To fully consider the impact of asphalt pavement rut on steering stability of autonomous vehicles, the sensitivity of various indicators of rut shape to vehicle stability was comprehensively measured, and pavement rut control standards based on comfort demands of autonomous vehicles were investigated. Firstly, a steering control system for autonomous vehicles was built in Simulink according to fuzzy control theory. Then, through orthogonal experiment design theory, different rut shape indicators are simulated in CarSim. The influence sensitivity of different rut shape indicators and the allowable rut range considering driving comfort were studied. The results show that both the rut depth and the rut side angle have a greater effect on the vehicle vertical acceleration within a certain parameter range. The maximum roll angle of vehicle body is mainly affected by the rut depth, and the rut width has a small effect on the vehicle driving stability. Meanwhile, considering human comfort, the rut side angle should not be greater than 1° when the rut depth reaches 2 cm. For autonomous driving, the rut depth should not exceed 2.5 cm. When the rut depth exceeds 2.5 cm, the vehicle body roll angle caused by the rut exceeds the inertial centrifugal force of the vehicle itself, which has a significant impact on the passenger comfort and safety.
At present, asphalt pavement is adopted over 80% of all kinds of roads built in the world [
Typical rut distress of asphalt pavement.
With the rapid development of driverless technology around the world, the unmanned driving of vehicles has also put forward higher requirements for road engineering. As the direct carrier of autonomous vehicles, the condition of road surface is undoubtedly the most important and direct impact on the driving safety. The existence of ruts will not only affect the driving comfort, but also the lateral stability and safety of the vehicle when it runs on the road. At present, the main type of the base of asphalt pavement in China is semirigid base, and the rut caused by the shear failure of pavement structure is fairly common. With the bump and pothole on the road surface, the rut makes it easy for water to gather and cause hydroplaning, which increases its influence on driving comfort, stability, and safety. Therefore, it is of great significance for the driving safety and applicability of autonomous vehicles to propose the corresponding rut threshold control standards.
A large number of experiments and practical investigations have been made on asphalt pavement rut [
In some developed countries, rut control is stipulated in relevant asphalt pavement specifications [
From the aspect of the vehicle, most of the researchers used CarSim to simulate the driving stability of vehicles [
In view of above research shortcomings, in order to provide reference for the control standard of ruts in the future engineering application, the influence of different rut indexes on driving stability and comfort of autonomous vehicles was investigated in this study. Then, rut threshold of asphalt pavement under different evaluation indexes of autonomous vehicle stability was put forward. We firstly established the steering control system based on the fuzzy control theory and then established the vehicle-road coupling models for different rut conditions in CarSim. Afterwards, the significance analysis of rut shape evaluation indexes was carried out by using orthogonal test design.
Based on the driving characteristics and human comfort demands of autonomous vehicles, this paper studies the threshold of asphalt pavement rut control for autonomous vehicles. In this study, we focus on the steering control behavior of autonomous vehicles built by CarSim/Simulink co-simulation. With considering vehicle steering stability and road surface rut shape, rut control threshold for different rut shape evaluation indexes was put forward according to orthogonal experimental design theory. The objectives and main contributions of this study are as follows: In CarSim, the typical A-class hatchback car model is selected as the vehicle body parameter simulated. To reflect the real rutting shape on road surface, rutting shape after geometric trapezoid regularization is defined in the uneven information of road cross section in CarSim. A steering control system for autonomous vehicles was built in Simulink according to fuzzy control theory, which can simulate the steering behavior by cosimulation of CarSim and Simulink. Limit steering rate and planning path are obtained to study the lane change process of autonomous vehicle. In Simulink, a triangular membership function is used in fuzzy control. Through the 7 fuzzy control subsets and 35 fuzzy control rules, the autonomous vehicle during the lane change process is realized. The orthogonal experimental design theory is applied to simulate the steering stability of autonomous vehicle by CarSim and Simulink cosimulation, rut threshold for different vehicle stability indexes is obtained. As far as we know, this is one of the first attempts in the self-driving area to evaluate steering stability considering road surface rut shape. In our opinion, this approach is of big significance to improve brake safety and comfort of autonomous vehicles.
Many kinds of vehicle models are preset in the CarSim database, including sedans, SUVs, and vans. According to relevant research [
We adopted the “Class A, Hatchback” model in the CarSim database, as shown in Figure
The data of A-class hatchback car in CarSim.
This paper aims to fully study the sensitivity of different indicators of rut shape on the driving stability of vehicles. In fact, the cross section of asphalt pavement with rut is usually an asymmetrical irregular shape formed by curves. Therefore, it is difficult to directly describe the actual rut shape with multiple indexes, so it is necessary to first geometric regularize the cross section to simplify it to trapezoid, as shown in Figure The elevation difference from the bottom of the rut to the highest point of the two shoulders is defined as The average inclination angle of the side of the rut is defined as The width at half of the rut depth is defined as
Architecture of rut shape of asphalt pavement. (a) Rut cross section. (b) Rut shape index.
The rut shape is defined in the “irregularity information” of the cross section in CarSim, in which the cross-section coordinates are equally divided at every 0.2 m along the width direction of the pavement with the pavement surface elevation recorded similarly. Meanwhile, to eliminate the sharp points of ruts after geometric regularization, further coordinate encryption is carried out on the basis of the original 0.2 m equidistant coordinate point. As this study mainly measures the influence of different rut shape indicators on the lateral stability of vehicles, the longitudinal change of rut shape is not considered [
Pavement rut parameter setting in CarSim.
Generally, during the normal lane change of the vehicle, the steering angle of the front wheel is the smallest, and the maximum steering angle is usually stable around 15°. Under the conditions of the vehicle turning around, it is usually necessary to take the limit steering angle of the vehicle front wheel, that is, about 40°. And during the turning process, the front wheel angle is usually between 15° and 40°. At present, in the steering control system of an autonomous vehicle, the above three different steering conditions are usually separated and controlled separately by different subsystems. At the same time, through a unified control center, the steering conditions required for autonomous vehicles are distinguished, and different subsystems are activated to control the steering process of the autonomous vehicles under different driving conditions. The Simulink toolbox in MATLAB was applied to compile the subsystem of lane change for autonomous vehicles. Furtherly, the Simulink control system was connected to the CarSim simulation interface to carry out the simulation of the lane change process of the autonomous vehicle to fully measure the influence of different rut patterns on the vehicle stability and driving comfort under the condition of autonomous driving.
In the lane change subsystem, the angle If If If If If If If If If If If If If If If If If If If If If If If If If If If If If If If If If If If
The fuzzy domain for the input and output variables is defined as [−3, 3]. As for the three different variables, their actual physics domains are different. For the actual physics domain, the lateral deviation
Regarding the determination of the membership function, the definition of two input variables
Membership functions of parameters. (a) Input parameter,
In this study, it is assumed that there is a virtual steering wheel in the autonomous vehicle. In the Simulink program, the steering angle of the wheel will be converted into the steering wheel rotation angle by a simple fixed expansion factor. Thus, by controlling the rotation angle of the virtual steering wheel, the steering angle of the front wheels is controlled indirectly. Among them, the relationship between the angle of the steering wheel and the lateral displacement of the steering lever is shown in Figure
Relationship between steering angle and lateral displacement of steering lever during steering process. (a) Angle of steering wheel-lateral displacement of steering lever. (b) Lateral displacement of steering lever-steering angle of rear wheel.
From Figure
In the path processing and lane changing system module in Simulink, the current location of the unmanned vehicle is located, so as to determine the corresponding line coordinate matrix data line for calculation control and output of the wheel steering angle. The coordinate matrix of path planning is [A
Architecture of the path matrix.
When the distance between the center of the vehicle mass and the end point coordinates
In order to ensure that the vehicle does not interfere with the operation of the vehicle in the third lane during the lane change process, the offset of the vehicle body centerline should not be greater than 5 m. The specific control program in Simulink is shown in Figures
Path handling and lane change subsystem.
Architecture of vehicle distance during lane change.
In the steering rate control process, this study uses the ratio to describe, that is, the ratio of the distance traveled by the vehicle in the driving direction to the vehicle lateral offset distance. In order to determine the limit steering rate under different vehicle speeds in the case of the automatic fuzzy control system, ased by steps of 5 m, and the lateral displacement of the vehicle after the lane change is 4 m. Each running speed corresponds to two adjacent lane change rates to determine the final limit lane change rate of autonomous vehicle at different speeds. In order to ensure that the vehicle body can be kept within the design path, the maximum steering rate simulated at different speeds, as shown in Figure
Limit steering rate design for different speeds. (a) Steering rate of 25 : 4 with a speed of 60 km/h. (b) Steering rate of 35 : 4 with a speed of 80 km/h. (c) Steering rate of 40 : 4 with a speed of 100 km/h. (d) Steering rate of 50 : 4 with a speed of 120 km/h.
At the speed of 120 km/h, setting the steering rate as 50 : 4 during normal driving process, the vehicle can reach the limit state where the body does not invade the third lane during operation. The maximum offset of the vehicle is close to 5 m, but the vehicle body remains in the preset lane. In the following simulation of rut threshold, the limit steering rate was adopted at the speed of 120 km/h, and the coordinate matrix of planning path (L (120)) is as follows:
The influence of road rutting on vehicle driving stability is mainly reflected in the two indexes of the vehicle vertical acceleration and vehicle body roll angle. The passenger comfort mainly depends on the change of speed, that is, vehicle vertical acceleration. Meanwhile, the ISO 2631–1 [
As the vehicle speed is large while the friction between tire and road surface is low, the vehicle will have a serious uncontrollable phenomenon during the steering process. In CarSim, set the vehicle speed of 120 km/h with steering rate of 25 : 1. With the friction coefficient of 0.1, the steering control process is conducted by the fuzzy control system for autonomous vehicles built in Simulink, and vehicle body coordinate point during lane change is as shown in Figure
Simulation with a vehicle speed of 120 km/h and friction coefficient 0.10. (a) The simulation interface in CarSim. (b) The vehicle lateral displacement plot.
During the process of vehicle change lane, the steering force provided by small road friction is too low, and the vehicle cannot achieve sufficient self-aligning torque. As a result, the vehicle cannot be controlled in the target lane in time, causing the body to invade the outer lane seriously, which seriously affects the safety of the vehicle when changing lanes. According to adjust the friction coefficient properly, as the friction coefficient is 0.14 at the speed of 120 km/h, the vehicle can reach the limit state where the body does not invade the third lane during operation, as shown in Figure
Simulation with a vehicle speed of 120 km/h and friction coefficient 0.14. (a) The simulation interface in CarSim. (b) The vehicle lateral displacement plot.
In order to study the influence degree of different rut shape indexes on vehicle stability during steering process, the combination design of different rut shape indexes was carried out by orthogonal experimental design theory in CarSim simulation. Three influence factors including rut depth, average rut width, and rut lateral angle are considered in the study. Thus, the L-9-3-4 orthogonal design table was selected for the combined design scheme, and set three levels for each factor. Then, the design scheme for the CarSim simulation is shown in Table
Results of orthogonal experimental design.
Test number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1.5 | 1.5 | 1.5 | 2 | 2 | 2 | |
1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | |
80 | 100 | 120 | 100 | 120 | 80 | 120 | 80 | 100 |
For rut mainly affects the lateral unevenness of the road surface, lateral lane change behavior is added in the simulation, so that the vehicle crosses the uneven section. Considering the most unfavorable situation, the limit speed of the highway is 120 km/h as the simulated speed, and the steering rate of the vehicle is 25 : 1 with road surface friction coefficient of 0.14.
In the simulation process, the vehicle vertical acceleration and roll angle are not only caused by rutting, but also the inertial centrifugal force of vehicle and suspension system performance. Therefore, in order to avoid the inertial effect of the vehicle during the steering process, it is necessary to deduct the simulation results of the vehicle on a completely flat road under the same working conditions. The simulation interface and the lateral displacement of the vehicle are obtained as shown in Figure
Simulation results of the orthogonal experiment design.
Test no. | Rut depth | Rut slide angle | Average rut width | Maximum vertical acceleration (g’s) | Vehicle roll angle (deg) |
---|---|---|---|---|---|
1 | 1.0 | 1 | 80 | 0.01668 | 0.026954 |
2 | 1.0 | 2 | 100 | 0.02207 | 0.022685 |
3 | 1.0 | 3 | 120 | 0.023782 | 0.019744 |
4 | 1.5 | 1 | 100 | 0.017902 | 0.039066 |
5 | 1.5 | 2 | 120 | 0.020326 | 0.031618 |
6 | 1.5 | 3 | 80 | 0.026792 | 0.037611 |
7 | 2.0 | 1 | 120 | 0.025492 | 0.066289 |
8 | 2.0 | 2 | 80 | 0.033325 | 0.054974 |
9 | 2.0 | 3 | 100 | 0.037105 | 0.046514 |
According to Table
Analysis results of the vehicle maximum vertical acceleration.
Factors | |||
---|---|---|---|
Average value 1 | 0.021 | 0.020 | 0.026 |
Average value 2 | 0.022 | 0.025 | 0.026 |
Average value 3 | 0.032 | 0.029 | 0.023 |
Range | 0.011 | 0.009 | 0.003 |
Analysis results of the maximum vehicle roll angle.
Factors | w (cm) | ||
---|---|---|---|
Average value 1 | 0.023 | 0.044 | 0.040 |
Average value 2 | 0.036 | 0.036 | 0.036 |
Average value 3 | 0.056 | 0.035 | 0.039 |
Range | 0.033 | 0.009 | 0.004 |
From Table
Selecting the maximum roll angle of the autonomous vehicle as the control index, only the rut depth needs to be considered. The allowable threshold was calibrated for the maximum rut depth. In the study, the rut depth was set as 1 cm, 1.5 cm, 2 cm, 2.5 cm, and 3 cm, respectively. When the vehicle drives on a completely straight road under the same condition, the maximum roll angle during the lane change process is 1.1063610°. The maximum roll angle of the autonomous vehicle caused by rut is shown in Figure
Simulation results of the vehicle maximum roll angle.
Based on the principle that the maximum roll angle of the vehicle body caused by rutting should not exceed the maximum roll angle of the vehicle during the lane change process, the rut depth under unmanned driving conditions should not exceed 2.5 cm. When the rut depth exceeds 2.5 cm, the vehicle body roll angle caused by the rut exceeds the inertial centrifugal force of the vehicle itself, which has a significant impact on the passenger comfort.
For further simulation of the maximum vertical acceleration of the vehicle, rut depth and rut side angle were selected as variables. When the rut side angle is set as 1°, the rut depth cannot reach 2.5 cm and deeper depth under the normal rut width range. However, when the rut side angle changes from 2° to 3°, the rut depth can reach 3 cm within the rut width range. Therefore, when the rut depth is greater than or equal to 2.5 cm, the rut side angle is only 2° and 3°. When the rut depth is less than 2.5 cm, there are three rut side angles, such as 1°, 2°, and 3°.
As the rut depth and rut side angle increase, the maximum vertical acceleration of autonomous vehicle will increase significantly. However, the maximum vertical acceleration of the vehicle did not exceed 0.5 m/s2. According to the standard ISO 2631–1, the passenger comfort level for different acceleration ranges is specified corresponding. The simulation experiment results are distinguished according to the two categories of “comfortable” and “slightly uncomfortable”, as shown in Table
Comfort zone division based on the standard ISO-2631.
Comfortable | Slightly uncomfortable | ||||
---|---|---|---|---|---|
1.0 | 1 | 0.163464 | 2.0 | 2 | 0.326634 |
1.0 | 2 | 0.216286 | 2.0 | 3 | 0.363678 |
1.0 | 3 | 0.233044 | 2.5 | 2 | 0.337512 |
1.5 | 1 | 0.17542 | 2.5 | 3 | 0.462756 |
1.5 | 2 | 0.199234 | 3.0 | 2 | 0.321538 |
1.5 | 3 | 0.262542 | 3.0 | 3 | 0.486766 |
2.0 | 1 | 0.249802 | — | — | — |
The results in Table When the rut depth is 1.5 cm or less, regardless of the rut side angle value (not more than 30°), the vehicle vertical acceleration can be kept within the “keep comfortable” range. When the rut depth is increased to 2 cm, only the rut side angle is less than or equal to 1°, the vertical acceleration of the vehicle can be kept within the “keep comfortable” state. If the rut depth or rut side angle continues to increase, passenger will feel “slightly uncomfortable.” As the rut side angle reaches 3° and the rut depth reaches 2.5 cm or 3 cm, the maximum vertical acceleration of the vehicle during the lane change process will be close to 0.5 m/s2, and the passenger comfort will be significantly affected.
According to the above analysis, for the maximum vertical acceleration of autonomous vehicles, the rut depth should generally not be greater than 1.5 cm considering the passenger comfort. Moreover, when the rut depth reaches 2 cm, the rut side angle should not be greater than 1°.
Based on the cosimulation of CarSim and Simulink, the fuzzy control theory is used to build the steering control system of autonomous vehicles. The orthogonal experimental design theory was adopted to combine different rut shape indexes. And the driving stability of autonomous vehicles on the rut road during the lane change process was simulated in CarSim. Reference to the allowable rut range of passenger comfort, rut control threshold of asphalt pavement was studied. The main research conclusions are as follows: Rutting has a significant effect on the stability of the autonomous vehicle. When considering the maximum vertical acceleration of the car body during the lateral crossing of the rut, the rut depth and the rut side angle both have significant impact, while the rut width influence can be ignored. For the roll angle of the vehicle, only the influence of rut depth needs to be considered. Considering the influence of pavement rut, the rut depth should generally not be greater than 1.5 cm to ensure the passenger comfort. Moreover, when the rut depth reaches 2 cm, the rut side angle should not be greater than 1°. Under unmanned driving condition, the rut depth should not exceed 2.5 cm. When the rut depth exceeds 2.5 cm, the vehicle body roll angle caused by the rut exceeds the inertial centrifugal force of the vehicle itself, which has a significant impact on the passenger comfort. In the rut threshold control standard, because the influence of rut width on the maximum roll angle and the maximum vertical acceleration of the vehicle body is small in the simulation analysis of the orthogonal test, the rut width may not be regarded as the control standard.
Due to the lack of relevant evaluation standards for human comfort for the roll angle of vehicle, this study does not give the rut control threshold recommendations for the roll angle as an evaluation index. Furtherly, this work still needs to be studied combing with the field test.
The simulation data used to support the findings of this study are included within the article.
The authors declare that they have no conflicts of interest regarding the publication of this paper.
The study was financially supported by the National Natural Science Foundation of China (no. 51778139).