Research on Adaptive Cruise Systems Based on Adjacent Vehicle Trajectory Prediction

Abstract

Vehicles in the adjacent lane making abrupt lane changes is a common and frequent action during traffic movement. Being aware of adjacent vehicles ahead of time, determining their cut-in intention, monitoring their cut-in trajectory in real time, and actively adjusting following speed are all critical for adaptive cruise systems for vehicles. This study proposes a flexible following-factor-calculation approach that considers the driver’s willingness to take risks for the purpose of identifying cut-in intent, predicting trajectory, and narrowing the window for following cruise speed adjustment to improve passenger ride comfort. To begin, a lane-change trajectory prediction algorithm based on driver adventitious factor correction is proposed in order to correctly predict the lane-change trajectory of adjacent vehicles in urban road traffic scenarios. Second, the flexible following factor and the flexible switching factor of the following target are constructed to overcome the influence of the uncertainty caused by internal and external disturbances on the vehicle following the motion process, and to reduce the impact of cut-in events on passenger comfort. An anti-disturbance rejection control and an adaptive cruise controller based on the vehicle’s longitudinal inverse dynamics model are proposed in order to compensate for and suppress the internal perturbations caused by the vehicle’s internal parameter changes and the random disturbances caused by external road environment changes. The results of simulation and real-world testing showed an average of 28% improvement in passenger comfort.

1. Introduction

In the United States, driver error is to blame for 93% of accidents according to the National Highway Traffic Safety Administration. There are no adequate accident prevention strategies from the driver’s perspective alone, even though the number of accidents has fallen due to technological advancements. A more advanced variation of the cruise control system is ACC [1,2,3], in which information about the intended vehicle is gathered using millimeter waves, and through specific target screening algorithms and control tactics, the vehicle moves at a strategic output speed and follows the vehicle in front of it [4]. Most companies that actively deploy the ACC system take into account environmental data linked to safety [5,6,7,8]. Mitsubishi, the first firm to suggest ACC, created a preview distance control system that immediately matches a vehicle’s speed to the laser ranging system. While this method was being developed, numerous businesses performed in-depth studies of cruise control systems [9,10].

Speed control is the core factor determining the following effect and performance, and the common ACC speed control algorithmincludes traditional control methods and hierarchical control methods. The class control method can optimize the whole system by using a loss function trained in a data-driven manner without building physical models such as vehicle models and environment models. This method greatly reduces the workload of researchers and mainly uses fuzzy control, natural heuristic optimization technology, neural network control, and hybrid control. Similar to traditional control methods, hierarchical methods mainly use PID control, model-based control, sliding film control, LQR control, model predictive control (MPC), fuzzy control, and stochastic optimization control [11].

Hadi Kazemi et al. [12] designed a specific stochastic model predictive controller (SMPC) that is responsible for adjusting the dynamics parameters of the vehicle and incorporating the cut-in probability output through a neural network to enhance its response to dangerous cut-in maneuvers. Xue-Wen Chen et al. [13] proposed a multi-objective fuzzy controller of lane changes for critical targets on straight roads that pre-judges dangerous lane changes. Wei Yuan et al. [14] proposed a lane-change maneuver prediction method for the vehicle ahead by constructing a hidden Markov model to optimize the control algorithm of the adaptive cruise control system used to evaluate the target vehicle. Jun Yao et al. [15] trained a sliding window support-vector-machine-based lane-change intention prediction algorithm to identify the lateral position lane-change intention of the current vehicle in the current lane. Next, the target vehicle selection algorithm was studied under three different conditions—safe lane change, dangerous lane change, and lane-change cancellation—based on the lane driving intention and collision threat of the target vehicle. The results showed that the target vehicle selection algorithm was able to ensure the smooth transfer of the target vehicle when safely changing the lane-change maneuver of the target vehicle, thus reducing the longitudinal acceleration fluctuation of the target vehicle. The proposed target vehicle selection algorithm had a faster response than the target vehicle selection method of the conventional ACC system in hazardous lane-change situations. Hyun Soo Park et al. [16] proposed multiple classifications for various driving situations using a multilevel SVM. This method provided better performance in predicting object motion behavior compared to conventional radar systems, enabling ACC systems to decelerate early or accelerate smoothly. Aris Polychronopoulos et al. [17] proposed algorithms with a hierarchical structure to combine traffic environment data with vehicle dynamics to accurately predict the trajectory of intelligent vehicles, allowing active safety systems to notify and warn the driver or intervene when an emergency occurs, which can enhance adaptive cruise control and continuous fluctuation by reducing the false alarm rate. Donghan Lee et al. [18] proposed a combination of convolutional-neural-network (CNN)-based lane-change intention inference and a prediction controller to address the impact of adjacent lane vehicle cut-in on adaptive cruise control systems. The algorithm provides superior inference performance and improves safety and comfort. Another paper by Donghan Lee [19], using a graphical modeling framework and probabilistic inference, synthesized human driver intent inference algorithms that can predict the lane changes of other traffic participants in advance, using only data from standard vehicle sensors to predict lane changes approximately 1.5 s earlier than commercial systems. N.K. et al. considered a strategy to map the state of the driving environment to the parameter weights of MPC through a deep neural network to compute the weight changes when there is a vehicle cut-in scenario with discrete binary states in order to improve situational awareness while enhancing the overall tracking performance of the algorithm [20]. Dominik et al. studied a simplified stochastic short-term prediction model for the lane-change trajectories of peripheral traffic participants [21]. The prediction model inputs are the actual lateral position in the lane, speed, and turn signal, and the model was incorporated into an MPC-based ACC approach, of which the results showed that the merging of prediction models can significantly improve comfort and efficiency when vehicles merge in front of intelligent vehicles. Yoon et al. proposed a method based on a radial basis function network (RBFN) using an artificial neural network to accurately compute the likelihood of multiple target lanes and trajectories of surrounding vehicles [22]. The collision uncertainty associated with the future uncertainty of the proposed prediction algorithm can be handled using the chance-constrained model predictive control (CCMPC) constraint. Multiple risky cut-in scenarios are targeted to achieve higher collision avoidance success rates while using smaller actuator inputs and providing higher ride comfort. However, due to the limitations of the control method structure, the above methods have disadvantages such as not considering driver characteristics and traffic constraints, resulting in lower prediction intention and trajectory accuracy, while not considering the influence of internal and external disturbances on the longitudinal control of the vehicle; thus, the anti-interference ability for the vehicle interior and exterior is low, i.e., when the internal and external environment changes, the control effect will be affected to different degrees. To cope with handling different numbers of heterogeneous target agents and jointly considering multiple factors that may affect their future movements, Mo et al. [23] proposed a three-channel framework and a novel heterogeneous edge-enhanced map network (HEAT), which produced a final displacement error (FDE@3sec) of 0.66 m in the test results, demonstrating the feasibility and effectiveness of the proposed method. S. Dai et al. [24] proposed eighty targeted solutions and a trajectory prediction model integrating a semi-supervised graph (AOG), and a spatio-temporal LSTM (ST-LSTM) was built. The concept of submaneuvers was introduced in order to improve vehicle motion classification based on a given coarse maneuver label. Experiments showed that it is a flexible and fast model for trajectory prediction in various driving scenarios. Z. Zhao et al. [25] proposed a graph-based information sharing network (GISNet) that allows information sharing between a target vehicle and its surrounding vehicles. At the same time, the model encodes the historical trajectory information of all vehicles in the scene. Quantitative and qualitative experimental results showed that this model significantly improved the trajectory prediction accuracy by 50.00% compared to existing models.

ADRC controllers are widely used in ACC control systems to solve the problem of poor control due to perturbation of the control layer by internal and external factors. Qing Yuan et al. investigated cruise control strategies through hierarchical control architectures [26]. ADRC was used to design the lower controller, and the results showed that the ADRC not only ensured the stability of the closed-loop system during load changes, but also overcame the influence of roadside slopes. H. Kai et al. designed an ADRC to implement traction control for electric vehicles to suppress the effects of parameter uncertainty and unknown disturbances [27], improve the safety and stability of the longitudinal driving of electric vehicles, and reduce the loss of drive energy. In addition, the comparison of the simulation results of the ADRC and PID controller showed that the ADRC performed better in suppressing the effects of parameter uncertainty and unknown disturbances. Yang et al. proposed an adaptive cruise control (ACC) algorithm based on model predictive control (MPC) and active anti-disturbance control (ADRC) [28]. The upper controller uses MPC aided by acceleration prediction estimation and the lower controller uses feedforward control based on a vehicle dynamics model (VDM) and ADRC-based compensation control to improve control accuracy and suppress the effects of internal and external disturbances. The results showed that the ACC with APE can precisely control the tracking of the host vehicle with less acceleration fluctuation than the conventional ACC controller. In addition, the ACC–APE–ADRC controller was still able to control the vehicle to track the required acceleration quickly and accurately when the mass of the vehicle and the road gradient changed. Ruan Jiuhong et al. [29] proposed a new method for vehicle acceleration control based on ADRC. Firstly, the vehicle longitudinal motion dynamics model is established and the coordination strategy between engine and brake for acceleration control is designed. Then, we derive the affine models of two dynamics subsystems—engine–vehicle acceleration and brake–vehicle acceleration—and design the vehicle acceleration ADRC using a linear discrete algorithm. The results showed that the self-anti-disturbance control method can achieve fast and high-precision vehicle acceleration control. Abir Hezzi et al. [30] proposed a linear active disturbance-resistant control (LADRC) for the speed control of a five-phase permanent magnet synchronous motor (PMSM) driving an electric vehicle (EV). The LADRC had high disturbance immunity in addition to high performance speed response and robustness.

An analysis of the adjacent lane cut-in following scheme reveals that the prediction methods summarized above suffer from the failure to consider driver characteristics as well as traffic constraints, resulting in reduced prediction and trajectory accuracy. Driver heterogeneity (in the same environment and vehicle, different drivers operate differently) is an important factor that affects the operating state of vehicles. The above control methods for ACC, due to the limitation of the control method structure, do not consider the influence of internal and external disturbances on the longitudinal control of the vehicle; therefore, the anti-interference ability is low, i.e., when the internal or external environment changes, the control effect will be affected to different degrees.

To address these issues, this paper proposes that the predicted trajectory of the cut-in vehicle be optimized using a driver adventitious factor, followed by flexible following of the cut-in vehicle using a flexible corrector and an anti-disturbance controller. The remainder of this paper is structured as follows. The Section 2 describes the proposed method for predicting trajectories as well as the control strategy for flexible following. Section 3 describes the method’s simulation validation using joint simulation. Section 4 presents a practical validation of the method using an experimental vehicle. Finally, in Section 5, the conclusions are presented.

In this paper, we propose an innovative CS-LSTM based on driver adventitious factor optimization. Based on the convolutional social pool trajectory prediction architecture, the driver character factor algorithm and the model and sampling short-term optimization algorithm are used to improve the distribution of future trajectory points in the time domain process of autonomous driving prediction, and to reduce the trajectory error of vehicle prediction. A single-vehicle following control algorithm based on a flexible corrector and an anti-disturbance controller is also proposed to achieve flexible and comfortable following for adjacent vehicle cut-in conditions.

2. System Structure

2.1. ACC Based on Front Vehicle Prediction

The algorithm framework designed in this paper is shown in Figure 1. The algorithm module consists of a long short-term memory (LSTM) artificial neural network module based on social context information recognition (Module 1), a driver risk-taking factor correction module (Module 2), an overlap calculation module (Module 3), a dual second-order time-varying filter (Module 4), a softening following distance module (Module 5), a self-rejecting control module (Module 6), and an inverse longitudinal dynamics model (Module 7).

As shown in Figure 1, Module 1 is a prediction method for the interaction of pedestrian trajectories in a reference population developed by researchers at the University of California [31] that solves the problem of target vehicle trajectory prediction in multi-vehicle scenarios [32]. This article refers to this method as the basic architecture of a data-driven method for predicting the future trajectories of vehicles in the adjacent lane, with the module input being the historical trajectories of all vehicles. Module 2 constructs a driver intrusion factor based on four factors: road ID, vehicle speed, vehicle acceleration, and vehicle size; this factor is added to the driver’s lane-change behavior characteristics to further modify the base model and increase the accuracy of long-term lane-change trajectory prediction for vehicles in the adjacent lane. The anticipated trajectory of the vehicle in the adjacent lane is utilized again to inject a two-dimensional Gaussian distribution function into the vehicle longitudinal control system. Module 3 outputs the degree of overlap with the center of the target lane based on the predicted trajectory of the entering vehicle. Module 4 outputs the flexible following factor and flexible switching factor of the following target. Module 5 calculates the flexible following speed based on the speed of the vehicle and the flexible following factor. Module 6 is an instantaneous observation approach based on the expansion state observer and is proposed to correct for and suppress both the internal disturbance generated by changes in the internal vehicle parameters and the random disturbances induced by changes in the external road environment. In Module 7, the autonomous bus is finally directed to follow the target vehicle using an inverse longitudinal dynamics model that incorporates both a vehicle dynamics model and a motor–battery model.

2.2. Social-LSTM Based on Driver Risk-Taking Factor Correction

Traffic scenarios involve many targets traveling in various directions and at varying speeds. Therefore, a model must be created to learn the motion characteristics of targets with various properties based on features extracted from a small number of initial observations. To avoid gradient disappearance, this paper uses one of the most powerful dynamics classifiers recognized in academia, the long short-term memory neural network LSTM, as a base model [33]. The LSTM is a special kind of recurrent neural network. This network differs from the general feedforward neural networks in that the LSTM can analyze the input using a time series. Proposed by Hochreiter and Schmidhuber (1997) and later improved and generalized by Alex Graves [33], LSTMs have been shown to successfully learn and generalize isolated sequences, for example in handwriting recognition and speech recognition techniques. Therefore, we design an LSTM for each individual considered in this paper to learn their current states and estimate their unknown future states using shared LSTM weights. A single LSTM, however, is unable to capture the interaction behavior of individuals in an image. The proposed model overcomes this problem by using a novel pooling layer technique. This technique utilizes a network-based pool to combine data while maintaining geographical information. The University of California makes use of such techniques to perform vehicle trajectory prediction in complex settings. We use this method as our basic framework and propose a model optimization method, as shown in Figure 2.

The first component on the left side of Figure 2 is the predictive model encoder (LSTM-ENCODER), which employs an LSTM-encoder to learn the dynamics of vehicle motion. The middle section of Figure 2 shows the convolutional social pooling layer. This layer uses a convolutional layer and a pooling layer on the social tensor to determine the final position of the vehicles around the vehicles in the adjacent lane based on the output of the LSTM-encoder. To create the social context encoding, two convolutional processes and one maximum pooling operation are used. The lane definition grid is used to set the social tensor in this work. The target vehicle is surrounded by a 13 × 3 spatial grid, where each column represents a lane and each row is separated from the next by 4.5 m, or roughly one car’s length. To extract the vehicle dynamics coding, the LSTM states of the vehicles in the adjacent lanes are also sent through a fully linked layer. The whole trajectory code is created by connecting the two codes, which is then sent to the decoder. The driver adventitious factor is calculated by Equation (1); the correction factor with different degrees of adventitiousness that is the output for different driver characteristics and the input to the flexible factor module, which is the correction structure, is a data-driven trajectory prediction model for the driver adventitious factor. The correction structure is for the convolutional social pooling layer, and after two convolutional operations and one pooling operation, the fully connected module for the target vehicle and the social tensor pooling layer for the surrounding vehicles output the contextual encoding information and the vehicle dynamics encoding information of the adjacent vehicle, respectively, which are corrected according to different driver adventitious factors; the correction formula is shown in Equation (2). Finally, the trajectory distribution and maneuvering probability are output by the predictive model decoder (LSTM-DECODER).

We have added a module for the driver risk-taking factor to the framework. In this study, a factor model is built to evaluate the driving risk connected to each contributing factor that could result in an accident, and prior research [34] has shown that a multinomial logit model (MLM) can facilitate the calculation of the coefficients of various variables for various drivers who are exposed to driving risk. The driver risk-taking factor constructed in this paper requires theoretical support. When the obtained data are combined subjectively and objectively, the multinomial logit model (MLM) establishes a probability model to evaluate the driving risk associated with each contributing factor of potential accidents. The basic expression of the MLM model is as follows, and the driver risk-taking factor is mutated on this basis. In Equation (1), $X_n$ is the influence factor and ${\beta }_n$ is the proportion of different influence factors.

$$MLM=\frac{EXP\left({\beta }_n{X}_n\right)}{1+EXP\left({\beta }_n{X}_n\right)}.$$

(1)

A unit function can also be used to examine the model’s relative risk. To maximize the data-driven predictions based on the data, the driver aggressiveness factor function below was built. According to the relevant research, aggressive drivers engage in more lane changes than less aggressive drivers, and the average headway time distance, the original lane in which the car was traveling, the driver’s aggressiveness, and the type of vehicle all have an impact on driving behavior [35].

According to the statistical results of Ref [35], a larger average time headway will reduce the possibility of a lane change (in the case without congestion, the possibility of a lane change is small, because changing lanes to improve mobility is not a priority). Lane ID vehicles traveling in the right lane (slower lane) are more likely to change lanes at will, because this may improve speed. Driver aggressiveness is measured by the average absolute value of the vehicle acceleration or deceleration rate, measured in 0.1 s increments. The probability of a lane change can be increased based on these data [35]. Regarding vehicle size, large vehicles (7 feet wide and 15 feet long) are on average less likely to change lanes (due to their large size and poor acceleration and deceleration characteristics). Based on the above factors and the MLM, the following formula is constructed.

$${\tau }_{character}=\frac{e^{-\frac{\alpha ·A+\beta L_{ID}}{\omega ·T+\gamma ·W_{vehicle}}}}{1+e^{-\frac{\alpha ·A+\beta L_{ID}}{\omega ·T+\gamma ·W_{vehicle}}}}$$

(2)

$$P_{predicted-driver}=P_{lanechange-fusion} \ast {\tau }_{character}.$$

(3)

where $P_{predicted-driver}$ is the social tensor of the social pool layer input. T is the headway time distance, where each 1 ft increase reduces the probability of a lane change occurring by 0.0014, and ω is the headway time distance as a percentage of the negative influence on the factor affecting driver risk-taking. $L_{ID}$ is the lane type, with the slow lane having a 0.5813 higher probability of lane change than the fast lane, and β is the percentage of headway time distance as a factor positively influencing the driver’s risk-taking factor. A is the level of aggression due to acceleration, with each 1 ft/s² increase in acceleration/deceleration increasing the probability of a lane change by 0.0404, and α is the percentage of acceleration/deceleration that positively affects the driver aggressiveness factor. $W_{vehicle}$ is the vehicle size. For smaller cars, the probability of a lane change is decreased by 0.3717 and γ is the percentage of the car model accounting for the negative influence on the factor affecting driver risk-taking. α, β, ω, and γ are four parameters whose values are assigned according to the probability of a lane change.

This model’s design essentially satisfies the requirements of forecasting the future trajectory, which allows the simulation test to proceed. The NGSIM dataset comes from the Next Generation Simulation project. NGSIM covers areas such as intersections on structured roads and high-speed gates. The dataset was collected from four different regions in the U.S.: southbound US 101 in California, the Lankershim Boulevard map in Los Angeles, California, eastbound I-80 in Emeryville, California, and Peachtree Street in Atlanta, Georgia. This dataset is the preferred test set for a large number of vehicle prediction algorithm researchers. This dataset can also be applied to the study of vehicle–road collaboration roadside systems. In this study, public NGSIM datasets are used to validate the algorithm’s validity, as shown on the left side of Figure 3 eight segments make up the trajectory, of which three serve as the historical trajectory and five serve as the predicted range.

After setting the simulation conditions, model training is carried out. The server used for the training of the prediction model parameters in this paper is RT-BRAIN’s DEVTOP AIX2950. This server is powered by an Intel Core i9 X series processor with M.2 NVMe SSD. The training model in this paper adopts the end-to-end training mode, i.e., it minimizes the negative log-likelihood.

$$P\left(Y\right|X)=-\mathit{log}\left({\sum }_i{P}_{\Theta }\left(Y\right|m_i,X\left)P\right(m_i\left|X\right)\right).$$

(4)

However, each training instance performs only one of the maneuvers in the actual execution process. Therefore, this paper minimizes the negative log-likelihood function for training, as shown below.

$$P\left(Y\right|X)=-\mathit{log}\left({\sum }_i{P}_{\Theta }\left(Y\right|m_{true},X\left)P\right(m_{true}\left|X\right)\right).$$

(5)

This paper uses the Adam optimizer with a learning rate of 0.001 to train the model. The LSTM encoder has a 64-dimensional state, while the decoder has a 128-dimensional state. The size of the convolution social pool layer is shown in Figure 2. A full link layer with a size of 32 dimensions is used to obtain the vehicle dynamics code. Finally, a leaky rectified linear unit (ReLU) activation layer is used. All modules in this model are built using the LSTM function library in PyTorch. ${Traj}_{social-lstm}$ is defined here as data-driven trajectory prediction, where ${Traj}_{social-lstm}$ = ($u_x,u_y$).

To confirm the efficacy and accuracy of the aforementioned techniques, numerous datasets that satisfy the study scenario of this paper must be chosen for testing, and the format of the test dataset should be identical to the format of the NGSIM dataset after processing. In this study, we use a freely accessible dataset from UTE [36] which was gathered by academics from Southeast University and other traffic sensing institutions. The data in this dataset were collected by hovering unmanned aerial vehicles (UAVs), and have been aligned to NGSIM. Both large and small vehicles are represented in the raw data, which are divided into four parts for each type of road. The video data include 2222 s of footage of 18,500 unique cars with speed ranges of 0 to 80 km per hour. These data are complete and can be used to support the determination of the adjacent lane vehicle cut-in study conditions in this report. The right side of Figure 2 shows the locations where the data were collected. The data format of the test set, in which some information has been reorganized, must be identical to that of the NGSIM dataset. Therefore, data reconstruction is mainly performed for the trajectory points, lane IDs, and vehicle types, and the output is given as horizontal and vertical coordinates.

2.3. Softening Correction Model

The calculation of the overlap degree is shown in Figure 4. The process of passing the centerline of the lane during a lane change is a factor in the evaluation of the extent of a vehicle’s coverage of the adjacent lane; more specifically, the degree of intersection between the adjacent vehicle’s cut-in process and the centerline of the lane during the lane change exhibits Gaussian changes as the lane change proceeds.

The overlap degree is calculated as shown in Figure 5. To obtain the overlap degree in changing lanes, we set the trajectory prediction of the two-dimensional Gaussian distribution of the five parameters, calculate its maximum value and the value of the intersection point with the lane line, and then multiply these two values together. The formula for the computation is as follows:

$$Overlap\left(u_{x-lane},u_{y-lane}\right)=\frac{p_{lane}\left(x\right|\mu ,\Sigma )}{p_{max}\left(x\right|\mu ,\Sigma )}=\frac{\frac{1}{\sqrt{{\left(2\pi \right)}^{N}det\Sigma }}\mathit{exp}\left(-0.5{\left({\mu }_{x-lane}-\mu \right)}^T{\Sigma }^{-1}\left({\mu }_{y-lane}-\mu \right)\right)}{\frac{1}{\sqrt{{\left(2\pi \right)}^{N}det\Sigma }}\mathit{exp}\left(-0.5{\left({\mu }_{x-max}-\mu \right)}^T{\Sigma }^{-1}\left({\mu }_{y-max}-\mu \right)\right)}.$$

(6)

The flexible following factor must then be calculated, as shown in the next diagram. However, due to the excessive number of spikes, it cannot be easily normalized for use. The filter is a dual second-order time-varying filter. A digital dual fourth-order filter in signal processing is a second-order recursive linear filter with two poles and two zeros. The term “Biquad”, which stands for “Biquadral”, indicates the ratio of two quadratic functions in the Z-domain whose transfer function is:

$$H\left(z\right)=\frac{b_0+b_1{z}^{-1}+b_2{z}^{-2}}{a_0+a_1{z}^{-1}+a_2{z}^{-2}}.$$

(7)

where the coefficient is usually normalized. Higher-order infinite impulse response (IIR) filters are prone to instability because of their sensitivity to the quantization of their coefficients. Higher-order filters are frequently implemented as serially cascaded dual quadratures (with a first-order filter if necessary), since first-order and second-order filters are substantially less difficult to work with. The stability of the dual quad filter depends on the location of the poles within the unit circle. This generally holds true for all discrete filters, i.e., for a filter to be stable, all poles must be contained within the unit circle in the Z domain. When multiple spikes still exist because of the constructed function in the late stage of the lane change, which cannot be logically switched, the factor is calculated using the state equation transformation function of the dual second-order time-varying filter. The factor is then constructed as follows:

$${\rho }_{flex}=\frac{0.2+0.3z^{-1}+0.2z^{-2}}{1-0.9z^{-1}+0.001z^{-2}}.$$

(8)

$${\tau }_{object}=\frac{0.2+0.3z^{-1}+0.2z^{-2}}{1-z^{-1}+0.001z^{-2}}.$$

(9)

Equation (8) fuses the flexible following factor _flex into the speed control framework, and Equation (9) flexibly switches the target switching factor object at the time of target switching, thereby preventing target switching when the switching factor is below a certain threshold. The parameters in Equations (8) and (9) can be selected by means of enumeration. In this paper, the parameters are matched to the above parameters by a large number of enumerations and simulation tests.

The flexible following factor calculated using Equation (8) is used to calculate the flexible following speed by combining Equation (10) with the target vehicle’s entry speed; Equations (11) and (12) are used to determine whether to use these two factors. When the calculated value of the factor is greater than the threshold, flexible switching is performed. If it is less than the threshold, then the flexible calculation is not performed.

$$v_{flex}=v_{Following}(1+{\rho }_{flex})$$

(10)

$$\left\{\begin{array}{c}{\tau }_{object}<{\tau }_{threshold}, \mathrm{no}\\ \mathrm{otherwise}, \mathrm{yes}\hfill \end{array}\right..$$

(11)

$$\left\{\begin{array}{c}{\rho }_{flex}<{\rho }_{threshold}, \mathrm{no}\\ \mathrm{otherwise}, \mathrm{yes}\hfill \end{array}\right..$$

(12)

2.4. Active Disturbance Rejection Control

The automatic disturbance rejection control algorithm simplifies the vehicle longitudinal dynamics system into a second-order system, and the factors that have a dynamic impact on the system (such as resistance, system model simplification, and real-time changes in road environment such as slope curvature, etc.) are represented by the total disturbance term. ESO is established to observe the total disturbance of the system in real time, and feedback control terms are used to eliminate the disturbance influence. A longitudinal vehicle speed ADRC algorithm based on a third-order linear extended state observer is designed. Its basic structure is shown in Figure 5. The extended state observer and feedback control module are part of the ADRC feedback control algorithm. The third-order ESO is designed to observe the system state (such as vehicle speed and acceleration) and estimate the total disturbance of the system; then, the feedback is provided to the control module for real-time compensation, thereby ensuring that the longitudinal speed control has certain anti-interference characteristics. The inverse longitudinal dynamics model in the algorithm determines whether to start driving or braking by receiving acceleration/braking switching logic, and outputs a driving or braking force to the entire vehicle model through the expected acceleration.

$$\left\{\begin{array}{c}\dot{z}=[A-LC]z+[B,L]u_c\\ y_c=z\hfill \end{array}\right..$$

(13)

where $u_c=[u y{]}^T$ is the input variable of the observer, including the control quantity output by the control algorithm and the state variable output by the system. $y_c$ is the output of the observer, including the vehicle speed $v$, the first derivative of the vehicle speed $\dot{v}$, and the estimated value of the disturbance $f$. After parameterization, the poles of the characteristic equation can be placed at the same position ($-{\omega }_o$), where ${\omega }_o$ is the observer bandwidth, that is, the gain matrix $L=[3{\omega }_0 3{{\omega }_0}^2 {{\omega }_0}^3{]}^T$ of the observer is taken. After parameter tuning, the ADRC longitudinal control algorithm in this paper sets ${\omega }_0$ to 30. Thus far, the third-order linear extended state observer for the longitudinal control system has also been designed. As shown in Equation (13), the model of this observer can be built in Simulink to observe the values of the system output state variables and disturbances in real time, which lays a foundation for subsequent controller design.

One of the criteria for evaluating the merit of ACC systems is passenger comfort, and this paper uses the inverse of acceleration, or jerk, as a parameter to evaluate this criterion. In this paper, the smaller the jerk value, the more comfortable the passenger is as the criterion for comfort improvement.

3. Simulation Test

The algorithm proposed in this article is applicable to structured running scenarios. Structured operating scenarios refer to autonomous driving scenarios where the lane information of vehicle driving conditions is clear, the geometric features of the road are obvious, and the driving environment of other traffic participants is relatively clear. Structured scenes are mostly urban roads and highway sections. This section designs a scenario case of structured roads, using simulation experiments and real vehicle road testing experiments to verify the feasibility and effectiveness of the algorithm proposed in this article. The simulation experiment is conducted on the Simulink/PreSCAN simulation platform to construct a virtual road based on the Tianjin University test site, and the effectiveness of the prediction algorithm and the following algorithm is verified.

3.1. Trajectory Prediction Simulation

According to the analysis of the actual driver lane-change process, the proposed method determines the trajectory over the next 4 s. We take the beginning of the lane change as the initial time, the completion of the lane change as the end time, and the processing of the lane change as $t_c=t_{end}-t_{init}$. After analyzing many real-world experimental datapoints, the distribution of vehicle lane-change times at different speeds is [4.62, 5.33] s.

It has been demonstrated that the prediction model put forward in this research has a high degree of adaptability for various working situations based on the simulation results of the aforementioned four categories of typical working conditions. Finally, the prediction performance index is used to assess the accuracy of the model’s predictions. The equation below calculates the root-mean-square error (RMSE), where $(x_k^i,y_k^i)$ is the observed location and $({\widehat{x}}_k^i,{\widehat{y}}_k^i)$ is the projected position of the $i_{th}$ sequence at time t. N is the total number of sequences in the database subset used for the calculation.

$$RMSE\left(k\right)=\sqrt{\frac{1}{N}{\sum }_{i=1}^N\left[\right(x_k^i-{\widehat{x}}_k^i{)}^2+(y_k^i-{\widehat{y}}_k^i{)}^2]}.$$

(14)

Table 1. Statistics of Trajectory Prediction Methods.

Forecast Range	1	2	3	4	5
Vanilla LSTM	0.68	1.65	2.91	4.46	6.27
CS-LSTM(D)-NGSIM	0.62	1.32	2.21	3.32	4.34
CS-LSTM(D)-UTE	0.61	1.27	2.20	3.06	4.33

displays the RMSE computation results. The method put forward in this research can be used to simulate data from a variety of open-source datasets from around the world thanks to the Vanilla LSTM trajectory prediction algorithm. The proposed method in this paper improves the accuracy of trajectory prediction by 8.8% on average compared to Vanilla LSTM.

3.2. Simulation and Verification of the Softening Corrector

In this article, we evaluate the efficacy of the softening corrector using the scenario depicted in Figure 6. The autonomous bus is gray in the illustration, the adjacent car is orange, and the guiding car in this lane is dark gray.

In Simulation 1, the vehicle speed is 10 km/h, and the adjacent lane car merges into the lane at a speed of 14 km/h. Figure 7 shows the speed tracking, headway time (HWT) change, and relative distance change with and without the intelligent prediction system. In the figure, the result without the softening corrector is shown in red, and the result with the softening corrector is shown in black.

In Figure 8, red represents the speed following effect without the prediction module and black represents the speed following effect with the prediction module; the speed variation between the two modes is compared over the time during which the orange vehicle merges into the lane, or between 6 and 10 s. It is obvious from the figure that the speed fluctuation of 1.3 m/s can be minimized as much as possible, ensuring the smoothness of the autonomous bus’s speed in the situation of a mid-distance cut-in.

In Simulation 2, the speed of the vehicle is 15 km/h, and the adjacent lane car merges into the lane at a speed of 14 km/h. From the results in Figure 9, it can be concluded that for vehicles in the adjacent lane, the system with an intelligent prediction module can mitigate sudden changes in distance. As shown by the red curve in the figure, when the vehicles in the adjacent lane merge into the lane within 7.5 s, the distance between the vehicle and the vehicles in the adjacent lane suddenly decreases; with the prediction system, the autonomous bus can decrease its speed approximately 1.5 s before the vehicle has fully merged into the lane. From the results in Figure 9, it can be concluded that when as many vehicles merge from the adjacent lane as possible, the system with the intelligent prediction module can reduce the speed change rate. Due to the intelligent prediction system, approximately 1 s before the completion of the lane change in the adjacent lane, the guide vehicle can carry out early flexible switching, causing the speed fluctuation rate of the following autonomous bus to be reduced by 58%.

3.3. Joint Simulation Verification of the Disturbance Rejection Controller and Flexible Corrector

To jointly test the anti-interference controller and softening corrector of the single-vehicle intelligent observation adaptive cruise system, the experiment in this section establishes a straight road with a length of 100 m and two one-way lanes, and three working conditions are tested. The speeds of the driverless bus and the vehicle in front are the same; the three working conditions set these speeds to 20 km/h, 40 km/h, and 60 km/h, and the vehicles in the adjacent lane are inserted into the lane at a speed 3–4 km/h slower than the following speed. This is used to verify the following effect under different cruising speeds as well as the following effect of the softening corrector when vehicles in the adjacent lane cut into the driverless bus lane. The speed error in the legend is the difference between the speed of the car in front and the speed of the driverless bus.

First, the autonomous bus and the front vehicle run at a cruising speed of 20 km/h. In Figure 10, the left side shows the speed of the front vehicle and the speed of the autonomous bus, and the right side shows the acceleration comparison of the two tests. The lane-change behavior can be recognized 2.19 s in advance by the control algorithm modified by the softening corrector, and the lane change reaction can be carried out in advance. As shown in the Figure 10 the acceleration is reduced by 0.21 m/s² by the control algorithm modified by the softening corrector, and the acceleration is reduced by 0.25 m/s² and 0.04 m/s² by the control algorithm without softening; therefore, the comfort is increased by 19 %.

Second, the autonomous bus and the front bus are traveling at a cruising speed of 40 km/h, as shown in Figure 11 below. In the figure, Figure 11a is the speed difference between the front bus and the driverless bus and Figure 11b is the speed difference between the two tests. The speed of the driverless bus with the flexible corrector is adjusted to between 6 s and 7.5 s. Compared with the case of the autonomous bus without the flexible corrector, there is a relatively slow speed reduction process, and the speed difference between the two vehicles is also relatively soft.

A further analysis of the acceleration changes in Simulation 2 is shown in Figure 12, which shows the time period with large local acceleration changes during the lane-change process. The maximum reduction in acceleration of this vehicle after optimization by the flexible correction factor is 1.75, but the maximum reduction in acceleration during the lane change without the softening corrector is 2.5, and the acceleration difference is 0.75, which means the comfort level is improved by 30%. Additionally, in the late stage of the lane change, the acceleration of the vehicle with the flexibility corrector changes less frequently than that with the controller without the flexibility corrector.

Third, the autonomous bus and the front bus run at a cruising speed of 60 km/h, as shown in Figure 13 below, where Figure 13a is the speed difference between the front bus and the driverless bus and Figure 13b is the speed difference between the two tests. The autonomous bus with the flexible corrector in Figure 13a can identify the lane-change intention of the vehicles in the adjacent lane 1 s in advance. From the different speed curves between 6 s and 13 s in Figure 13b, it can be seen that the controller with the flexible corrector has a more stable performance in following the vehicle in front; the controller with the flexible corrector leads to a sudden change of 4 km/h in the speed of the autonomous bus, which is 2 km/h less than that of the controller without the flexible corrector.

As shown in the figure, after the optimization of the flexible corrector, the acceleration increase of the autonomous bus is 0.175 compared to 0.25 before optimization; the acceleration is reduced by 0.075 and the comfort is improved by 42%.

According to the above simulation verification, by comparing the speed information and acceleration information of different working conditions with and without the softening corrector, it can be concluded that the anti-disturbance control and softening controller proposed in this paper can effectively reduce the speed fluctuation of the driverless bus during the adjacent lane cut-in process, and ensure a relatively low acceleration change rate, which can improve ride comfort.

4. Real Vehicle Verification

The road for the real vehicle verification of the longitudinal follow-up control algorithm was a straight road at the automatic driving test field of Tianjin University. The road scenarios and vehicles are shown in Figure 14. This section verifies the effectiveness of the single-vehicle intelligent predictive adaptive cruise control algorithm. As shown in Figure 14 below, the cut-in vehicle was a BYD SUV and the autonomous bus was an Ankai autonomous bus.

A low speed of 15 km/h was selected as the cruising speed of the autonomous bus, and it was driven on a straight road. Comparing the cut-in curve and prediction curve of the actual target vehicle (Figure 15) with the variables and evaluation criteria of the first real vehicle test, it can be observed that the test results of the trajectory prediction algorithm developed in this paper using a real vehicle can largely meet the requirements.

Analyzing Figure 15 in terms of the tradition model without a prediction module, in the real vehicle test 1 the speed fluctuation was large and the maximum fluctuation rate reached 9 km/h. Meanwhile in the cruise system with a prediction module, the speed fluctuation was significantly reduced, the maximum fluctuation rate was reduced to 4.5 km/h, and the comfort level was improved by 50%. Analyzing Figure 16, in the cruise system without a prediction module, the speed fluctuation was larger, and the maximum fluctuation rate reached 3 km/h. In the cruise system with the prediction module, the speed fluctuation was significantly reduced, the maximum fluctuation rate was reduced to 2.5 km/h, and the comfort level was improved by 16%. The average improvement in comfort for the two real-world tests was 33%. It was concluded that the softening corrector developed in this paper can be effectively used in real vehicle tests with enhanced ride comfort.

5. Conclusions

In this research, we presented a lane-change trajectory prediction method based on a driver adventitious factor correction, which incorporates the driver characteristics in urban road traffic scenarios, in order to accurately predict the lane-change trajectories of adjacent cars.

The polynomial logit model (MLM) was used to generate the driver adventitious factor, which takes into account four categories of historical data (headway time distance, acceleration, lane ID, and vehicle type) and the size of adjacent vehicles. The LSTM model’s parameter training was finished using the minimization of the negative log-likelihood function. The basic architecture is a convolutional-social-pooling-layer-optimized (long short-term neural network) LSTM network (CS-LSTM). The two-dimensional Gaussian distribution function on the road centerline was introduced as the lane-change overlap degree, and the flexible following factor and the flexible switching factor of the following target were constructed by the double second-order time-varying filter for flexible tracking after the mode switch in order to overcome the effect of adjacent vehicle cut-in on the comfort of the vehicle.

An instantaneous observation method based on the dilated state observer and an adaptive cruise controller based on the vehicle longitudinal inverse dynamics model were proposed to compensate for and suppress the internal perturbations caused by the internal parameter changes of the vehicle and the random disturbances caused by the external road environment changes.

The simulation and real-world results showed that the comfort level was improved by an average of 28%. This was performed to ensure a flexible response to vehicles merging from the adjacent lane.

6. Discussion

This article has limitations in terms of the real-time optimization of prediction models, testing conditions, and actual vehicle testing conditions. Further exploration can be made in the following areas in the future:

(1) In the future, the training module of the prediction model can be synchronously run in the cloud to update model parameters in real time, and continuous optimization and updating methods can be used to improve the adaptability of the algorithm in various scenarios.

(2) Due to the continuous development of the future transportation environment, future research can focus on other typical operating conditions in the entire city, such as traffic merging conditions, and intersection conditions. These conditions are more complex and require higher requirements for the prediction and control of unmanned vehicles.

(3) On the premise of obtaining an autonomous driving license plate for testing while ensuring safety, actual testing on open roads can be carried out, thereby continuously collecting a large amount of test data and optimizing the model in real-world scenarios.