Slot control optimization of intelligent platoon for dual-lane two-way overtaking behavior

CHEN Jun-jie; CAI Bo-gen; SHANGGUAN Wei; WANG Jian; CHAI Lin-guo

doi:10.19818/j.cnki.1671-1637.2019.02.016

Volume 19 Issue 2

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Article Contents

Abstract

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0. 引言

1. Bidirectional Two lane SVOP Model

2. Stepwise SVOP algorithm

3. 仿真结果分析

4. 结语

References

Article Navigation > Journal of Traffic and Transportation Engineering > 2019 > 19(2): 178-190

CHEN Jun-jie, CAI Bo-gen, SHANGGUAN Wei, WANG Jian, CHAI Lin-guo. Slot control optimization of intelligent platoon for dual-lane two-way overtaking behavior[J]. Journal of Traffic and Transportation Engineering, 2019, 19(2): 178-190. doi: 10.19818/j.cnki.1671-1637.2019.02.016

Citation:

CHEN Jun-jie, CAI Bo-gen, SHANGGUAN Wei, WANG Jian, CHAI Lin-guo. Slot control optimization of intelligent platoon for dual-lane two-way overtaking behavior[J]. Journal of Traffic and Transportation Engineering, 2019, 19(2): 178-190. doi: 10.19818/j.cnki.1671-1637.2019.02.016

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Slot control optimization of intelligent platoon for dual-lane two-way overtaking behavior

doi: 10.19818/j.cnki.1671-1637.2019.02.016

CHEN Jun-jie^{1, 2
,},
CAI Bo-gen^{1, 2, 3
,},
SHANGGUAN Wei^{1, 2, 3
,},
WANG Jian^{1, 2, 3},
CHAI Lin-guo^{1, 2}

1.
School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing 100044, China
2.
Beijing Engineering Research Center of EMC and GNSS Technology for Rail Transportation, Beijing Jiaotong University, Beijing 100044, China
3.
State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China

More Information

Author Bio:
CHEN Jun-jie (1989-), male, doctoral student, junjiechen@bjtu.edu.cn

CAI Bai-gen (1966-), male, professor, PhD, bgcai@bjtu.edu.cn

SHANGGUAN Wei (1979-), male, professor, PhD, wshg@bjtu.edu.cn
Received Date: 2018-11-03
Publish Date: 2019-04-25

Abstract

Abstract

A model of single vehicle overtaking a platoon on the dual-lane two-way road was established, and the key factors affecting the range of dangerous overtaking zone were analyzed. The step-by-step algorithm was designed when single vehicle overtakes the platoon. The relationship among the speeds of the vehicles before and after the safety slot, the speed of the overtaking vehicle entering the platoon and the safety slot range of the platoon was studied. The speed matching scheme with the minimum safety slot required for the vehicle to overtake the platoon was proposed. The objective function of the algorithm was established, and the following assumptions were made in the maximum allowable overtaking time: the overtaking vehicle and platoon travelled the longest distance, the overtaking vehicle overtaked the platoon by the most vehicles, and the acceleration and deceleration of front and rear vehicles were the minimum in the forming process of safety slot. The hierarchical constrained multi-objective optimization method based on the improved particle swarm was proposed to provide the algorithm with the optimized three-level speed guidance strategy. Analysis result shows that the overtaking dangerous zone on dual-lane two-way road is positively correlated with the number of vehicles in the platoon and the velocities of the opposite vehicles. The improved particle swarm optimization algorithm has stronger robustness and faster convergence than the traditional algorithm, and the average convergence time reduces by 39.2%. In the step-by-step process that the single vehicle overtakes the platoon, the average speed of the vehicles in the platoon increase by 9.04%, which means that in the forming process of safety slot, although the speeds of some vehicles decrease, the overall average speed of the platoon increases. The average speed of overtaking vehicle increases by 16.8%, which means that in the overtaking process, not only is the safety of overtaking vehicle guaranteed, but also its operating efficiency is improved.
- traffic information engineering,
- dual-lane two-way road,
- intelligent platoon,
- algorithm of single vehicle overtaking platoon,
- safety slot,
- slot optimization,
- step-by-step overtaking

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0. 引言

Overtaking and lane changing can improve road utilization to a certain extent. In response to the basic information of vehicle interaction provided by the future vehicle road collaborative environment, Li Xun et al. proposed a collaborative lane changing model that considers local area vehicle state optimization^[14]Milan é s et al. developed a fuzzy logic based controller that simulates the overtaking process by inputting information from a location-based system consisting of visual systems, global positioning systems, and inertial measurement units, and outputting actions on vehicle actuators such as the steering wheel, accelerator, and brake pedal^[15].

At present, research on overtaking behavior of vehicles mainly focuses on overtaking vehicles and overtaking fleets composed of multiple vehicles without vehicle to vehicle communication^{[16, 17, 18]}For vehicle overtaking, there is vehicle to vehicle communication^[19]However, there is little research on the swarm intelligence fleet, and some scholars have studied the necessary message response methods for bicycles to surpass the fleet in an ideal state^{[20, 21, 22, 23]}However, there has been no research on the control of the distance between vehicles within the convoy during overtaking and the restrictions on overtaking vehicles returning to their original lane. In fact, when overtaking a convoy in a two-way two lane road, if the driver misjudges the distance to the oncoming vehicle and the length of the convoy, the vehicle is easily trapped in a dangerous area where it cannot complete overtaking or return to the original lane^{[24, 25, 26]}Causing the overtaking vehicle to be forced to make an emergency stop or collide with the oncoming vehicle, or the overtaking vehicle to forcefully merge into the original lane convoy, resulting in a collision with the convoy vehicles. At the same time, two-way two lane highways such as the Qinghai Tibet Highway, which are responsible for the main transportation of materials, have the characteristics of long queues, multiple queues, and fast driving speeds for large vehicles traveling in groups^{[27, 28, 29]}The overtaking defects of the above-mentioned vehicles on the transportation fleet will be more pronounced.

This article establishes a kinematic model for a single vehicle overtaking convoy, theoretically analyzing and demonstrating the existence of a dangerous area where vehicles face the dilemma of "overtaking giving up" when overtaking on a two-way two vehicle road section. The influencing factors of the dangerous area are determined through the model; Studied the relationship between the speed of overtaking vehicles and the safety clearance of the convoy when completing overtaking actions or giving up overtaking and returning to the original lane; Finally, a bidirectional two lane stepwise Single Vehicle Overtaking Platoon (SVOP) algorithm based on dynamic safety clearance was proposed, and a hierarchical constrained multi-objective optimization method based on improved particle swarm optimization was designed to provide a multi-objective optimization scheme for the three-level speed guidance of overtaking vehicles and vehicles in front and behind the safety clearance in the stepwise overtaking algorithm, including mileage, number of overtaking vehicles, and comfort.

1. Bidirectional Two lane SVOP Model

1.1 Establishment of SVOP model

In a two-way two vehicle road section, when an overtaking vehicle occupies the opposite lane for overtaking, if the distance between adjacent vehicles in the overtaking fleet is not sufficient to meet the overtaking requirements of the overtaking vehicle, a vehicle appears in the opposite lane, causing the line of sight to be less than the safe overtaking line of sight requirement. The overtaking vehicle often falls into the danger zone of overtaking, where it cannot overtake or return to the original lane.

Here we define the critical position and critical time for overtaking vehicles. Assuming that there is always a chance to give up overtaking and safely return to the original lane before the overtaking vehicle enters the overtaking lane and reaches the critical position, and when the overtaking vehicle crosses the critical position point on the overtaking lane, it enters the overtaking danger zone; The critical time is the time when a overtaking vehicle reaches the critical position from the start of overtaking.

The conditions for safely completing the overtaking maneuver are: avoiding collision between the overtaking vehicle and the oncoming vehicle; The necessary safety distance should be maintained between the overtaking vehicle and the leading vehicle of the overtaken convoy. Shan Xiaofeng and others provided detailed explanations on the conditions for safe overtaking^[30]For the convenience of explaining the implementation of the SVOP algorithm, only a brief explanation is provided below

$\begin{array}{l} o \geq (v_{0} + v_{1}) (t_{0} + t_{1}) + J_{1} (1) \\ J_{1} = (v_{0} + v_{1}) h_{1} (2) \\ J_{2} = v_{2} h_{2} (3) \\ J_{2} + l_{1} = v_{0} (t_{0} + t_{1}) + J_{3} - \\ v_{2} (t_{0} + t_{1}) - (Ν - 1) v_{2} h_{3} (4) \end{array}$

The line of sight conditions for safe overtaking are

$\begin{array}{l} o_{1} \geq \frac{(v_{0} + v_{1}) {v_{2} [h_{2} + (Ν - 1) h_{3}] + l_{1} - J_{3}}}{v_{0} - v_{2}} + \\ (v_{0} - v_{1}) h_{1} (5) \end{array}$

In the formula:oFor the lower limit of safe driving sight distance;v₀The speed of the overtaking vehicle after acceleration;v₁To determine the speed of the oncoming vehicle for overtaking;v₂For the speed of the fleet;t₀For critical time;t₁The remaining overtaking process time after the critical moment;J₁The minimum safe distance between the overtaking vehicle and the oncoming vehicle at the end of overtaking;J₂To complete overtaking, the distance between the rear of the overtaking vehicle and the front of the leading vehicle in the overtaking convoy;J₃The distance between the front of the overtaking vehicle and the rear of the overtaking fleet after acceleration;h₁doJ₁The safe time interval;h₂doJ₂The safe time interval;h₃To be overtaken by the front distance of the convoy;l₁To overtake the driver;NNumber of vehicles in the fleet;o₁For safe overtaking visibility.

The conditions for a overtaking vehicle to safely return to its original lane after giving up overtaking during the overtaking process are: the overtaking vehicle should maintain a certain safe distance from the oncoming vehicle and downstream vehicles when returning to its original lane, and at the same time, the speed of the overtaking vehicle should not be too low when decelerating and returning to its original lane to avoid obstructing the normal driving of vehicles behind. The condition is

$\begin{array}{l} J_{4} = h_{4} (v_{0} - d t_{2}) = \\ v_{2} (t_{0} + t_{2}) - l_{2} - J_{3} - v_{0} t_{0} - v_{0} t_{2} + \frac{d t_{2}^{2}}{2} (6) \\ o_{2} \geq v_{0} t_{0} + v_{0} t_{2} - \frac{d t_{2}^{2}}{2} + v_{1} (t_{0} + t_{2}) + J_{5} (7) \\ J_{5} = (v_{0} - d t_{2} + v_{1}) h_{1} (8) \end{array}$

The line of sight conditions that allow giving up overtaking are

$\begin{array}{l} o_{2} \geq (v_{2} + v_{1} + h_{4} d) t_{2} + (v_{2} + v_{1}) t_{0} - l_{2} - \\ J_{3} - h_{4} v_{0} + (v_{0} - d t_{2} + v_{1}) h_{1} (9) \end{array}$

$o = \min {o_{1}, o_{2}} (10)$

In the formula:J₄The distance between the front of the overtaking vehicle and the rear of the convoy when returning to the original lane;h₄doJ₄The safe time interval;dReduce the speed of overtaking vehicles;t₂The process time from giving up overtaking and slowing down to returning to the original lane;l₂For the fleet leader;J₅The minimum safe distance between returning to the original lane and the oncoming vehicle;o₂To allow the abandonment of overtaking sight distance.

When the line of sight conditions are less than the safe overtaking and allowed to abandon overtaking line of sight, the vehicle is in a dangerous situation of overtaking and abandoning overtaking.

1.2 Factors affecting SVOP hazardous areas

The danger zone for overtaking refers to the area from the front of the convoy to the critical position of the overtaking vehicle. For the purpose of analyzing the factors that affect the range of overtaking danger zones, it is assumed that when overtaking is completed, the distance between the rear of the overtaking vehicle and the front of the overtaking vehicle is 2 seconds; The headway between vehicles in the overtaking convoy is 3 seconds; All vehicles have a length of 5 meters; The safe time interval between the front of the overtaking vehicle and the rear of the downstream vehicle when returning to the original lane is 2 seconds; The speed of the oncoming vehicle when overtaking is 60 km/h^-1The speed of the overtaking vehicle after acceleration during overtaking is 80 km/h^-1The fleet speed is 60 km · h^-1The distance between the front of the overtaking vehicle and the first downstream vehicle after acceleration is 20 meters; At the end of overtaking, the minimum safe distance between the overtaking vehicle and the oncoming vehicle is 3 seconds. The critical time obtained from equation (10)t₀By substituting equations (7) and (9), the relationship between the overtaking danger zone and the number of vehicles in the overtaking convoy, as well as the speed of oncoming vehicles, can be obtainedFigure 1.

Figure 1. Surface plot of dangerous overtaking area

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Figure 2. Step-by-step overtaking

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causeFigure 1It can be seen that the emergence of overtaking danger zones is not only related to the line of sight judgment at the beginning of overtaking, but also to the number of vehicles in the convoy and the speed of oncoming vehicles. The overtaking danger zone increases with the increase of the number of vehicles in the convoy and the speed of oncoming vehicles.

2. Stepwise SVOP algorithm

This paper proposes a "step-by-step" SVOP algorithm to address the overtaking abandonment dilemma faced by vehicles when overtaking a convoy in a two-way two lane road. SeeFigure 2, A~E are fleet vehicles; F is the overtaking vehicle; O is a vehicle traveling in the opposite lane. The cloud computing center is responsible for collecting vehicle information on road sections and calculating the optimal overtaking plan.

In a two-way two lane road, when overtaking vehicle F overtakes a convoy composed of vehicles A~E (there is no limit to the number of vehicles in the convoy), vehicle O comes from the opposite lane. To avoid overtaking vehicles entering the overtaking danger zone, the cloud computing center guides the overtaking vehicles and convoy vehicles in terms of speed. Vehicle F follows the speed guidance information provided by the cloud computing center to perform overtaking behavior. Vehicle B and its preceding convoy, vehicle C and its following convoy follow the speed guidance information provided by the cloud computing center to form a safe gap for vehicle F to enter the convoy (vehicles B and C are selected by the cloud computing center through calculation). Vehicle F first overtakes vehicles C~E in the convoy and enters the convoy. After the oncoming vehicle O passes by, vehicle F follows the speed guidance information provided by the cloud computing center to form a safe gap for vehicle F to enter the convoy (vehicles B and C are selected by The published speed guidance information drives and overtakes vehicles B and A, This is the overtaking goal that the step-by-step overtaking algorithm aims to achieve for the vehicle to the convoy.

In summary, the step-by-step overtaking algorithm process is as follows.

2.1 超车车辆速度与安全间隙匹配

Table 1. Relationship among v₅, v₆and v₇

方案	v₅与v₆关系	v₅与v₇关系	图示
1	v₅ > v₆	v₅ > v₇	3 (a)
2	v₅≤v₆	v₅ > v₇	3 (b)
3	v₅ > v₆	v₅≤ v₇	3 (c)
4	v₅≤v₆	v₅≤v₇	3 (d)

| Show Table

DownLoad: CSV

Figure 3. Safety distance distributions under different velocity relationships

DownLoad: Full-Size Img PowerPoint

2.2 车队安全间隙位置选取

3. 仿真结果分析

Table 2. Simulation parameters of step-by-step overtaking

参数	数值
s₃/m	600
H/m	0.5
l₁、l₂/m	5
N/veh	30
a₂/ (m·s^-2)	4
a₃/ (m·s^-2)	4
a₄/ (m·s^-2)	7
v₀/ (m·s^-1)	12
v′k/ (m·s^-1)	10
v₁/ (m·s^-1)	10
t₃/s	1
t₄/s	0.2
t₁₁/s	3

| Show Table

DownLoad: CSV

Figure 4. Relationship curves between speeds of front and rear vehicles and safety distance when overtaking velocity is 36 km·h^-1

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Figure 5. Relationship curves between speeds of front and rear vehicles and safety distance when overtaking velocity is 72 km·h^-1

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Figure 6. Relationship curves between speeds of front and rear vehicles and safety distance when overtaking velocity is 90 km·h^-1

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Table 3. Optimal control strategy of step-by-step overtaking

车辆行驶距离/m	超越车队车辆数/veh	安全间隙后车减速度/ (m·s^-2)	安全间隙前车加速度/ (m·s^-2)	超车车辆入队减速度/ (m·s^-2)	超车车辆减速时间/s
169.69	4	4.27	2.11	4.28	2.19
169.58	3	4.77	3.07	3.52	1.70
169.48	3	4.51	2.98	4.58	1.54
169.19	4	4.32	2.54	4.63	1.16
169.18	3	4.41	2.64	3.71	2.21
︙	︙	︙	︙	︙	︙
168.22	3	4.42	2.69	4.47	2.08
167.59	3	4.79	3.01	4.07	1.65
167.58	3	4.87	2.76	4.39	1.23
167.19	3	4.65	3.58	3.92	2.15
167.11	4	5.23	2.92	4.25	2.13
︙	︙	︙	︙	︙	︙
166.88	3	4.63	3.05	3.96	1.70
166.76	3	5.09	3.00	3.82	1.52
166.69	3	5.03	3.78	3.39	1.27
166.63	4	5.47	3.04	3.84	2.00
166.42	3	4.22	2.45	4.73	0.94

| Show Table

DownLoad: CSV

Figure 7. Fitness degree curves

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Figure 8. Velocity of overtaking vehicle in step-by-step overtaking strategy

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Figure 9. Velocity of platoon in step-by-step overtaking strategy

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4. 结语

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Slot control optimization of intelligent platoon for dual-lane two-way overtaking behavior

doi: 10.19818/j.cnki.1671-1637.2019.02.016