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 right-turning vehicle’s collision warning and avoidance. We put forward an algorithm based on Monte Carlo simulation to calculate the collision probability between the right-turning vehicle and another vehicle (or pedestrian) in intersections. We drew collision probability curves which used time-to-collision as the horizontal axis and collision probability as the vertical axis. We established a three-level 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 two-stage braking strategy is applied. Taking four right-turning collision conditions as examples, the two-stage 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 two-stage 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 two-stage braking strategy are validated and analysed. The results verified the rationality of the collision probability curve calculation algorithm and the two-stage braking strategy.

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 right-turning 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 right-turning condition was special and relatively complex [

In intersections, the intelligent vehicle’s turning condition was a complex traffic scene which possesses a high accident rate [

The current research is summarized as follows:

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 right-turning vehicles.

The current research focused on pedestrian intention prediction and identification, without considering the right-turn 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.

At present, AEB early warning and active intervention were mature, but there was relatively little research on early warning of traffic conflicts during the right-turn process. Current research lacked the calculation of collision probability for a vehicle on a right-turning course. The early warning mechanism should be introduced into the field of right-turn collision warning.

In order to calculate the collision probability accurately, extensively covering all possible collisions during right-turning, and actively avoiding a collision, the system described in this paper not only calculated the collision probability and designed the three-level 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 right-turning vehicle’s collision warning and avoidance. We established a three-level 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 two-stage braking strategy was applied. Therefore, we calculated the probability of collision, through the warning level and active intervention to improve the safety of the right-turning process and reduce the accident rate.

Our study analysed the right-turning condition and predicted four different collision modes during the right-turning process. The CWS was designed for each collision scenario, and the two-stage 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 two-stage braking strategy were validated and analysed. This control scheme’s technical roadmap is shown in Figure

The control scheme’s roadmap.

Schematic diagrams of the four modes.

The collision warning and avoidance algorithm’s main process was as follows:

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 right-turning 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 right-turning vehicle (scenario 3); and a collision between a right-turning vehicle merging into the lane and another vehicle existing in the lane (scenario 4). The four modes are shown in Figure

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 three-level warning figure.

We output the warning level through the three-level warning region and performed the two-stage braking strategy in the specific scenario.

In our study, we adopted the collision safety model based on time-to-collision (TTC) [

The total delay was as follows: the time in which driver included stimulation (_{1}), identification and decision time (_{2}), time to control action (_{3}), and braking system delay time (

To ensure safety, it was necessary to ensure the safety time threshold (_{s}) greater than the sum of delay (_{sum}), so the CWS needed to take actions before _{sum}, as expressed by the following equations:

_{sum} was generally within 3 s [_{s} should be greater than 3 s. To reach reliable intelligent vehicle safety during right-turning conditions, the collision warning and avoidance algorithm was designed for a TTC of 5 s.

The three warning levels for right-turning collisions of intelligent vehicles [

I-level: it is low collision probability; vehicle’s right-turning process was safe, so the warning system did not warn the driver.

II-level: the intelligent vehicle had a certain collision probability; the warning system reminded the driver by displaying a yellow light in the dashboard.

III-level: 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 two-stage 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 [

Division of three-level collision warning regions.

Three-level warning mechanism | TTC | TTC |
---|---|---|

I-level region (I-region) | { | { |

II-level region (II-region) | { | {PC | TTC/30 + 7/30 ≤ PC ≤ 0.1 TTC + 0.3} |

III-level region (III-region) | { | { |

Three-level collision warning regions.

The vehicle’s right-turning 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 right-turning vehicle was _{1} and the width W_{1}. A second vehicle’s length was _{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 right-turning vehicle is _{1}, and the angle with the _{1}. Another vehicle’s velocity was _{2}, and the angle with the _{2}. The vehicle’s coordinate system is shown in Figure _{1}) crossed into the second vehicle’s or pedestrian’s safety profiles, a collision occurs.

Vehicle’s coordinate system.

Many scholars regarded the car as a contour [

When another vehicle collides with the right-turning 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 (_{1} + _{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

Vehicle’s safety profile.

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 (_{1})/2. The pedestrian’s safety profile is shown in Figure

Pedestrian’s safety profile.

Monte Carlo simulation theory was based on the central limit theorem and the large number theorem [_{i} was unknown, Σ_{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 {_{i}} as an independent random variable and part of a sequence of identically distributed random variables, with an expected value of ^{2}, as shown in

_{i} were obtained, the closer the distribution was normal, which was the basis of Monte Carlo simulation theory for collision probability.

_{1} and _{2} and the right-turning radius ^{2} as the variance [

Flowchart of the collision probability calculation algorithm based on Monte Carlo simulation.

The calculation process of collision probability for four modes was as follows. First, the right-turning vehicle’s angle (_{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 _{1} and the right-turning vehicle’s coordinates (_{1}(_{2}(

The calculation of angle _{1} was shown in

To calculate the position coordinates (_{1},_{,} the second vehicle was regarded as stationary and the reverse speed _{2}(

When the condition met the scenario 1, the right-turning vehicle’s coordinates (

When the condition met the scenario 2, the right-turning vehicle’s coordinates (

When the condition met scenario 3, the right-turning vehicle’s coordinates (

When the condition met scenario 4, the right-turning vehicle’s coordinates (

The second step, in the _{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 (

The collision between the right-turning 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 (

An intelligent right-turning vehicle collision warning and avoidance algorithm needed a braking strategy to realize active collision avoidance.

We established the two-stage braking strategy. The two-stage braking strategy could select the braking strength independently according to the TTC so that high-efficiency 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 two-stage braking strategy was as follows:

II-stage braking: if the collision probability reached 50% within 1 s (whether it reached III-level warning within 1 s), we used the II-stage braking with the amount _{max}. In the braking process, we considered the braking deceleration (

I-stage braking: if the collision probability reached 50% within 1-2 s (whether it reached III-level warning within 1-2 s), we used the I-stage braking with the amount _{min}. For the same reason as in the II-stage braking process, we considered the braking deceleration (

The two-stage braking strategy.

The time-domain integral operation of the acceleration obtained the decrease in velocity, Δ

The two-stage braking strategy had two sets of formulas, and equation (

Equation (

Therefore, in each simulation, the right-turning vehicle speed _{1}(

The position coordinates (_{t}, _{t}) of the vehicle were updated at time

Scenario 1: collision probability curve (

Scenario 2: when the vehicle turned right into the lane, it was difficult to find pedestrians who were crossing the road in the lane, so it was easy to cause serious traffic accidents. The parameters in this scenario were defined as follows: pt = 0.01 s, _{1} = 8 m, _{1} = 2 m, and _{1}, _{2}, and _{1} ∼ _{2} ∼ _{2} represented the velocity of the pedestrian in this case. We used the two-stage braking strategy; the specific parameters were as follows: _{max} = 6 m/s^{2}, _{min} = 3 m/s^{2}, and

Scenario 2: collision probability curve (

Scenario 3: because the driver had blind spots in vision, it is possible for the right-turning vehicle to collide with pedestrians crossing the road. The parameters in this scenario were defined as follows: pt = 0.01 s, _{1} = 8 m, _{1} = 2 m, and _{1}, _{2}, and _{1} ∼ _{2} ∼ _{2} represented the velocity of the pedestrian in this case. We used the two-stage braking strategy; the specific parameters were as follows: _{max} = 6 m/s^{2}, _{min} = 3 m/s^{2}, and

Scenario 3: collision probability curve (

Scenario 4: the parameters in this scenario were defined as follows: pt = 0.01 s, _{1}, _{2}, and _{1} ∼ _{2} ∼ _{max} = 6 m/s^{2}, _{min} = 3 m/s^{2}, and

Scenario 4: collision probability curve (

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, _{1}, _{2}, and _{1} ∼ _{2} ∼ _{max} = 6 m/s^{2}, _{min} = 3 m/s^{2}, and

Through the simulation results from the four modes, by comparing the collision probability curve (

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

Parameters of three different initial positions (

Initial positions | _{1} (m/s) | _{2} (m/s) | pt (s) | ||||
---|---|---|---|---|---|---|---|

Position 1′ | 9 | 12 | _{1} ∼ | _{2} ∼ | 0.01 | 5 | |

Position 2 | 8 | 11 | _{1} ∼ | _{2} ∼ | 0.01 | 5 | |

Position 3 | 7 | 10 | _{1} ∼ | _{2} ∼ | 0.01 | 5 |

The collision probability curves (

Collision probability curves (

From Figure

For the same reason, to verify the rationality of the two-stage braking strategy, we compared and analysed the collision probability curves after two-stage 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

Parameters of three different initial positions (

Initial positions | _{1} (m/s) | _{2} (m/s) | pt (s) | T (s) | _{max} (m/s^{2}) | _{min} (m/s^{2}) | ||||
---|---|---|---|---|---|---|---|---|---|---|

Position 1′ | 9 | 12 | _{1} ∼ | _{2} ∼ | 0.01 | 5 | 6 | 3 | 0.3 | |

Position 2 | 8 | 11 | _{1} ∼ | _{2} ∼ | 0.01 | 5 | 6 | 3 | 0.3 | |

Position 3 | 7 | 10 | _{1} ∼ | _{2} ∼ | 0.01 | 5 | 6 | 3 | 0.3 |

The collision probability curve (

Collision probability curve (

From Figure

Compared with the safety distance model, the safety model based on TTC can more intuitively reflect the degree of danger. The two-stage braking strategy can lower the warning level. Aiming to reduce an intelligent right-turning vehicle’s collision probability, we established a three-level warning mechanism and drew the warning figure. Based on Monte Carlo stochastic simulation, we established the collision probability calculation algorithm for an intelligent right-turning 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.

The two-stage braking strategy was established to actively avoid a collision if the collision probability reaches 50% within 2 s. We analysed four modes for a right-turning vehicle and simulated the collision probability curve (

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 two-stage 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.

The collision probability curve calculation algorithm and the two-stage 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 two-stage braking strategy were reasonable.

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 right-turning 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.

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.

The authors declare that there are no conflicts of interest.

This project was supported by the National Natural Science Foundation of China (Grant nos. 51875237, 51675224, and 51675224).

The supplemental files are the program file compression package.