This paper presents the design of an integrated longitudinal and lateral controller for autonomous vehicle and field tests with an electric vehicle. First, the longitudinal design was studied which includes the spacing policy as the upper level controller and throttle and brake control as the lower level controller. A safety spacing policy was proposed considering both the vehicle states and the vehicle capability. A coordinated throttle and brake controller was also designed to ensure the vehicle pursuing the desired acceleration. Second, a multimodel lateral controller was proposed which can perform the lane tracking and lane changing manoeuvres. Then, an integrated control structure was proposed to manage both the longitudinal and lateral controller. Finally, simulation and visualization works were carried out to validate the proposed solutions. An electric vehicle experiment platform was also built, and field tests showed encouraging results.
With the increasing demands of traffic safety, efficiency, environment protection etc., the automated vehicle and electric vehicle have been the hot topics for researchers and automobile manufactures. Normally, automated vehicle and electrified vehicle belong to different research fields, and significant progresses have been made in both fields separately in the past decades. However, progress regarding the integration of the two fields is still insufficient. Combining the two technologies within one vehicle appears to be an attractive and promising solution to cope with the many challenges of the future transportation [
The concept of vehicle automation was introduced by the General Motors Futurama exhibited at the 1940 New York World’s Fair [
Longitudinal and lateral controls are the two main aspects in automated vehicle control. The longitudinal control system needs to handle several challenges, such as vehicle safety, fuel economy, string stability and traffic flow stability, and riding comfort. The longitudinal control system can be designed to be hierarchical with upper and lower levels, where the upper level controller determines the desired acceleration of the controlled vehicle, while the lower level controller decides the operations of the accelerate and brake actuators to pursuit the desired acceleration [
The spacing policy and its associated control law constitute the upper level controller, where the vehicle is considered a mass point, and the vehicle powertrain dynamic is neglected. Constant (velocity independent) as well as variable spacing policies (velocity dependent) have been proposed by Rajamani et al. [
The lower level controller within the longitudinal control system is closely associated with the vehicle powertrain dynamics. Fixed gain and gain scheduling PID controllers and a multiple surface sliding control method were proposed and validated through simulation and field test for the traditional powertrain vehicles [
Lateral control research is also a challenging issue to be further studied to improve traffic safety, mobility, and efficiency. Lane keep and lane change are the basic functions of the lateral control system. Similarly, the control architecture can also be designed to be hierarchical with two levels: strategy level and control level. Regarding the strategy level, different approaches have been proposed, such as trapezoidal acceleration trajectory for the lane change manoeuvers in [
In the control level, for the traditional Ackermann steering system, many results have been given in former researches. In [
Integrated longitudinal and lateral control is also a challenging issue. In [
In this work, at first, we propose a longitudinal control system including a safety spacing policy and a coordinate accelerate and decelerate controller to improve vehicle safety and efficiency. Second, a vehicle velocity-adaptive lateral control system is proposed, which does not need the exact vehicle model and can deal with vehicle model uncertainty. Then, the integration of longitudinal and lateral control system is proposed. Finally, simulation works are carried out to verify the proposed control method, and a case study on a low-speed electric vehicle platform is also demonstrated.
Figure
Structure of the vehicle longitudinal control system (reproduced from [
When a human driver decides the intervehicle spacing, he considers not only the vehicle states but also the vehicle capability and environment conditions. Inspired by this, we proposed a safety spacing policy (SSP) as follows [
Then, the spacing error of SSP is given by
In Figure
Intervehicle spacing with different safety coefficients
Parameters value.
Parameters |
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Value | 6.5 m | 4.5 m | 0.1 s | 0.4 | −7.32 m/s2 |
The string stability of a string of vehicles refers to a property in which spacing errors are guaranteed not to amplify as they propagate towards the tail of the string [
Let
Taking Laplace transforms of (
Therefore, from the requirement of inequality (
The inequality constrain is always satisfied if
The traffic flow stability refers to a macroscopic property associated with speed and density of traffic in a section of a highway. The traffic flow is stable if the gradient of the traffic flow volume with respect to highway vehicle density is positive [
For the SSP, the traffic density at the steady state is given by
We can get the aggregate velocity
Then, the traffic flow is
The
The coordinated throttle and brake control system is proposed to realize vehicle longitudinal control, and it contains throttle controller, brake controller, and switching block, as shown in Figure
Coordinated throttle and brake switching control system.
The vehicle speed error
To imitate human driver’s experiences, the vehicle speed error
Hence, the vehicle longitudinal control task is represented as “IF-THEN” linguistic format, and each of member functions is divided into 5 sets; i.e.,
Variables of the throttle fuzzy controller.
Rule table of the throttle fuzzy controller.
Input 2: acceleration error | ||||||
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Nb | Ns | Null | Ps | Pb | ||
Input 1: speed error | Nb | D-inten | D-inten | D-sof | D-sof | Null |
Ns | D-inten | D-sof | D-sof | Null | A-sof | |
Null | D-sof | D-sof | Null | A-sof | A-sof | |
Ps | D-sof | Null | A-sof | A-sof | A-inten | |
Pb | Null | A-sof | A-sof | A-inten | A-inten |
The structure of the brake controller is actually the same with the throttle controller, except for the brake incremental value
The current brake output becomes
In order to make the separated throttle and brake controller working coordinately, a logic switch block is required. The basic functions of the logic switch are as follows: Avoid simultaneously operations at both throttle and brake pedals Before stepping down the throttle, step off the brake and vice versa Avoid frequent switches from one pedal to the other
To achieve these purposes, a switching logic is constructed by the vehicle current status to determine which action should be operated, i.e., throttle output
Flowchart of switch logic.
A “bicycle model” of the vehicle lateral dynamics with two degrees of freedom is considered. The bicycle model can be represented into the standard state space equation [
It can be found that the longitudinal velocity
Based on the divide-and-conquer strategy, the multimodel fuzzy controller is designed to deal with the parameter variations in vehicle lateral dynamics. Multimodel approaches develop local controllers corresponding to typical operating regions. The global control output is obtained by the integration of local ones.
With the consideration of the vehicle velocity in highway operation, we divide the velocity range into four regions. In addition, an overlap of 10 km/h is set for two adjacent regions to avoid the hard switch between the adjacent controllers. The operating regions are shown as low [0, 35], medium-low [25, 65], medium-high [55, 95], and high [85, 120] km/h.
The frame of the multimodel lateral control system is illustrated in Figure
Multimodel fuzzy controller structure.
For each local controller, the fuzzy algorithm with the same structure is used for steering angle control. However, more simple structure is adopted for each local controller, compared with the longitudinal controller, which benefits from the subdivision of vehicle lateral dynamic. The lateral deviation
Variables in the multimodel fuzzy controller (reproduced from [
Membership function variables (reproduced from [
Local controllers | ||||
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Low | Medium-low | Medium-high | High | |
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−0.2/0.2 | −0.3/0.3 | −0.4/0.4 | −0.5/0.5 |
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−10/10 | −6/6 | −4/4 | −3/3 |
|
−20/20 | −12/12 | −8/8 | −6/6 |
Fuzzy rule base (reproduced from [
Input 2: angular error | ||||
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Left | Center | Right | ||
Input 1: lateral error | Left | RightB | RightS | Center |
Center | RightS | Center | LeftS | |
Right | Center | LeftS | LeftB |
The fusion block is designed to integrate the four local controllers into a global one. In fact, the fusion block determines the weighting coefficient of each local controller. It can be described as
The longitudinal and lateral controllers have been designed in the previous sections. However, a global control system, which can perform the two control tasks simultaneously, is preferred for vehicle automatic driving. Hence, the integration of longitudinal and lateral controllers is presented in this section.
The uncoupled longitudinal and lateral control system has been proposed by Wijesoma et al. [
Uncoupled longitudinal and lateral control system.
It has been noticed that vehicle velocity can severely impact both longitudinal and lateral dynamics in the previous sections. The velocity is the variable controlled by the longitudinal controller, while it is the input variable of the lateral controller. Therefore, the integrated control system, in which the longitudinal and lateral controllers are coupled, is developed to perform better performance, as shown in Figure
Integrated control system.
A two-vehicle platoon is considered. The leader is a manually driven vehicle, and the follower is an automatic vehicle equipped with the proposed longitudinal control system which includes the upper and lower controllers, as described in Section
The horizontal road condition is first considered. The simulation scenario is described as follows: at beginning, the two vehicles run at a constant speed of 10 m/s. And then, the leading vehicle’s speed is gradually increased to a high speed of 26 m/s. After that, it begins to decelerate to the speed of 5 m/s. Successionally, the leading vehicle accelerates back to the speed of 20 m/s. The profile of the leading vehicle’s speed and acceleration is detailed in Figures
Leading (a) vehicle speed and (b) vehicle acceleration.
The follower’s speed and speed error are shown in Figures
Following (a) vehicle speed and (b) vehicle speed error.
Figures
Control results of (a) throttle and (b) brake (horizontal road) percentage.
In this test, the road grade is considered. We use the same two-vehicle platoon and the same scenario that we used in the former test. The road grade profile is given in Figure
(a) Road grade. (b) Speed error. (c) Throttle percentage and (d) brake percentage (control output (inclined road)).
The results of the following vehicle’s speed error are given in Figure
The proposed lateral controller is also tested with a bicycle model. The parameters can be found in Table
Parameter of the vehicle model.
Parameters |
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Value | 1485 kg | 2872 kg·m2 | 1.1/1.58 m | 42000/42000 N/rad |
Vehicle lateral control results (a, c, and d are reproduced from [
Furthermore, the uncertainties of the vehicle parameters are also considered. From equation (
Parameter variations.
Mass (kg) | Movement inertia (kgm2) | Cornering stiffness (N/rad) | |
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Case 1 | 1300 | 3000 | 36500 |
Case 2 | 2300 | 4000 | 55000 |
Vehicle lateral control results under different loads: (a) lateral position errors; (b) lateral acceleration responses.
The cosimulation with Matlab/Simulink and AMESIM is also carried out to test the proposed control system with more realistic vehicle models and test environments. Furthermore, the visualization of simulation can also be realized by using AME Animation function, which can facilitate the analysis and demonstration of the results.
A vehicle dynamics model with 15 degrees of freedom is established in AMESIM, including suspension module, aerodynamic module, tire, road, sensors, powertrain unit, braking system, and steering system. The testing path is also designed by using the Reference Trajectory Designer APP of AMESIM. The track is 1.54 km long with various road profiles, as shown in Figure
Test in Matlab and AMESIM cosimulation platform: (a) test path; (b) desired vehicle velocity; (c) vehicle steering angle output; (d) vehicle lateral position error; (e) visulization scenario.
The path tracking lateral position error and steering angle, which are measured by the virtual sensors of AMESIM libraries, are shown in Figures
The Rapid Control Prototype was established based on a modified low-speed electric vehicle using dSPACE MicroAutoBox II to test the proposed control algorithms. The vehicle is a rear-wheel drive vehicle using a central electric motor, and the front axle is the steering axle. The throttle, brake, and steering system of the vehicle were well modified to perform the autonomous driving task, as shown in Figure
Low-speed electric vehicle experiment platform.
Different scenarios of longitudinal and lateral motion control experiments were carried out. The velocity following scenario including acceleration and deceleration operations was performed, as shown in Figure
Longitudinal and lateral control test results: (a) velocity control results; (b) steering control results.
In this paper, the integrated longitudinal and lateral control system for autonomous vehicles has been studied, and a case study on a low-speed electric vehicle was carried out to validate the proposed solutions. Some conclusions are obtained: A safety spacing policy was proposed, which considers both the vehicle states and vehicle capabilities. A coordinated throttle and brake controller was also designed for the vehicle to pursue the desired acceleration while ensuring smooth operation to reduce energy waste. The proposed fuzzy based controller is not a model-based approach, and it controls only the pedals. Therefore, it can be applied in either traditional powertrain or electrified powertrain. A multimodel fuzzy controller was applied to deal with the vehicle lateral control, which considers the influence of vehicle velocity variations on lateral dynamics. An integrated control structure was proposed, in which the longitudinal and lateral controllers were coupled for the fully automated vehicle motion control. It is robust to the variations in vehicle speed and coupling effects between longitudinal velocity and lateral dynamics. Simulations and visualization works were carried out to validate the proposed controllers. A low-speed electric vehicle platform was also built to carry out field tests, and the results showed the proposed integrated control system can manage the longitudinal and lateral control task of the electric vehicle.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
The authors would like to express gratitude for funding from the National Natural Science Foundation of China (51965008), Science and Technology Projects of Guizhou ([2018]2168), and Excellent Young Researcher Project of Guizhou ([2017]5630).