A variable weight adaptive cruise control strategy based on lane change recognition of leading vehicle

The traditional adaptive cruise system is responsible for delay in recognizing the cut-in/cut-out behaviour of front vehicle, and there is significant longitudinal acceleration of the vehicle fluctuation leading to reduced driver’s comfort level and even dangerous situation. In this paper, the next generation simulation data set and back propagation (BP) neural network are used to train the vehicle lane change recognition model to recognize the lane change behaviour of the preceding vehicle. The higher controller adopts variable weight linear quadratic optimal control to adjust the weight parameters according to the recognition results of front vehicle to reduce the fluctuation of vehicle acceleration. The lower layer adopts fuzzy proportional-integral-derivative (PID) control to follow the expected acceleration and builds the vehicle inverse dynamic model. Through CarSim/Simulink co-simulation, the results show that, under the cut-in or cut-out and working conditions, the behaviour of the leading vehicle can be recognized, following target can be switched in advance, weight parameters can be adjusted and the large fluctuation of longitudinal acceleration can be reduced.


Introduction
Adaptive cruise control (ACC) system is an advanced auxiliary driving system developed with the foundation of the steady speed cruise, which can obtain the information of front vehicle speed and distance. With the data available from sensors and based on the application algorithm, the controlling behaviour of the vehicle remains stable with front car by significantly reducing the fatigue of the drivers [1]. In case of the adaptive cruise system, the main task of target identification is to select the main purpose of vehicle tracking and to carry out the acceleration control of vehicle based on the motion status information of the main target. When the vehicle at the front cuts into or cuts out of the main lane, an ACC system should have necessary or even advance response capability [2]. In this process, ACC vehicles may have challenges of late braking and excessive braking [3]. Therefore, managing to identify and respond to the behaviour of vehicles in front in advance is of great significance to improve the performance of the ACC system.
Many scholars have carried out in-depth research on the ACC system. Gao et al. [4] designed an ACC system that can identify driver online requirement to meet the needs of different driving modes. Liu et al. [5] proposed a new safe distance model based on the analysis of real driving test data to optimize the safety and comfort economy of the ACC system. In terms of control algorithms, there are several methods such as PID control, optimal control, model predictive control and other commonly used control algorithms [6]. Yang et al. [7] proposed ACC algorithm combining model predictive control and active disturbance rejection control by adopting hierarchical control algorithm. However, the online optimization process of model predictive control algorithm needs repeated optimization calculation, and the calculation cost is high, so it is difficult to ensure the real-time requirements of the system [8,9]. Xu et al. [10] proposed a control strategy based on optimal control in which adaptive cruise and lane keeping system can run simultaneously. Due to the complexity of actual traffic, linear quadratic optimal (LQR) control with fixed weight coefficient is unable to meet the performance requirements of the ACC system. Based on this, a variable weight LQR control algorithm is proposed to solve the expected follow acceleration in real time.
ACC system mostly adopts the hierarchical control structure. The upper control algorithm produces the desired acceleration required for safe follow according to the current driving environment. The lower controller switches control through throttle and brake, so that the actual acceleration of the vehicle can track the expected acceleration of the upper controller [11]. However, due to the vehicle's own nonlinear and external interference factors, the lower controller has poor robustness and the control effect is difficult to achieve the desired effect [12]. Therefore, fuzzy PID control is used in the lower layer as described in this paper, so that the actual acceleration can quickly and stably follow the expected acceleration.
Currently, most studies on the ACC system are only able to control the vehicle target in the main lane, and the following target can only be replaced when the vehicle in the adjacent lane completely cuts into or cuts out of the main lane [13]. This leads to the phenomenon of lag in cutting recognition of the front vehicle, increasing the driver's sense of panic and excessive braking reduces ride comfort. Therefore, the ACC system based on cut-in vehicle recognition has important practical significance. Moon et al. [14] calculated the lane change probability of leading vehicle through the fuzzy controller to perform the target fusion of leading vehicle. Chen et al. [15] proposed a method to identify and quantify the possibility of vehicle access. Lane changing behaviour of vehicles has certain regularity. In the recent years, many scholars use machine learning methods to identify lane changing behaviour of vehicles. Zeisler et al. [16] used the information collected by sensors to predict the cut-in behaviour of surrounding vehicles using Bayesian network. Díaz-Álvarez et al. [17] used artificial neural network to build the lane change decision model. Remmen et al. [18] used machine learning algorithms such as support vector machines to identify the cutting vehicles. Jin et al. [19] proposed a lane changing behaviour decision-making model based on the Gauss mixture hidden Markov model. In addition, Do et al. [20] proposed different lane changing behaviour models based on various scenarios.
Through analysis, it is found that most of the existing studies have the following limitations. First, the prediction time is delayed, the information source is single, and the lane changing behaviour of drivers cannot be fully characterized, and the prediction accuracy is low. Second, most of the test data are obtained by driving simulators, which are very different from the real environment and the driver's psychological state. Based on this, in this paper, next generation simulation (NGSIM) data set of American expressways is used to train the lane change recognition model of the vehicle ahead using BP neural network.
Aiming at the above problems, a variable weight ACC strategy based on lane changing behaviour recognition of the vehicle ahead is proposed in this paper. The main contributions are summarized as follows: (1) The lane changing characteristics of vehicles are extracted using NGSIM data set, and the vehicle lane changing recognition model is obtained using BP neural network offline training. According to the information collected by sensors, the lane changing behaviour of the vehicle in front is identified online. The results show that the trained model can accurately identify the lane changing condition of the vehicle in front, switch to follow the main target in advance and reduce the driver's discomfort caused by the sudden jump of the main target. (2) According to different driving conditions of the vehicle in front, the weight coefficient adjustment strategy of the LQR control algorithm is designed. Compared with the fixed weight algorithm, the proposed control algorithm can adjust the objective function in real time and reduce the fluctuation of acceleration. This makes ACC control more in line with the driver's decision-making process and improves driving safety and riding comfort. (3) The design details of the ACC system which is provided in this paper adopt a hierarchical control structure, and the upper layer adopts LQR control to obtain the expected acceleration considering relative velocity, relative distance and selfacceleration. In order to avoid time-varying vehicle parameters and external interference, fuzzy PID control is adopted in the lower layer to make the actual acceleration track the expected acceleration quickly and accurately.
The rest of this paper is organized as follows. Section 2 introduces the overall design framework of the ACC system. Section 3 introduces how to train the lane changing recognition model based on BP neural network using NGSIM data set. The ACC layered control algorithm and weight adjustment strategy are introduced in Section 4. In Section 5, details of the simulation analysis and comparison experiments carried out to verify the effectiveness of the control strategy are provided. Finally, the summary of the main conclusions is provided in Section 6.

Overview of the ACC system
The overall design framework of the ACC system is shown in Figure 1. The speed, acceleration, and position information of the leading vehicle can be calculated based on the relative distance and speed between the main vehicle and the leading vehicle information collected by the sensor. Based on the vehicle lane changing data available from US highway data set NGSIM, the vehicle lane changing recognition model was obtained by offline training with BP neural network, in order to identify the lane changing condition of the previous vehicle online. The ACC strategy adopts layered control, and the upper layer adopts variable weight LQR control algorithm, which adjusts weight parameters according to different driving conditions of the vehicle in front. The lower layer adopts fuzzy PID control to avoid the influence of external interference and vehicle parameter consolidation which makes the actual acceleration difficult to track the expected acceleration quickly and accurately. In order to avoid vehicle accelerating and braking simultaneously, the braking and driving switching logic is designed. In addition, the corresponding throttle opening and braking master cylinder pressure are obtained through the vehicle inverse dynamics model. After acting on the main vehicle, the feedback adjustment is performed continuously according to the vehicle state at the next moment, so as to realize the function of the ACC system.

Introduction to recognition of front vehicle lane changing behaviour
Since there is no communication between the front and rear vehicles, for the rear vehicles, the intention of front vehicle's behaviour cannot be directly known, but the motion state parameters of the front vehicle can be calculated through the relative motion relationship of the surrounding vehicles detected by the sensor. The traditional adaptive cruise main target selection algorithm only controls the main target vehicle in the main lane. In order to accurately follow the main target and to reduce the discomfort feeling of the driver, the NGSIM data set is selected to extract the lane changing characteristic parameter of driving vehicles. Driving behaviour intention is divided into three types: lane change left, lane change right, and lane keep. The lane changing behaviour recognition was established based on the BP neural network model. Figure 2 shows the analysis of driving behaviours such as lane keeping and left-right lane changing when the vehicle is driving on a straight road. When the vehicle is in lane keeping state, its lateral movement will not have a large range, instead only a small change, and it will not appear a fixed movement state in a certain direction. In the process of lane change, the movement of vehicles in the lateral direction has an obvious trend

Data set selection and processing
In this paper, the vehicle trajectory data of US-101 provided by the NGSIM project of the Federal Highway Administration of the United States is selected as the research data [21]. This project uses the camera to sample every 0.1 s and obtains the vehicle trajectory data through video software processing, such as vehicle acceleration, speed, lane, and so on. Therefore, this data set is used in this paper to study the vehicle lane change recognition model, and the NGSIM data set to study the road section area as shown in Figure 3. In this study, vehicles in the NGSIM data set were selected as the research object to analyze their lane change characteristics. In order to avoid the influence of forced lane change behaviour and to obtain data on vehicles on and off the ramp, the data of lanes 1-5 were selected for this study. Table 1 shows the data on width of lanes in US-101 [22]. According to the lane width and the distance between the head centre and the left edge of the section, the distance between the vehicle and the lane line on the left side of the initial lane can be obtained.
The original NGSIM data is not filtered and has certain measurement error and noise. In order to reduce the influence of error, the Kalman filtering is adopted to process the vehicle trajectory data. Since the vehicle speed in the NGSIM data set is the speed in the driving direction, the longitudinal and transverse velocity data of vehicle cannot be obtained. Therefore, the changing rates of the horizontal and vertical coordinates of the vehicle can be obtained. Figure 4  transverse velocity fitting curve, and Figure 4(c) shows the longitudinal velocity fitting curve. As it is evident from these results, the transverse displacement data has no obvious change after filtering, while the transverse velocity and longitudinal velocity data smooth the fluctuation of data change after filtering and still reflect the driving behaviour characteristics of vehicles while changing lanes. Therefore, the filtered data is replaced with the original data. After

Lane change recognition of leading vehicle based on BP neural network
The method of vehicle lane changing condition recognition based on feature extraction combined with classification algorithm has been proved to have good feasibility and practicability [25]. In this paper, BP neural network is used to train lane changing intention recognizer based on vehicle lane changing data collected from actual road, and it is used to recognize lane changing condition online. According to the surrounding vehicle information obtained by the sensor, the specified characteristic parameters are extracted from the data and input into the trained recognition algorithm to output the real-time driving condition category. Considering the driving characteristics of vehicles, driving intention is divided into three categories: left lane changing, right lane changing, and lane keeping. Based on the corresponding driving behaviour characterization parameters, a lane changing intention recognition model of the vehicle in front is established. The working process of lane changing recognition is shown in Figure 5.
BP neural network usually includes input layer, hidden layer, and output layer, which is often used to deal with classification and nonlinear prediction problems. This algorithm has strong nonlinear mapping and self-learning ability, which is conducive for improving the identification accuracy [26]. The designed vehicle lane changing condition recognition network structure is shown in Figure 6. After the correlation analysis between characteristic parameters and lane changing conditions, the longitudinal velocity, lateral velocity, and the distance between the head centre and the left

Design of upper controller
The main purpose of the ACC system is to control the workshop spacing of two vehicles to ensure the safety of driving, and on this basis, it is optimized to meet the requirements of comfort, economy, and other multi-objectives [27]. In this paper, the upper controller is designed using LQR algorithm, and the longitudinal kinematic diagram of the two workshops is shown in Figure 9. The relative distance between the two vehicles is d, the expected distance of the following vehicle is d des , and the error of the expected distance is d.
In consideration of the complexity and practical safety of the model, the calculation method provided in Ref. [28] of the expected car-following distance using the timing distance is applied. The calculation formula for calculation is as follows: where τ h is the time interval between vehicles, v f is the vehicle speed, and d 0 is the minimum safe distance. The relationship between the actual acceleration and the expected acceleration of the main vehicle is regarded as the first-order inertial link: Taking d, v, and a f as state variables, a f as control input, and a p as system disturbance, the state equation can be obtained as follows: where For the car-following system, the controlling strategy is to make the actual distance between the main vehicle and the leading vehicle approach to the expected distance, and the speed of the main vehicle approach to the speed of the leading vehicle. That is, the vehicle distance error d and the relative speed v are required to approach zero.
A control index function considering vehicle distance, relative speed, and main vehicle acceleration is established as shown in Equation (4): where q 1 , q 2 , and q 3 are the weight coefficients of vehicle distance error, relative speed, and main vehicle acceleration, respectively; r is the weight coefficient limiting the jitter of the expected acceleration. Based on the LQR control theory, the minimum expected vehicle following acceleration of the index function J is sought.

Weight adjustment strategy
Compared with the traditional fixed weight coefficient LQR algorithm, a variable weight coefficient LQR controller for the driving condition of the vehicle in front is designed in this paper, so as to reduce the influence of large fluctuation of longitudinal acceleration caused by following the main target switch. Weight adjustment strategies are designed for different lane changing conditions of the front vehicle, as shown in Figure 10. Based on the coordinate information of the surrounding vehicles obtained by the sensor, the lane of leading vehicle relative to the main vehicle was analysed, the lane changing condition of the vehicle was identified by using the BP neural network, and the weight parameters were adjusted. The setting of parameter adjustment rules is divided into three cases. The first is that the leading vehicle cuts out of the lane, and the main car switches to the vehicle farther down the lane. The second is that the side car cuts into the lane, and the main car recognizes the target and switches to the cutting vehicle. The third is that the leading vehicle stays in the main lane, and the main car recognizes the target unchanged.
In the LQR algorithm, the larger the values of q 1 , q 2 , and q 3 , the more significant the expected distance, velocity difference, and acceleration are in the performance function, and the larger the value of r, the more important the control constraints are. In this paper, the values of q 1 , q 2 , and q 3 are adjusted, and r is selected as a fixed value. By analyzing the NGSIM data set and in combination with the practical situation of the road, it is found that cut into the main lane is usually due to vehicles in front and the vehicle speed is low, and lane changing the distance between car in left and the new target vehicle is greater than the expected distance, d positive, both relative velocity decreases, v is negative, should smooth deceleration. Therefore, q 2 and q 3 should be larger, q 1 is small, and the parameter is adjusted for (q 1 −, q 2+ , q 3+ ). When other lane to the main lane is generally slow down in turn into the main lane, lane changing the distance between the left in the car and the new target vehicle is less than expected, the relative velocity is smaller, d and v are negative, should slow down as soon as possible. Therefore, q 1 and q 2 should be larger, q 3 is relatively low, to avoid collision, and the parameter adjustment for (q 1+ , q 2+ , q 3− ). When the vehicle accelerates and cuts into the main  lane, v is positive. For the sake of driving safety, the weighted value of q 2+ is still adopted.

Lower controller design
Based on the strong nonlinear characteristics of the vehicle dynamics model, the precision of lower controller and the control performance are the precondition of the upper controller control functions. The actual road condition and of vehicles on the road are complicated, and because the engine in the vehicle dynamics and tyre model are showing strong nonlinear characteristics of conventional PID, it is difficult to achieve stable control effect. Fuzzy PID control, which can adjust PID parameters in real time through fuzzy rules, is suitable for nonlinear and time-varying control systems [29].
In order to make the actual acceleration track, the expected acceleration quickly and accurately, the lower controller adopts the fuzzy PID control principle in this study, and the fuzzy PID controller structure design block diagram is shown in Figure 11.
Deviation e is the difference between the expected acceleration a des and the actual acceleration a f of the vehicle; e c is the deviation change rate; k p , k i and k d are the three parameters of the PID controller; E and Ec are the input fuzzy values of the fuzzy controller, respectively. To establish the inverse dynamic system with PID controller module connection, the Simulink is used, and CarSim for the joint simulation for vehicle dynamics system. Under the simulation environment, by trial and error method, PID parameters adjusted repeatedly, parameters to get ideal value rule is analyzed, and fuzzy controller is used to adjust parameters k p , k i and k d .
In this paper, two-dimensional fuzzy control is used to realize real-time parameter tuning. Seven language variables are set, namely PB  The scaling factor k acon is The fuzzy set of language variables is described by a membership function. The input membership function adopts Gaussian membership function, and the output membership function adopts triangular membership function, as shown in Figure 12.
The essence of fuzzy control rules is to summarize the control experience obtained by experts in this field according to a large number of experiments, and then obtain the set of fuzzy conditional statements. The fuzzy rule table is formulated by referring to the summary of simulation experience of parameters at different times, as shown in Table 2. Figure 13 shows the output surface viewer, which can intuitively show the corresponding relationship between the input and output of the three parameters k p , k i and k d .
The designed fuzzy PID controller was joined with the vehicle inverse dynamics module, and the cosimulation was conducted with the vehicle dynamics system in Carsim to verify the control performance of the designed controller. The simulation condition is that the initial speed of the vehicle is set as 100 km/h, and the expected acceleration signals of step variation are set as −2 m/s 2 and −4 m/s 2 . The simulation time is 10 s. After simulation verification, the obtained vehicle acceleration curve is shown in Figure 14.
As can be seen from the simulation results, the control output of the actual acceleration in about 0.17 s to   Table 4. Main parameters of LQR controller.
Parameter Value reach the desired acceleration has rapid response ability and is able to control the actual stable output to a desired acceleration. Moreover, this can steadily control the actual acceleration, and the simulation results show that controller has strong robustness.

Comparative analysis simulation
In order to verify the correctness of the algorithm proposed in this paper, the ACC system model and layered control algorithm based on BP neural network for lane change identification of leading vehicle are built in the Matlab/Simulink environment. Key parameters of LQR controller are obtained according to the methods mentioned in Refs. [30,31] and simulation test results were obtained. The simulation parameters of Carsim are shown in Table 3, and the key parameter settings of LQR controller are shown in Table 4. In this study, two different scenarios are simulated, in which the main vehicle is always on road, but due to the different behaviours of the vehicle in front, the autonomous vehicle is adjusted accordingly to meet the control requirements. In order to better conform to the actual road scenario, the vehicle simulation environment is set according to the US-101 road environment. Trad-LQR is a LQR control method based on traditional target recognition, Pre-LQR is a LQR control method with fixed weight combined with BP neural  the relative velocity v = −5 m/s. The fixed weight will cause a large fluctuation of acceleration. In this case, a steady deceleration is required, and the weight parameter should be adjusted as (q 1− , q 2+ , q 3+ ), as shown in Figure 16 The test results are shown in Figure 17.
As can be seen from Figure 17, Pre-LQR recognizes the entry of a vehicle in an adjacent lane 1.68 s before the lane change point, and the deceleration peak is about −1.44 m/s 2 , while Trad-LQR deceleration peak is −1.69 m/s 2 . As shown in Figure 17(c), although Pre-LQR can operate the actuator in advance, the fixed weight coefficient LQR acceleration fluctuates significantly. When the target switches to C, the expected spacing error d = 18 m, the relative speed v = −4 m/s and the adjustment of variable weight coefficient is shown in Figure 17(d). The results show that the peak deceleration of Pre-VM-LQR is about −0.89 m/s 2 , which is 47.33% lower than that of Trad-LQR, and the acceleration change is smoother and the overshoot is smaller. ACC vehicles can slow down in advance and reduce braking strength.
As it can be seen from Figure 19, the lane changing behaviour recognition model based on BP neural network training recognized the lane changing behaviour recognition model based on BP neural network training at 4.48 and 0.87 s earlier than the traditional adaptive cruise algorithm. When the target switches to F , the expected spacing error d = −12.5 m and the relative speed v = −4 m/s. In this case, it is necessary to slow down as soon as possible, adjust the value of the weighting parameter to (q 1+ , q 2+ , q 3 −), and the weight coefficient change curve is shown in Figure 19(d). According to Figure 19(c), the maximum deceleration rate of Trad-LQR is −2.96 m/s 2 , the maximum deceleration rate of Pre-VM-LQR is   Figure 20.
As can be seen from Figure 20, the Pre-LQR recognizes the entry of the vehicle in the adjacent lane 1.52 s before the lane change point, and the peak deceleration is about −2.18 m/s 2 , with gentle acceleration change and small overshoot. As shown in Figure 20(c), the peak value of Trad-LQR deceleration is −2.88 m/s 2 , and the peak value of Pre-LQR deceleration is −2.58 m/s 2 . When the target switches to C, the expected spacing error d = −7.1 m and the relative speed v = −3.6 m/s. The adjustment of variable weight coefficient is shown in Figure 20(d). The results show that the peak deceleration of Pre-VM-LQR is 24.31% lower than that of Tard-LQR and 15.50% lower than that of Trad-LQR. The control strategy proposed in this paper can identify the cutting condition of the vehicle ahead earlier, avoid the phenomenon of forced movement of the vehicle and reduce the fluctuation of acceleration.

Conclusion
In this paper, a variable weight ACC control strategy based on BP neural network to identify the lane changing behaviour of the vehicle in front is proposed. The main purpose is to solve the problems of the ACC system being insensitive to the lane changing behaviour of the vehicle in front, braking too late or too fast. The lane changing characteristics of vehicles were extracted from NGSIM data set, and BP neural network was used to train the lane changing behaviour recognition model of the vehicle ahead offline. The lane changing behaviour recognition of the vehicle in front is integrated into ACC control strategy, and ACC vehicle is controlled before the vehicle arrives at the lane changing point. According to different working conditions of the vehicle in front, the weight coefficient adjustment strategy is designed to improve the LQR control algorithm. ACC system adopts hierarchical control strategy, and the lower controller adopts fuzzy PID control, so that the actual acceleration of the vehicle can follow the expected acceleration stably. In this paper, CarSim and Matlab/Simulink are used for co-simulation, and different experimental conditions are established to analyze and compare the proposed control strategy.
The simulation results show that under different lane changing conditions, lane changing recognizer can identify different lane changing behaviours in advance, and ACC vehicles can switch to follow the main target in advance. The variable weight LQR controller can adjust the weight coefficient according to different working conditions to avoid the occurrence of strength braking and even danger. This not only ensures the driving safety of driver but also ensures the riding comfort, and reduces the fear caused by the late switching of following the target.
Due to the limited experimental conditions, only simulation analysis is carried out in this study. If the subsequent conditions allow, further hardware-in-theloop or real vehicle tests will be carried out to verify the control algorithm and to make the control strategy more accurate. The ACC system proposed in this paper only considers the longitudinal control of the vehicle, but for the actual driving process of the vehicle, such as turning, the lateral and longitudinal movement of the vehicle is inseparable. Therefore, in future studies, the influence of main target identification and lateral control of the ACC system on the system under curves will be comprehensively considered.

Disclosure statement
No potential conflict of interest was reported by the author(s).