In this study, we propose an adaptive path planning model and tracking control method for collision avoidance and lane-changing manoeuvres on highways in rainy weather. Considering the human-vehicle-road interaction, we developed an adaptive lane change system that consists of an intelligent trajectory planning and tracking controller. Gaussian distribution was introduced to evaluate the impact of rain on the pavement characteristics and deduce adaptive lane-change trajectories. Subsequently, a score-based decision mechanism and multilevel autonomous driving mode that considers safety, comfort, and efficiency were proposed. A tracking controller was designed using a linearised model predictive control method. Finally, using simulated scenarios, the feasibility and effectiveness of the proposed method were demonstrated. The results obtained herein are a valuable resource that can be used to develop an intelligent lane change system for autonomous vehicles and can help improve highway traffic safety and efficiency in adverse weather conditions.
Weather is an important factor that affects traffic and road safety. Nearly, 75% of all traffic accidents are caused due to slippery pavement and around 47% of traffic accidents occur on the rainy days of the year [
An intelligent lane change system for autonomous vehicles must address two critical issues—path planning and tracking control. Path planning for lane changing is a localised motion that occurs in real-time and is closely related to the vehicle dynamics and parameters relating to the external environment, such as the decision time and adhesion coefficient of pavement. Tracking control is based on the goal defined by path planning and must provide tracking accuracy and robust stability. Over the past few years, a significant amount of progress has been achieved in this field [
Classical path planning strategies using search-based and random sampling methods, such as A
Based on the lane-change path planning method, the decision system determines a reasonable path, and a control module executes the selected lane-change trajectory. A significant amount of research has been conducted on control methods [
Traditional methods of path planning and control have played a positive role in the study of autonomous vehicles. However, most existing models only consider vehicle dynamics and seldom consider the impact of the characteristics of an intelligent driver and the road on driving safety in rainy weather. Furthermore, previous studies have focussed primarily on straight roads, without paying much attention to curved sections. Vehicle lane changing on a curved highway to avoid a collision is a relatively complex working condition that synchronously involves both steady-state and transient steering, coupled with a wide range of real-time state changes. Therefore, it is prone to instability and can cause chain rear-end collisions, especially in rainy weather.
There are three main considerations in this scenario: the first is to determine the safe distance for lane changes on a typical dangerous curved and slippery road section, which clarifies the influence of the road environment on active obstacle avoidance and path planning; the second involves a method to generate an intelligent decision, called hierarchical scoring, through which the system can make an optimal driving decision, considering multiple and conflicting objectives; the third is a real-time trajectory planning and following architecture that is designed based on different lane-change scenarios. Overall, we present a systematic approach from behavioural decision making and path planning to control execution for autonomous vehicles, based on Gaussian distribution, scoring, and convex optimisation, such that optimal paths and velocity profiles are generated to safely execute vehicle movement. This study can serve as a reference to develop the environmental suitability of an autonomous vehicle control system and improve the safety and efficiency of the advanced transportation system.
This study considers lane changing in an autonomous vehicle on a curved highway in rainy weather, which is a relevant real life situation. The rest of this paper is laid out as follows: Section
tRainfall, especially moderate to heavy rainfall, reduces visibility, blurring the sight of the driver and increasing response time. According to [
Distribution box diagram of vehicle speed in various rainfall conditions.
In rainy weather, a water film layer exists between the tyre and the pavement, decreasing the road adhesion coefficient, maximum lateral force, and brake force. The thickness of the water film is mainly affected by the rainfall intensity, slope length, slope angle, and roughness of the road surface [
Setting
Rain has a significant influence on the adhesion coefficient of the road and the vehicle tyres, which can decrease by about 60%. As a result, the tyre saturated lateral force cannot supply the vehicle steering centrifugal force. Consequently, sideslip is more to likely to occur while steering on a highway. In general, the vehicle acceleration threshold in rainy conditions is lower and can be calculated as
The typical performance when vehicle sideslip occurs is a sharp turn, as shown in Figure
Comparison of vehicle driving tracks on normal and slippery roads.
The plane movement of a vehicle lane-change manoeuvre on a curved road is shown in Figure
Plane movement of vehicle lane-change on curved road.
As shown in Figure
The steering inputs can be divided into two separate inputs: steady state cornering with fixed radius and transient steering with variable radii. Based on this idea, the vehicle lateral dynamics can be integrated by the turning motion and the lane changing motion, and the vehicle lateral velocities in
In general, the minimum radius of a curve on highways in plains and hilly areas is more than 600 m. Thus, the road curvature and vehicle yaw angle while changing lanes at high speed on a curved highway section are relatively small. Introducing the improved Gaussian distribution from [
Generally, a vehicle brakes or changes lanes to avoid a colliding with an obstacle or a slower vehicle. Changing lanes is better than braking as it is more efficient. In addition, owing to the high speeds and lower adhesion coefficient on highways during rainy weather, a longer safe distance should be taken to avoid collisions. Therefore, a combination of lane changing and longitudinal speed control is a safer and more efficient alternative. Two lane changing modes with constant speed and deceleration are discussed herein.
On account of the small yaw angle of the vehicle (generally, < 10°), the vehicle longitudinal velocity in the ground coordinate system
The safe distance is defined as the minimum distance required for the vehicle to safely change lanes or avoid a collision with the vehicle or obstacle ahead. To calculate the minimum safe distance, the critical lane changing state must be analysed based on the critical position relationship with the vehicle ahead, as shown in Figure
Critical position relationship for safe lane change.
As shown in Figure
Figure
The minimum safe distance is defined as the longitudinal driving distance required to just complete obstacle avoidance. It is closely related to the relative speed and the critical time
The relative speed can be obtained using GPS or sensors, and consequently, the key to calculate the minimum safety distance is to determine
According to equation (
The proposed model was validated using the autopilot mode of a physics-based simulation platform called PreScan, developed by Siemens, Germany. As an active safety experimental platform, PreScan can build scenes based on the actual road environment and sensor model and is an advanced and professional development tool. Therefore, it is widely used in the automotive industry to develop Advanced Driver Assistance Systems (ADASs) and autonomous vehicles.
Using PreScan, a vehicle lane-change scenario for collision avoidance was simulated, considering a two-way four-lane highway with a curved section and moderate rainfall. The vehicle and road parameters were set up as listed in Table
Basic parameters of the simulation vehicle and road.
Road width (m) | Road adhesion coefficient | Curve radius (m) | Initial velocity (m/s) | Vehicle width (m) |
---|---|---|---|---|
3.75 | 0.53 | 650 | 30 | 2 |
Comparative verifications with different simulation tools. (a) Lateral velocity at constant speed and 0.4 Hz steering. (b) Global trajectory at constant speed and 0.4 Hz steering.
As shown in Figure
Detailed comparison by different simulation tools.
Mode | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
PreScan | 30 | 650 | 0.5 | 0 | — | 0.4 | 3.5110 | 0.0904 | 2.1151 | 2.52 | 80.5250 |
−2 | 3.5908 | 0.1020 | 2.1485 | 2.46 | 75.0523 | ||||||
Lane-change model | 0 | 5.4 | 3.3707 | 0.0736 | 2.0666 | 2.41 | 77.3690 | ||||
−2 | 5.3 | 3.4417 | 0.0849 | 2.0991 | 2.36 | 72.3509 | |||||
Error % | 0.4 | 4.00 | 18.58 | 2.29 | 4.37 | 3.92 | |||||
4.15 | 16.76 | 2.30 | 4.07 | 3.60 |
As shown in Figure
An autonomous vehicle must be able to make the right decision and plan a reasonable path according to the external situation detected by the perception sensors on the vehicle, such as radar, CCD, and inertial gyroscopes. Consequently, the decision mechanism must generate an appropriate path and provide the basis for the control inputs, making it an important part of an autonomous driving system. Considering driving safety, comfort, and efficiency, we propose a scoring reference-based lane-change decision mechanism for collision avoidance on a curved road with low adhesion and formulate a four-mode decision-making rule based on the safe lane-change model.
Considering a relative velocity of 30 m/s between the autonomous vehicle and the vehicle (or obstacle) ahead and using simple driving modes (e.g., constant speed and braking with a deceleration of 2 m/s2), we proposed decision-making scoring references, as listed in Table
Hierarchical scoring reference with relative velocity of 30 m/s.
Hierarchy | Performance | Driving mode steering frequency (Hz)/brake deceleration (m/s2) | Maximum acceleration, | Minimum safe headway, | Evaluation parameter | Score |
---|---|---|---|---|---|---|
1 | Overall | — | — | — | — | |
2 | Safety | — | ≤ | Δ | Δ: difference between headway and minimum safe headway | |
3 | Comfort | 0.1/0 | 1.5973 | 192.5480 | Maximum acceleration | |
0.2/0 | 2.0718 | 117.2420 | ||||
0.1/2 | 2.5900 | 146.2759 | ||||
0.3/0 | 2.7085 | 90.8600 | ||||
0.2/2 | 2.9122 | 102.3528 | ||||
0.4/0 | 3.3707 | 77.3690 | ||||
0.3/2 | 3.3839 | 83.1736 | ||||
0.4/2 | 3.9806 | 72.1616 | ||||
0.5/0 | 4.2781 | 68.8610 | ||||
0.5/2 | 4.8007 | 65.1585 | ||||
4 | Efficiency | 0.5/2 | 4.8007 | 65.1585 | Minimum safe headway | |
0.5/0 | 4.2781 | 68.8610 | ||||
0.4/2 | 3.9806 | 72.1616 | ||||
0.4/0 | 3.3707 | 77.3690 | ||||
0.3/2 | 3.3839 | 83.1736 | ||||
0.3/0 | 2.7085 | 90.8600 | ||||
0.2/2 | 2.9122 | 102.3528 | ||||
0.2/0 | 2.0718 | 117.2420 | ||||
0.1/2 | 2.5900 | 146.2759 | ||||
0.1/0 | 1.5973 | 192.5480 |
Table
Based on the scoring references under specific circumstances, a four-level lane-change mode for collision avoidance is proposed, as listed in Table
Four-level lane-change mode for collision avoidance.
Mode | Host vehicle initial velocity (m/s) | Application condition | Optional driving mode steering frequency (Hz)/brake deceleration (m/s2) | Score | Optimal driving mode steering frequency (Hz)/brake deceleration (m/s2) |
---|---|---|---|---|---|
1 | 30 | 0.2/0 | 8.4 | 0.2/0 | |
0.3/0 | 6.8 | ||||
0.2/2 | 5.8 | ||||
0.4/0 | 5.2 | ||||
0.3/2 | 4.2 | ||||
0.4/2 | 3.5 | ||||
0.5/0 | 2.7 | ||||
0.5/2 | 1.9 | ||||
2 | 0.3/0 | 6.8 | 0.3/0 | ||
0.2/2 | 5.8 | ||||
0.4/0 | 5.2 | ||||
0.3/2 | 4.2 | ||||
0.4/2 | 3.5 | ||||
0.5/0 | 2.7 | ||||
0.5/2 | 1.9 | ||||
3 | 0.4/0 | 5.2 | 0.4/0 | ||
0.3/2 | 4.2 | ||||
0.4/2 | 3.5 | ||||
0.5/0 | 2.7 | ||||
0.5/2 | 1.9 | ||||
4 | 0.5/2 | 1.9 | 0.5/2 |
Table
Model predictive control (MPC) was developed in the late 1970s and includes methods such as dynamic matrix control (DMC) and model algorithmic control (MAC). It is a well-known and effective control algorithm and has found widespread acceptance in industry. The major advantage of MPC is its ability to handle multivariable interactions and operating constraints in a systematic manner. Essentially, it is a type of optimisation method based on objective functions, and rolling horizon optimal control is achieved by model-based state prediction, optimisation with constraints in a finite time domain, and feedback correction. This section presents a detailed MPC controller derived from a nonlinear four-degree-of-freedom (4-DOF) vehicle model that can simultaneously track the reference planned path and velocity.
Considering the longitudinal and lateral coupling movement of a vehicle during typical steering dynamics, we established a 4-DOF vehicle model based on reasonable simplification, involving front wheel steering and vehicle longitudinal, lateral, and yaw motions:
Setting
The function of a controller is to guarantee tracking and robust stability considering the nonlinear effect of the vehicle.
For an MPC controller, linearisation and discretisation can be used to improve the real-time performance of the controller. The nonlinear vehicle dynamic model can be linearised as a linear time invariant (LTI) state space form, using the first order approximation of the Taylor expansion. Subsequently, the linearised model can be discretised as
While designing the controller, constraints must be set to ensure that the autonomous vehicle can precisely and stably track the trajectory references generated during intelligent path planning. The constraints designed herein primarily include two aspects—one related to the vehicle control quantity and the other related to the vehicle state quantity:
In addition to tracking the reference precisely and stably, the controller must also keep the vehicle running at the desired speed. The cost quadratic function is
According to [
The solution of the quadratic program problem can be solved using
Figure
Structure of the safe lane-change intelligent control system.
Two typical scenarios were defined to verify the performance of the designed controller. The first is a simple lane-change scenario to evaluate the controller against other conventional methods, such as single preview and PID. The second scenario is a continuous curve with multiple lane-changes. The details of the two scenarios are as follows: An autonomous vehicle travelling at 20 m/s, with a steering frequency of 0.2 Hz and a decision time of 1.5 s, on a straight highway. An autonomous vehicle travelling at 30 m/s, with a steering frequency of 0.4 Hz and a distance of 80 m to avoid collision with obstacles, on a continuous curved road composed of three parts with circular arcs of 600 m radii.
The control performance of the first scenario was verified by comparing the proposed controller with conventional control algorithms, such as a PID controller and a controller without path planning, as shown in Figure
Model comparative study of controller. (a) Global path. (b) Tracking error. (c) Lateral velocity. (d) Yaw angle.
Figure
The multiple decision-making and anticollision control performance of the MPC controller were verified based on the second scenario. The simulation results are shown in Figure
Control effects of specific modes for anticollision on a curved road. (a) Global path. (b) Tracking error. (c) Longitudinal velocity. (d) Lateral velocity. (e) Lateral acceleration. (f) Yaw rate. (g) Control inputs of AFS and DYC. (h) Control inputs of longitudinal forces.
Figure
Based on the vehicle steering and lateral dynamics in rainy weather, we introduced Gaussian distribution to the lateral dynamics of an autonomous vehicle for decision making and path planning. In particular, the scenario of an autonomous vehicle travelling on a curved highway section in rainy weather was considered herein. The main conclusions are The Gaussian distribution function could perfectly describe the lateral dynamics of the vehicle. The related parameters were easily fitted, and the characteristics of autonomous vehicles, including reaction, response, pavement condition, and lane-change status, were accurately and quantitatively obtained. The reaction time of decision-making and path planning, steering frequency, delay times of vehicle lateral dynamics, road adhesion coefficient, and completion probability of lane change were determined as well. In a typical scenario, the proposed lane-change model could be applied to the path planning process of a vehicle lane-changing manoeuvre. Based on the lane-change model, the minimum safe distance for collision avoidance was obtained. The lane-change decision mechanism utilises a scoring system that considers driving safety, comfort, and efficiency and serves as a reference for intelligent path planning. Using convex optimisation, an MPC controller with AFS and DYC was designed and verified. The results of the typical scenarios considering an autonomous vehicle in rainy weather demonstrated that the proposed controller has good tracking and robust stability. This study offers practical value as it considers the cooperative relationship between humans, vehicles, the road, and the environment and can serve as valuable reference in the development of autonomous driving systems.
The results obtained herein are of significant importance for numerous applications and provide a valuable reference for future studies involving actual vehicles. Compared to traditional studies on lane-change manoeuvres, the novel trajectory model, decision mechanism, and control algorithm proposed herein can describe the system characteristics under various road alignments and operational environments. However, considering the complex environmental influences on man-machine interactions, further research is required. The multifactor coupling characteristics of the environmental impact must be studied further. Typical examples include the interference between the perception sensors on the vehicle that detect the external environment. Notably, human driving behaviour always forms the basis for autonomous vehicle development. Consequently, a systematic study of personified decision-making is required to ensure coordination between humans and the environment. Furthermore, considering the field of cooperative vehicle-infrastructure systems, a cooperative decision-making and control strategy with swarm intelligence for multiple vehicles or vehicle fleets should be studied in depth.
The data used to support the findings of this study are available from the first author and the corresponding author upon request.
The authors declare that there are no conflicts of interests regarding the publication of this article.
This work was partially sponsored by the State Key Laboratory of Automotive Safety and Energy under Project No. KF2013, the Joint Laboratory for Internet of Vehicles, Ministry of Education, China Mobile Communications Corporation, under Project No. ICV-KF2018-02, the National Natural Science Foundation of China (No. 51775565), the Tianjin Science and Technology Project (Grant Nos. 16PTGCCX00150, 17ZXRGGX00070, 18YFZCGX00380, and 119YFSLQY00010), the Tianjin Development and Reform Commission Project (Grant No. TJZNZZ1811), the University Foundation of Tianjin University of Technology and Education (Grant No. KYQD 1710), and the Fundamental Research Funds for the Central Universities (Grant No. 18lgpy83). The first author would like to thank Dr. Su L.L., Dr. Guan Z.W., Dr. Hou H.J., Li J.K., Liu X.L. and Tong Y.K. for valuable discussions to improve the quality and presentation of this paper.