Emerging Technologies in Traffic Safety Risk Evaluation, Prevention, and Control
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Chuanliang Shen, Shan Zhang, Zhenhai Gao, Binyu Zhou, Wei Su, Hongyu Hu, "Study on a RightTurning Intelligent Vehicle Collision Warning and Avoidance Algorithm Based on Monte Carlo Simulation", Journal of Advanced Transportation, vol. 2020, Article ID 9405760, 11 pages, 2020. https://doi.org/10.1155/2020/9405760
Study on a RightTurning Intelligent Vehicle Collision Warning and Avoidance Algorithm Based on Monte Carlo Simulation
Abstract
With the development of intelligent vehicle technology, the demand for advanced driver assistant systems kept increasing. To improve the performance of the active safety systems, we focused on rightturning vehicle’s collision warning and avoidance. We put forward an algorithm based on Monte Carlo simulation to calculate the collision probability between the rightturning vehicle and another vehicle (or pedestrian) in intersections. We drew collision probability curves which used timetocollision as the horizontal axis and collision probability as the vertical axis. We established a threelevel collision warning system and used software to calculate and simulate the collision probability and warning process. To avoid the collision actively when turning right, a twostage braking strategy is applied. Taking four rightturning collision conditions as examples, the twostage braking strategy was applied, analysing and comparing the anteroposterior curve diagram simultaneously to avoid collision actively and reduce collision probability. By comparison, the collision probability 2 s before active collision avoidance was more than 80% and the collision probability may even reach 100% in certain conditions. To improve the active safety performance, the twostage braking strategy can reduce the collision probability from exceeding 50% to approaching 0% in 2 s and reduce collision probability to less than 5% in 3 s. By changing four initial positions, the collision probability curve calculation algorithm and the twostage braking strategy are validated and analysed. The results verified the rationality of the collision probability curve calculation algorithm and the twostage braking strategy.
1. Introduction
With the development of vehicle active safety systems, ADAS can solve traffic safety problems in challenging crashes situations. The current ADAS focuses mainly on turning left, and studying the rightturning process was also important for improving traffic safety. Considering that the driver in mainland China was sitting on the left side, there was a large blind spot in the process of turning right, and the algorithm was designed by taking the right turn as an example. The rightturning condition was special and relatively complex [1] because drivers needed to give attention to pedestrians crossing the road while avoiding vehicles coming from the left side and drivers had a visual blind spot during the rightturning [2]. Therefore, the rightturning condition of an intelligent vehicle was studied and analysed.
In intersections, the intelligent vehicle’s turning condition was a complex traffic scene which possesses a high accident rate [3, 4]. There are increasing numbers of collisions between rightturning vehicles and pedestrians (or other vehicles) [5, 6]. Therefore, it was necessary to reduce the collision probability by technical means. At present, most previous studies focused on the forward collision warning (FCW) system and active collision avoidance [7]; however, there was a lack of research on the collisions caused by rightturning vehicles. Some researchers estimated the motion state of vehicles and pedestrians [8, 9]. By establishing a probability model, Hashimoto et al. predicted and identified a pedestrian’s crossing decision in advance [10]; however, this research lacked the calculation of collision probability for a vehicle on a rightturning course. In rightturning collisionrelated research, Sitao et al. put forward an intersection optimization design to reduce the collision probability between rightturning vehicles and pedestrians [11], but it cannot cover all possible rightturning collisions in intersections. Zhao et al. have conducted research in intelligent vehicles active collision avoidance related fields [12]. Choi and Zhao et al. adopted the autonomous emergency braking (AEB) system to avoid collisions [13, 14]. However, these studies were not combined with the intelligent vehicle’s rightturning condition. In this paper, Monte Carlo simulation was used to establish a random simulation algorithm which simulates the rightturning intelligent vehicle’s collision probability.
The current research is summarized as follows:(1)At present, most previous studies focused on the forward collision warning (FCW) system and autonomous emergency braking (AEB) system; however, there was a lack of research on the collisions caused by rightturning vehicles.(2)The current research focused on pedestrian intention prediction and identification, without considering the rightturn condition. The existing research on the right turn was not comprehensive enough, and the research should be extended to the vehicle and pedestrian protection during the right turn.(3)At present, AEB early warning and active intervention were mature, but there was relatively little research on early warning of traffic conflicts during the rightturn process. Current research lacked the calculation of collision probability for a vehicle on a rightturning course. The early warning mechanism should be introduced into the field of rightturn collision warning.
In order to calculate the collision probability accurately, extensively covering all possible collisions during rightturning, and actively avoiding a collision, the system described in this paper not only calculated the collision probability and designed the threelevel collision warning system (CWS) but also actively avoided the collision to reduce the collision probability.
According to the algorithm based on Monte Carlo simulation to calculate the collision probability, we have improved the performance of the active safety systems, which contributed to rightturning vehicle’s collision warning and avoidance. We established a threelevel collision warning system and used software to calculate and simulate the collision probability and warning process. To avoid the collision actively when turning right, a twostage braking strategy was applied. Therefore, we calculated the probability of collision, through the warning level and active intervention to improve the safety of the rightturning process and reduce the accident rate.
2. Establishing the Collision Safety Model and Warning Mechanism
2.1. Collision Safety Model Based on TimetoCollision
Our study analysed the rightturning condition and predicted four different collision modes during the rightturning process. The CWS was designed for each collision scenario, and the twostage braking strategy was designed for each scenario to actively and simultaneously avoid collisions. Finally, by changing four initial positions, the collision probability curve calculation algorithm and the twostage braking strategy were validated and analysed. This control scheme’s technical roadmap is shown in Figure 1.
The collision warning and avoidance algorithm’s main process was as follows:(1)The information gathering process needs to collect the vehicle’s velocity information and classify it into four modes. The four modes were as follows: a collision between a vehicle which turned right into the lane and another vehicle which merged into the same lane from the left side (scenario 1); a collision between a rightturning vehicle merging into the lane and pedestrians crossing the road in the same lane (scenario 2); a collision between the pedestrians crossing the road ahead and a rightturning vehicle (scenario 3); and a collision between a rightturning vehicle merging into the lane and another vehicle existing in the lane (scenario 4). The four modes are shown in Figure 2.(2)We calculated the collision probability for these four modes and used the vehicle’s and pedestrian’s safety profile as the collision’s criteria. We generated random variables for velocity and turning radius and simulated the collision probability curve using a collision probability calculation algorithm based on Monte Carlo simulation. We accumulated collision probability and plotted the collision probability curve on the threelevel warning figure.(3)We output the warning level through the threelevel warning region and performed the twostage braking strategy in the specific scenario.
In our study, we adopted the collision safety model based on timetocollision (TTC) [1]. The driver’s danger perception caused a delay, and the braking system also caused a delay.
The total delay was as follows: the time in which driver included stimulation (D_{1}), identification and decision time (D_{2}), time to control action (D_{3}), and braking system delay time (d).
To ensure safety, it was necessary to ensure the safety time threshold (D_{s}) greater than the sum of delay (D_{sum}), so the CWS needed to take actions before D_{sum}, as expressed by the following equations:
D_{sum} was generally within 3 s [15]; therefore, D_{s} should be greater than 3 s. To reach reliable intelligent vehicle safety during rightturning conditions, the collision warning and avoidance algorithm was designed for a TTC of 5 s.
2.2. Establishment of Collision Warning Mechanism
The three warning levels for rightturning collisions of intelligent vehicles [16, 17] were defined as follows: Ilevel: it is low collision probability; vehicle’s rightturning process was safe, so the warning system did not warn the driver. IIlevel: the intelligent vehicle had a certain collision probability; the warning system reminded the driver by displaying a yellow light in the dashboard. IIIlevel: a collision could happen immediately, and the warning system reminded the driver to take action. If the TTC was within 2 s, the intelligent vehicle would perform the twostage braking strategy to actively avoid the collision.
Many researchers believed that a collision between the vehicle and other vehicles or between the vehicle and pedestrians should have different collision warning figures, collision warning icons should be different according to the crashing objects, and their systems generated different collision warning figures based on different collision objects [18, 19]. We used a conservative warning figure as the only collision warning figure, which can simultaneously simplify the collision warning mechanism and ensure security. The specific areas of the CWS are shown in Table 1 and drawn, as shown in Figure 3. During the simulations, the area where the collision probability curve was located is the warning level.

2.3. Geometric Modelling of Vehicle’s and Pedestrian’s Safety Profiles
The vehicle’s rightturning process was regarded as a rigid body motion, and the vehicle’s centre (O_{1}) was placed on its geometric centre. The length of the rightturning vehicle was L_{1} and the width W_{1}. A second vehicle’s length was L_{2}, and the width was W_{2}. The coordinate system was based on O_{1}, and another vehicle’s centre was O_{2} at coordinates (a, b). The velocity of the rightturning vehicle is V_{1}, and the angle with the Xaxis was θ_{1}. Another vehicle’s velocity was V_{2}, and the angle with the Xaxis is θ_{2}. The vehicle’s coordinate system is shown in Figure 4. During the simulation, the second vehicle’s or pedestrian’s position was unchanging, and reversed speed equal to the speed of the second vehicle or pedestrian was applied to the turning vehicle. If the rightturning vehicle’s centre (O_{1}) crossed into the second vehicle’s or pedestrian’s safety profiles, a collision occurs.
Many scholars regarded the car as a contour [20, 21]; based on this, the second vehicle’s and pedestrian’s safety profiles were developed. In this study, we expanded the contour of another vehicle or pedestrian, and the expansion size was the size of the turning vehicle and used this size to establish the vehicle’s and pedestrian’s safety profiles. If the turning vehicle’s centre crossed into the safety profiles, the collision occurred.
When another vehicle collides with the rightturning vehicle, this situation could be used as the safe contour threshold. The vehicle’s safety profile was built up as follows.
The front of the vehicle’s safety profile was a circle with the front centre S_{2} as the centre point and (L_{1} + W_{2})/2 as the radius. The vehicle’s rear safety profile was constructed in the same way as the front, and the transition part was a rectangle. The vehicle’s safety profile is shown as Figure 5.
In the same way, the pedestrian’s safety profile was centred on the pedestrian, and the pedestrian’s geometric area was enlarged to determine whether the vehicle’s centre (O_{1}) crossed into the pedestrian safety profile, which was the collision criterion. When the vehicle’s front side collided with the pedestrian, this situation was the pedestrian’s safety profile threshold. We defined the pedestrian’s profile as a circle with a centre O_{2} and radius D/2, and the pedestrian’s safety profile was a circle with centre O_{2} and radius (D + L_{1})/2. The pedestrian’s safety profile is shown in Figure 6.
3. RightTurning Vehicle Collision Probability Calculation Algorithm
Monte Carlo simulation theory was based on the central limit theorem and the large number theorem [22, 23]. The central limit theorem showed that although the distribution of each random variable M_{i} was unknown, ΣM_{i} obeyed a normal distribution and could be converted to a standard normal distribution; therefore, it could be processed using the standard normal distribution properties. We defined {M_{i}} as an independent random variable and part of a sequence of identically distributed random variables, with an expected value of O and variance of k^{2}, as shown in
Φ(m) represented the value of the standard normal distribution. According to equation (3), the more the samples of random variable M_{i} were obtained, the closer the distribution was normal, which was the basis of Monte Carlo simulation theory for collision probability.
N random numbers were generated for each random variable V_{1} and V_{2} and the rightturning radius r. The random variables were assumed to obey the normal distribution with μ as the expected value and σ^{2} as the variance [24, 25]. The intelligent vehicle’s position was continuously updated as sampling time increases. Sampling time is pt; each simulation calculated the collision probability within the collision analysis period (T), shown in Figure 7, to calculate whether a collision will occur in T; according to the vehicle’s and pedestrian’s safety profiles, PC represented the collision probability. If a collision occurred, the probability is accumulated, and the probability curve is drawn on the threelevel warning figure by software.
The calculation process of collision probability for four modes was as follows. First, the rightturning vehicle’s angle (θ_{1}) and coordinate calculation algorithm were introduced. The four modes were slightly different in calculation due to different initial velocity directions and initial positions, but the basic calculation principle was the same. We introduced the calculation process for θ_{1} and the rightturning vehicle’s coordinates (x(t), y(t)). In the i times simulation, the velocity of the rightturning vehicle was V_{1}(i), turning radius was r(i), and the velocity of the second vehicle was V_{2}(i). We represented TTC with t, and t represented the simulation time.
The calculation of angle θ_{1} was shown in
To calculate the position coordinates (x(t), y(t)) at the time t using θ_{1},_{,} the second vehicle was regarded as stationary and the reverse speed V_{2}(i) was applied to the rightturning vehicle.
When the condition met the scenario 1, the rightturning vehicle’s coordinates (x(t), y(t)) were shown in
When the condition met the scenario 2, the rightturning vehicle’s coordinates (x(t), y(t)) were shown in
When the condition met scenario 3, the rightturning vehicle’s coordinates (x(t), y(t)) were shown:
When the condition met scenario 4, the rightturning vehicle’s coordinates (x(t), y(t)) were shown in
The second step, in the i times simulation, was to judge if a collision will occur. We needed to judge whether the rightturning vehicle centre O_{1} crossed the vehicle’s or pedestrian’s safety profile. When the condition met the scenario 1 or scenario 4, the safety profile condition of the vehicle was given in equation (9), and the probability was accumulated according to the safety profile condition:
The collision between the rightturning vehicle and the pedestrians was judged by the pedestrian’s safety profile condition, when the condition met the scenario 2 or scenario 3, which was given in the same way as equation (9). The probability was accumulated according to the pedestrian’s safety profile condition; the pedestrian’s safety profile condition was shown in
4. TwoStage Braking Strategy
An intelligent rightturning vehicle collision warning and avoidance algorithm needed a braking strategy to realize active collision avoidance.
We established the twostage braking strategy. The twostage braking strategy could select the braking strength independently according to the TTC so that highefficiency braking could be achieved, and emergency braking could be avoided to prevent the driver from being nervous and misoperating the car. The specific flow of the twostage braking strategy was as follows: IIstage braking: if the collision probability reached 50% within 1 s (whether it reached IIIlevel warning within 1 s), we used the IIstage braking with the amount a_{max}. In the braking process, we considered the braking deceleration (a) approximately linearly increasing with the braking delay (d) and performed a timedomain integral operation on a, so the speed reduction amount could be obtained, thereby obtaining the vehicle speed at each sampling time. Istage braking: if the collision probability reached 50% within 12 s (whether it reached IIIlevel warning within 12 s), we used the Istage braking with the amount a_{min}. For the same reason as in the IIstage braking process, we considered the braking deceleration (a) approximately linearly increasing with the braking delay (d) and performed a timedomain integral operation on a. The twostage braking strategy is shown in Figure 8.
(a)
(b)
The timedomain integral operation of the acceleration obtained the decrease in velocity, ΔV(t), during the twostage braking process; thereby, we obtained the speed change by timedomain integration of acceleration:
The twostage braking strategy had two sets of formulas, and equation (12) represented the IIstage braking, which was within 1 s:
Equation (13) represented the Istage braking, which was within 12 s:
Therefore, in each simulation, the rightturning vehicle speed V_{1}(i) was obtained, and then, the updated speed was obtained, which was shown in
The position coordinates (x_{t}, y_{t}) of the vehicle were updated at time t, and the updated coordinates were shown in
5. Simulation Results and Comparative Analysis
5.1. Simulation Results of Each of the Four Modes
Scenario 1: the driver was sitting on the left side and needed to view the right, and it was not convenient to observe the movement of the vehicle in the left side, so it was easy to collide with another vehicle. The parameters in this scenario were defined as follows: pt = 0.01 s, T = 5 s, L1 = 8 m, W1 = 2 m, L2 = 8 m, and W2 = 2 m; the second vehicle’s coordinates were (−9, 12). V_{1}, V_{2}, and R consist of 10,000 normally distributed random numbers; V_{1} ∼ N (12, 1), V_{2} ∼ N (15, 1), and R ∼ N (20, 1). We used the twostage braking strategy; the specific parameters were as follows: a_{max} = 6 m/s^{2}, a_{min} = 3 m/s^{2}, and d = 0.3 s. The collision probability curve (A curve) and the collision probability curve (B curve) after twostage braking are shown in Figure 9.
5.2. Simulation Results Analysis of Four Modes
Through the simulation results from the four modes, by comparing the collision probability curve (A curve) and the collision probability curve (B curve) after twostage braking, the twostage braking strategy could reduce the collision probability that was more than 50% within 2 s to nearly 0%. The twostage braking strategy shifted the collision probability curve (A curve) to the right so that most of the curve falls in the Ilevel region. Before the twostage braking, most of the curve fell in the IIlevel and IIIlevel regions. Finally, the simulation results showed that the intelligent rightturning vehicle collision probability calculation algorithm could calculate collision probability and the twostage braking algorithm significantly reduced the collision probability which can improve safety.
5.3. Comparative Analysis
To verify the rationality of the collision probability curve calculation algorithm, we compared and analysed the collision probability curves generated using three different initial positions. Taking scenario 1 as an example and leaving the size of the two vehicles unchanged, we designed three different initial positions and changed the initial coordinates of the second vehicle, as shown in Table 2.

The collision probability curves (A curve) for the three different initial positions are shown in Figure 13.
From Figure 13, we can conclude that the collision probability was increasing from position 1 to position 3 within the period from 1 to 4.5 s, and the closer the distance between the two vehicles was, the higher the collision probability is. Therefore, the calculation algorithm of the collision probability curve (A curve) can be verified.
For the same reason, to verify the rationality of the twostage braking strategy, we compared and analysed the collision probability curves after twostage braking generated using three different initial positions. Taking scenario 1 as an example and leaving the size of two vehicles unchanged, we designed three different initial positions and changed the initial coordinates of the second vehicle, as shown in Table 3.

The collision probability curve (B curve) after twostage braking using three different initial positions is shown in Figure 14.
From Figure 14, we can conclude that the collision probability was increasing from position 1 to position 3 within the period from 2.5 to 4.5 s, and the closer the distance between the two vehicles is, the higher the collision probability is. Therefore, the twostage braking strategy can be verified.
6. Conclusion
(1)Compared with the safety distance model, the safety model based on TTC can more intuitively reflect the degree of danger. The twostage braking strategy can lower the warning level. Aiming to reduce an intelligent rightturning vehicle’s collision probability, we established a threelevel warning mechanism and drew the warning figure. Based on Monte Carlo stochastic simulation, we established the collision probability calculation algorithm for an intelligent rightturning vehicle at an intersection and plotted the collision probability curve on the warning figure. The area where the probability curve was located outputs the warning level.(2)The twostage braking strategy was established to actively avoid a collision if the collision probability reaches 50% within 2 s. We analysed four modes for a rightturning vehicle and simulated the collision probability curve (A curve) and the collision probability curve (B curve) after twostage braking. Finally, we changed the initial position for comparative analysis and verification.(3)The simulation results from the four modes showed that the collision probability reached 80% in the 2 s before active collision avoidance, and the collision probability of some modes could reach 100%. The twostage braking strategy reduced the collision probability to nearly 0% in 2 s, and the collision probability was reduced to less than 5% in 3 s, which improves safety significantly.(4)The collision probability curve calculation algorithm and the twostage braking strategy were verified and analysed. By comparing three different initial positions, the comparison results showed that the collision probability curve calculation algorithm and the twostage braking strategy were reasonable.(5)We used the Monte Carlo method to calculate the collision probability; collision warning and avoidance were carried out to reduce the collision probability of a rightturning vehicle. Our research laid the foundation for future experiments, and we will carry out experimental analysis better in future. Through future experiments, we can perfect the collision warning and avoidance algorithm.
Data Availability
All data generated or analysed during this study were included in this article. All data and models used during the study appear in the submitted article. Part data were calculated from the algorithm and the code.
Conflicts of Interest
The authors declare that there are no conflicts of interest.
Acknowledgments
This project was supported by the National Natural Science Foundation of China (Grant nos. 51875237, 51675224, and 51675224).
Supplementary Materials
The supplemental files are the program file compression package. (Supplementary Materials)
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Copyright © 2020 Chuanliang Shen 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.