2. State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China;
3. Research Center for Military Computational Experiments and Parallel Systems Technology, National University of Defense Technology, Changsha 410073, China;
4. Mechanical and Mechatronics Engineering Department at the University of Waterloo, 200 University Avenue West Waterloo, ON, N2L 3G1, Canada;
5. Department of Automotive Engineering, Cranfield University, Bedfordshire MK43 0AL, UK;
6. School of Water, Energy and Environment, Cranfield University, Bedfordshire MK4 30AL, UK
With the rapid development of parallel control and management theory and its numerous applications in transport automation and vehicle intelligence over the past decade [1], [2], parallel steering control, which is an aspect of parallel driving, has been steadily developed and applied in practice [3], [4]. Moreover, furthered by emerging developments in connected and automated vehicles [5], [6], parallel steering control has become a hot topic and has been garnering increased attention from both academic and industrial researchers [7].
Parallel steering control systems are composed of three components: an intelligent vehicle, a human driver and a parallel steering controller. The steering operation of the human driver and the computed steering wheel angle by the parallel steering controller are coupled by the intelligent vehicle [8], [9]. To ensure that an intelligent vehicle runs in a safe and stable manner, the final steering operation should be compared and evaluated between the human driver and the parallel steering controller, therein employing vehicle dynamic states and traffic conditions [10]. Due to its online optimization, preview performance and constrainthandling capabilities, model predictive control (MPC) represents an opportunity to provide parallel steering control for an intelligent vehicle while satisfying safety constraints [11].
Among many of the studies related to the parallel steering control issue, several schemes can be classified based on the stage of the research. One type of approach simply guides a driver that does not actively control the vehicle. In [12], an MPC approach was employed to generate optimal paths to help guide a human driver using information about the surrounding environment. In [13], a copilot driving scheme was expanded and improved, and an automated driving capability is presented. In these approaches, the vehicle is always controlled by the human driver. The parallel steering controller only provides driving advice. The controller cannot effectively avoid traffic in situations of improper operation, driver distraction or driver inattentiveness.
Another approach is to directly switch control between a human driver and a parallel steering controller. In [14], a switching strategy was presented to govern the driverassistance interaction by describing the hybrid system as an inputoutput hybrid automation. In this situation, the judgmentandswitch strategy is conducted by analyzing the state of the human driver and both traffic and road conditions. However, the stability at the switching point needs to be further discussed in this scheme.
In contrast to the abovementioned switch control, the interpretation of the driver's driving intention is adopted and described as a reference path, and a controller is designed to follow the path. In [15], a lanekeeping strategy was designed to share control of the steering wheel with the driver in an optimal manner by describing the problem as an
In addition to the abovementioned schemes, there is a parallel steering control approach that issues a final steering command by blending human driver steering operation and an optimal controller. In [16], a shared control framework for obstacle avoidance and stability control was presented using an MPC approach. The final steering command was a blended value decided by a human driver and a parallel controller simultaneously. The objective of this approach mainly follows the operation of a human driver. This will be hazardous when a human driver improperly operates the vehicle or is under certain driving conditions whereby an intelligent vehicle cannot be controlled by the human driver.
In this manuscript, motivated by the shared control scheme in [16], a parallel steering control framework is developed by blending the operation of a human driver and a parallel steering controller using a moving horizon optimization approach. The path following error and the steering operation error are employed to evaluate the current hazardous situation of the intelligent vehicle. Under the hazard evaluation, the intelligent vehicle will be mainly operated by the human driver when the vehicle runs in a safe and stable manner. In addition, the automated steering driving objective will play an active role and regulate the steering operation applied to the intelligent vehicle based on the hazard evaluation. Moreover, lateral stability, collision avoidance and actuator saturation are considered by the parallel steering controller. To verify the effectiveness of the proposed hazardevaluationoriented moving horizon parallel steering control approach, various validations are conducted and compared with a parallel steering scheme not considering the automated driving situation.
The two main contributions of this manuscript are as follows: 1) a parallel steering control framework is developed using a moving horizon optimization whereby the operation by the human driver is dominant during safe operating conditions but whereby the automated steering driving objective will regulate the steering operation in hazardous situations. 2) The hazard evaluation is performed for the parallel steering control whereby the road hazard and the steering operation error are employed to evaluate the current hazardous situation of the intelligent vehicle.
The remainder of this paper is organized as follows: In Section Ⅱ, the intelligent vehicle model and the problem description are presented. In Section Ⅲ, the parallel steering control framework using moving horizon optimization is presented, and the hazard evaluation is discussed. In Section Ⅳ, a highprecision verification vehicle model is built, and then, joint veDYNASimulink simulations are performed under various driving conditions. Finally, in Section Ⅴ, the conclusions are presented.
Ⅱ. VEHICLE MODEL AND PROBLEM DESCRIPTION A. Vehicle ModelA human driver makes decisions according to traffic conditions and a vehicle's position and dynamic states. Therefore, the vehicle model used in parallel steering control should also describe the vehicle position and lateral dynamics.
Under the assumption that the intelligent vehicle is a rigid body with nondeformable wheels, the longitudinal and lateral positions as well as the yaw angle of the vehicle can be described according to the geometric relationship described in Fig. 1(a):
$ \dot{x}_o=v\cos(\psi+\beta)\notag\\ \dot{y}_o=v\sin(\psi+\beta)\notag\\ \dot{\psi}=r $  (1) 
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Fig. 1 Vehicle model. 
where
$ \dot{x}_o=v\notag\\ \dot{y}_o=v(\psi+\beta)\notag\\ \dot{\psi}=r. $  (2) 
Considering that the lateral dynamics of the intelligent vehicle is also needed in the parallel steering control, the vehicle body coordinate system with the origin at the CoG is defined as shown in Fig. 1(b), where the positive direction of the
$ \begin{eqnarray} m{v}(\dot \beta + r) &\hspace{0.2cm}=&\hspace{0.2cm} {F_{xf}}\sin {\delta _f} + {F_{yf}}\cos {\delta _f} + {F_{yr}}\nonumber\\ {I_z}\dot r &\hspace{0.2cm}=&\hspace{0.2cm} a({F_{xf}}\sin {\delta _f} + {F_{yf}}\cos {\delta _f})  b{F_{yr}} \end{eqnarray} $  (3) 
where
Using a small angle for the front steering wheel angle
$ \begin{align*} m{v}(\dot{\beta}+r)&={F_{yf}}+{F_{yr}}\notag\\ {I_z}\dot{r}&=a{F_{yf}}b{F_{yr}}. \end{align*} $  (4) 
The lateral tire forces
$ \label{ieeeseqtire} \begin{aligned} F_{yf}&={C}_f\alpha_f\\ F_{yr}&={C}_r\alpha_r \end{aligned} $  (5) 
where
$ \begin{align} {\alpha_{f}}&=\beta+\frac{ar}{v}\delta_f\notag\\ {\label{ieeeequalphab}\alpha_{r}}&=\beta\frac{br}{v}. \end{align} $  (6) 
Then, substituting (5) and (6) into (4) and combining with (2), the lateral dynamics of an intelligent vehicle can be obtained as follows:
$ \begin{eqnarray} \dot{y}_o&\hspace{0.2cm}=&\hspace{0.2cm}v(\psi+\beta)\nonumber\\ \dot{\psi}&\hspace{0.2cm}=&\hspace{0.2cm}r\nonumber\\ \dot{\beta}&\hspace{0.2cm}=&\hspace{0.2cm}\frac{C_f+C_r}{mv}\beta+\Big(\frac{aC_fbC_r}{mv^2}1\Big)r\frac{C_f}{mv}\delta_f\nonumber\\ \dot{r}&\hspace{0.2cm}=&\hspace{0.2cm}\frac{aC_fbC_r}{I_z}\beta+\frac{a^2C_f+b^2C_r}{I_zv}r\frac{aC_f}{I_z}\delta_f. \end{eqnarray} $  (7) 
The steering system is assumed to be designed such that there is a proportional relationship between the steering wheel angle and the front wheel steering angle. Accordingly, given the relationship between the front wheel steering angle
$ \begin{align*} &\dot{x}=Ax+B \delta_{f}\notag\\ &y=Cx \end{align*} $  (8) 
where
$ \begin{align*} & A \!=\!\left[\!\! \begin{array}{cccc} 0\!&\!v\!&\!v\!\!&\!\!0\\ 0\!&\!0\!&\!0\!\!&\!\!1\\ 0\!&\!0\!&\!\frac{C_f+C_r}{mv} \!\!& \!\!\frac{aC_fbC_r}{mv^2}\!\!1 \\[2mm] 0\!&\!0\!&\!\frac{aC_fbC_r}{I_z} \!\!& \!\!\frac{a^2C_f+b^2C_r}{I_zv} \end{array} \!\!\right]\!, \;\; B \!= \!\left[\!\! \begin{array}{c} 0\\ 0\\ \frac{C_f}{mv} \\[2mm] \frac{aC_f}{I_z} \end{array}\nonumber \!\!\right]\!, \;\; C \!=\!\left[\!\! \begin{array}{c} 1\\0\\0\\0 \end{array}\nonumber \!\!\right]^{T}\!. \end{align*} $ 
The linear singletrack model is employed here to describe the dynamics of an intelligent vehicle and the parameters can be obtained in [6]. When the intelligent vehicle runs into the nonlinear region, the modelling error will become large. However, the objective of parallel steering control is ensuring the intelligent vehicle to run in the linear region, which can be satisfied by the constraints of MPC optimization. Therefore, the linear singletrack model is enough to discuss the parallel steering control here. To verify the precision of the proposed vehicle model, a comparison with the measured behavior of a test vehicle and the simulated output of a highprecision vehicle model implemented in veDYNA is performed, and the validation results are shown in Fig. 2. Moreover, it can be seen from Fig. 2 that the precision of the intelligent vehicle model is sufficient to address the parallel steering control problem. Then, by discretizing (8) at the sample time
$ \begin{eqnarray} &x(k + 1) = {A_d}x(k) + {B_d}{\delta _{f}}(k) \nonumber\\ &{y}(k) = {C_d}x(k) \end{eqnarray} $  (9) 
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Fig. 2 Model validation results for a standard doublelanechange maneuver with 
where
For the intelligent vehicle operating on the road shown in Fig. 3 with a constant longitudinal velocity, the steering operation that is integrally decided upon by the human driver and autonomous driving system should be performed to follow the desired path. The steering operation by the human driver is accepted and kept invariant when the vehicle operates safely in this situation. In contrast, if the human driver steers the intelligent vehicle too far from the desired path or makes the intelligent vehicle unstable, the parallel steering control system will correct the steering operation of the human driver until the intelligent vehicle follows the desired road safely.
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Fig. 3 Schematic diagram of the intelligent vehicle operating on the road. 
In the abovementioned parallel steering control framework, the road shown in Fig. 3 is represented by three curves: the centerline of the road,
Considering that traffic and road conditions are constantly varying, a parallel steering control system must assist human drivers in making an intelligent vehicle complete steering tasks, ensure the safety of the intelligent vehicle, and avoid colliding with the road boundaries. This represents a multiobjective and multiconstraint optimization problem in essence. Therefore, MPC is introduced to discuss the parallel steering control issue for an intelligent vehicle. Accordingly, the structure of the parallel shared steering control employing the MPC approach is shown in Fig. 4. Here, we mainly discuss the MPCbased parallel steering control, which includes the steering relations between the human driver and the parallel steering system, a description of the vehicle's stability and collision avoidance, and weighting matrix selection based on hazard evaluation.
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Fig. 4 Human and automatic parallel steering control structure. 
1) State and Output Prediction for the Intelligent Vehicle: Because vehicle state estimation schemes have already been discussed extensively in [18], [19], it is reasonably assumed that the vehicle velocity, yaw angle, sideslip angle and tireroad friction coefficient can be estimated. Moreover, the control of the steering motor is not discussed in this manuscript.
Suppose that the predictive horizon is
$ \begin{equation} \label{controller4} \begin{aligned} x(k+1k)=&A_dx(k)+B_d\delta_f(k)\nonumber\\[2mm] x(k+2k)=&A^2_dx(k)+A_dB_d\delta_f(k)+B_d\delta_f(k+1)\nonumber\\[2mm] % x(k+3k)&=A_cx(k+2k)+B_cu(k+2)\\ % &=A^3_cx(k)+A^2_cB_cu(k)+A_cB_cu(k+1)+B_cu(k+1)\\ &\vdots\\[2mm] x(k+mk)=&A^m_dx(k)+A^{m1}_dB_d\delta_f(k)+A^{m2}_dB_d\delta_f(k+1)\nonumber\\[2mm] &+\cdots+B_d\delta_f(k+m1)\nonumber\\[2mm] &\vdots\\[2mm] x(k+pk)=&A^p_dx(k)+A^{p1}_dB_d\delta_f(k)+A^{p2}_dB_d\delta_f(k+1)\nonumber\\[2mm] &+\cdots+\sum\limits_{i=1}^{pm+1}A^{i1}_dB_d\delta_f(k+m1)\nonumber. \end{aligned} \end{equation} $ 
The control input is assumed invariant when the sampling instants are beyond the control horizon
$ \begin{equation} \label{controller5} \begin{aligned} y(k+1k)=&C_dA_dx(k)+C_dB_d\delta_f(k)\nonumber\\ y(k+2k)=&C_dA^2_dx(k)+C_dA_dB_d\delta_f(k)+C_dB_d\delta_f(k+1)\nonumber\\ &\vdots\\ y(k+mk)=&C_dA^m_dx(k)+C_dA^{m1}_dB_d\delta_f(k)\nonumber\\ &+\cdots+C_dB_d\delta_f(k+m1)\nonumber\\ &\vdots\\ y(k+pk)=&C_dA^p_dx(k)+C_dA^{p1}_dB_d\delta_f(k)\nonumber\\ &+\cdots+\sum\limits_{i=1}^{pm+1}C_dA^{i1}_dB_d\delta_f(k+m1).\nonumber \end{aligned} \end{equation} $ 
Define the input sequence
$ \begin{equation*} { U(k)=\left[\!\! \begin{array}{c} \delta_f(k) \\ \delta_f(k+1)\\ \vdots\\ \delta_f(k+m1)\\ \end{array}\!\!\right], \\ Y(k+1k)}=\left[\!\! \begin{array}{c} y(k+1k) \\ y(k+2k)\\ \vdots\\ y(k+pk)\\ \end{array}\!\!\right]. \end{equation*} $ 
Accordingly, the
$ \begin{equation} \label{controller8} \begin{aligned} &Y(k+1k)=S_xx(k)+S_uU(k)\\ \end{aligned} \end{equation} $  (10) 
where
$ \begin{equation} S_u= \left[\!\! \begin{array}{cccc} C_dB_d&0&\cdots&0\\ C_dA_dB_d&C_dB_d&\cdots&0\\ \vdots&\vdots&\ddots&\vdots\\ {C_dA^{p1}B_d}&C_dA^{p2}B_d &\cdots&\sum\limits_{i=1}^{pm+1}C_dA_d^{i1}B_d\\ \end{array}\!\!\nonumber \right] \\ S_x=\left[ \begin{array}{cccc} C_dA_d &C_dA^2_d &\cdots &C_dA^p_d \end{array}\right]^T. \end{equation} $  (11) 
2) Stable Formulation: Considering the steadystate condition in (4), that is,
$ \begin{equation} \label{jas:equ:rsteady} mvr_{ss}=F_{yf}+F_{yr}. \end{equation} $  (12) 
Assuming that the longitudinal tire forces are zero and that the effects of weight transfer are neglected, the following relationship can be obtained [20]:
$ \begin{equation} \label{jas:equ:fyfmax} F_{yf, {\text{max}}}+F_{yr, {\text{max}}}=mg\mu \end{equation} $  (13) 
where
Combining (12) and (13), the maximum steadystate yaw rate can be obtained as follows:
$ \begin{equation} \label{jas:equ:yawrss} r_{ss, {\text{max}}}=\frac{g\mu}{v}. \end{equation} $  (14) 
Another important consideration for vehicle lateral stability is the saturation of the tire sideslip angle. As described in (6b), the sideslip angles of the rear tires can be approximated as
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Fig. 5 Phase diagram of tire sideslip angle with different initial values of 
Accordingly, the bound of the tire sideslip angle can be obtained as follows:
$ \begin{equation} \beta_{\text{max}}=\alpha_{r, sat}+\frac{br}{v}. \end{equation} $  (15) 
Based on the abovementioned safety considerations, the yaw rate and sideslip angle should satisfy the following constraints:
$ \begin{eqnarray} &r_{ss, \min}\le r \le r_{ss, \max}\nonumber\\ &\beta_{\min} \le \beta \le \beta_{\max} \end{eqnarray} $  (16) 
where the minimum yaw rate and sideslip angle can be chosen as
$ \begin{equation} \label{jas:equ:stablecon} C_s x(k+1)\le b_s \end{equation} $  (17) 
where
$ \begin{equation*} C_s=\left[\! \begin{array}{cccc} 0&0&0&1 \\ 0&0&1 &\frac{b}{v_x} \\ 0&0&0 &1 \\ 0&0 &1& \frac{b}{v_x} \end{array}\! \right], \;\;\; b_s=\left[\!\begin{array}{c} \frac{ g \mu}{v_x} \\ \alpha_{r, sat} \\ \frac{g \mu}{v_x} \\ \alpha_{r, sat} \end{array}\! \right]. \end{equation*} $ 
3) Collision Avoidance: To ensure that the intelligent vehicle does not collide with other vehicles, it is better to keep it running in its own lane.
The abovementioned objective can be achieved by restricting the lateral positions of the vehicle front end
$ \begin{equation} \label{jas:equ:yo} y_r{'}+\omega_{p} \le y_i \le y_l{'}\omega_{p}, \;\; i=F, R \end{equation} $  (18) 
where
The relationship among the vehicle lateral position, front end
$ \begin{eqnarray} &y_F=y_o+l_f(\psi+\beta)\nonumber\\ &y_R=y_ol_r(\psi+\beta) \end{eqnarray} $  (19) 
where
Substituting (19) into (18), collision avoidance can be achieved by restricting the lateral position of the intelligent vehicle to satisfy the following constraints:
$ \begin{equation} \label{jas:equ:cr} C_rx(k+i)\le b_r \end{equation} $  (20) 
where
$ \begin{equation*} C_r=\left[\! \begin{array}{cccc} 1& l_f & l_f&0 \\ 1&l_r &l_r&0 \\ 1& l_r&l_r&0 \\ 1& l_r&l_r&0 \end{array}\! \right], \;\; b_r=\left[\!\begin{array}{c} y_l\frac{w}{2}\omega_p \\ y_r\frac{w}{2}\omega_p \\ y_l\frac{w}{2}\omega_p \\ y_r\frac{w}{2}\omega_p \end{array} \!\right].\end{equation*} $ 
4) Actuator Saturation Formulation: To avoid saturation of the mechanical system, the steering action of the steering wheel motor should be limited. The corresponding requirement is formulated as the constraints
$ \begin{equation} \label{jas:equ:actuator} \delta_f(k+i)\le \delta_{f, sat} \end{equation} $  (21) 
where
In addition, to ensure that the steering operation is smooth, the control action between two sample instants should be minimized:
$ \begin{equation} \label{jas:equ:controlaction} \Delta \delta_f(k+i)\le \dot{\delta}_{f, sat} T_s. \end{equation} $  (22) 
5) Moving Horizon Parallel Steering Control: As shown in Fig. 4,
$ \begin{equation} \label{jas:equ:j1} J_1=\delta_f(k)\delta_h(k). \end{equation} $  (23) 
In addition, considering the mechanical characteristics of the steering actuator and to ensure the smooth performance of the control system, the difference between two steering actions should be limited. The corresponding requirement is described as follows:
$ \begin{equation} \label{jas:equ:j2} J_2=\sum\limits_{i=1}^p\left(\Delta \delta_f (k+i)\right)^2 \end{equation} $  (24) 
where
To minimize
$ \begin{equation} \label{jas:equ:ja} J_H=\Gamma_h\delta_f(k)\delta_h(k)+\Gamma_d \sum\limits_{i=1}^p\left(\Delta \delta_f (k+i)\right)^2 \end{equation} $  (25) 
where
Considering the fact that the intelligent vehicle will deviate from the road centerline or experience instabilities resulting from improper operation by the human driver, it is necessary to consider the roadfollowing and stability performance of parallel steering control. Accordingly, an additional objective function is introduced as follows:
$ \begin{equation} \label{jas:equ:jaauto} J_A=\Gamma_y\Y(k+1)Y_c(k+1)\+\Gamma_{\beta} \\left(\beta(k+i)\right)\ \end{equation} $  (26) 
where the first element
From (26), the autonomous driving condition is considered in the objective function of the parallel steering control to make the intelligent vehicle follow the road centerline and ensure stability. To minimize both
$ \begin{equation} \label{jas:equ:objectiveall} J(y(k), \;\; U(k), m, p)=J_H+\Gamma J_A \end{equation} $  (27) 
where
According to the objective function defined in (27) and the constraints described in (17), (20), (21) and (22), the MPCbased optimization problem for parallel steering control can be defined as follows:
$ \begin{align} &\mathop {\min }\limits_{U(k)} (27)\notag\\ {\text{s.t.}}\quad&x(k + 1) = {A_d}x(k) + {B_d}\delta_f(k)\notag\\ &y(k + 1) = {C_d}x(k)\notag\\ &x(kk)=x(k)\notag\\ &C_rx(k+i)\le b_r \notag\\ &C_sx(k+i)\le b_s \notag\\ &i=1, 2, \ldots, p\notag\\ &\delta_f(k+j)\le \delta_{f, sat}\notag\\ &\Delta\delta_f(k+j)\le \dot{\delta}_{f, sat}T_s\notag\\ &j=1, 2, \ldots, m. \end{align} $  (28) 
At each execution of the controller, the optimization problem defined in (28) is solved for each sample instant, and the optimal input corresponding to the lowest objective value is used. As is common with MPC, the first element of the optimal control sequence is applied to the intelligent vehicle, and the optimization problem is resolved in the next sample instant. Thus, parallel steering control by a human driver and autonomous driving system can be achieved.
The difference between the scheme in [6] and the approach in this manuscript is that the control issue is differentiated from path following and parallel steering control. Despite MPC control approach is used in these two control issues, the cost functions are selected to be different and the safety constraints are additional considered in the proposed scheme here.
C. Weighting Factor Selection Based on Hazard EvaluationIt is concluded from (27) that the weighting factor
The road hazard is employed to describe the vehicle position dangerous for the intelligent vehicle as follows:
$ \begin{equation} E_{road}=(y(k)y_c(k))^{E_A} \end{equation} $  (29) 
where
The road hazard is not sufficient enough to balance the weights of the driver and the autocontroller without knowing the information of the current driver's status. Several aspects should be considered when choosing the parameter to reflect the current driver's behavior. The first one is that the parameter should be selected to reflect the performance of driver's behavior. The second is that the adopted system's information under the current scheme should not introduce additional sensor information. The third is that the information from the parallel steering controller should be sufficiently considered and used.
$ \begin{equation}\label{jas:equ:30} E_{driver}=\frac{\delta_{human}(k)\delta_f(kk1)}{E_B} \end{equation} $  (30) 
where
The relationship of the weighting factor
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Fig. 6 Membership function for road hazard, human driver hazard and weighting factor. 
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Fig. 7 Weighting factor based on hazard evaluation. 
In this section, the Hongqi intelligent vehicle is built to verify the proposed parallel steering controller. Then, the joint SimulinkveDYNA simulations are performed to determine the effectiveness of the proposed hazardevaluationoriented parallel steering controller.
A. Vehicle Model for Control Performance VerificationTo investigate the performance of the proposed hazardevaluationoriented moving horizon parallel steering control scheme for an intelligent vehicle, the versatile vehicle dynamics simulation software veDYNA
To reflect the dynamic characteristics of an intelligent vehicle, a highly efficient vehicle model that can reflect most of the vehicle dynamics under normal and critical operating conditions is needed. Therefore, an intelligent vehicle model of a Hongqi HQ430 passenger car shown in Fig. 8(a) is utilized to be cosimulated and to verify the effectiveness of the controller proposed in this manuscript. The detailed model structure of the Hongqi HQ430 intelligent vehicle can be seen in Fig. 8(b); the vehicle is established and extended based on the vehicle dynamics software veDYNA. The basic and empirical parameters of the HQ430 can be obtained from its technical documentation. The characteristic parameters of the HQ430 can be identified from experimental data obtainable from various types of characteristic experiments. Moreover, because veDYNA does not contain an automatic transmission and because an A761E automatic transmission is equipped on the Hongqi HQ430, it is essential to discuss the modeling of the transmission to improve the accuracy of the Hongqi HQ430 intelligent vehicle model.
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Fig. 8 Actual picture and simulation model of Hongqi HQ430 vehicle. 
Based on the above model and the identified parameters of the Hongqi HQ430 passenger vehicle, the longitudinal and lateral dynamics are both validated through representative vehicle experiments. Accordingly, the average longitudinal dynamic precision is 91.3%, and the average lateral precision can be obtained as 79.4%. The detailed verification was introduced in [22].
B. Simulation ResultsAccording to the hazardevaluationoriented parallel steering control issue described by (28), the predictive horizon and the control horizon are selected as
1) Safe Driving Verification: To verify the effectiveness of the proposed hazardevaluationoriented parallel steering control in safe driving situations, the simulation verification is performed under the condition of a slalom maneuver on an asphalt road with a friction coefficient of
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Fig. 9 Simulation results for parallel steering control under slalom maneuver. "No auto" denotes parallel steering control without considering the roadfollowing and stability performance 
It can be seen from Figs. 9(a) and (b) that the yaw rate and sideslip angle are small, which indicates that the intelligent vehicle is operating safely during the slalom maneuver. Because the human driver can operate the intelligent vehicle and complete this operating task at a relatively low velocity, the parallel steering control scheme only needs to follow the operation of the human driver and ensure that the difference between two steering actions is not excessive, which can be described by
2) Hazardous Driving Verification: To validate the performance of the proposed parallel steering control approach under hazardous operating conditions, a doublelanechange maneuver is performed on a wet asphalt road with a friction coefficient of
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Fig. 10 Simulation results for parallel steering control under the doublelanechange maneuver.
"No auto" denotes parallel steering control without considering the roadfollowing and stability performance 
It can be observed from the sideslip angle shown in Fig. 10(a) that the maximum sideslip angle is larger than 0.1 rad. This indicates that the intelligent vehicle tended to lose stability. Moreover, it can be concluded from Fig. 10(a) that the sideslip angle obtained from the approach in this manuscript is smaller than that in the scheme that did not consider the hazard evaluation. The result indicates that the proposed hazardevaluationoriented parallel steering control scheme is more effective than that not considering the hazard evaluation. The conclusion can also be obtained from the yaw rate shown in Fig. 10(b). The intelligent vehicle can perform the doublelanechange maneuver under the control of these two parallel steering control schemes, as can be seen from Fig. 10(c). This indicates that these two parallel steering control approaches can regulate steering operations implemented by a human driver. Moreover, compared with the parallel steering control scheme that did not consider the hazard evaluation, the parallel steering control approach introduced in this manuscript obtains better performance, as shown in Fig. 10(c), by regulating the front steering wheel angle shown in Fig. 10(d). This is because the hazard evaluation plays an active role in the hazardous situation, thereby obtaining better performance.
In addition, the road hazard factor
3) Improper Operation by Driver: We further validate the performance of the proposed hazardevaluationoriented parallel steering control scheme for the situation of improper operation by the human driver. The verification results are shown in Figs. 11 (a)(d).
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Fig. 11 Simulation results for parallel steering control considering improper operation by the human driver. "No auto" denotes parallel steering control without considering the roadfollowing and stability performance 
It can be concluded from the trajectory of the intelligent vehicle shown in Fig. 11(a) that the human driver operates the intelligent vehicle beyond the driving lane in this situation. In this case, both the parallel steering control scheme proposed in this manuscript and the approach that does not consider the hazard evaluation can regulate the front steering wheel angle, as shown in Fig. 11(b). This is because the constraints play an effective role and restrict the lateral movement of the intelligent vehicle. Moreover, because the hazardevaluationoriented parallel steering control scheme also considers the road centerline tracking and stability performance in the objective function described in (28), the approach proposed in this manuscript is more effective than that not considering the hazard evaluation, which can be seen from the sideslip angle and yaw rate shown in Figs. 11(c) and (d) , respectively.
Ⅴ. CONCLUSIONIn this paper, a parallel steering control framework is proposed for an intelligent vehicle using a moving horizon optimization approach that considers the lateral stability, collision avoidance and actuator saturation sufficiently and describes them as constraints. Hazard evaluation is performed to ensure the safe operation of the intelligent vehicle based on the road hazard and the steering operation error. The intelligent vehicle will be mainly operated by the human driver when the vehicle runs in a safe and stable manner. The automated steering driving objective will play an active role and regulate the steering operation applied to the intelligent vehicle based on the hazard evaluation. The proposed hazardevaluationoriented moving horizon parallel steering control has been confirmed to be an effective approach in humanmachine cooperation under both conventional conditions and hazardous conditions.
In the future works, considering the current steering difference between human driver and actual front steering wheel angle may cause some drastic switch jitter which may cause driver more nervous, the minimization problem of (23) should be considered as
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