3.1. Driving Intention Classification
Generally, drivers must turn on the turn signal in the corresponding direction before performing a lane change operation. However, statistics show [
40] that turn signals are used while turning in only 64% of cases, but some drivers signal only after starting a lane change and fail to use their turn signals in 70% of cases when other vehicles are nearby. Therefore, it is not enough to use turn signals alone as an identification feature for driving intention, and other feature parameters need to be used to distinguish driving intention.
In order to solve the problem of the unclear driving intention of the preceding vehicle, the FCM algorithm is used to classify driving intentions. The FCM algorithm is used to solve the problem of the unclear driving intention of the front vehicle. The final output of the FCM algorithm is the magnitude of the degree to which each object belongs to each class, rather than providing only high-level predictions of vehicle behavior that do not accurately describe the problem of operating intentions.
Using the relative offset of the current prediction window lateral and longitudinal coordinates and the current vehicle speed as feature parameters, respectively, the vehicle driving intentions are classified, and the driving intentions are categorized as drastic lateral change, lateral slow change, lateral uniform change, drastic longitudinal change, slow longitudinal change, and longitudinal uniform change driving. The vehicle’s tendency to change in longitudinal and lateral directions is described in the form of probabilities to classify the vehicle’s driving intentions and improve the classification’s accuracy. Driving intentions are classified in terms of how drastically they change in the lateral and longitudinal directions so that if moving at a constant acceleration, driving intentions will classify this situation as a uniform change.
In order to classify driving intentions,
Table 1 shows the selected characteristic parameters.
A portion of the real vehicle data is selected as the training set, Where is the data of the th vehicle at time t, is the speed information of the th vehicle at time t, and is the relative position offset of the th vehicle in the lateral and longitudinal directions at time t. As an example of classifying the driving intention of vehicle 1 for the next 1 step, the historical 4-step and the current moment data are composed as a set of data . When classifying lateral driving intentions, is calculated by Equation (1) with the value of in Equation (3). When classifying longitudinal driving intentions, is calculated by Equation (2) with the value of in Equation (3). When classifying lateral driving intentions, Equation (5) outputs , which is the probability of belonging to class j of lateral driving intentions at time t. When classifying the longitudinal driving intentions, Equation (5) outputs the result as , which is the probability of belonging to class j longitudinal driving intentions at moment t. Ultimately, the FCM model outputs the result of the vehicle’s affiliation function in the lateral direction and the result of the affiliation function in the longitudinal direction.
The FCM algorithm is applied to determine the clustering center and affiliation matrix.
where
is the objective function,
denotes the clustering center of class
j,
denotes the affiliation degree of sample
belonging to class
j,
N is the dataset size, and
m is fuzzy partition matrix exponent for controlling the degree of fuzzy overlap, with
m > 1.
After initializing the affiliation function, according to Equations (4) and (5),
and
are continuously iterated and updated so that minimize Equation (3) under the condition that
and finally reaches a stable state, and the values of
,
in this state are the final affiliation matrix and clustering centers.
For a single sample , the sum of the affiliation degree for each class is 1. The closer the affiliation degree is to 1, the higher the degree of belonging to , and the affiliation function , which takes the value in the interval (0,1), is used to characterize the degree of belonging to .
For the driving intention classification problem, the current and historical four-step sampling moment data are used as a group during the vehicle’s actual driving, and the group’s feature values are extracted. Moreover, the distance from the current moment data to each cluster center and the corresponding affiliation function are calculated using Equation (3) to characterize the probability that it belongs to that cluster center, and this probability is used as the weight coefficient of the trajectory prediction results based on different driving intentions. The accuracy of driving intention classification is improved by forming a combination of probabilities of different driving intentions.
3.2. Trajectory Prediction
The vehicle trajectory prediction problem is impacted by uncertainty in dynamical properties. Deep neural network architectures have been applied to many machine learning tasks and can generalize the nonlinear problems between real data and the environment. Among the existing deep neural network architectures, recurrent neural networks (RNNs) are widely used to analyze the structure of time series data, and RNNs have better results in targeting time series data. This paper uses a long short-memory (LSTM) model to predict the front car trajectory. LSTM is a variant in RNN, which has the same ability to learn long-term dependencies from the dataset and handle time series data as RNN. The LSTM algorithm can avoid the gradient disappearance/explosion problem of traditional RNN algorithms. In terms of structure, LSTM and RNN are dynamic structures containing repetitive blocks forming a chain. Within the repetition block, the difference between LSTM and traditional recurrent neural network is mainly its added gate structure, which is the forgetting gate, input gate, and output gate [
41].
The relevant formula for LSTM is.
where
denotes the forgetting gate, which controls the proportion of selectively forgotten information and
denotes the input gate; when predicting the lateral trajectory,
is calculated by Equation (6) and predicts the lateral trajectory with the value of
. When classifying longitudinal driving intentions,
is calculated by Equation (7) and predicts the lateral trajectory with the value of
.
denotes the state update, and the role of the input gate is to control the proportion of the state update
added to the
t-th step memory cell.
denotes the output gate, which determines the proportion of output information.
denotes the final output value and when classifying the lateral driving intention, the output of Equation (13) is
, which indicates the predicted result of the trajectory of car l in the lateral direction at the moment
t. When classifying the longitudinal driving intention, Equation (13) outputs the result as
, which indicates the predicted result of the trajectory of car l in the longitudinal direction at the moment
t and the final output of the LSTM is determined by both the output gate and the cell state.
,
,
,
,
,
,
denotes the weight coefficient,
,
,
,
denotes the bias, and
is the activation function.
Based on the FCM, the driving intention of the front vehicle is classified, and the LSTM algorithm predicts the trajectory of the front car. First, the LSTM model is trained using data with different driving intentions, the three LSTM prediction models based on the drastic lateral change, the slow lateral change, and the lateral uniform change, and the three LSTM prediction models based on the drastic longitudinal change, the slow longitudinal change, and the longitudinal uniform change, were formed, respectively. Additionally, the LSTM algorithm takes the historical four-step length and current trajectory data as input and the future one-step trajectory as output to derive the LSTM prediction results under different driving intentions. When predicting the lateral trajectory, the three LSTM lateral prediction models with different lateral driving intentions yielded
. The three LSTM longitudinal prediction models with different longitudinal driving intentions yielded
when predicting the longitudinal trajectory. Then the vehicle data are input to the FCM algorithm, combined with the FCM algorithm to determine the probability of different driving intent, and the probability is used as the weight coefficient of the trajectory prediction results. Furthermore, finally, the multi-model prediction results are fused to derive the trajectory prediction results based on driving intention classification. Take the future trajectory prediction of vehicle 1 with 1 step length as an example, and input the historical four-step length and current data into FCM driving intention classification model and LSTM trajectory prediction model. The FCM model outputs the result of vehicle affiliation function
in the longitudinal direction and
in the lateral direction. The LSTM model outputs the future longitudinal coordinate
and lateral coordinate
under different driving intentions. The future one-step trajectory prediction result
for the final vehicle 1 is shown in Equations (14) and (15).
The structure of the algorithm for trajectory prediction for 1-step is shown in
Figure 2.
3.3. Vehicle Interaction Correction
The predicted object is influenced by other traffic participants around it during its movement. However, the data-driven method does not consider the influence of other surrounding traffic participants in the prediction results. The purely data-driven method lead to prediction results that are inevitably detached from the essential characteristics of the predicted object and therefore needs to be corrected by environmental influences and the vehicle kinematic model of the predicted object itself to improve the algorithm’s environmental adaptability and accuracy. In this study, the artificial potential field (APF) method is used to calculate the repulsive field of the vehicle around the prediction object, and based on the vehicle dynamics model, the longitudinal and lateral safety distances are calculated to determine the influence range of the repulsive field, and finally, the trajectory prediction results are corrected.
The basic principle of the APF method is to assume the vehicle as a point that moves in a virtual force field, which is composed of the gravitational field of the target point to the vehicle and the repulsive field of the obstacle to the vehicle. Different from the traditional trajectory planning scenario, in this paper, APF is applied to trajectory prediction without using the gravitational field-related content, and the vehicle safety distance is used as one of the parameters in the repulsive field to achieve the correction of the prediction results, as shown in Equation (16).
is the vehicle’s coordinate, is the repulsive field, and is the sum of the repulsive fields.
The forces on the vehicle in the potential field are shown in Equation (17).
is the combined force on the vehicle, and
is the repulsive force that keeps the vehicle away from the obstacle point. The repulsive field is as in Equation (18).
where
is the repulsive force gain constant,
is the obstacle coordinates.
is the maximum influence distance. The repulsive force is calculated as (19).
In the scenario of multiple traffic participants, the repulsive field and repulsive force should be the sum of the repulsive field and the repulsive force of multiple traffic participants on the vehicle.
In this paper, the artificial potential field method is used to establish the surrounding vehicle potential field based on the vehicle safety distance, which is used to correct the predicted trajectory results and the erroneous results that lead to accidents of vehicles.
According to [
42], Equations (18) and (19) are used for the calculation of longitudinal safety distance and lateral safety distance as follows:
is the reaction time, is the maximum longitudinal acceleration, is the minimum longitudinal braking required to avoid a collision, and is the maximum longitudinal braking acceleration.
The potential field combines longitudinal and lateral safety distances to limit the minimum distance of the predicted vehicle from surrounding vehicles under the current driving intention and establishes a repulsive field of surrounding vehicles to predict the vehicle trajectory. The final prediction position is shifted to the edge of the repulsive field both horizontally and vertically to reduce the problem of ignoring the actual scenario constraints caused by the purely data-driven approach to predict trajectories and to improve the interaction with the surrounding environment in the trajectory prediction process.
3.4. Multi-Step Prediction
Multi-step prediction methods are mainly divided into direct and iterative methods. The iterative method uses the result of the previous prediction step as the input for the next prediction step until rolling the prediction up to the expected step. The direct method is to predict directly up to the kth step, but the trained model has to match the predicted step size, and models with different prediction steps cannot be substituted for each other [
43]. Moreover, the direct method prediction model requires much more training data than the iterative method [
44,
45].
However, the iterative method is affected by the problem that the prediction error accumulates with the prediction step. To solve this problem, in this paper, driving intention is identified at each prediction step, and the APF algorithm is used to determine and correct the results for collision risk. The k-step prediction indicates that the data at the current moment is used to predict the next k sampling moments. For example, the five-step prediction indicates that the current moment data is used to predict the trajectory for the next five sampling moments. Taking the prediction of the future two-step trajectory as an example, firstly, the FCM algorithm is used to classify the driving intention. The input data are the historical three-step long and current moment trajectory information, the predicted future one-step trajectory information, and the driving intention affiliation function of this data set is output. Then, the LSTM algorithm is used to predict the future two-step trajectory and combined with the affiliation function calculated by FCM, and the trajectory prediction result based on driving intention is obtained. Finally, the APF algorithm is used to determine whether there is a collision risk at the predicted points and to correct the predicted points with a safety risk, resulting in the final trajectory prediction results.