1. Quotes
Since the first motorways were built in the 1920s and the 1930s, traffic accidents and congestion caused by extreme weather conditions on highways have remained an unresolved issue. Traffic police departments basically take traffic control (including road closure) measures to cope with highway vehicle passage, especially in foggy environments. This not only restricts the full functioning of the highway, but also, in a sense, transfers accidents from the highway to other roads [
1]. Therefore, it is essential to develop a driving assistance system for lane changes that can guide drivers to drive on multiple lanes in foggy motorway environments.
Extensive research has been carried out in an attempt to solve the problem of low traffic passage rates in foggy environments. Huang Y [
2] proposed driving as a convoy under unused fog visibility and travel speed control restrictions to establish a car-following model; the real-time adjustment of the following distance of the model then ensures that the vehicles in the foggy environment are safely driving. Qiu YS [
3] proposed an object detection algorithm for low-to-light traffic environments, combining image defogging and enhancement methods to detect and identify obstacles in foggy environments, thereby allowing drivers to obtain real-time information about the movement of neighboring vehicles. Tan JH [
4] presented an extended model of car tracking on a sloped highway to judge driver misjudgment of car-following distance and active speed reduction behavior in low visibility conditions and correcting driving behavior in dense fog conditions.
Most of the aforementioned studies on driving assistance systems on foggy highways are based on overall vehicle driving. Few studies have been conducted on driving assistance systems focusing on lane changes on foggy highways. However, lane-changing operations on motorways are one of the main traffic actions and can significantly improve the traffic passage rate. Studying driving assistance systems for lane changes on foggy highways is vital for analyzing traffic safety [
5] and exploiting detailed traffic flow characteristics [
6]. Research on driving assistance systems for lane changes is equally topical. Kusuma A [
7] proposed a random utility formulation to study the lane-change mechanism for different lanes, using maximum likelihood estimation techniques and vehicle trajectory data to calibrate the model parameters. Hou Y [
8] developed a decentralized cooperative lane-change controller using proximal policy optimization and proposed a cooperative lane-change solution based on deep reinforcement learning, networking, and automated vehicle technology to provide lane-change solutions for different highway traffic conditions. He YM [
9] established a lateral acceleration model and a collision avoidance model with minimum safety spacing using a five-polynomial lane-change trajectory model and employed simulation methods to verify the accuracy of the model. The results showed that the safety of vehicles driving on the highway was effectively improved. Xu T [
10] developed a hybrid model for highway lane-change detection by extracting feature parameters associated with lane-change behavior from track records and using vision techniques to identify lane-change behavior. Zhang Q [
11] studied a deep learning, image processing-based vehicle lane-change warning algorithm to detect vehicle lane-change behavior on a highway from a first-person perspective. The results showed that the lane change detection accuracy was 94.5%. Wang JY [
12] proposed an automatic lane-change system for arbitrary lane-change scenarios in highway driving, implementing dual-target tracking via an adaptive cruise controller that used a low-level controller to track trajectories and predict vehicle motion, in addition to the use of environmental envelopes and maneuvers as constraints. Liu W et al. [
13,
14,
15] conducted a series of studies on lane-changing driving assistance systems, using a global navigation satellite system (GNSS) to measure the speed and position of the vehicle and lane-line information obtained from cameras equipped in the vehicle. Additionally, they proposed a visual lane-changing assistance system incorporating GNSS and vision technologies. The abovementioned studies were all based on vision sensor technology for highway lane-change driving assistance systems under normal weather conditions. Nevertheless, in foggy conditions, the vision sensors on the vehicles are subject to changes in the environment, resulting in reduced recognition of the surrounding environment, which in turn affects the safety of lane-change driving.
Therefore, in response to these research gaps, a lane positioning technology, based on vertical iterative methods for vehicle lane-change driving on foggy highways, is proposed. The rapid development trend of centimeter-level positioning and high-precision electronic map technologies enables vehicles to obtain real-time lane information in foggy motorway conditions. Owing to vehicle-to-vehicle (V2V) technology, research on lane-change safety distance and warning rules ensures the safety of vehicles when changing lanes on foggy highways to achieve the purpose of foggy highway multi-lane traffic and improve the efficiency of foggy highway traffic.
4. Vehicle Lane Recognition
As can be seen in
Figure 3, when a vehicle is driven to a certain location on the road, the flow of the driving assistance system for the lane-change onboard unit determines the lane the vehicle is in. The system first determines whether the driver is making a lane-change operation based on the CAN bus or onboard unit. If the CAN bus collects a turn signal or the onboard unit receives a signal indicating the driver intends to change lanes, the vehicle performs or prepares to perform a lane-change operation, and the onboard unit sends a lane-change message to the surrounding vehicles and performs the lane-change operation. At this point, the lane positioning technology obtains the information of the current midpoint of the front and rear axle centerlines (vehicle center) through a high-precision BDS, including the position coordinates of the vehicle center in the plane coordinate system, heading angle, and other data. The information stored in the high-precision map, such as the lane boundary, lane centerline, lane number, and heading angle of the highway where the vehicle is currently driving, is retrieved, and the onboard unit projects the real-time BDS data of the vehicle center onto the high-precision map of the present road section of the moving vehicle, obtains the real-time position and heading angle of the vehicle center on the high-precision map during the lane-change driving process, and then measures the lateral distance between the vehicle center on the high-precision map and the centerline of the nearest lane on the left and right sides using the vertical iteration method, determines the lane number, and sends the information to the surrounding vehicles simultaneously. It seems obvious that the real-time calculation of the lateral distance between the center point of the vehicle and the centerline of the nearest lane on the left and right sides is the core technology for lane discrimination in vehicle driving.
In this study, the vertical iterative method was used to calculate the lateral distance between the vehicle center point and the centerline of the nearest lane on the left and right sides. The specific method for solving for the lateral distance using the vertical iterative method is shown in
Figure 4 and
Figure 5.
According to
Figure 5, assuming that in the plane coordinate system [
21], the coordinates of the projection point
A of the vehicle center on the electronic map are
, the heading direction is
, the heading angle is
, the expression of the lane centerline is
, the expression for the lane centerline heading angle is
[
16], the error threshold is set to
, and the specific calculations of the vertical iterative method to solve the lateral distance are as follows:
(1) A straight line through point
A and perpendicular to
is drawn, the equation of which is as follows:
(2) The equation of the line in Equation (3) is combined with the equation of the lane centerline to find the coordinates of the intersection point , and the coordinates of the intersection point are then substituted into the lane centerline heading angle equation to obtain the heading angle at point on the lane centerline .
(3) A straight line
is drawn through point
and along the heading angle
, the equation of which is as follows:
Another straight line is drawn through point
and perpendicular to line
, the equation of which is as follows:
(4) Equation (5) is combined with Equation (4) of the line
to find the coordinates
of the intersection
; Equation (5) is combined with the equation of the lane centerline
to find the coordinates
of the intersection
. Finally
, the distance between
and
is calculated as follows:
If , then let , , and go to Step (8).
(5) If
, the coordinates (
) of intersection
are substituted into the equation for the heading angle
of the lane centerline to obtain the heading angle
at point
on the lane centerline
, and a straight line
is drawn along the heading angle
through point
, the equation of which is
A straight line through point
and perpendicular to line
is drawn, the equation of which is as follows:
(6) Equation (8) is combined with Equation (7) of the line
to find the coordinates
of the intersection point
; Equation (8) is combined with the equation of the lane centerline
to find the coordinates
of the intersection point
. Finally,
of the distance between
and
is calculated as follows:
If , then let , , and go to Step (8).
(7) If , continue to calculate according to Steps (5) and (6) until Step K is iterated. For the intersection of the line passing through point and perpendicular to the line with line at point , the intersection of a line passing through point A and perpendicular to the line with the lane centerline at point , when the distance of between and , let , , and go to Step (8).
(8) The lateral distance
D between point
A and the lane centerline is as follows:
It should be noted that as the permitted lateral deviation distance “n” between all vehicles and the centerline of the lane is set at 40 cm, and the positioning accuracy of the positioning system and of the electronic map need to be less than or equal to 22.5 cm, the lateral distance of the vehicles in the car-following scenario should be within 40 + 22.5 = 62.5 cm. When the vehicle changes lanes from lane to lane , if the lateral distance between the center of the vehicle and the centerline of the nearest lane on the left and right sides (lanes and ) is measured on the high-precision map as and , respectively, and if is less than or equal to the set threshold value of 62.5 cm, the lane number is judged to be . If is less than or equal to the set threshold value of 62.5 cm, then the lane number is judged to be . Otherwise, the vehicle is judged to be in the lane-change state.
5. Safety Distance for Lane Change and Design of Lane-Change Warning Rules
5.1. Determination of Safe Distances for Changing Lanes
As the foggy highway driving environment is more complex, this study, based on the theory of minimum safe distance, considers the psychological impact of the foggy environment on the driver and the impact of communication delay in a vehicle–vehicle communication environment, and determines the safe distance for vehicle lane change on foggy highways. A simplified graph of the car braking time versus car braking acceleration when the driver performs a braking operation under emergency conditions is shown in
Figure 6 [
22].
As shown in the diagram, the braking distance
S of the car under normal conditions is calculated as follows:
where
is the braking distance (m),
is the reaction time of the driver,
is the pedal change time of the driver,
is the time for the brake to act,
is the time for the braking force to be applied,
is the starting braking speed (km/h),
is the braking deceleration (m/s
2).
Studies [
23] have opined that after the driver has stopped safely, a distance d needs to be retained between the front and rear vehicles to ensure absolute safety, generally taken as a distance of 2–5 m. Depending on the actual situation, the time from point
to point b is the reaction time between the driver discovering the situation and taking braking action, which is generally 0.3–1.0 s for a normal person. Point b to point e is the time between the brake starting to generate braking force and reaching the maximum braking deceleration, generally 0.2–0.9 s. Considering that the vision of a driver is restricted in a foggy environment,
is 1 s,
is 0.1 s,
is 0.4 s, and
d is 5 m [
24], Equation (11) can be simplified as follows:
In addition, considering the time-division multichannel communication mechanism used by V2V technology, it takes 100 ms to complete an effective communication, while a single vehicle can, at most, record the driving information of eight nearby vehicles [
25]; therefore, the longest time of communication cycle (communication delay time) of two vehicles associated with each other is 800 ms. By adding the distance traveled by the vehicle during the communication delay time (i.e., the delay time multiplied by the initial vehicle speed) to Equation (12), the following equation is obtained:
To fully and reasonably improve the capacity of the highway in foggy weather, the system sets the upper limit of the driving speed for different visibility conditions: the lower the visibility, the slower the specified traveling speed, and the greater the distance maintained between vehicles. From Equation (13), a summary table of the safety distance parameters is generated, as shown in
Table 1:
5.2. Design of Lane-Change Warning Rules
When a vehicle needs to perform a lane-change operation, required because of a change in the number of lanes, vehicle breakdown, vehicle leaving the motorway, etc., occurring while the vehicle is traveling on the highway, the driving assistance system for lane changes should provide an appropriate warning strategy based on the four following states of lane-changing vehicles and other related vehicles. The warning strategy is illustrated in
Figure 7.
Status 1: No other vehicles within the communication range of the target lane.
Status 2: Presence of a potentially dangerous vehicle in front of the target lane
Status 3: Presence of a potentially dangerous vehicle at the rear of the target lane.
Status 4: Presence of potentially dangerous vehicles in front of and at the rear of the target lane.
For status 1, there are no other vehicles traveling within the communication range in the target lane, and the lane-change operation can be performed directly with the assistance of the onboard unit.
For status 2, if the distance between the vehicle in the target lane ahead of the lane-change vehicle and the lane-change vehicle satisfies the lane-change safety distance requirements, the lane-change operation can be performed directly with the assistance of the onboard unit. If the distance between the vehicle in the target lane ahead of the lane-change vehicle and the lane-change vehicle does not satisfy the lane-change safety distance requirements, the lane-change vehicle performs a deceleration operation until the lane-change safety distance condition is satisfied.
For status 3, if the distance between the vehicle in the target lane at the rear of the lane-change vehicle and the lane-change vehicle satisfies the lane-change safety distance requirements, the lane-change operation can be performed directly with the assistance of the onboard unit. If the distance between the vehicle in the target lane at the rear of the lane-change vehicle and the lane-change vehicle does not satisfy the lane-change safety distance condition, the vehicle in the target lane at the rear of the lane-change vehicle performs a deceleration operation until the lane-change safety distance condition is satisfied.
For status 4, if the distance between the vehicles in the target lane in front of and in the rear of the lane-change vehicle and the lane-change vehicle satisfies the lane-change safety distance condition, the lane-change operation can be exercised directly with the assistance of the onboard unit; if the distance between the vehicles in the target lane in front of the lane-change vehicle and the lane-change vehicle does not satisfy the lane-change safety distance condition, the vehicles at the rear of the lane-change vehicle and the lane-change vehicle simultaneously perform deceleration operation until the lane-change safety distance condition is satisfied; if the distance between the vehicle at the rear of the lane-change vehicle and the lane-change vehicle does not satisfy the lane-change safety distance condition, the vehicle at the rear performs the deceleration operation until it satisfies the lane-change safety distance condition; if both the distances between the vehicle in front of and at the rear of the lane-change vehicle and the lane-change vehicle do not satisfy the lane-change safety distance condition, the vehicle at the rear and the lane-change vehicle perform the deceleration operation at the same time, giving priority to satisfying the lane-change safety distance condition between the lane-change vehicle and the vehicle in front, and then the situation is analyzed according to the distance between the vehicle at the rear and the lane-change vehicle until both satisfy the lane-change safety distance condition.