order of the convoy in the final set is determined according to the first-come-first-served rule provided by the first-come-first-served model; combined with the third final set The time when the inner convoy enters the unsignalized intersection is used to determine the optimal traffic plan under this decision variable and calculate the total vehicle delay.
本例优化模型基于Matlab软件中的优化工具箱进行求解，非线性规划模型基于Gurobi优化求解软件进行求解。The optimization model in this example is solved based on the optimization toolbox in Matlab software, and the nonlinear programming model is solved based on Gurobi optimization solution software.
基于Matlab开展数值仿真实验以验证本例所提方法(记为AIM_O)的有效性，与先到先服务规则(FCFS)、最长队伍优先(LQF)规则以及分层优化方法(AIM_H)相比，进行10次随机试验，结果如图4-8及表1所示。三种对比方法均为基于编队的方法，即先利用聚类方法划分车队，然后FCFS方法根据最先到达的车队先通过规则确定车队通行顺序，LQF中则车道车辆数越多优先级越高，AIM_H方法则建立优化模型确定最优顺序。图4、5为纯CAV环境(CAV渗透率100％)，在不同交通需求下车辆的平均延误与最大延误结果对比图，当交通需求为1600veh/h时，本例所提方法与其他三种方法相比，车辆的平均延误分别降低了50.1％、44.6％和21.9％；图6、7为不同CAV渗透率(假设全部CV都服从，即都愿意接受速度建议)，且交通需求为1200veh/h下，车辆的平均延误与最大延误结果对比图；图8为采用本例所提供的方法与采用其他三种方法的车辆燃油消耗指标展示图。表1为CAV渗透率为30％，交通需求为1200veh/h时，不同CV服从率下车辆的平均延误与最大延误结果。由表1可知，在LQF和FCFS规则下，CV被认为总是遵守通行规则，而有通行次序优化的AIM_H和AIM_O方法则会受到CV服从率的影响。Numerical simulation experiments based on Matlab are carried out to verify the effectiveness of the proposed method (denoted as AIM_O) in this example. Ten random experiments are conducted to compare it with the first-come-first-served rule (FCFS), the longest queue first (LQF) rule, and the hierarchical optimization method (AIM_H). The results are shown in Figures 4-8 and Table 1. The three comparison methods are all based on formation methods, that is, the fleet is first divided by the clustering method, and then the FCFS method determines the fleet passage order according to the rule that the first fleet to arrive first passes. In LQF, the more vehicles in the lane, the higher the priority. The AIM_H method establishes an optimization model to determine the optimal order. Figures 4 and 5 are comparisons of the average delay and maximum delay results of vehicles under different traffic demands in a pure CAV environment (CAV penetration rate 100%). When the traffic demand is 1600veh/h, the average delay of vehicles in the proposed method is reduced by 50.1%, 44.6% and 21.9% respectively compared with the other three methods; Figures 6 and 7 are comparisons of the average delay and maximum delay results of vehicles under different CAV penetration rates (assuming that all CVs obey, that is, they are willing to accept speed suggestions) and traffic demand is 1200veh/h; Figure 8 is a display of the fuel consumption indicators of vehicles using the method provided in this example and the other three methods. Table 1 shows the average delay and maximum delay results of vehicles under different CV compliance rates when the CAV penetration rate is 30% and the traffic demand is 1200veh/h. As shown in Table 1, under the LQF and FCFS rules, CV is considered to always comply with the traffic rules, while the AIM_H and AIM_O methods with traffic order optimization will be affected by the CV compliance rate.
表1不同CV服从率下车辆的平均延误与最大延误结果Table 1 Average and maximum delay results of vehicles under different CV compliance rates
运用本例所提方法对无信号交叉口车辆编队方案、车队通行顺序同时进行优化，同时考虑车辆通行公平性与CV的不服从率，接着基于优化结果为CAV头车提供最优轨迹，为服从的CV头车提供速度建议。数值实验表明：运用本例所提方法相较于只优化通行顺序的方案，在交通需求为2000veh/h时，车辆的平均延误降低了19.8％。同时，随着CAV渗透率的增加，无信号交叉口的车辆平均延误呈下降趋势。另外，当CV的不服从率为25％的时候，运用本例所提方法也能够大大提高通行效率。The method proposed in this example is used to optimize the vehicle formation plan and the fleet traffic order at the unsignalized intersection at the same time, taking into account the fairness of vehicle traffic and the disobedience rate of CV. Then, based on the optimization results, the optimal trajectory is provided for the CAV lead vehicle, and the speed recommendation is provided for the compliant CV lead vehicle. Numerical experiments show that compared with the scheme that only optimizes the traffic order, the average vehicle delay is reduced by 19.8% when the traffic demand is 2000veh/h. At the same time, with the increase in CAV penetration, the average vehicle delay at unsignalized intersections shows a downward trend. In addition, when the disobedience rate of CV is 25%, the method proposed in this example can also greatly improve the traffic efficiency.
通过仿真实验对比，运用本例所提方法能够有效降低车辆的平均延误、最大延误，并降低油耗。另外，本例所提方法在无信号交叉口各进口道交通需求不均的情况下同样具有适用性。Through simulation experiment comparison, the proposed method can effectively reduce the average delay and maximum delay of vehicles and reduce fuel consumption. In addition, the proposed method is also applicable to the case of uneven traffic demand at the entrances of unsignalized intersections.
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