1. Introduction
With the rapid development of computers, electronics, and sensor technology, advanced driver assistance systems (ADAS) have now become an important direction for development of the automotive industry because they have great advantages in improving transportation efficiency [
1] and driving safety [
2]. As an important branch of ADAS, ACC systems have a wide range of applications in car-following scenarios. However, complex driving scenarios, such as cut-in scenarios, are still challenging for ACC systems [
3]. When facing the lane-change maneuvers of a nearby car, a vehicle with an ACC system has to switch the following target to the cut-in vehicle and follow its trajectory. In this process, there may be a problem of braking too late as well as excessive braking. In order to ensure driving safety and driving comfort, the cut-in possibility of a nearby car needs to be determined. When facing a vehicle cut-in, the host vehicle with the ACC system needs to cooperate with the cut-in vehicle at the same time, and smoothly follow the cut-in vehicle.
In ACC control, the aim is to solve the optimal control law of the host vehicle under the condition of satisfying constraints. Therefore, ACC can be considered as a constrained optimization problem. For constrained optimization methods, Garone et al. [
4] and Nicotra et al. [
5] proposed a novel scheme called the explicit reference governor (ERG) for the control of constrained systems characterized by fast dynamics and that are subject to non-convex constraints. Hosseinzadeh et al. [
6] proposed a systematic approach for applying the ERG to linear systems subject to combinations of intersections and unions of concave constraints. In addition, Forsgren et al. [
7] first utilized the barrier functions in constrained optimization. In constrained optimization, a barrier function is a continuous function in which the value of a point increases to infinity as the point approaches the boundary of the feasible region; therefore, a barrier function is used as a penalizing term for violations of constraints [
8]. However, in the process of following a preceding vehicle, the motion state of the preceding vehicle changes dynamically, so the control method of the host vehicle needs to be continuously adjusted. Model predictive control (MPC) can divide the time domain into infinite finite horizons. In each horizon, which is a sample time, the system experiences an error with the reference trajectory. With this error minimization as the control objective, the optimal control law is solved under constraints, and then the control law is used as the input of the system at the next horizon until the system reaches the reference trajectory. This is considered a rolling optimization process. Therefore, MPC is more suitable for the following control of a host vehicle. In addition, MPC can take the acceleration of the preceding vehicle as a disturbance in the system control, which compensates for the uncertainty caused by the preceding vehicle. For instance, Bageshwar et al. [
9] proposed an MPC-based headway control algorithm, which explicitly incorporates acceleration limits to meet the requirements of ride comfort and safety.
Except for MPC, many studies have contributed to the ACC control method. Milanés et al. [
10] proposed the design, development, implementation, and testing of a cooperative adaptive cruise control system. Yi et al. [
11] analyzed an ACC system using the method of transition state variables and obtained a desired acceleration. Mobus et al. [
12] studied the motion characteristics of an adaptive cruise system using a non-linear method with finite time constraints. Shakouri et al. [
13] optimized the non-linear characteristics of a vehicle into linear characteristics, thereby using the linear time-invariant model to control the ACC tracking index. Li et al. [
14] conducted real-time research and observations on a vehicle dynamic model, and optimized the adaptive cruise system algorithm by using the minimum tracking method. Paul et al. [
15] designed a full-speed-range ACC system using the fuzzy control theory. The genetic algorithm, particle swarm algorithm, and differential evolution algorithm have been used to optimize the parameters of the fuzzy controller. The designed ACC system can be used in urban traffic and highways. Considering the time-consuming problem of adaptive control design, caused by the combination of different characteristics and situation-dependent behaviors, Naus et al. [
16] proposed a systematic method of parameterized adaptive control design, based on explicit model predictive control. Schakel et al. [
17] investigated the driving state of a driver when the driver did not use the ACC function for comparison experiments, and collected information, such as acceleration and vehicle spacing, which was taken in the form of observations of lane changes.
In addition to the study of ACC control strategies, many studies have taken the driving characteristics of a driver in the design of ACC into account. Wang et al. [
18] developed an adaptive longitudinal driving assistance system based on driver characteristics using the recursive least squares method to identify the parameters of the driver model based on manual operation, and applied those parameters to real-time control. Lefèvre et al. [
19] used a set of offline driving data to teach a driver model instead of a human driver, and proposed a new intelligent longitudinal speed control (LVC) framework, which included a driver model and a model predictive controller. Kuderer et al. [
20] applied a feature-based demonstration learning method, in which the driver model is trained to produce a driving trajectory, similar to that shown by a driver, during vehicle following. Lefevre et al. [
21] designed a self-learning driver model that used the hidden Markov model (HMM) and Gaussian mixture model (GMM) to identify and predict a driver’s steering intention and acceleration, combining it with the MPC algorithm to design an ACC system controller. The system could adapt to different types of drivers and ensure driving safety. Butakov et al. [
22,
23] also designed different assisted driving strategies for ADASs, based on different types of drivers. Bifulco et al. [
24] proposed a full-speed ACC; by activating the electronic control unit (ECU), they used a few minutes of the online learning mode to learn a driver’s preferences and attitudes, and then updated the parameters to achieve a full-speed ACC that conformed to the driver’s behavior characteristics. Although the above papers show various studies on ACCs, the cut-in scenarios are still a challenge. Therefore, an ACC control strategy needs to consider cut-in possibility, and controls a vehicle to make a decision accordingly, which is meaningful to improve ACC driving safety and comfort.
The ACC for cut-in scenarios based on the model predictive control algorithm in this paper is structurally illustrated in
Figure 1. To begin this process, a finite state machine (FSM) was adopted to introduce different cut-in scenarios, which generated a reference trajectory for vehicle control. The second method used to recognize potential cut-in vehicles and to quantify the cut-in possibility based on nearby vehicle states was proposed. By comparing, judging the position of a potential cut-in vehicle with the position of the host vehicle, a potential cut-in vehicle on both sides of a lane was determined. Through analysis of the lateral displacement and lateral velocity of a potential cut-in vehicle, the cut-in possibility of a potential cut-in vehicle was quantified and then used as the reference for MPC to realize a coordinated control between the host vehicle and the cut-in vehicle. In addition, considering a straight lane and a curved lane, a safety distance model of the cut- in vehicle was proposed in this paper. When a nearby vehicle cuts into the lane, by considering the state change among the cut-in vehicle, the host vehicle and the preceding vehicle in front of it in the lane, a safety distance model of the cut-in vehicle was established, which is used to manage the transition of the FSM. In the end, considering the constraints of driving safety, comfort, and taking the possibility of cut-in of a nearby vehicle as a reference, an ACC control strategy based on MPC (MPC–ACC) was developed. Through the control strategy proposed in this paper, the host vehicle can judge and recognize a cut-in vehicle, and, at the same time, for a cut-in vehicle in different states, the host vehicle is controlled in coordination with the MPC–ACC to achieve safe and smooth processes in cut-in scenarios. The contributions of this paper are the following aspects:
(1) A finite state machine is used to divide the cut-in scenarios, and a method of screening and quantifying potential cut-in vehicles is proposed, which can be used as a reference for vehicle control to cooperate with a cut-in vehicle.
(2) The safety distance model of the cut-in vehicle is proposed. Comprehensively considering the movement state of the vehicle, the preceding vehicle ahead of the host in the lane as well as the cut-in vehicle, the safety distance model of the cut-in vehicle is established, which performs the conversion of the management finite state machine so that vehicle control can be taken appropriately when a cut-in vehicle changes lanes.
(3) Facing the cut-in vehicles in different states, the MPC–ACC control strategy is developed to realize the follow-up control for cut-in vehicles. At the same time, driving safety and comfort are taken as the constraints of the MPC–ACC to make the host vehicle follow an optimized control trajectory.
The rest of this paper is as organized follows. Cut-in vehicle identification and quantification are shown in
Section 2.
Section 3 describes the cut-in vehicle safety distance model.
Section 4 introduces the MPC–ACC control strategy model. In
Section 5, the simulation result research is given. The conclusions are presented in
Section 6.
2. Cut-In Scenario Classification and Cut-In Possibility Quantification
Cut-in scenarios are divided by the FSM according to the state of the surrounding vehicles. With the presence of nearby vehicles on both sides of a host vehicle, whether the vehicles cut in is judged and the cut-in possibility is quantified, so as to control the host vehicle accordingly.
2.1. Finite State Machine for Cut-In Scenarios
The finite state machine is shown in
Figure 2. The host vehicle can adopt different control strategies when facing a cut-in vehicle through the conversion of the FSM. The FSM includes two states in total, in which the cut-in vehicle state contains two sub-states; corresponding to three scenarios.
Driving scenario 1: When the cut-in vehicle does not exist, or completes a lane change, the FSM remains in the following the preceding vehicle state, which means that the host vehicle can use the preceding vehicle in front of it in the lane as a reference to stably follow the object.
Driving scenario 2: When the host vehicle recognizes a potential cut-in vehicle using the target screening method mentioned below, if the longitudinal relative distance (which can be measured using a corner radar equipped on the front of the host vehicle) between the host vehicle and the preceding vehicle in front of it in the lane meets the cut-in vehicle safety distance model, the FSM is switched to follow the cut-in state. At this time, the host vehicle does not need to brake in advance to maintain a safe relative distance with the cut-in vehicle. When the cut-in vehicle reaches the center line of the lane, the host vehicle stably changes the follow object, from the preceding vehicle, to the cut-in vehicle.
Driving scenario 3: When a nearby vehicle performs a cut-in maneuver, and the relative distance between the host vehicle and the cut-in vehicle does not meet the safety distance model, the FSM is switched to yield to the cut-in vehicle state. Before the nearby vehicle cuts in, the host vehicle changes the following target to the cut-in vehicle. At the same time, the cut-in possibility is used as a reference trajectory for the MPC. At this time, the host vehicle under the control of the MPC–ACC start to perform a braking action, which increases the relative distance from the preceding vehicle in front of it in the lane to provide a safe space for the nearby vehicle to cut into. With the successful cut-in maneuver completed, the host vehicle can smoothly follow the cut-in vehicle.
2.2. Potential Cut-In Vehicle Screening
In the cut-in scenario, a nearby vehicle performs a lane change operation from the original lane to in front of the host vehicle, which is considered as the cut-in behavior of the nearby vehicle. If all vehicles around the host vehicle are used for cut-in recognition, the calculations of the ACC system will be increased. Therefore, it makes sense that vehicles in the two adjacent lanes are considered as potential cut-in vehicles.
Using the width of a city lane as a reference and the center of the vehicle directly in front of the host as the base point, the maximum lateral distance and minimum lateral distance of the area where the next vehicle exists is determined, as shown in
Figure 3.
and
can be written as:
where
is the width of the lane and
is the width of the host vehicle.
By calculating the lateral distance of surrounding vehicles relative to the host vehicle, the vehicle of which the lateral distance meets the interval
is regarded as the adjacent lane vehicle. As shown in
Figure 4, nearby vehicles A and B are in the forward direction of the host vehicle, and the azimuth angles of the nearby vehicles are
and
, respectively.
and
are the relative distances between the nearby vehicles and the host vehicle. Therefore, the relative lateral distances
and
between the nearby vehicles and the host vehicle are expressed as follows.
When the lateral distances, and , of nearby vehicles A and B meet the interval , the nearby vehicles are both regarded as adjacent lane vehicles.
In the cut-in scenario, in addition to the relative lateral distance of the surrounding vehicles, the relative longitudinal distance of the next vehicle also needs to be considered. Only the cut-in behavior of vehicles on both sides that are closest to the host vehicle in the longitudinal direction affect the driving state of the host vehicle. Therefore, the vehicles on both sides are selected as potential cut-in vehicles that are closest to the host vehicle in the longitudinal direction. As shown in
Figure 5, H is the host vehicle. Assume that there are four target vehicles P(1), P(2), P (3), and P(4) in front of host vehicle H. P(1) is the follow target of host vehicle H. Since P(2) and P(3) are in the left and right lanes with the smallest relative longitudinal distance to the host vehicle, P(2) and P(3) are regarded as potential cut-in vehicles.
2.3. Quantification of Cut-In Possibility Based on Lateral Distance and Lateral Relative Velocity
When a nearby vehicle cuts into the lane, the lateral distance and lateral velocity of the vehicle change quite obviously [
25]. Therefore, this paper studies the cut-in possibility of nearby vehicles in the lateral distance and with a relative lateral velocity.
2.3.1. Lateral Distance Criterion
When a nearby vehicle performs a cut-in maneuver, the continuous change of the nearby vehicle’s lateral displacement is the most intuitive. The driver’s judgment of the cut-in vehicle is generally based on whether the lateral distance of the nearby vehicle has an impact on the current driving trajectory of the host vehicle. As shown in
Figure 6, if the nearby vehicle’s body and the host vehicle’s body overlap in the longitudinal direction, the driver will take measures to adjust the vehicle, according to the driving state of the two vehicles. Therefore, cut-in possibility is determined according to a change in the vehicle’s lateral distance.
As the lateral displacement of a nearby car increases, the cut-in possibility of the vehicle becomes greater. The cut-in possibility is the greatest when the body of the nearby vehicle overlaps with the body of the host vehicle in the longitudinal direction. Therefore, the cut-in possibility of the nearby vehicle is quantified as the value of [0,1] according to the vehicle’s lateral distance.
where
is the cut-in possibility based on lateral distance. When
, it is considered that the nearby vehicle will definitely cut in. On the contrary, when
, it is considered that the nearby vehicle cannot cut in. In addition, because the lateral distance of the nearby vehicle is positively related to the cut-in possibility, the sigmoid function is selected to link the lateral displacement with the cut-in possibility.
where
is the lateral distance of the nearby vehicle,
and
are both parameters that are related to the width of the lane line and the width of the host vehicle.
As the relative lateral distance decreases, the cut-in possibility of the nearby vehicle increases gradually. When the nearby vehicle body and the host vehicle body have any overlap in the longitudinal direction,
, and is regarded as cut-in behavior. The cut-in possibility based on lateral distance
and lateral distance
are shown in
Figure 7.
As shown in
Figure 7, the ordinate is the cut-in possibility based on lateral distance
, the abscissa is the lateral distance of nearby vehicle,
,
is the width of the vehicle, and
is the width of the lane. As shown in
Figure 7a, with the lateral distance of a nearby vehicle decreases, the cut-in possibility,
, becomes greater. When a nearby vehicle shifts laterally until it overlaps with the host vehicle body in the longitudinal direction and touches the red dotted line in
Figure 7a, the cut-in probability is considered to be 1, which means
when
.
2.3.2. Relative Lateral Velocity Criterion
There can be a minor misjudgment in recognizing cut-in behavior only using the lateral distance. As shown in
Figure 8, in the curve scenarios, for the cut-in vehicle, if the cut-in recognition is only performed using lateral distance, the turning behavior of the nearby car will be recognized as a cut-in behavior, which is obviously unreasonable. Therefore, the relative lateral velocity of the nearby car is used as another reference factor.
During the cut-in process of a nearby vehicle, similar to the lateral distance, the lateral speed of the nearby vehicle also gradually increases, and then gradually decreases until the cut-in maneuver is successful [
26]. At the same time, in curve scenarios, a nearby vehicle also has a large lateral speed. Therefore, in order to avoid judging the turning behavior of a vehicle as a cut-in behavior, this paper uses the relative lateral speed between the host vehicle and the nearby vehicle as a reference.
where
is the relative lateral velocity,
is the relative lateral velocity of the nearby vehicle, and
is the lateral velocity of the host vehicle.
Similar to the lateral distance judgment method, as shown in
Figure 9, the sigmoid function is used to fit the relationship between cut-in probability and the relative lateral distance.
where
is the cut-in possibility of the lateral relative velocity and
is the parameter.
In a straight lane scenario, as a nearby vehicle cuts in, the lateral velocity of the vehicle gradually increases, but the lateral velocity of the host vehicle is 0, so the relative lateral velocity between the host car and the nearby vehicle gradually increases, and the cut-in possibility becomes greater. In a curve scenario, both the host vehicle and the nearby vehicle have large lateral speeds, so the relative lateral velocity is small, which means that the cut-in possibility is low and the situation where a nearby vehicle that is driving normally on a curve is judged as a cut-in vehicle is avoided. If the nearby vehicle performs a cut-in maneuver, the vehicle needs to generate a greater lateral velocity than the host vehicle to cut in the front of the host vehicle successfully. Therefore, the relative lateral velocity criterion is effective when judging the cut-in possibility.
2.3.3. Quantification of Cut-In Possibilities
For the quantification of the cut-in possibility of vehicles on both sides, lateral distance
and lateral relative velocity
are comprehensively considered. Because the lateral distance and lateral relative velocity have different influences on the cut-in possibility of a nearby vehicle under different road scenarios, the lateral distance
and the lateral relative velocity
are set with different weights to adapt to the quantification of the cut-in possibility in different road scenes, so the cut-in possibility of the cut-in vehicle is finally expressed as
where
is the cut-in possibility of the side car,
,
is the weight.
Figure 10 shows the quantified cut-in possibility of nearby vehicles under different weights. The maximum value of cut-in probability
is 1, and the extreme value changes with different weights, so that the road scenarios factor is taken into account in the quantification of the cut-in behavior of a nearby vehicle, which avoids the wrong estimation of cut-in probability when facing changing road scenarios.
In cut-in scenarios, as a nearby vehicle gradually cuts in, the cut-in possibility also changes at any time. In the host vehicle control, the generated cut-in probability value is used as a reference variable for the MPC–ACC, so that it can control the state of the host vehicle in a coordinated way to adapt to the cut-in vehicle according to the changing cut-in possibility. Finally, under the condition that the nearby vehicle safely cuts in, the host vehicle can achieve a smooth target conversion process.