Research Article  Open Access
Research on Safety Lane Change Warning Method Based on Potential Angle Collision Point
Abstract
In order to ensure safe lane change and avoid traffic accidents, an effective lane change assist system is required. In a lane change assist system, it is very important to obtain the following elements in time, such as actual distance between vehicles, minimum safety distance, and warning signal. To this end, this paper analyzed four kinds of lane change angle collision scenes. Initial position, initial velocity, acceleration, heading angle, and kinematics of vehicles were used to calculate the position of potential angle collision points between lane change vehicle and obstacle vehicles. Then, actual distance model was constructed based on potential angular collision points. The minimum safety distance model was also established under the two most unfavorable conditions. In order to achieve the lane change warning, three early warning rules were formulated. We verified the validity of models and early warning rules using vehicle driving video data of Interstate 80 in California. Models and early warning rules constructed in our research can be applied to the advanced active safety systems of vehicle, such as vehicle lane change assist system and active collision early warning system, which can improve the active safety and reduce traffic accidents.
1. Introduction
Lane change is a relatively complicated process for driving vehicles. Drivers’ improper operation during lane change may cause traffic delays and accidents. According to incomplete statistics, lane change accidents account for 410% of all traffic accidents [1]. Safety is affected by the type, position, speed, acceleration, and deceleration of obstacle vehicles in the present lane and the target lane. In order to ensure safe lane change and avoid angle accidents, the vehicle lane change assist system needs to calculate actual distance between lane change vehicle and obstacle vehicles and make decisions and early warning by comparing the minimum safety distance [2–7].
In terms of actual distance estimation between lane change vehicle and obstacle vehicles, C. L. Wang [8] processed data using statistical mean model and then applied RSSI (Received Signal Strength Indication) to estimate the distance between the two vehicles. C. Wang [9] determined actual distance between these two vehicles by calculating the distance between the microwave radar in the rear bumper of preceding vehicle and that in the preceding bumper of rear vehicle, as well as the included angle of axle wire. J. Feng et al. [10] assumed that the lateral acceleration of lane change vehicle satisfied the positive and negative trapezoidal constraints and determined the position of lane change vehicle by predicting its lane change path. Meanwhile, the distance between those vehicles is estimated by considering their length. G. Xu et al. [11] predicted the lane change trajectory to determine positions of lane change vehicles by trapezoidal lateral acceleration, spline curve, commutation trajectory of convoluted curve, polynomial function, and artificial potential field. Parameters such as the length of vehicles were considered in estimating the distance between vehicles. Y. G. Luo et al. [12] achieved actual distance measurement with other vehicles by establishing a fivetime polynomial lane change trajectory tracking model for time. H. Z. Zhu et al. [13] proposed that vehicles equipped with RUPS (relative urban positioning system) can perceive their trajectory information and then perceive the relative distance between vehicles by exchanging, comparing, and identifying overlapping positions between their own and adjacent vehicle trajectories. Y. Zhu et al. [14] detected the position of the corresponding vehicle using fish swarm algorithm. After simplifying vehicle coordinates, the corresponding actual distance was obtained by calculating their Euclidean distance. C. OlaverriMonreal et al. [15] stereoscopically captured and processed images through the rear camera to obtain positional relationships between vehicles, with the distance between the preceding and rear vehicles calculated.
In the past studies, actual distance between lane change vehicle and obstacle vehicles was calculated by considering the coordinates of the centre points and the length of the vehicle bodies as well as the angle coordinate of lane change vehicle. In actual lane change, the collision of two vehicles depends on the space between potential angle collision points. Based on this, our research analyzed coordinates of potential angle collision points in lane change and established actual distance model for lane change vehicle and the adjacent obstacle vehicle by considering initial position, initial speed, acceleration, and heading angle of vehicle.
In terms of minimum safety distance, Q. Luo et al. [16] considered the gradual process of state and speed of preceding vehicle and established the minimum safety distance model in the motionlessness, uniform speed, and uniform deceleration of the preceding vehicle. S. M. Wang et al. [17] regarded the lateral acceleration as a sinusoidal characteristic function of time and derived the critical position of vehicle collision by derivation. Then the minimum safe distance condition was obtained to avoid vehicle collision. R. S. Tomar et al. [18] extracted the relative velocity, acceleration, and other parameters between lane change vehicle and the surrounding vehicle through support vector machine, which was used to calculate the minimum safety distance. In actual lane change, the minimum safety distance changes with the running state of vehicle, and most of the above studies cannot reflect realtime running state of vehicle [19]. A. Kanaris et al. [20] proposed that the preceding vehicle braking should be considered to calculated the minimum safety distance, so the remaining vehicles have enough time and space to adjust and avoid collision. Based on it, this paper analyzed the most unfavorable situations in lane change and combined the realtime running state of vehicle to establish the minimum safety distance model between the preceding and rear vehicles in the emergency braking of the preceding vehicle as well as the minimum safety distance model when the speed of rear vehicle is higher than that of preceding vehicle.
Different from the existing research, this paper studied functions of potential angle collision point positions under four lane change scenes to determine the actual distance model of lane change vehicles and surrounding obstacle vehicles. And then, according to the minimum safety distance, lane change risks were classified and corresponding warning rules were formulated, which assisted driver to adjust vehicle’s state in time and improve vehicle’s active safety.
2. Methods
2.1. Relevant Vehicle Definitions and Scenes of Angle Collision during Lane Change
2.1.1. Relevant Vehicle Definitions Involved in the Lane Change
In Figure 1, it is defined as follows: CLcar is the lane change vehicle; Pfront the preceding obstacle vehicle before lane change; Pback the rear obstacle vehicle before lane change; Tfront the preceding obstacle vehicle after lane change; Tback the rear obstacle vehicle after lane change.
2.1.2. Scenes of Angle Collision during Lane Change
Figure 2 shows the scenes of angle collision during lane change, that is, the angle collision of CLcar and Pfront, that of CLcar and Pback, that of CLcar and Tfront, and that of CLcar and Tback. Our research analyzed positions of potential angle collisions of lane change vehicles in the four scenes and established relevant models.
(a) The angle collision between Tback and CLcar
(b) The angle collision between Tfront and CLcar
(c) The angle collision between Pback and CLcar
(d) The angle collision between Pfront and CLcar
2.2. Actual Distance Model between Two Vehicles
2.2.1. Assumptions
This paper has made the following assumptions:
Tback, Pback, Tfront, and Pfront drive straight on the respective roads without lane change, and the speed and acceleration are in a horizontal state.
When the position of angle collision point is determined, lane change vehicles are regarded as a rectangle, and its coordinates are simplified to the geometric centre of the rectangle.
2.2.2. Lane Change Parameters and Coordinate Definition
Without loss of generality, modeling and analysis were carried out by taking the left lane change as an example. The lane change process was positioned by the absolute Cartesian coordinate system. The direction of the vehicle along the lane was defined as the positive direction of Xaxis; vertical to the lane and upward were defined as the positive direction of Yaxis (see Figure 3). The right edge line of the current lane is defined as Xaxis, and Yaxis is located at the geometric centre of the end obstacle vehicle at the beginning of lane change. Then the origin of coordinates can be obtained (see Figure 3). After the definition is completed, the coordinate system does not change with the change of vehicle position during lane change.
As shown in Figure 4, the position of each vehicle is (), with the unit of m; is the speed of each vehicle, with the unit of m/s; is the acceleration of each vehicle, with the unit of ; is the length of the vehicle, with the unit of m; is the vehicle width, where Tback, Pback, Tfront, Pfront, CLcar].
Figure 4 shows that the speed and acceleration of each vehicle are constantly changing during driving, so the start time of the lane change is defined to be zero, and the position of each vehicle can be expressed bywhere represents the initial position of the vehicle in the X direction; is the initial speed of the vehicle in the X direction; is the acceleration of the vehicle in the X direction. Similarly, the meanings of , and are similar.
When the lane change vehicle CLcar is driving, the heading angle is constantly changing. In Figure 5, is the heading angle of vehicle; is the shape parameter angle of vehicle.
The angles and can be calculated using
2.2.3. Calculation of the Preceding and Rear Angular Coordinates of Obstacle Vehicles
Figure 6 shows the preceding and rear angles of obstacle vehicles that are . And coordinates can be calculated from the position, length, and width of obstacle vehicles (see Table 1), wherein Tback, Pback, Tfront, Pfront].

2.2.4. Coordinate Calculation of Potential Angle Collision Points of Lane Change Vehicles
The preceding and rear angles of lane change vehicles are defined as , and the potential angle collision points of lane change vehicles are calculated by combining .
In the lane change scene of CLcar and Pfront, the potential collision coordinates of CLcar are calculated as follows.
Figure 7 shows that, in the lane change process 1, CLcar and Pfront generate a potential angle collision point ①, and the potential collision position of CLcar is at point . The coordinates are as follows:In the lane change process 2, CLcar and Pfront generate a potential angle collision point ②, and the potential collision position of CLcar is located within . The coordinates arewhere In the lane change scene of CLcar and Pback, the potential collision position coordinates of CLcar are calculated as follows.
Figure 8 shows that in the lane change process 1, CLcar and Pback generate a potential angle collision point ①, and the potential collision position of CLcar is at . The coordinates areAs shown in Figure 8, in the lane change process 2, CLcar and Pback generate a potential angle collision point ②, and the potential collision position of CLcar is located within . The coordinates arewhere In the lane change scene of CLcar and Tfront, the potential collision position coordinates of CLcar are calculated as follows.
As shown in Figure 9, in the lane change process 1, CLcar and Tfront generate a potential angle collision point ①, and the potential collision position of CLcar is located within . The coordinates arewhereIn the lane change process 2, CLcar and Tfront generate a potential angle collision point ②; the potential collision position of CLcar is at ; its coordinate is .
In the lane change scene of CLcar and Tback, the potential collision position coordinates of CLcar are calculated as follows.
Figure 10 shows that, in the lane change process 1, CLcar and Tback generate a potential angle collision point ①, and the potential collision position of CLcar is located within . The coordinates arewhereFigure 10 shows, in the lane change process 2, CLcar and Tback generate a potential angle collision point 2; the potential collision position of CLcar is at ; its coordinate is .
2.2.5. Determination of Actual Distance
According to the preceding and rear angular coordinates of obstacle vehicles and the coordinates of potential angle collision points of lane change vehicle, we calculate actual distance between lane change vehicle and obstacle vehicles during the twostage lane change in four scenes. Figure 11 shows that when , the potential angle collision position of CLcar is at , and the actual distance between the two vehicles can be calculated by Similarly, actual distance between lane change vehicle and obstacle vehicles in other scenes can be obtained (see Table 2).

2.3. Minimum Safety Distance Model
For the assisted driving system, after measuring actual distance between lane change vehicle and obstacle vehicles, it is necessary to determine the corresponding minimum safety distance for safe lane change. Decision and early warning are made by comparison [21]. The minimum safe distance refers to the necessary separation distance between the rear and preceding vehicles to avoid collision.
In lane change, there are two most unfavorable scenes: one is emergency braking of the preceding vehicle and the other is the speed of rear vehicle which is greater than that of preceding vehicle. For the first type, when preceding vehicle is parked under emergency braking, the rear vehicle should adjust its deceleration and speed to make the vehicle stop within the shortest distance for safety [22]. The second type is that, during lane change of continuous driving, the rear vehicle needs to decelerate to the same speed as preceding vehicle for safety.
In view of the abovementioned most unfavorable scenes, based on kinematics principle of vehicle, this paper established the minimum safety distance model between preceding and rear vehicles when the preceding vehicle is in emergency braking and the minimum safety distance model between preceding and rear vehicles when the rear vehicle is adjusted to the same speed as the preceding vehicle.
2.3.1. Minimum Safety Distance Model between the Preceding and Rear Vehicles during Emergency Braking of the Preceding Vehicle
The vehicle braking time consists of driver response time, brake coordination time, brake acceleration growth time, and continuous braking time [23], wherein vehicle tires, suspension, and ground have the impact on brake coordination time [24, 25]. The sum of driver response time and brake coordination time is generally 0.81.0 s [26, 27]. The deceleration buildup time of the preceding vehicle is generally 0.1 to 0.2 s, and is the braking time of preceding vehicle, with the unit of s. is the deceleration buildup time of the rear car, generally 0.10.2 s, and is the rear brake time, with the unit of s [28]. The braking principles of different vehicles are different [29, 30], and the maximum braking force is not exactly the same. The maximum average braking acceleration in the horizontal direction of the vehicle during emergency braking is determined as [27, 31]. Since the driver of the rear vehicle takes action after the preceding vehicle brakes, the change of the braking acceleration of rear vehicle will be delayed relative to the preceding vehicle. When the minimum safety distance is calculated, the acceleration changes of preceding and rear vehicles are shown in Figures 12 and 13.
Then the braking distance of the rear vehicle iswhere represents the speed of the rear vehicle in X direction; is the maximum braking acceleration of the rear vehicle in X direction.
Similarly,The braking distance of the preceding vehicle iswhere represents the speed of the preceding vehicle in X direction; is the maximum braking acceleration of the preceding vehicle in X direction.
Similarly,The minimum safety distance under emergency braking of the preceding vehicle isSimilarly,
2.3.2. Minimum Safety Distance Model between Preceding and Rear Vehicles When the Rear Vehicle Is Adjusted to the Same Speed as the Preceding Vehicle
If the speed of the preceding vehicle is greater than the speed of the rear vehicle, the actual distance between the two vehicles increases with time, and no angle collision and rearend collision occur. Therefore, the minimum safety distance is zero [32]. If the speed of the preceding vehicle is less than the speed of the rear vehicle, the minimum safe distance isSimilarly,
2.4. Definition of Early Warning Rules
According to the position of the potential angle collision point, we can obtain the actual distance between the rear vehicle and preceding vehicle, the minimum safety distance under the emergency braking of the preceding vehicle, and the minimum safety distance between preceding and rear vehicles when the rear vehicle is adjusted to the same speed as the preceding vehicle. The comparison of , , and divides the early warning into no early warning, mild early warning, and high early warning, and the colors of the early warning lights are green, yellow, and red, respectively. Specific definitions are shown in Table 3.

3. Result and Discussion
3.1. Introduction to Data Sources
The model validation data in our research was obtained from vehicle travel video data of Interstate 80 in Emeryville, California, collected by the Berkeley Highway Laboratory, from 4:00 pm to 4:15 pm on April 13, 2005. The US federal highway management software NGSIM was used to transcribe video data at 10 frames per second and then obtain data such as the length, width, coordinates, acceleration, and other data of vehicle in each frame.
3.2. Model Verification Parameters and Preprocessing
This paper analyzed the lane change video of the vehicle 1078, which considers preceding and rear obstacle vehicles before and after lane change. Thus, vehicle 1078 is defined as CLcar, vehicle 1062 as Pfront, vehicle 1077 as Tfront, vehicle 1083 as Tback, and vehicle 1084 as Pback (see Figure 14). According to the definition of coordinates origin and coordinate axis in Section 2.2.2, at the beginning of lane change, the end obstacle vehicle is vehicle 1083, so Yaxis in coordinate system is located at the geometric centre of vehicle 1083, and Xaxis is on the right edge of the lane where vehicle 1084 and vehicle 1062 are located. Table 4 shows the data involved in model validation.

Since the data is extracted by frame, it is necessary to fit the acceleration of vehicle. MATLAB is used to determine the acceleration of lane change vehicle and obstacle vehicles. Figures 15–20 show the vehicle acceleration versus time curve, and Table 5 shows the corresponding fitting effect indicators.

3.3. Early Warning Analysis
According to the established actual distance model, minimum safety distance model, and early warning rule definition, this paper drew the time variation curves of actual distance and the minimum safety distance between the lane change vehicle 1078 and its adjacent obstacle vehicles, and the curve of vehicles speed changes with time (see Figures 21–24). Through comparing with video recording, the actual distance variation curve between vehicles is consistent with the change of the distance between vehicles in the video, and the validity of the model constructed in the work is verified. At the same time, according to early warning rules, warnings and prompts can be given to potential conflict vehicles. The early warning analysis is as follows.
3.3.1. Early Warning Analysis of CLcar and Pfront
Figure 21 shows in the early stage of the potential angle collision point ① that is always greater than , resulting in the decrease of and the increase of and . Since is always greater than and at this stage, which satisfies the safety conditions, CLcar needs no early warning.
In the middle and late stages of the potential angle collision point ①, is always greater than , resulting in the decrease of and the increase of and . is always greater than and less than . Then, CLcar should be given the mild early warning and pay attention to the emergency brake of preceding vehicle with appropriate deceleration.
During the potential angle collision point ②, is always greater than , but the change of potential angle collision point increases and decreases and . Since is always greater than and less than , CLcar should be given mild early warning and pay attention to the emergency braking of preceding vehicle with appropriate deceleration. When there is no potential angle collision point between two vehicles, the early warning is terminated.
3.3.2. Early Warning Analysis of CLcar and Pback
Figure 22 shows that since CLcar travels to the left road edge line in the lane, there is potential angle collision point ② between vehicles instead of potential angle collision point ①. In the early stage of potential angle collision point ②, is less than and greater than . Pback can be given mild early warning and pay attention to the emergency braking of preceding vehicle with appropriate deceleration. The speed of the lane change vehicle CLcar is basically in increase trend; there is a slight increase for in the early period, but the sharp decline in the later period. The speed difference between the two vehicles gradually increases; the actual distance between the two vehicles increases; is in the decrease trend; is zero and remains unchanged. When is greater than , which satisfies the safety conditions, the early warning for Pback ends.
3.3.3. Early Warning Analysis of CLcar and Tfront
Figure 23 shows in the early and middle stage of potential angle collision point ① that since is always larger than , increases, and is zero and remains unchanged. Because is less than the minimum safety distance and greater than , CLcar should be given the mild early warning and pay attention to the emergency brake of preceding vehicle with appropriate deceleration.
In the late stage of the potential angle collision point ①, decreases sharply with a large deceleration. Then becomes small, and and become large, reflecting the sensitivity and effectiveness of the minimum safety distance model in the work. Since is always greater than and less than , CLcar should be given the mild early warning at this stage and pay attention to the emergency braking of preceding with appropriate deceleration.
In the early stage of the potential angle collision ②, for the sudden decrease of in the later period of potential angle collision point ①, CLcar reacts rapidly and then decelerates, and increases with a larger acceleration and exceeds . It makes increase, decrease, and become zero. Since is greater than , which meets safety conditions, CLcar needs no early warning. In the middle and late stages of the potential angle collision point②, since is always larger than , the early warning for the CLcar is changed from the mild early warning to no early warning.
3.3.4. Early Warning Analysis of CLcar and Tback
Figure 24 shows that CLcar appears as the preceding vehicle and the vehicle Tback as the rear vehicle. At the process of potential angle collision point ①, is always greater than , which decreases and increases and . Since is always greater than and less than . Tback should be given the mild early warning and pay attention to the emergency brake of the rear vehicle with appropriate deceleration.
In the early stage of the potential angle collision ②, is still higher than . It makes even less than . Tback should be given the severe early warning and decelerate immediately for safety.
In the middle and late stage of the potential angle collision point ②, for the sudden decrease of in the early stage, Tback perceives and then decelerates, which makes less than and become zero. Then the two cars drive at a relatively stable speed difference, with the little change of and . Since is greater than and less than , Tback should be given mild early warning and pay attention to the front emergency brake with appropriate deceleration.
4. Conclusions and Outlook
The innovation of this paper is that we analyzed more comprehensive lane change scenes, and, based on this, position functions of potential angle collision points on the sides, front, and rear of lane change vehicles and obstacle vehicles were studied in this paper. At the same time, different early warning rules were formulated according to the relationship between the actual distance and the two kinds of minimum safety distances.
Under assumptions, this paper can use the constructed models to judge the potential collision risk of different degrees in the process of changing lanes in a timely and effective manner. The driver’s behavior can be guided in real time according to early warning rules. Models and early warning rules established in this research could be applied to smart cars equipped with IOT (Internet of Things). The parameters such as speed and acceleration required by models were obtained through data acquisition and data interaction. Then, through the calculation and analysis of vehicle intelligent system, drivers were assisted to complete the safe lane change. The research content of this paper had good application value and practical significance for the development of advanced vehicle active safety system and the reduction of traffic accidents caused by lane change.
Models in this paper are mainly applicable to the analysis and early warning of lane change in long straight sections and longitudinal slope sections. Therefore, in the followup research, it is necessary to analyze the flat and curved sections. At the same time, the followup research will consider the influence of driver’s psychological role and the external environment on the minimum safe distance model and then modify the model.
Data Availability
The data for the five vehicles used in the work comes from the video data of vehicles travelling on Interstate 80 in Emeryville, California, collected by Berkeley Highway Laboratory (accessibility of data acquisition: ops.fhwa.dot.gov/trafficanalysistools/ngsim.htm).
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this article.
Acknowledgments
The work was funded by the National Natural Science Foundation of China (Grant no. 51308249).
References
 G. Gu, Cooperative Lanechanging Trajectory Planning ofIntelligent Vehicles with Consideration of DriverCharacteristics, South China University of Technology, 2008.
 H. Jula, E. B. Kosmatopoulos, and P. A. Ioannou, “Collision avoidance analysis for lane changing and merging,” IEEE Transactions on Vehicular Technology, vol. 49, no. 6, pp. 2295–2308, 2000. View at: Publisher Site  Google Scholar
 J. A. Laval and C. F. Daganzo, “Lanechanging in traffic streams,” Transportation Research Part B: Methodological, vol. 40, no. 3, pp. 251–264, 2006. View at: Publisher Site  Google Scholar
 H. Wan, Z. Liu, and H. Wang, “Rearend and lanechanging collisions avoidance theoretical models of the multilane freeway in disaster weather,” Procedia  Social and Behavioral Sciences, vol. 96, pp. 70–81, 2013. View at: Publisher Site  Google Scholar
 C. Hatipoglu, U. Ozguner, and K. Redmill, “Automated lane change controller design,” IEEE Transactions on Intelligent Transportation Systems, vol. 4, no. 1, pp. 13–22, 2003. View at: Publisher Site  Google Scholar
 A. Vahidi and A. Eskandarian, “Research advances in intelligent collision avoidance and adaptive cruise control,” IEEE Transactions on Intelligent Transportation Systems, vol. 4, no. 3, pp. 143–153, 2003. View at: Publisher Site  Google Scholar
 Z. Shiller and S. Sundar, “Emergency lanechange maneuvers of autonomous vehicles,” Journal of Dynamic Systems, Measurement, and Control, vol. 120, no. 1, pp. 37–44, 1998. View at: Publisher Site  Google Scholar
 C. L. Wang, Research on Highway AntiCollision Alarm System Based on Zigbee, Harbin Institute of Technology, 2010.
 C. Wang, Research on Several Key Problems of Vehicle Lane Change Warning, Chang'an University, 2012.
 J. Feng and J. Ruan, “Study on intelligent vehicle lane change path planning and control simulation,” in Proceedings of the 2006 IEEE International Conference on Information Acquisition, ICIA 2006, pp. 683–688, China, August 2006. View at: Google Scholar
 G. Xu, L. Liu, Y. Ou, and Z. Song, “Dynamic modeling of driver control strategy of lanechange behavior and trajectory planning for collision prediction,” IEEE Transactions on Intelligent Transportation Systems, vol. 13, no. 3, pp. 1138–1155, 2012. View at: Publisher Site  Google Scholar
 Y. Luo, Y. Xiang, K. Cao, and K. Li, “A dynamic automated lane change maneuver based on vehicletovehicle communication,” Transportation Research Part C: Emerging Technologies, vol. 62, pp. 87–102, 2015. View at: Publisher Site  Google Scholar
 H. Z. Zhu, S. Chang, W. Zhang, F. Wu, and L. Lu, “Online vehicle front–rear distance estimation with urban contextaware trajectories,” IEEE Transactions on Vehicular Technology, vol. 67, no. 2, pp. 1063–1074, 2018. View at: Publisher Site  Google Scholar
 Y. Zhu and J. Chen, “Research on the minimum safe distance of vehicle lane changing based on fish swarm grouping behavior,” Software Guide, vol. 17, no. 3, pp. 23–27, 2018. View at: Google Scholar
 C. OlaverriMonreal, G. C. Krizek, F. Michaeler, R. Lorenz, and M. Pichler, “Collaborative approach for a safe driving distance using stereoscopic image processing,” Future Generation Computer Systems, vol. 95, pp. 880–889, 2019. View at: Google Scholar
 Q. Luo and L. H. Xu, “Carfollowing model based on the minimum safety distance and simulation study,” Science Technology and Engineering, vol. 10, no. 2, pp. 569–573, 2010. View at: Google Scholar
 S. M. Wang, J. Y. Xu, Q. Luo et al., “A safety warning model for lane changing on highway,” Journal of South China University of Technology (Natural Science Edition), vol. 42, no. 12, pp. 40–50, 2014. View at: Google Scholar
 R. S. Tomar, S. Verma, R. S. Kushwah, and G. S. Tomar, “Collision avoidance warning for safe lane change,” in Proceedings of the 2013 International Conference on Communication Systems and Network Technologies (CSNT 2013), vol. 12, pp. 385–389, April 2013. View at: Publisher Site  Google Scholar
 Y. Luo, Y. Xiang, K. Cao, and K. Li, “A dynamic automated lane change maneuver based on vehicletovehicle communication,” Transportation Research Part C: Emerging Technologies, vol. 62, pp. 87–102, 2016. View at: Publisher Site  Google Scholar
 A. Kanaris, E. B. Kosmatopoulos, P. A. Loannou et al., “Strategies and spacing requirements for lane changing and merging in automated highway systems,” IEEE Transactions on Vehicular Technology, vol. 50, no. 6, pp. 1568–1581, 2001. View at: Publisher Site  Google Scholar
 X. Q. Yin, P. J. Liu, X. D. Zou et al., “Optimization and simulation of the minimum safety distance of car following model,” Information Technology Journal, vol. 12, no. 17, pp. 4101–4105, 2013. View at: Google Scholar
 Y. H. Wu, J. X. Xie, L. H. Du, and Z. Hou, “Analysis on traffic safety distance of considering the deceleration of the current vehicle,” in Proceedings of the 2009 Second International Conference on Intelligent Computation Technology and Automation, pp. 491–494, Changsha, China, October 2009. View at: Publisher Site  Google Scholar
 H. Yuan, G. Shi, X. Huang, and J. Cheng, “Braking model of stopping sight distance,” Journal of Southeast University (Natural Science Edition), vol. 39, no. 4, pp. 859–862, 2009. View at: Publisher Site  Google Scholar
 R. H. Zhang, Z. C. He, H. W. Wang, F. You, and K. Li, “Study on selftuning tyre friction control for developing mainservo loop integrated chassis control system,” IEEE Access, vol. 5, pp. 6649–6660, 2017. View at: Publisher Site  Google Scholar
 X. J. Sun, H. Zhang, W. J. Meng, R. Zhang, K. Li, and T. Peng, “Primary resonance analysis and vibration suppression for the harmonically excited nonlinear suspension system using a pair of symmetric viscoelastic buffers,” Nonlinear Dynamics, vol. 94, no. 2, pp. 1243–1265, 2018. View at: Publisher Site  Google Scholar
 B. Park, Y. Chen, and J. Hourdos, “Opportunities for preventing rearend crashes: Findings from the analysis of actual freeway crash data,” Journal of Transportation Safety & Security, vol. 3, no. 2, pp. 95–107, 2011. View at: Publisher Site  Google Scholar
 N. H. Jiang and J. G. Yu, “Study on rearend avoidance model of highway based on RBF neural network,” Forest Engineering, vol. 26, no. 5, pp. 60–65, 2010. View at: Google Scholar
 B. E. Heinrichs, B. D. Allin, J. J. Bowler, and G. P. Siegmund, “Vehicle speed affects both preskid braking kinematics and average tire/roadway friction,” Accident Analysis & Prevention, vol. 36, no. 5, pp. 829–840, 2004. View at: Publisher Site  Google Scholar
 H. Y. Xiong, X. L. Zhu, and R. H. Zhang, “Energy recovery strategy numerical simulation for dual axle drive pure electric vehicle based on motor loss model and big data calculation,” Complexity, vol. 2018, Article ID 4071743, 14 pages, 2018. View at: Publisher Site  Google Scholar
 J. Rehkopf, Automobile Brake Systems, Pearson Prentice Hall, Upper Saddle River, NJ, USA, 2008.
 J. Y. Lian and X. Y. Hua, “Study of mathematics model for rear end collision avoidance system,” China Journal of Highway and Transport, vol. 18, no. 3, pp. 123–126, 2005. View at: Google Scholar
 H. Wang, S. Zhang, W. Quan, and X. Liu, “Study on safety distance model of fleet based on vehicle communication,” Procedia  Social and Behavioral Sciences, vol. 96, no. 6, pp. 2698–2705, 2013. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2019 Tongqiang Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.