1. Introduction
Benefiting from the advancement of science and technology, such as computer science, communication networks, and smart chips, autonomous driving technology has progressed rapidly in recent years. The Society of Automotive Engineers (SAE) used a six-level system (ranging from level 0 to level 5) in 2014 to define the degree of automation [
1]. The current research on autonomous driving mainly focuses on the degree of level 3 [
2], which allows for switching between fully autonomous and fully manual driving modes. However, a variety of unresolved issues need to be addressed before fully autonomous driving can be achieved, including ethical issues, laws and regulations, and technical bottlenecks [
2,
3,
4,
5]. In addition, keeping the driver out of the control loop for a long time will lead to driver over-reliance and situational awareness decline [
4,
6]. However, it is worth noting that automation control systems surpass humans in information storage, computing power, etc., while human drivers exceed automation in moral judgment and reasoning [
2]. Shared control technology in intelligent driving can make full use of the strengths of human drivers and automation systems to compensate for each other’s weaknesses, which has been considered a transition to fully autonomous driving [
7]. The concept of shared control was first proposed by Sheridan and Verplank in the field of industrial robots in 1978 [
8]. Subsequent research developed it towards intelligent vehicles and derived the idea of a human–machine shared control vehicle (HSCV) [
2,
4,
6].
The standard shared control system in an HSCV consists of a human driver, an automation control system, a control mechanism, and a controlled vehicle system [
6]. The driver in a shared control system sits in the driving seat and controls the future movement of the vehicle by turning the steering wheel and adjusting the accelerator and brake pedals. The unique aspect of shared control in an HSCV is that the driver and the automation control system are simultaneously kept in the control loop to complete a specific driving task together [
2]. The control mechanism is used to integrate the driver’s control commands and the control actions of the automation system and ultimately input them into the vehicle system. Based on the different control mechanisms, the shared control system in an HSCV can be divided into a haptic shared control system and an input mixing shared control system. The main difference between them is whether the control mechanism is mechanically coupled. Haptic shared control usually uses an electric power steering system to directly increase auxiliary torque to intervene and guide the driver’s control commands [
9]. In contrast to haptic shared control, a steer-by-wire system can be used by an input mixing shared control system to allow the steering wheel to be mechanically decoupled from the road wheel. It then uses an intermediate controller to modify control commands entered by the driver before they are applied to the vehicle steering system [
2].
Designing a proper control policy for the automation system is always one of the critical issues in the shared control system. An appropriate control policy is expected to consider drivers’ personalization and commands to minimize human–machine conflicts and guarantee driving safety and stability in changeable traffic scenarios [
4,
6]. For shared control, integrating driver modeling into the system to characterize driver behavior can increase mutual understanding between the driver and the automation system, thereby reducing human–machine conflicts [
2,
10]. Many studies based on driver models have been conducted, including the single-point preview model [
2] and the two-point preview model [
11,
12], which are used to simulate the driver’s steering behavior in lane keeping scenarios and obstacle avoidance scenarios. Li et al. [
13] adopted the idea in the work [
14] that driver steering behavior can be simulated by model predictive control (MPC), and they designed a driver steering model based on MPC. A brain emotional learning circuit model (BELCM) was designed in [
15] to simulate driver steering behavior, but it did not consider human–vehicle interaction. In terms of shared longitudinal control in an HSCV, the main contribution of this research direction focuses on using the haptic accelerator to perform vehicle following tasks [
16,
17]. In particular, the integrated control framework of driver steering control and speed control models in HSCVs requires more research.
For automation control systems, it is necessary to design shared controllers to assist drivers in driving safely and smoothly and to make timely interventions in dangerous situations. And there are a variety of shared controllers in HSCVs, which include a linear quadratic regulator (LQR) [
18], Takagi–Sugeno (T-S) fuzzy control [
11],
control [
19], and MPC [
20]. Compared with the above controller, MPC has the advantage of being suitable for solving multi-constraint and multi-variable optimization problems, and it has received widespread attention in the design of shared controllers for HSCVs [
4,
6,
21]. In 2013 [
22], Anderson et al. used constrained MPC to design a shared controller and then used a weighted summation method to integrate the control commands of the driver and the automation control system. However, this method ignored the adaptability of the shared controller to the driver’s control input. A novel shared controller is designed in [
20,
23], in which the driver’s control commands are integrated into the MPC’s cost function to form an optimization problem. Considering that the driver’s unreasonable operation will pose a safety threat to the vehicle, Liu et al. [
24] added a driving control authority allocation strategy based on fuzzy logic in the shared controller. Another reference-free shared control framework based on MPC was designed by Huang et al. [
25]. In this shared controller, constrained Delaunay triangles and collision time are used to determine the safe area, vehicle sideslip angle, and yaw angular rate, which are used to design stability constraints. Na et al. [
26,
27] use a non-cooperative MPC method to simulate the interaction between the driver and the controller, in which the driver steering controller and the automation controller need to minimize the cost function of cumulative trajectory errors while also considering the impact of their control outputs on each other. The above studies on shared controllers in HSCVs mainly focus on obstacle avoidance and lane keeping scenarios. However, previous research mentioned above on HSCV shared controllers focused primarily on static driving environments, such as safe avoidance of static obstacles on the road or lane keeping on a road without other vehicles, and it lacks consideration of the impact of complex factors such as vehicle interaction.
In the complex traffic environment of the future, it will be necessary for HSCVs to share the road with adjacent traffic participants. Some research on how to design a safe and effective control scheme for HSCVs to avoid SVs or static obstacles safely was conducted. In [
20], a method was demonstrated that integrates driver control commands into a constrained MPC and defines an environmental envelope and a stable handling envelope in the shared controller to ensure safe and stable obstacle avoidance driving. In [
28], the elliptical driving safety field is used to design a strategy to avoid surrounding vehicles for human–machine shared control. Yue et al. [
29] developed a spatial collision risk system that allocates driving authority between the driver and the automation system to avoid surrounding vehicles. In [
27], MPC and game theory are used to simulate the impact of the interaction between the driver and the automation system in obstacle avoidance scenarios. However, the status of obstacles or surrounding vehicles (SVs) is static or determined in the above studies while ignoring the influence of the behavioral changes of SVs. Advances in sensors and vehicle-to-vehicle communication technology have facilitated the development of connected autonomous vehicles (CAVs) [
30]. The impact of the different driving styles (aggressive, normal, cautious) of vehicles on interactive behavior in lane changing and unsignalized roundabout scenarios has been studied in the field of CAVs [
30,
31,
32]. However, current HSCV studies need to give more attention to complex traffic conditions, especially multi-vehicle interaction scenarios with different driving styles.
How to ensure safe driving between HSCVs and SVs in uncertain traffic environments, especially in multi-vehicle interaction scenarios with different driving styles, is still an open issue. Based on a non-cooperative game, this paper designs a safe, interactive control method for HSCVs with surrounding vehicles with different driving styles. The main contributions are as follows. (1) The driver’s control commands in the HSCV, as well as the uncertain driving behavior of SVs, especially the aggressive behavior of neighbor vehicles that suddenly change lanes or accelerate to occupy the road, are taken into account by the automation control system of the HSCV to ensure safe driving. (2) The coupling optimization problem of the HSCV in a multi-vehicle interaction scenario is transformed into a non-cooperative game obstacle avoidance control problem. The iterative optimal response method is adopted to find Nash equilibrium solutions for these non-cooperative games.
The structure of the article is as follows. Problem formulation and the overall system framework are described in
Section 2.
Section 3 displays the vehicle dynamics model and a comprehensive driver model considering lateral and longitudinal control. Then,
Section 4 establishes the human–machine shared control model and shared control strategy and demonstrates the non-cooperative game interaction method between HSCV and SVs, considering different driving styles. In
Section 5, the feasibility of the algorithm is tested and analyzed in different scenarios.
Section 6 concludes this study.
2. Problem Formulation
As introduced in
Section 1, existing research on the traffic participants that HSCV needs to avoid in safe driving are usually set as static obstacles, or SVs, with fixed driving characteristics, and the motion state remains unchanged. However, there are significant differences in the driving styles of different drivers, and the research methods related to driving style recognition include the Markov model, K-means clustering, Bayesian learning, and other methods [
31]. Usually, the three labels of aggressive, moderate, and cautious are used in many studies to distinguish driver styles [
30,
33,
34,
35]. Aggressive drivers often pursue traffic efficiency and perform sharp acceleration and steering behaviors. For example, an aggressive driver may suddenly accelerate and seize the road, preventing neighbor vehicles from changing lanes. Aggressive drivers even have the dangerous behavior of suddenly changing lanes and ignoring the existence of neighbor vehicles. However, cautious drivers worry about driving safety and will choose a lower speed and maintain a longer following distance. This article focuses on the impact of the dangerous behavior of SVs on HSCVs and how to safely control HSCVs rather than the classification of driving styles. The driving style of SVs will be designed based on the driving style cost function, in which two critical indicators of driving safety and travel efficiency that reflect personalized driving style will be taken into consideration.
Lane changing is a typical driving behavior of vehicles which is also prone to lead to traffic accidents, especially in high-speed scenarios. This paper mainly focuses on ensuring the safety control of an HSCV in the lane changing scenario, including the HSCV’s avoidance of the sudden lane changes of neighbor vehicles (NVs). The driving environment module in
Figure 1 shows common driving scenarios in which the red vehicle driving on road 2 is an HSCV controlled by a human driver and an automation system. The vehicles on either side of the HSCV are represented as NV1 and NV2, respectively. The vehicles in front of the road are represented as leader vehicles (LVs). The HSCV is the subject of this study, and it can also be expressed as an ego vehicle, and all NVs and LVs around the HSCV can be called SVs. For the convenience of expression, superscript symbols
e and
are proposed to distinguish the HSCV from SVs, where
i is the index of SVs.
The overall safety obstacle avoidance control framework of the HSCV is illustrated in
Figure 1. Firstly, before the HSCV executes vehicle control commands, its automation control system needs to integrate the control commands of the driver and the control system based on the allocated driving authority. The driver’s control commands are simulated by the brain emotional learning circuit model (BELCM), and the driving control authority between the driver and the control system is dynamically adjusted in real time by the driving safety field simulated by the driving environment information. In addition to the driver control input, the HSCV automation control system must also consider the interaction with SVs with different driving styles, which the driving style cost function will simulate. Finally, the non-cooperative game method was adopted to find the optimal solution for the HSCV to achieve safe control and obstacle avoidance.
5. Experimental Results and Analysis
HSCVs must share the road with surrounding vehicles in future complex traffic environments, especially in lane change scenarios prone to traffic accidents. The automation control system in an HSCV not only needs to assist the driver in safely changing lanes but also needs to consider how to safely avoid SVs that suddenly change lanes. This section designs two experimental scenarios of HSCV active lane change and HSCV passive avoidance of vehicles that suddenly change lanes to verify the feasibility and effectiveness of the designed safety control scheme, as shown in
Figure 5. Scenario 1 shows the impact of NV1’s behavior of slowing down to give way or accelerating to seize the road when the HSCV changes lanes. The dangerous situation of NV2 suddenly changing lanes to compete with the HSCV and occupy the middle lane is considered in Scenario 1. Finally, Scenario 2 demonstrates how a lane-keeping HSCV in a middle lane can safely avoid neighbor vehicles that suddenly change lanes.
Assume that the ego vehicle is an HSCV and all neighbor vehicles of the HSCV are CAVs. All experimental scenarios were simulated in Matlab. The vehicle and driver characteristic parameters are given in
Table 2, which include vehicle control input limitations.
Table 3 displays the initial desired trajectory state and expected vehicle speed of the HSCV and SVs in the above two scenarios. It is worth noting that all lanes have a maximum speed limit of 25 m/s.
5.1. Scenario 1 Test
In Scenario 1, a common HSCV single lane change case was tested, and it was assumed that the lanes of the HSCV, NV1, and NV2 were represented as lane 1, lane 2, and lane 3, respectively. In this designed scenario, the HSCV driver in lane 1 is affected by the low speed of LV1 (assuming it keeps moving forward at a speed of 15 m/s), which leads to the lane-changing behavior of the human driver in the HSCV. Subsequently, in cases a and b, NV2 is set to lane keeping in lane 3, and only the effect of the different responses of NV1 on the HSCV is studied. NV1 in case a has a moderate level of aggressiveness, while NV1 is set with a high level of aggressiveness in case b. Case c and case d are supplements to the first two cases. NV1 is set to a low aggressiveness level, and the impact of the sudden lane changing behavior of NV2 with a high level of aggressiveness on the HSCV is studied. In all cases of Scenario 1, the initial velocities of the HSCV and LV1 are 18 m/s and 15 m/s, respectively, and the initial positions of the HSCV, NV1, NV2, and LV1 are , respectively. The initial velocities of NV1 and NV2 are 20 m/s and 15 m/s in cases a and b, and they are both 16 m/s in cases c and d.
Figure 6,
Figure 7 and
Figure 8 show the experimental results of vehicle trajectory, vehicle longitudinal speed, and longitudinal position, respectively, under the influence of different driving styles of NV1 and NV2. It can be found that NV1 will slow down and give way when it is in a low or moderate level of aggressiveness. The difference between low-level and moderate-level aggressive NV1 is that the former will maintain a greater distance between vehicles. In case a, the human driver in the HSCV can safely and smoothly change lanes. In case b, high-level aggressive NV1 will accelerate to occupy the road, and the automation control system in the HSCV will modify the driver’s control commands to avoid NV1 safely. As the collision threat caused by the acceleration of NV1 increases, the automation control system gradually decelerates the HSCV and corrects the steering angle to maintain a safe distance from NV1. Until the HSCV safely avoids NV1, it gradually releases control authority to the driver, restores the driver’s desired speed, and assists the driver in changing lanes. Cases c and d show the experimental results that the HSCV automatic control system can ensure the safe avoidance of NV2 under two driving conditions: driver giving up lane change and driver insisting on lane change.
Figure 9 and
Figure 10 present the HSCV front steering angle and the curve of the driving control authority between the driver and the automation control system, respectively. In case a, since the safety threat posed by NV1’s deceleration is very small, the automation control system in the HSCV only plays an auxiliary role, and the steering angle of the vehicle is mainly controlled by the driver. Cases b, c, and d show the situation where the SV and HSCV compete for the same lane. The HSCV automation control system will quickly deprive the driver of the control authority and perform safe avoidance until the driver senses the danger and returns to the original road, or it will assist the driver who insists on changing lanes. As shown in
Figure 10, the automation control system increases intervention as environmental risks increase, and the driver’s control authority
gradually decreases. After the driver completes the lane change or gives up the lane change, the environmental danger is reduced, and the driver’s control authority
gradually approaches 1.
5.2. Scenario 2 Test
Scenario 2 consists of cases e, f, g, and h and considers HSCV passive avoidance of sudden lane changes by adjacent vehicles. In this scenario, the HSCV, NV1, and NV2 are in lane 2, lane 1, and lane 3, respectively. Faced with the competitive lane change behavior of NV1 to lane 2, the driver in the HSCV may choose to change lanes to avoid collision or slow down to give way. In cases e and f, the impact of the different driving styles of NV2 on the HSCV of passive lane change to road 3 to avoid NV1 was tested. Cases g and h tested the HSCV that insisted on lane keeping and safely avoided the NV1 that changed lanes from different locations. In all cases of Scenario 2, the initial speed of the HSCV and NV2 is set to 18 m/s. The initial speed of NV1 is 16 m/s in cases e and f, while it is 18 m/s in cases f and g. The initial position of the HSCV is in all cases of Scenario 2. The initial position of NV1 is in cases e, f, and g and in case h. The initial position of NV2 is in cases e and f, while it is in cases g and h.
Figure 11,
Figure 12 and
Figure 13 show the vehicle trajectory, vehicle speed, and vehicle position in Scenario 2. In case e, it can be found that when the aggressiveness level of NV2 in lane 3 is low, the driver in the HSCV can smoothly change lanes to avoid NV1 which suddenly changes lanes to lane 2. Case f supplements case e and tests the situation where NV2 competes with the HSCV for lane 3. As the threat of collision between the HSCV and NV2 increases, the automation control system in the HSCV will intervene in vehicle speed and wheel angle to avoid collision with NV2 until the driver gives up the lane change and desired vehicle speed and returns to the original road at a low speed. Case g shows that the human driver and the HSCV avoid NV1’s lane change by actively slowing down, slightly steering, and gradually returning to the driver’s desired speed after completing the safe avoidance. Case h shows the dangerous situation of NV1 suddenly accelerating and changing lanes from the blind spot behind the HSCV, which is invisible to human drivers. The automation control system in the HSCV performs emergency collision avoidance on NV1 by decelerating and controlling the steering angle until the avoidance is successful and then assists the driver who chooses to follow the leader vehicle at a low speed to maintain lanes.
Figure 14 and
Figure 15 show the control of steering angle by the driver and automation system in HSCV and the dynamically allocated driving control authority, respectively. In the case of e, due to NV2 slowing down to give way, HSCV is mainly controlled by the human driver and can change lanes smoothly to avoid NV1, which suddenly changes lanes. However, in case f, NV2 with a high aggressiveness level will bring a higher collision threat. The automated control system in the HSCV will reduce the driver’s control authority until the driver gives up the lane change. Then, the value
of the driver’s control authority will gradually increase to close to 1. In cases g and h, as the collision threat caused by NV1’s sudden lane change increases, HSCV will allocate more driving authority to the automation control system to intervene in driving. The difference between cases g and h is that in case g, the NV1 that changes lanes in front of the HSCV reserves more space for the HSCV to decelerate and avoid collisions without requiring automation system intervention in the steering angle. In contrast to case g, HSCV in case h needs more steering control to avoid collision when facing NV1 changing lanes behind it.