Emergency collision avoidance control strategy based on four-wheel steering and differential braking


 Path tracking control strategy of emergency collision avoidance is the research hotspot for intelligent vehicles, and active four-wheel steering and integrated chassis control such as differential braking are the development trend for the control system of intelligent vehicle. Considering both driving performance and path tracking performance, an active obstacle avoidance controller integrated with four-wheel steering (4WS), active rear steering (ARS) and differential braking control (RBC) based on adaptive model predictive theory (AMPC) is proposed. The designed active obstacle avoidance control architecture is composed of two parts, a supervisor and an MPC controller. The supervisor is responsible for selecting the appropriate control mode based on driving vehicle information and threshold of lateral and roll stability. In addition, a non-linear predict model is employed to obtain the future states of the driving vehicle. Then the AMPC is used to calculate the desired steering angle and differential braking toque when the driving stability indexes exceed the safety threshold. Finally, the proposed collision avoidance path tracking control strategy was simulated under emergency conditions via Carsim-Simulink co-simulation. The results show that the controller based on AMPC can be used to tracking the path of obstacle avoidance and has good performance in driving stability under emergencies.


Introduction
Currently, active obstacle avoidance is becoming the standard associate system on most intelligent vehicles and it is regarded as the most effective way to reduce traffic crash accidents, including frontal crash, side crash, rear-end crash and so on [1][2]. The obstacle avoidance control mainly includes two ways of turning and braking according to the specific traffic scenes. For obstacle avoidance control, most researchers utilize a path planner and a tracking controller [3][4]. Claussmann, et al [5] presented a review of path planning techniques over the last decade for highway autonomous driving, and described their features, applications, challenges, and open issues in details for path planning. For path tracking in obstacle avoidance conditions, steering control is the most common and effective method. Thus, various types of steering control systems for intelligent vehicles have been proposed to enhance driving stability. The first proposal was four-wheel steering (4WS) system, mainly including active front steering (AFS) [6][7] and active rear steering (ARS) [8]. However, the active steering systems affect the path tracking performance greatly with respect to yaw rate tracking under emergency. And incorporating other actuators into the control system can improve the tracking and driving performance of a vehicle, especially in emergencies [9]. As the initial stage of the autonomous driving, advanced driving assistant systems can enhance driving safety by real-time obstacle warning and conditional intervention. But the ability is limited in emergency scenarios when an obstacle suddenly appears in the middle of the road [10].
The obstacle avoidance strategies mainly include smooth curve planner [11], fuzzy-based control [12], and optimal control methods [13]. However, the vehicle cannot safely track the planned path in emergency situations, and rollover also happens frequently in highspeed collision avoidance, which can cause fatal injuries accidents and has raised much concern, especially in the vehicle with high center of gravity (CG), such as van, bus and SUV [14].
The vehicle loses stability usually due to the maneuvering in limit conditions by human factor aspects [15]. Although the active safety control technology has been commonly used in passenger cars [16][17]. For intelligent vehicles with high CG, rollover accidents maybe still occur. Thus, many approaches have been proposed to enhance the rollover stability, such as the active steering [18], active suspension [19], and differential rollover braking control (RBC) [20]. Emergency steering in highspeed obstacle avoidance is easy to cause rollover due to the generation of the large lateral acceleration [21]. Studies show differential braking and active steering are two useful strategies to restrain the rapid increasing of vehicle lateral acceleration, and prevent rollover indirectly [22].
Moreover, for path tracking and stability control in emergency situations, the rollover performance indicator is often ignored in tracking performance evaluation, which may cause the vehicle deviation from the target path under emergency. Thus, design of an integrated path tracking controller for highspeed obstacle avoidance is a hot problem [23]. Cui, Ding, Wu, and Zhou [24] designed an integrated collision avoidance system by active steering and active braking. To calculate the steering angle and improve the driving stability, a feedforward controller and a separate subsystem are used, simultaneously.
However, it may not achieve the collision avoidance objectives when the control actions of the stability controller conflict with the path tracking controller. Qian, Wang, and Zhao [25] designed a front steering controller based on MPC and integrated with differential braking by SMC, which can ensure the accuracy of path tracking and achieve sufficient rollover stability. While parametric uncertainties, speed varying, bring a great challenge to the MPC controller.
The present work uses previous knowledge to improve the path tracking performance and lateral stability by front steering and braking control. We focus on vehicle path tracking and rollover prevention for emergency collision avoidance system used ARS and RBC. To this end, a composite control strategy composed of a supervisor and an MPC controller considering tracking performance, yaw stability characters, and anti-rollover performance is proposed. The executive AMPC module based on ARS and RBC is utilized to carry out the requirements of the supervisor module. Moreover, we are interested in both driving stability and tracking performance for vehicle active obstacle avoidance system, especially the roll stability under emergency, to do this, a priority weight will be given to the yaw and roll aspect of the AMPC even though the path tracking performance became worse. We compare our method versus the classic version of MPC with a uniform weight distribution, versus a AMPC version with the distribution skewed by the priority weight and versus a classic version of PID. We show that our method reduces the peak value of vehicle yaw rate, roll angle by 40% under sufficient tracking accuracy, which means the proposed controller can be used to tracking the path of obstacle avoidance and did well in driving stability. In addition, our results provide evidence that the method can prevent rollover under high-speed emergency.
Taking an SUV vehicle (SF5) as control object and the key parameters are shown in Table 1. The rest of this article is organized as follows. Section 2 describes the used vehicle dynamic models. The obstacle avoidance controller by 4WS and ARS based on AMPC theory is setup in Section 3. Then an integrated emergency collision avoidance controller is described in Section 4. Finally, conclusions are drawn in Section 5.

Vehicle dynamics model
Two DOF vehicle model where, m is the mass of vehicle, vx, vy are the longitudinal and lateral velocity, lf and lr are the distances from CG to front and rear axle, respectively, Fyf and Fyr are vehicle's lateral forces, δf is the steering angle of front wheel, Iz is the yaw moment of inertia.
The slip angle of the front and rear tire is obtained as ( Then, the linear tire model can be expressed as where kf, kr are the vehicle cornering stiffness. Then, the vehicle's dynamic equations are obtained as 2-DOF linear model is regularly used by most scholars on active rear wheel steering design. The rear tire slip angle is obtained as where δr is the active rear wheels steering angle. Equation (6) can be expressed as Written in state equation of the equation (8), as where, x=[vy, γ], u=[δf, δr]. Also Finding the characteristic roots of equation (9), can be written as where, . It can be concluded from equation (13) that the 4WS vehicle is In stationary situations, y v =0,  =0. Equation (8) can be expressed as It has been proved that the lateral stability evaluation index of γ is adjustable by control δr before a vehicle reaching on limit operating condition (see Li, Zhao, Lin, & Xiao, 2019). According to equation (16), the rear steering controller can be designed as Front steering by preview-follower A ten-point preview steering control model is designed in Figure 2. Figure 2. Preview-follower theory for steering control.
The preview distance is ∆d. The error of lateral position between the desired path and the vehicle path can be defined as [23] where   d i y t ,   i y t are the desired and actual lateral displacement, T is the preview time, and T=1 s. It presumes that the tracking error ∆yi can be eliminated after T. Thus, where, y a  is the ideal value of y a .
The realistic absolute value of vy v x. Thus, the total velocity v= 2 2 Since v =γR (vehicle turning radius), then, Substituted equation (23) for (17), then, the 4WS system is designed as To achieve y a  for front steering system ( r = 0 where   2 a 2 1 x y The hierarchical architecture of the front steering by preview-follower is illustrated in

Carsim SUV vehicle model
The Carsim simulation software is used for validation dynamics model and control strategy designed in this article. The four-wheel-steer controller can model in Matlab. Figure 4 shows a SUV simulated in CarSim. A 275/65R18 radial pneumatic tire and generic front and rear independent suspensions are selected. The important parameters are given in Table 1.  Roll damping coefficient CՓ 5825 Nm·s/rad Acceleration due to gravity g 9.81m/s 2

Path tracking control strategy design
Considering both handing performance and path tracking performance, an active obstacle avoidance path tracking controller integrated with 4WS, ARS based on AMPC theory is designed. The path tracking control structure is illustrated in Figure 5. General 4WS for obstacle avoidance system The hierarchical control architecture of the obstacle avoidance system by four-wheel steering is illustrated in Figure 6. To design the steering controller, the cornering stiffness of front and rear axle kf, kr are set 110367 N/rad, 70287 N/rad, respectively. According to equation (17), the gain coefficient of the four-wheel steering system S1=-1, S2 =     It can be observed from Figure 8 that the maximum of ℽ has reduced -46.04 % at 3.5 s and the roll angle cut down -30.1 % at 5 s by 4WS, respectively. However, the front steer angle increased 61.8% in the peak value at about 1.8 s, and the path tracking performance was also reduced. Which means the general 4WS can help to improve the driving stability but will increase the front steer angle and path tracking error simultaneously. Figure 9 shows the 3D result of this scenario, where the blue and red cars are respectively related to 2WS and 4WS. Figure 9. Dynamic visualization of obstacle avoidance path tracking (The blue and red cars are respectively related to 2WS and 4WS).

MPC Controller Design
Through rolling optimization strategy, the MPC system can not only address the issues of tracking capability, parameters uncertain but also ensure driving stability. Therefore, the MPC based active steering is designed to track the design path, and the adaptive MPC system is introduced in this part. For the linear vehicle model, the global y position: where ψ is yaw angle.
The relevant equation of state is: where, x=[y` ψ γ Y], u= [δf, δr], The discrete state space of equation (28) is achieved based on forward Euler method, as where, = +I, = x(k) are the vehicle states at k time, x(k+1) are the vehicle states at k+1 time, I is a unit matrix, T is the discretization time.
A unique feature of the MPC method is that it can forecast the system's future state. The predicted state within P control cycle as: where, x(k+1|k), u(k+1|k) are the states predicted at k+1 time, computed at k time, respectively, Np is the predictive step length, Nc is the control step length.
The system states of the future P control periods are predicted by discretization of the state equations as: Written in state matrix form, then where, Define a sequence of reference values in the predicted P time as: where, , , According to the cumulative error between the predicted state vector and the reference value, the optimization objective function considering the constraints is as follows: where Q and R are the weight matrixes.
The MPC is an optimal control method. Combining Equations (38-40), the optimization problems can be solved for the active rear steering controller as  Figure 11.  It can be found from Figure 12    In Figure 13, it concluded that the peak value of lateral station, yaw rate and rear wheel steering angle changed obviously, when vx=80km/h, tracking accuracy is good, but the stability index of yaw gets worse. When vx=120km/h, vehicle driving stability is best, but tracking accuracy gets worse. In other words, it means the proposed path tracking control strategy based on MPC cannot adapt to vehicle speed change completely.

Adaptive MPC Controller Design
In  Figure 14 showed the structure of the adaptive MPC. Figure 14. The structure of the adaptive MPC controller.
The pre-built function of the adaptive MPC takes vx, steering angle and vehicle state as inputs. To make the vehicle path tracking controller fit for emergency collision avoidance, the preferred weights will be applied to the stability aspect and active rear wheel based on AMPC will be used even though the path tracking performance became worse. The "high-speed" denotes the dynamic velocity greater than 80km/h in this article.
The tracking accuracy and stability indexes by different controllers are displayed in Figure   15. In Figure 15, vehicle yaw rate reduced more than 30% in peak value by AMPC+4WS compared with general vehicle (2WS), and the AMPC+4WS is better adapt to variable speed condition under tracking obstacle avoidance compared with MPC+4WS controller.

Integrated active obstacle avoidance control design
For SUV vehicle, rollover maybe still occur even with 4WS+ARS system on account of the high CG. In this section, an improved active collision avoidance controller integrated with 4WS, ARS and RBC based on AMPC theory is designed. Figure 16 shows the control flow charts of the integrated controller. The supervisory module decides the corresponding mode based on the ADAS sensors signal and safety thresholds. The underlying controller is based on 4WS, ARS, and RBC to carry out the supervisory module's requirements. Figure 16. Structure of the integrated active obstacle avoidance system.

Rollover braking control strategy
The hierarchical control architecture of the AMPC rollover controller is illustrated in Figure 17. Figure 17. Hierarchical control architecture of the AMPC.
For the rollover control, design a rollover prediction module is needed. Load transfer ratio (LTR) is commonly used as where, r l , z z F F are right, left vertical loads on wheel.
By analyzing the vehicle mechanism of roll, the LTR rewrite as (see Li, Lu, Wang, & Chen, 2017): If |LTR| is larger than 0.8, it means vehicles in danger of rollover greatly. So, the threshold value of LTRS=0.8. When rollover is about to occur, the braking instruction is ordered for rollover control, however, the brake force may too large and to prevent wheels from locking, the ABS controller [26] is also added.
To get the braking force as |LTR|> LTRS, an adaptive MPC is used to calculated the braking torque. Taking the 4-DOF vehicle model as the bases for rollover controller which is given in Figure 18.
  f f r r bfl brl bfr brr Then, its discrete and incremental form is represented as: where, Considering the actuator's ability, the input of the AMPC controller should satisfy input is conducted to the vehicle at different speed, and Figure 19 shows the transient response of LTR at different initial speed. Figure 19. Transient response of LTR at different initial speed. Figure 19 indicates that the rollover risk increases with increasing the vehicle speed, especially vehicle speed over 70 km/h. And the vehicle rollover index reaches its maximum threshold limit (LTR≈1) when avoiding the obstacles with the same "Sine" steering input. Rollover status approaching at t=3.3 s and LTR can estimate the point.
A traffic accident accrued ahead of the vehicle in highway is adopted to verify the rollover control based on AMPC, and suppose that the 4WS+ARS is not working. The vehicle needs to avoid the obstacles immediately. The dynamic visualization is displayed in Figure 20, and vx=110 km/h.   Note that in Figure 21 Figure 22 shows AMPC control inputs of differential braking. Figure 22. Active braking torque of 4 wheels by AMPC.
In Figure 22, the rollover controller by AMPC generates a braking torque of 960 N·m to prevent rollover occurrence at 3.6 s, and the vehicle speed also decreases rapidly which can prove that the braking controller has come into play.

Integrated obstacle avoidance control
The supervisor of the integrated obstacle avoidance control is as follows: According to the vehicle status signal, the yaw rate γ and rollover index LTR are obtained.
Then, they are compared with the γs (ideal yaw rate) and rollover threshold value LTRs. If the deviation of the actual and the ideal yaw rate is less than ∆γs, the active rear steering controller is not working, or the ARS is working. When the actual LTR is over LTRs, the RBC is open. The control strategy of the supervisory decision model is shown in Table 2. To verify the effectiveness of the integrated obstacle avoidance control (ARS+RBC) based on AMPC for highway obstacle avoidance, the dynamic visualization of obstacle avoidance is the same as Figure 20. The vs group are the ARS, RBC and no controlled vehicle. Figure 23 illustrates the path tracking performance by different controllers. Figure 24 shows the driving stability response of yaw and roll for emergency obstacle avoidance.  It implies from Figure 23 and Figure 24(a) that the no-controlled vehicle's yaw rate comes up to 54 deg/s, it means the vehicle is close to lose lateral stability. But, the controlled vehicle by RBC+ARS and ARS can maintain lateral stability. In addition, the tracking performance is also improved.
In Figure 24(b), the peak value of vehicle roll angle reduced more than 40% in case of RBC+ARS and 10% in case of RBC compared with the regular vehicle at 3.7 s, in other words, the integrated controller can prevent rollover under emergency effectively.
Consequently, the RBC+ARS vehicle can adjust its driving states of steering angle and lateral acceleration to perform steering and braking maneuvers by the AMPC.
In summary, the proposed integrated collision avoidance strategy based on APMC can coordinate the tracking accuracy and driving safety, and can prevent rollover in emergency.

Conclusions
An integrated collision avoidance strategy based on AMPC is proposed in this paper, which can not only guarantee the path tracking accuracy of the vehicle but also enhance the driving stability under emergency. The control architecture of the proposed novel active system consists of a supervisor and an adaptive MPC. The supervisory module decides the corresponding mode based on the critical safety threshold and ADAS sensors signal. The executive controller of 4WS+ARS based on AMPC is used to carry out the supervisory module's requirements. To enhance the roll stability of intelligent vehicle in highspeed obstacle avoidance, RBC is beginning to work as the LTR over the safety threshold. Finally, the effectiveness of proposed obstacle avoidance control strategy is validated by Carsim-Simulink co-simulation. The results are summarized as follows.
For ARS model with a high weight on lateral displacement, the steering angle of rear wheels and yaw rate responses are larger than the controller with low weight, and ARS with a high weight of yaw rate index can obtain a better stability control performance.
The designed ARS and RBC work alone have limited effect on obstacle avoidance tracking characteristic and driving stability in emergency.
The active obstacle avoidance strategy integrated with ARS, and RBC based on APMC can coordinate the tracking accuracy and driving safety, and can prevent rollover in emergency.