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Liu Yanbo 1 , Sun Weiqi 2 , Du Haikuo 3 , Xu Wenchao 4 , Xiong Xin 5 , Hao Li 6 , Qu Ling 7 , Liu Shiji 8
1. Teaching development and Student Innovation Center of SEIEE , Shanghai Jiao Tong University
2. Xin Dong Interactive Entertainment Company Ltd
3. Department of automation , Shanghai Jiao Tong University
4. Shanghai Key Laboratory of Multidimensional Information Processing , East China Normal University
5. Huawei Cloud , Huawei Technology Company Ltd
6. Asset Management and Laboratories Division , Shanghai Jiao Tong University
7. Student Innovation Center , Shanghai Jiao Tong University
8. Michigan Colleger , Shanghai Jiao Tong University
Abstract: This paper takes the scheduling of multiple low-speed vehicles at multiple intersections as the main research content,studies the vehicle scheduling and motion control from the perspective of vehicle motion planning,and provides experimental verification based on the miniature vehicle experimental platform.In the formation scheduling,the leader vehicle of the formation plans the forward trajectory,and the follower vehicle plans the trajectory through the consistency method to realize the synchronization of the vehicles within the fleet.Vehicles in the same lane that are relatively close together form a team,and often pass through multiple intersections for coordinated intersection scheduling.In the experimental part,this article will build miniature vehicles and intersection scenes to test the effectiveness of the algorithm in this article for scheduling and control in miniature scenes.
Key words: Multi-vehicle scheduling,Path planning,Vehicle-to-road communication,Intersection collaboration
The traditional vehicle driving process is a process in which the driver performs real-time vehicle path planning and trajectory tracking according to road conditions and traffic environment [1] .With the coming of the era of autonomous driving,the form intersection scheduling method is based on the research and application of the communication and the collaboration.In the scenario,the high-precision sensors installed at the road end have a high reuse rate.Compared with installing the same sensor on the vehicle end,the weight load and calculation load of the vehicle will drop,and the total number of sensors required will be less [2] .The vehicle-road collaboration system is based on bicycle intelligence and V2X,which contains Vehicle to Vehicle(V2V)and Vehicle to Infrastructure(V2I)and Vehicle to Road(V2R),and Vehicle to Person(V2P),through the information sharing and data fusion,in order to achieve the communicational and collaborative work.In this way,more complete and accurate road environment information can be obtained,so that the vehicle can run stably,safely and efficiently [3] .
Computing equipment between the roadside and the cloud can undertake most of the data computing tasks,reducing the computing load of the vehicle [4] .When the vehicle density and traffic flow reach the optimal value,the traffic efficiency of vehicles can reach the maximum value [5] .The concept of Macroscopic Fundamental Diagram(MFD)is proposed to evaluate the running urban state of the road network [6] .The theory of the MFD is used to classify and stratify the traffic state of urban road network,and coordinate the control of vehicles at traffic intersections [7] .Through the iterative learning of the road network,the density of traffic flow in each section tends to the average density.Traffic flows are more evenly distributed.With the change of the MFD,the effect of this control measure on the traffic running state of the road network is measured [8] .For the planned sub-road network,the blind area of the on-board sensors can be eliminated by the integration of the information of the road-end and the vehicle-end sensors through the vehicle-road cooperative system [9] .
The position and speed of obstacles and other vehicles can be obtained more accurately, and the probability of collision can be reduced to meet the collision avoidance requirements of autonomous driving vehicles [10] .Inreference[11],the research on active collision avoidance between vehicles mainly relies on vehicle positioning acquisition and information interaction.In reference[12],V2V is used to exchange information between the following vehicle and the leading vehicle,and the safe distance between the main vehicle and the leading vehicle is calculated,thereby realizing collision avoidance.The collision warning and braking method based on the vehicle-road coordination system can be used to avoid collisions between pedestrians and vehicles in the scenarios of straight going,intersection and lane change.When the traffic volume is moderate,the algorithm proposed above can better realize the dispatch of intelligent vehicles at the intersection and improve the efficiency,but when the traffic volume is very large,the efficiency improvement brought by the algorithm is relatively limited.
This paper proposes an improved multi-vehicle cooperative multi-intersection scheduling algorithm to optimize the traffic scheduling of intersection vehicles.By summarizing the research results of congestion law and the characteristics of the MFD,the urban road network is divided into several local sub-regions.Autonomous vehicle dynamic priority scheduling and control with a two-tier road network divided into several sub-regions as the dispatch unit. The upper layer is responsible for inter-regional flow coordination,and the lower layer considers the traffic flow of each sub-regional intersection,to perform multi-intersection multi-vehicle optimization scheduling.
The rest parts of this paper are arranged as follows.Section II describes the overall framework of the system,and introduces the general requirements of the vehicle,road and network.Section III presents the vehicle model and vehicle control methods,including the longitudinal control and the lateral control.Section IV shows the experimental results.Section V concludes the paper.
The cooperative vehicle infrastructure system(CVIS)is in accordance with the road network requirements of unmanned intelligent vehicles,and can simulate the road network structure under different road types and scenarios.The system consists of three parts:vehicle,road equipment and network.In this paper,a kind of miniaturized vehiclesis equipped with lightweight sensing and computing equipment.Roadside equipment includes cameras,UWB,computers,traffic signs,etc.With a camera array and UWB equipment,we can obtain the positioning accuracy of centimeter level.The roadside computer is responsible for reference trajectory planning and motion control.The system network is equipped with 2.4g/5G industrial-grade WIFI module as V2R network,as shown as in Fig.1.
Miniaturized vehicle chassis for the Ackermann drive-by-wire chassis cover parts,includes the drive system,unmanned servo brake system,unmanned steering system and so on.System based on sensors and indoor positioning information,on-board processor complete path planning,and the reference path in the speed and course angle control input transmitted to MCU,again by MCU for signal processing and transmission,distributing to each System.The serial bus serves as the main communication protocol between systems.At the same time,intelligent roadside equipment and central control management system can also provide their own address and port,which can carry out research on vehicle AD hoc network technology(VANET).It can build a set of intelligent network communication system with global organization and open structure in combination with road network equipment and central control and scheduling system.
Fig.1 System Framwork
The application scenarios of intelligent road network system cover vehicle adaptive recognition of traffic lights,vehicle adaptive recognition of traffic signs,intersection blind zone warning,vehicle adaptive following,vehicle formation control,etc.Intelligent road network system will control the real-time state information of each vehicle,the CVIS,intelligent roadside equipment information integrated management.The driving state data of each vehicle is synchronized to the Internet of Vehicles(IoV)system in realtime.The IoV system calculates the characteristic information of the vehicle in real time.
The actual motion of unmanned vehicle is a complex,multi-degree-of-freedom(MDOF)nonlinear time-varying process [13] .The miniaturized vehicle used in this paper is a steering engine model with four-wheel drive and front wheel steering,as shown as in Fig.2.
The dynamic equation of the miniaturized vehicle is based on the kinematics and dynamics model.By studying the transverse kinematics and dynamics,it is obtained that the transverse motion includes the transverse position and the yaw motion.The dynamic model of the miniaturized vehicle is a linear 2-DOF bicycle model [14] .
The linear 2-DOF kinematics model is an automobile model with lateral and yaw motion,with two degrees of freedom,sup ported on the ground by two lateral-elastic tires.The model is established with the following assumptions and characteristics:
Fig.2 Kinematic Model of the Miniaturized Vehicle
1）In this model,the influence of steering system is ignored and the front wheel rotation Angle is directly taken as input.The relationship between steering wheel Angle and front wheel Angle is linear when miniaturized vehicle rotates the steering wheel.
2）The effect of suspension is ignored,and it is believed that the miniaturized vehicle only makes plane motion parallel to the ground.The displacement of the car along the Z-axis ,the pitch angle around the Y-axis and the roll angle around the X-axis are all zero,and the influence of air resistance on the suspension of the miniaturizedvehicle is not considered.
3）The moving speed of the miniaturized vehicle along the X-axis is regarded as unchanged.Therefore,the miniaturized vehicle has only two degrees of freedom:lateral motion along Y and yaw motion around Z .
4）The side-acceleration of the minicar is limited to less than 0.4g,and the side-deflection characteristic of the tire is in a linear range.The driving force is small,and the influence of ground tangential force on tire lateral characteristics is not considered.The change of tire characteristics caused by the load change of left and right tires and the effect of tire righting moment are ignored without the aerodynamic effect.The miniaturized vehicle wheels are in good rolling contact with the ground.
By studying the component of the acceleration of the vehicle′s center of mass in the vehicle coordinate system,and considering the relationship between the external force and the external moment around the center of mass and the external force,external moment and the vehicle's motion parameters,the equation of motion is obtained.Because the vehicle mass distribution parameters such as moment of inertia are constant to the vehicle coordinate system,the analysis is convenient.Under the assumption of small steering angle and linear tire model,the intelligent networked miniaturized vehicle is called vehicle i in the Tab.1.
Tab.1 Parameter of the Vehicle
The kinematic equations of the vehicle are as follows [15][16] :
where the range of t is from 0 to t f and t f can be a variable or a constant. Φ max 、 a max 、 v max 、 Ω max are the maximum values of each state or control variable respectively and satisfy the following conditions.
The coordinates ( A i , B i , C i , D i )are the four vertices of the vehicle body starting from the vertex near the left front wheel of vehicle i in a clockwise direction.The coordinates ( A i , B i , C i , D i ) are in the following.
In order to ensure that all intelligent networked vehicles do not collide,this paper adopts the method of dual-element uniform coverage to model.The two prims of each intelligent connected car do not want to collide with any circle of other intelligent connected cars.For vehicle i ,its contour is( A i , B i , C i , D i ),which can be covered by a circle with points( xr i , yr i )and( xf i , yf i )as the center of the circle and R i as the radius.
Accordingly,simplified collision avoidance constraints can be established as follows:
where the range of vehicle i and vehicle j is from 1 to N V and i ≠ j .
In order to build the MFD model in line with the actual situation,data is needed to estimate the road network flow and density.According to MFD theory,there is the following expression [6] :
In the Equation(10), q w and k w are respectively weighted flow(veh/h)and weighted density (veh/km) of the road network.Also q u and k u are the unauthorised heavy flow (veh/h) and density(veh/km)of the road network respectively.At the same time, q i , k i and o i are the flow rate (veh/h),density(veh/km)and occupancy of section I respectively. l i is the length of section I(km)and S is the average effective body length(km).
In this paper,Remote Traffic UWB Sensor Data(RTUSD)is used to estimate the MFD.RTUSD is the Traffic flow Data of a single lane with cross-section,which needs to be integrated into the cross-section Data during calculation,and is weighted by Traffic flow.The calculation formula is [17] :
where
is the number of lanes in the section
i
. Also
q
ij
and
k
ij
are respectively the flow and density of the lane j in the section
i
.
In this paper,License Plate Camera Recognition Data (LPCRD) is used to obtain the travel time of vehicles entering and departing sections.Its calculation formula is as follows:
where
is the travel time of the vehicle
n
in the section
i
.
Also
and
are respectively the last moment when the vehicle
n
is detected to enter the section
i
and the earliest time when the vehicle
n
is detected to leave the section
i
.
From Equation (12),
has abnormal data due to tempora ry parking or license plate detection errors in the road section, and the box diagram method is used to process the noise da ta. Assuming that all the processed data are effective travel time data, the average travel time of road section
i
is:
From Equation(13),the flow q i and density k i of the section i under license plate recognition data are [17]:
where N is the number of vehicles passing the detector within the statistical interval; N ma is the number of vehicles that can match to the travel time; T is the length of the statistical interval.
In reference [17],Traffic State Ratio ( R ) is adopted to evaluate MFD,that is,the distance Ratio between road network Traffic parameters and critical State at any time,and the following can be obtained:
where
and
are respectively non-congestion and congestion ratio under microwave data.
and
are respec tively non-congestion and congestion ratios under license plate recognition data. Defines
Δ
t
the MFD difference under different data source, the greater the
Δ
t
, the MFD difference is larger, the smaller instead. For any road section, if there is a license plate recognition detector, LPCRD is used to calculate the traffic and density of the road section. Otherwise, RTUSD is used for calculation.
The large road network is divided into several smaller sub-road networks,and the controllers are divided into different levels.The controller of each layer communicates with the corresponding controller above and below it.The upper controller is responsible for the coordinated control of the entire road network,receives all the information of the road network,and optimizes some variables of the sub-road network by setting some optimization objectives.The lower controller accepts the Settings of the upper level and carries out optimization control in the sub-road network.The objective function and constraint of subroad network optimization are changed.Make each subpath network to achieve local optimization.
If the distance between two adjacent intersections is Z ,the threshold distance of merging into the same sub-area is LH,and the threshold distance of separating into two different sub-areas is LF.When L < L H ,in order to effectively weaken the influence of queuing vehicles at the intersection on the arrival traffic flow,the adjacent intersection can be merged into the same traffic control sub-area for coordinated control.When L > L H ,the degree of dispersion of traffic flow between two adjacent intersections will increase with the increase of driving distance.Coordinated control is not appropriate at this time,and the adjacent intersections can be separated into different control sub-areas.
When the traffic volume of two adjacent intersections is similar and the traffic flow characteristics are similar,they can be merged into the same sub-area for coordinated control.At this time,the coordinated control efficiency of the sub-area is better.On the other hand,when the two adjacent intersections are in the traffic saturation state,the two intersections with large traffic flows are divided into the same control sub-area for signal coordination control,which is conducive to efficiently solving the local congestion problem of the road.
The correlation between two intersections will be affected by the traffic volume and length of the sections between the intersections [ 18] .Therefore,the coupling index is defined to describe the effect of the two main factors on the correlation.The calculation of the coupling index is as follows:
where, Q is the flow between two adjacent intersections; L ij is the distance between adjacent intersections from the section i to the section j .When the coupling index C value is small,it indicates that the coupling degree between the two intersections is low,so the correlation is weak.When the coupling index C value is larger,it indicates that the coupling degree between the two intersections is higher,so its correlation is higher.
Whitson model,as the recommended relational model in the Manual of American Traffic Control System,is widely used because it requires fewer traffic data types and simple calculation process [19] .Whitson model mainly considers the influence of intersection distance,road traffic volume and road travel time on intersection relevance.The calculation of interconnection index is as follows:
where, t is the driving time between adjacent intersections; n is the number of traffic flow from the upstream intersection into the intersection; q max is the maximum flow of the key lane in the coordinated phase of the upstream intersection.The range of I is from 0 to 1,and the threshold is 0.25.In other words,when I > is 0.25,it indicates that the two adjacent intersections have strong correlation and are suitable for coordinated control.
Algorithm for road network division and merger
（续）
Spatial division of road network at different levels is carried out,namely,ground road and elevated road are divided,and then the overall road network is razed according to location information.For each grid after rasterization.Merge operation,that is,the geographic partitions with similar traffic characteristics are merged to obtain the final topological partition.
The CVIS consists of two parts:hardware system and software system.On the hardware,it includes the central control server,10 gigabit routing switch equipment and intelligent vehicle-mounted communication terminal.In terms of software,it includes user management,map loading,intelligent car loading,online vehicle path planning,real-time display of vehicle and road information,real-time display of bicycle sensor data,online control of roadside equipment and remote driving.Paper Submission
In this subsection,we will introduce the hardwares of the CVIS,that is vehicle,roadside equipments and V2R network.The miniaturized intelligent car adopts Ackerman′s steering method,which is consistent with the real car,and is shrunk according to the 1:10 ratio with the real car's exterior structure.It is equipped with a six-core Cortex-A5 family of industrial processors,which can meet the requirements of long time and high computation and complex matrix calculations.
In addition,its Cortex-M3 series motion system processor can accurately control the motion cycle to 1ms.Equip with camera,9-axis IMU,high-resolution encoder,lidar module,2.4g/5G industrial WIFI module,ultrasonic ranging and other sensors, as shown as in Fig.3.The software environment of the mini vehicle is Ubuntu 18.04 and ROS-Melodic.We configure the ROS package,through which the motion command can be sent out from the USB port.The roadside equipments include computer and cameras and WiFi,as shown in Fig.4.Several HD cameras are used to cover the area for different sections.The computer used in our experiment is a laptop with Ubuntu 16.04 and ROS Kinetic installed.It translates the serial signal into PWM signal,then sends the signal to the steering engine and motor to drive the vehicle.The roadside computer is equipped with OpenCV library to re alize license plate recognition and upload data.
Fig.3 A miniaturized intelligent vehicle platform
Fig.4 Roadside equipments
In our experiment,the road scenario are divided into road side and vehicle side.The Location Detection node gets the position and orientation of vehicle with the method described above,and publishes it as the message named/location.The node called car_control subscribes the/location message,which plans the trajectory and carries out the velocity command according to the position of vehicle and the destination.The velocity command is sent to the vehicle through the network.The Move node will translate the command into the ROS message named/car/cmd vel and send it to the drive node.The drive node further turns it into serial signal,and makes the car move.
The upper network localizes the traffic density between different subroad networks through controller optimization,and evaluates and optimizes the traffic density of each subroad network.The lower layer network dispatches and controls the traffic flow dynamically through the regional sub-road network,which takes the formation as the dispatching unit,and improves the traffic efficiency to reach the estimated traffic flow of the upper layer shown in the, as shown as in Fig.5.
The experiment of autonomous vehicle scheduling at intersections is completed on a miniaturized intersection scene and experimental platform.There are altogether 6 vehicles in the scene,including 2 cars in lane 1,2 cars in lane 2,and 2 cars in lane 2(Fig.6).
The cooperative formation control of vehicles among the three vehicles can better test the effect of road network stratified planning proposed in section 3 of this paper on conflict avoidance and vehicle collision avoidance.The experimental results show that the algorithm proposed in this paper has a good effect on the vehicle scheduling in the micro-intersection scenario,and can complete the automatic scheduling of autonomous vehicles at the intersection.
Fig.5 Communication Graph of Nodes
Fig.6 Formation Scheduling process Record
Combined with the current traffic state of the road network and the path evaluation index,a feasible path space is planned for each vehicle participating in the control at the lower level.The main task of the lower level is to optimize the signal light setting at the intersection and the driving path of these vehicles through the game between the signal controller at a single intersection and the vehicles at the intersection in Fig.7.
Fig.7 Priority and time in Formation Scheduling Situatio
Considering that lane change operation is more difficult for vehicles closer to the intersection,at the beginning of the signal cy cle,we carry out path planning again for vehicles that cannot leave the intersection at the end of the signal cycle shown in Fig.8.
Fig.8 Speed and time in Formation Scheduling Situatio
The curve tends to be stable.Starting from a different position,each agent moves with a time-varying reference trajectory to track its desired designated position.Before each agent tracks its desired designated position,the relative velocity between each agent and the desired designated position gradually shrinks,and the forward velocity error of the corresponding agent also decreases accordingly.Therefore,the forward speed error of the agent is basically close to 0.8m/s,and the agent keeps moving at this speed to achieve the purpose of concerted movement.
Shown in Fig.9 and Fig.10,the tracking error curve shows the trend of sine wave in X-axis and Y-axis direction.Multiple agent formation systems track the desired designated position from different starting points with time-varying reference trajectories and keep consistent movement,which can be divided into tracking stage and holding stage.After 5s,the curve shows the trend of sine wave after coincidence.This indicates that the formation keeps consistent movement after tracking its forward direction and realizes the purpose of coordinated control,scheduling and tracking of the system.
Fig.9 Tracking error curve in X-axis direction
Fig.10 Tracking error curve in Y-axis direction
In the study of urban traffic intersections,the boundary sections of subsections are the key to regulate the traffic state of subsections,and the traffic state of adjacent subsections can be adjusted by controlling the number of vehicles passing through the boundary sections,and the traffic flow of the whole road network can be balanced.The urban road network is divided into several local sub-regions and the adaptive state transition probability model of the whole road network is established based on the regional stochastic macroscopic basic graph model.Put forward in the son has been divided into a number of local area network,calculated on a fleet of its transit priority for motion planning and control,to reduce the frequency of the vehicle with traffic,through the mechanism of dynamic priority,to solve the high-priority traffic near the conflict problem of reduction,and improve the efficiency of intersection autonomous vehicle scheduling.
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