The Indirect Shared Steering Control Under Double Loop Structure of Driver and Automation

Yantao Tian, Yanbo Zhao, Yiran Shi, Xuanhao Cao, and Ding-Li Yu

Abstract—Due to the critical defects of techniques in fully autonomous vehicles, man-machine cooperative driving is still of great significance in today’s transportation system. Unlike the previous shared control structure, this paper introduces a double loop structure which is applied to indirect shared steering control between driver and automation. In contrast to the tandem indirect shared control, the parallel indirect shared control put the authority allocation system of steering angle into the framework to allocate the corresponding weighting coefficients reasonably and output the final desired steering angle according to the current deviation of vehicle and the accuracy of steering angles. Besides, the active disturbance rejection controller(ADRC) is also added in the frame in order to track the desired steering angle fleetly and accurately as well as restrain the internal and external disturbances effectively which including the steering friction torque, wind speed and ground interference etc.Eventually, we validated the advantages of double loop framework through three sets of double lane change and slalom experiments, respectively. Exactly as we expected, the simulation results show that the double loop structure can effectively reduce the lateral displacement error caused by the driver or the controller, significantly improve the tracking precision and keep great performance in trajectory tracking characteristics when driving errors occur in one of driver and controller.

I. Introduction

ALTHOUGH our science and technology developed rapidly and realized epochal achievement in recent years,fully autonomous driving still cannot deal with the complicated and fast-changing traffic environment in an effective way. From another point of view, with the improvement of intelligence and automation technology,automation can bring great convenience to all aspects of human life such as transportation, sorting system of logistics and industrial manufacture. Therefore, man-machine shared control becoming an alternative solution to meet the needs of people in many fields [1]–[3], especially in the region of highly automated driving [4], [5]. One of the key issues of shared control is how to constitute the sharing control structure and design weighting allocation strategy so as to reduce the conflict between auxiliary system and driver as much as possible [6]–[8]. In other words, conflicts between the driver and systems for automated steering are important issues that affect the safety of driver and the acceptability of the system [9]–[11]. In order to solve the above problems,Griffiths proposed the concept of haptic feedback of shared control earlier in 2004 [12], [13], the experiments show that the use of haptic assistant on steering wheel can improve the performance of lane keeping by 30 percent, reduce the visual demand by 29 percent, and increase the reaction time by 18 ms,which illustrate that the shared controller reduces the visual demand and attention burden of driver. Generally speaking,shared control with haptic feedback was regarded as direct shared control because driver can perceive the torque from the controller by the steering wheel [14]–[17]. Balachandran et al.proposed the haptic feedback for obstacle avoidance prediction based on model predictive control in 2016 [18], the system can provide proper help or warning for driver through predicting the driver’s driving path and then the constraintbased approach of envelope control is further applied to the system to ensure vehicle safety while being minimally invasive to the driver [19]. Abbink proposed a new parameter named level of haptic authority (LoHA) which is applied to shared control system to achieve smooth transfer the control authority between driver and automation [6]. Moreover, in[20], a new haptic shared steering control framework for automated driving systems is proposed to improve the safety of driving tasks. In this framework, the steering controller minimizes its control when driver intervenes in the controlloop by adapting the relative weight in the cost function online. Reference [21] investigated human-machine cooperation when driving with different degrees of a shared control system. By means of a direct intervention on the steering wheel, shared control systems partially correct the vehicle’s trajectory and, at the same time, provide continuous haptic guidance to the driver. Recent researches put many efforts on the human-machine interaction for the sake of reducing intention conflicts or maneuver conflicts. For example, [22]proposed a new approach to consider such an interaction via a fictive driver activity parameter introduced into the roadvehicle system. By introducing a measured weighting parameter into the road-vehicle system, the assistance control actions can be designed in accordance with the real-time driving activity of drivers. In [23], the design of a driver steering assistance system is presented, which provides a corrective torque in order to guide the driver. Similarly, [24]proposed a shared control framework for driver’s override of automatic steering control. This framework formulates the control transfer between driver and system as a constrained optimization problem which is solved online by a model predictive controller. Furthermore, the question of ability limitation and absolute reliability of the current shared control systems is discussed in [25], [26].

However, there are some defects in direct shared control,first of all, driver can not identify auxiliary torque of control system under certain circumstances, because the torque act on the steering wheel involve the feedback torque from the steering system and tire, which all interfere the judgement about the torque of controller. Secondly, the conflicts between driver and controller will significantly influence the comfort of driving. For example, if the driver intends to deny the action of the control system due to different strategies or driver’s misunderstanding of regarding it as disturbance torque, he or she will increase the stiffness of arms to produce more force to resist it, which might seriously affect the driving experience and go against the original intention of driving assistance. In order to overcome the weaknesses of haptic shared control, Li et al. introduced the indirect shared control framework as an alternative solution [27]. The advantage of this frame is that the driver steering input signal was transformed and optimized by model predictive control(MPC) controller and the steering torque of controller’s will not be perceived by the driver. This method not only improves the safety and comfort of vehicle driving, but also makes the driving task more relaxed and labor-saving. Wang et al.proposed a new concept of parallel driving in cyber-physicalsocial system, which offers an ample solution for achieving a smooth, safe and efficient cooperation in future road transportation systems [28], [29].

Nevertheless, there still exist two weaknesses need to be improved and perfected. 1) Due to series connection of driver and controller, the faulty operation of controller will directly affect the driver’s operation and even threaten the safety of vehicle driving; 2) The output wheel angle can not track desired value accurately because of internal and external disturbances, which is ignored by previous work.

The main purpose of this paper is to further improve the safety of shared driving. Therefore, we proposed the indirect shared control under double loop structure of driver and automation. First of all, the controller independently calculates the steering angle, and then the steering angles of both driver and controller will be sent to the authority allocation system. Then, the ADRC will track the desired steering angle rapidly and precisely which is weighted by the authority allocation model. The advantages of double loop framework can be stated in following several aspects. First,the steering angle arbitration system based on fuzzy inference rules in this structure is to determine which angle is more accurate so as to improve the trajectory tracking precision of vehicle driving. Secondly, the steering angle arbitration system can allocate the weighting of steering angle reasonably according to the accuracy of the two steering angles, which could reduce the impact of faulty operations of driver or controller on driving safety. Lastly, the ADRC can track the desired angle rapidly and accurately with the effect of internal and external disturbances which including the steering friction torque, wind speed and ground interference, etc. The performance of proposed double loop structure has been validated through double lane change and slalom tests in CarSim. The relative results will be revealed in Section IV.

The main contributions of this paper can be described as two points. 1) the steering angle arbitration system based on fuzzy inference rules is introduced to the structure so as to determine which angle is more accurate, which can reduce the impact of faulty operations of driver or controller on driving safety; 2) The ADRC is added to the structure so as to restrain internal and external disturbances and then improve the tracking precision of steering angle, which can further enhance the safety of shared driving.

The construction of this paper is organized as follows: In Section II, the advantages of double loop structure as well as the main models included will be described. The specific description and modeling of framework mentioned above is realized in Section III. The experimental design and analysis of simulation results will be arranged in Section IV.Conclusions and future work are finally discussed in Section V.

II. Framework Description

The series connection structure is shown in Fig.1(a),obviously, the driver’s steering angle is transformed by controller and then the transformed steering angle will be transmitted to the vehicle system. However, the parallel connection structure described in Fig.1(b) turn the controller and driver into two independent closed loops. Then the authority allocation system allocates the weighting properly according to the accuracy of two steering angles. In other words, if the driver’s steering angle is accurate enough, the weight coefficient of driver’s will be increased. Conversely,more weight will be allocated to controller. Thus, the double loop frame guarantees the accuracy and safety of driving even though one of them appears faulty operation. ADRC control the motor to output corresponding torque to make the steering angle of vehicle more accurate. Besides, it can also effectively restrain the steering error caused by internal and external disturbances, which can improve the performance of antiinterference and robustness.

III. Modeling

A. Vehicle Model

Fig.1. Block diagrams of two shared control frameworks: (a) series connection; (b) double loop framework.

The vehicle model used in predict equation of MPC is two dimensional kinematic model shown in Fig.2 [30]. Its nonlinear state-space equation can be described as (1).(Xf,Yf) and (Xr,Yr) are coordinates of front axle and rear axle(the subscripts f and r represent the front wheel and rear wheel, respectively), φ is yaw angle, δfis front wheel angle,vris velocity of rear axle, l is wheelbase, R is steering radius,M and N are rear and front axle center. General form of (1)can be written as (2) and then the approximate continuous linear time-varying model (3) might be obtained by using the Taylor series at reference point εi=[xi,yi,φi], ui=[vi,δi] (the subscripts nli and c represent the nonlinear and continuous linear vehicle model, respectively).

where εc, uc, Ac, and Bccan be described as

B. Trajectory Tracking Controller

Fig.2. Vehicle model.

The theory and technology of MPC have realized remarkable achievements in recent years, and the study of nonlinear system control is a new trend in this field [31]. This paper uses MPC as the trajectory tracking algorithm, which including the design of prediction equation, cost function and constraint condition. More details about MPC algorithm can be seen in [32].

1) Prediction Equation: The discontinuous model is carried out through discrete transformation which can be represented as (8) according to (3) (the subscript s represent the discontinuous model).

where the εs(k), us(k) , As, Bs, and Cscan be written as follows:

The T and k in above equations are sample period and sampling instant, respectively. In order to eliminate the sudden change of controlled variable, we need to limit the increments within each sample period and then (14) is carried out

where

In (14), (k+1|k) represents the predicted value of sampling instant k+1 at sampling instant k. The k+1 before notation “|”represents the predictive state at sampling instant k+1 and the k behind notation “|” represents the current time instant is k.The subscript n represents the dimensional of state variables,m represents the dimensional of input variables, Npis predictive horizon and Ncis control horizon, more details was discussed in [33]. Thus, the values of state and output variables in predictive horizon can be calculated by

where

2) Cost Function: Appropriate cost function need to be devised to ensure that the vehicle can follow the desired trajectory quickly and gently, therefore, the (24) is carried out

where the Q and R are weighting matrices of state and input variables. The first item in (24) reflects the ability to follow the reference trajectory as well as the second reflects the restriction of increment to ensure the gentle change of output.Meanwhile, it is necessary to take constraints of u and ?u into account which can be expressed as

C. Authority Allocation of Steering Angle

The main meaning of this part is to allocate the weighting of steering angles of controller and driver reasonably according to the deviation level of vehicle and the accurate level of two steering angles. In other words, the driver’s steering angle is more precise and leads to less deviation, then the more weighting will be given to driver’s, otherwise, more weighting might be assigned to controller’s [34]. Therefore, it can be split into two sections, the calculation of variables and fuzzy inference system.

1) The Calculation of Variables: This section includes the computation of level of lane departure and relative accurate level of steering angle.

a) Level of lane departure

The level of lane departure can be described as

where ?y is the current lateral deviation of vehicle, ?ymaxis the value of maximum allowable lateral deviation, and then we can put forward the range of LDwhich is [0 1]. Therefore,LD=1 represents the vehicle has reached the maximum allowable deviation value, that is to say, there might be a danger of collision at any time.

b) Relative accurate level of steering angle

According to vehicle model, heading angle errors of both driver and controller at the next time can be obtained and then the relative error of heading angle could be gained(see Fig.3).

Firstly, suppose the current heading angle deviation is ?φ0,the input steering angle of driver and controller are θdand θc,from (1), we can know that

Fig.3. Heading angle errors of both driver and controller at the next time.

where ?φ is change rate of heading angle, θ is steering angle, i is steering ratio and T is sample period. Afterwards, the heading angle change rate of both driver and controller, the?φdand ?φc, can be carried out through (28)

Added current heading angle error ?φ0to (29) and (30),respectively, and then comes to the next time heading angle errors, the ?φTcand ?φTd

In order to present the equation more concisely and directly,we define

Then the variable ?φcdis introduced to represent the relative accurate level of steering angle which can be expressed as follows:

Obviously, the range of ?φcdis [?1,1], that is to say, the steering angle of controller is more accurate if ?φcd<0,otherwise the driver’s is more precise if ?φcd>0. It is means that the steering angle is equal if ?φcd=0. The values of|?ymax| and |?φc?d|maxwill be given in Section IV.

2) Fuzzy Inference System: Fuzzy inference system is used to realize the reasonable weighting distribution and then select the better angle to achieve complementary advantages of driver and controller. It contains the selection of fuzzy sets,membership functions and fuzzy inference rules.

a) Selection of fuzzy sets and membership functions

The inputs of fuzzy system are LDand ?φcd, output is the weighting of steering angle of the controller kc. The range of LD, ?φcd, and kcare [0,1], [?1,1], and [0,1], respectively.Appropriate fuzzy sets and corresponding membership functions of input and output variables can be selected through experimental method and experiences. The fuzzy sets of three variables in this paper can be written as

where Ljrepresents the lateral deviation level of vehicle, the level will increase with the raise of subscript j. CAfmeans that the controller’s steering angle is more accurate than driver’s and the relative precision level will increase with the raise of subscript f. Similarly, DAfmeans that the driver’s is more accurate. Eq. means that the steering angles of them are same. Wlis the weight level of kc, it will increase with the raise of subscript l. Then the membership function parameters of every fuzzy variables can be carried out (see Tables I–III)and corresponding function curves can be seen in Fig.4. The Trapmf(x,[a,b,c,d]) represents trapezoid membership function, where parameter a and d determine the bottom position of the curve, b and c determine the top position of the curve. Similarly, the Trimf(x,[a,b,c]) represents triangle membership function, where parameter a and c determine the bottom position as well as b determines the top position of the curve. According to large numbers of experiments and tests,these two membership functions can meet our requirement.Corresponding functions can be written as follows:

Due to space constraints, we have to use the abbreviations in Tables I–III. The meaning of FV, MF, Ta.(x,[a,b,c,d]),and Ti.(x,[a,b,c]) are fuzzy variable, membership function,Trapmf(x,[a,b,c,d]), and Trimf(x,[a,b,c]), respectively.

b) Fuzzy inference rules

The language form of fuzzy inference can be expressed as Ri: if LDis Ljand ?φcdis CAf(DAf/Eq.)then kcis Wl

where

The design of fuzzy rules can be expressed as four main principles.

i) Under the same lateral deviation LD, the weight of thecontroller kcwill increase if the steering angle of controller is more accurate than driver’s, otherwise the kcwill decrease.

TABLE I Membership Functions of LD

TABLE II Membership Functions of ?φcd

TABLE III Members hip Functions of kc

Fig.4. Membership functions of all input and output variables.

ii) Assume the steering angle of controller is more accurate than that of driver, then the kcwill raise with increasing lateral deviation LDunder same relative precision of steering angle?φcd.

iii) Assume the steering angle of driver is more accurate than that of controller, then the kcwill decline with increasing lateral deviation LDunder same relative precision of steering angle ?φcd.

iv) Assume the steering angles of driver and controller are equal, then the kcwill always be W5at any lateral deviation level LD.

According to the above principles, the fuzzy inference rules can be carried out and seen in Table IV. The weighting coefficient of driver’s can be given through

Consequently, only need to get the kcand then the kdcan be obtained. The final desired output steering angle can be expressed as

D. ADRC

ADRC has been widely applied to complex nonlinear systems with large disturbance, big delay and uncertainty due to its strong ability to restrain the internal and external disturbances such as localization and tracking control of manipulator [35] and attitude control of quadrotor during wind gusts and actuator faults [36]. Moreover, the ADRC is also used to further improve the performance of active front steering [37], [38]. Therefore, ADRC is used in this paper to follow desired steering angle quickly and precisely. The construction of ADRC (see Fig.5) includes arrangement of transition process, nonlinear error feedback control law(NEFCL) and extended state observer (ESO) [39].

Fig.5. The framework of ADRC.

1) Arrangement of Transition Process: Arrange an appropriate transition process is essential for controller to track input as quickly as possible without overshoot in order to solve the contradiction of rapidity and overshoot in classical control theory [40]. Tracking differentiator (TD) was used to arrange the transition process and its discrete form is shown in (36) [41].

where the T is sample period, x1(k) is the tracking signal of input and x2(k) is the differential signal of x1(k) at sampling instant k, θsw(k) is steering angle at sampling instant k, r is

adjustable parameter that determines the speed of tracking and h is filtering factor that can filter noises in the input signal.f st(·) can be calculated through

TABLE IV Fuzzy Rules

where

2) NEFCL: The nonlinear feedback function is used to remove steady-state error of system in ADRC [42]. Therefore,appropriate nonlinear function is constructed to improve feedback control performance of system, which is carried out

where the Id0is the control variable of nonlinear error feedback control law (NEFCL), b0is the compensating factor which determine the level of compensation, and Idis the control variable after disturbance is compensated. The k,α,δ are all adjustable parameters, which generally set as 0<α1<1<α2and δ1=δ2. fal(·) can be described as

3) ESO: According to [43], [44], the discrete extended state observer can be expressed as

where z1is the estimation of desired steering angle, z2is the estimation of differential signal of desired steering angle and z3is the extended state variable. β1,β2,β3are all adjustable parameters and then the integral form of ADRC can be presented as

E. Driver Model

Driver model used in this paper consists of error compensation and neuromuscular system. The error compensation model is constructed in CarSim which based on the theory of single point optimal preview model proposed by Macadam [45]. The input of this model are lateral error and error area of driver preview point and output is steering wheel angle, more details can be seen in CarSim. Preview point in this paper was chosen as 10m in front of the car, ?ypand ?Aprepresent lateral error and error area (see Fig.6) as well as ρ and σ represent the relative coefficients, respectively. In the Fig.6, the line TP represents lateral error ?ypand the area of quadrangle CDTP represents the error area ?Ap. Hence, the steering angle can be expressed as

Fig.6. Lateral error and error area.

In order to better reflect the driver steering characteristics,neuromuscular system is naturally introduced in driver model,which based on α?γ motor neurons proposed by Andrew James Pick in Cambridge [34], [46]. The system is composed of reference model, reflex controller, active stiffness as well as arm and steering dynamics (see Fig.7).

Fig.7. Neuromuscular model of driver [34].

Reference model:

Reflex controller:

Active stiffness:

Arm and steering dynamics:

where the Jdr,Bdr,Kdrand Jsw,Bsw,Kswrepresent inertia,damping and stiffness of driver and steering system,respectively. The value of parameters will be given in Table V.

IV. Experimental Results and System Analysis

A. Experimental Results

1) Double Lane Change Test: As a representative test method, double lane change test is often used to evaluate the controllability and stability of driver-vehicle closed-loop system. Furthermore, the controllability and stability of system can be interpreted as the tracking capability of vehicle.Thus, the vehicle trajectory tracking performance will be validated through double lane change test shown in Fig.8.

Fig.8. Double lane change test.

The control system is built in MATLAB/Simulink and then tested in CarSim. The corresponding parameters are listed in Table V. The vehicle traces under different conditions can be seen in Fig.9. The traces shown in Fig.9 illustrate that the parallel shared driving mode (purple line) is more accurate than alone driving (orange and red lines) and series shareddriving mode (green line). For instance, the overshoots at x = 50 m and x = 105 m occurred in driver alone driving can be obviously reduced by authority allocation system, which proved that the weighting allocation can effectively decrease the errors caused by either side in driving task. Moreover, the comparison of tracking precision is presented in Fig.10 in which we can clearly see that the value of parallel shared control is much lower than any other driving modes. The tracking error of series shared driving mode might caused by the loss of algorithm optimality [47]. Evaluation index of tracking precision of trajectory can be derived from [48] and

TABLE V Parameter Values of Vehicle, Controller, and Driver Models

Fig.9. The comparison of driving traces under normal driving status in double lane change test (vr = 80 km/h, Mu = 1, driver load only).

Fig.10. The comparison of tracking precision under normal driving status in double lane change test.

expressed as

where tnis the total time it takes to finish the whole course,f(t) is desired trajectory, r(t) is the actual driving trace of vehicle, E? is standard threshold for trajectory error which is chosen as 0.4m in this paper. Equation (48) should be transformed to discrete form due to computer arithmetics

where T is sample period which is chosen as 0.001 s in this paper, j is sampling point and n is the sum of sampling points which can be obtained by

2) Slalom Test: The slalom test (see Fig.11) is also carried out and then the similar results can be seen in Fig.12.Obviously, the parallel shared driving mode (purple line) is more accurate than that of alone driving (orange and red lines)and series shared driving mode (green line). Therefore, the parallel shared driving system can further meet the requirement of slalom test.

Fig.11. Slalom test.

Fig.12. The comparison of driving traces under normal driving status in slalom test (vr = 80 km/h, Mu = 1, driver load only).

B. System Analysis

1) Analysis of Driver’s Faulty Operation: Assume oversteering operation happened to driver during x = 100 m to x =105 m, meanwhile the controller is in normal working status,and then compare the trace differences among driver alone,series and parallel shared driving modes (see Fig.13(a)). We try to make the output value of driver to suddenly increase to a certain value and maintain for a period of time to represent the driver over-steering. The value of over-steering of driver is set as 1.02 rad and the duration is set as 0.6 s. Evidently, the trace of parallel shared driving mode (purple line) is much more precise than that of driver alone driving (orange line) and series shared driving (green line) modes and corresponding tracking precision of each driving mode is shown in Fig.14.In addition, the comparison of weighting allocation and steering angle between normal and over-steering status are shown in Figs. 13(b) and 13(c). From Fig.13(b), we can clearly see that the weighting coefficient of controller increased during t = 4.1 s to t = 4.7 s when driver oversteering (see Fig.13(c)) and then declined after driver back to normal operations. In conclusion, the parallel shared driving mode can effectively enhance the safety, controllability and stability of system under the condition of driver over-steering.

Fig.13. The comparison under driver over-steering status: (a) driving traces among series mode, parallel mode and driver alone driving (vr = 80 km/h,Mu = 1, driver load only); (b) weighting allocation between normal driving and driver over-steering status; (c) steering angle between driver and weighted steering angle.

Fig.14. The comparison of tracking precision under driver over-steering status in double lane change test.

2) Analysis of Controller Crashed: Assume system halted happened to MPC controller during x = 105 m to x = 125 m,meanwhile the driver is in normal driving status, and then compare the trace differences among controller alone, series and parallel shared driving modes (see Fig.15(a)). We try to make the output value of controller to maintain a certain value for a period of time to represent the controller crashed. The output value of controller is set as 0.62 rad and the duration is set as 1 s. Apparently, the trace of parallel shared driving mode (purple line) is much more precise than that of controller alone driving (red line) and series shared driving(green line) modes as well as the corresponding tracking precision of each driving mode is shown in Fig.16. In addition, the comparison of weighting allocation and steering angle between normal and system halted status are shown in Figs. 15(b) and 15(c). From Fig.15(b), we can clearly see that the weighting coefficient of controller decreased during t =4.5 s to t = 5.5 s when MPC crashed (see Fig.15(c)). In conclusion, the parallel shared driving mode can effectively enhance the safety, controllability and stability of system when the controller is crashed.

3) Analysis of ADRC: The purpose of adding ADRC into system is to effectively restrain the internal and external disturbances and enhance the anti-interference and robustness of steering system. From Fig.17, it is obvious that the driving trace with ADRC control is much more precise and stable than that without ADRC acted under the interference of feedback torque from steering system and tires. The effect of ADRC can be observed more directly through Fig.18 in which the steering angle tracking precision with ADRC (see Fig.18(b))is much more accurate than that with no ADRC (see Fig.18(a)). Consequently, the ADRC can improve the tracking precision significantly and effectively and corresponding tracking precisions are shown in Fig.19.

4) Analysis of Parametric Variation: The change of vehicle and environmental parameters such as vehicle speed, ground adhesion coefficient and passenger loads can more or less affect the tracking precision in double lane change test (see Fig.20). Therefore, the driving traces under different speed,friction coefficient, and passenger loads are plotted in Figs. 20(a), 20(b), and 20(c), respectively. From Fig.20(a),we can see that the vehicle pass through the test without obvious sideslip until vehicle speed reached 95 km/h. In other words, the vehicle is stable and controllable under speed of 90 km/h. Similarly, the vehicle pass through the test till friction coefficient Mudrop below 0.6 (see Fig.20(b)). However, the changes of passenger loads have little effect on tracking precision and stability of vehicle driving (see Fig.20(c)). The every passenger load is set as 80 kg and then observe the driving traces under different loads such as driver load only,driver with right side load of front row, driver with left side load of second row and driver with full passenger loads. In conclusion, the changes of vehicle speed and friction coefficient might affect the tracking performance of parallel shared driving system.

Fig.15. The comparison under MPC crashed status: (a) driving traces among series mode, parallel mode and MPC alone driving (vr = 80 km/h,Mu = 1, driver load only); (b) weighting allocation between normal driving and MPC crashed status; (c) steering angle between MPC and weighted steering angle.

Fig.16. The comparison of tracking precision under MPC crashed in double lane change test.

Fig.17. The comparison of driving traces with or without ADRC(vr = 80 km/h, Mu = 1, driver load only).

V. Conclusion and Future Work

The indirect shared control under double loop framework is proposed in this paper which divides driver and controller into two independent closed loops so as to obtain the weighted steering angle through authority allocation system. Moreover,the ADRC control the motor to follow the weighted steering angle precisely. The advantages of the structure can be reflected through several following reasons. First, the frame not only eliminates the driving discomfort caused by control conflicts between driver and controller in direct shared control, but also further improves the reliability, rapidity,accuracy and robustness of indirect shared control scheme.Secondly, if the abnormal driving state happened to either controller or driver, the weighting allocation system could distribute the weighting reasonably according to the state of vehicle. Thirdly, the transmission lag of driver’s steering angle caused by time-consuming of MPC can be solved to a certain degree by parallel connection of them. Lastly, the contribution of adding ADRC into frame is that not only can it follow the desired steering angle rapidly and accurately, but also effectively restrain the steering error caused by internal and external disturbances. Simulation results also prove that

Fig.19. The comparison of tracking precision with or without ADRC in double lane change test.

the vehicle trajectory tracking accuracy is significantly improved, meanwhile, the risk of lane departure is reduced after adding authority allocation system and ADRC into framework.

Fig.20. The comparison of driving traces with parameters change: (a) the driving traces under different speed (Mu = 1, driver load only); (b) the driving traces under different friction coefficient (vr = 80 km/h, driver load only); (c)the driving traces under different passenger loads (Mu = 1, vr = 80 km/h).

In the next work, the deep analysis of defects and shortcomings of system will be carried out. For example, only the status of temporary error driving is presented in this article, the analysis of continuous error driving is not mentioned at all. After analysis, this situation might be caused by abnormal driving state of driver and the different driving intention between driver and controller. Therefore, we try to avoid the above circumstances through putting driver observing system and intention recognition system into framework. Furthermore, the proper decision should be made to ensure the safety and stability of vehicle under the condition of both failed of driver and controller. Finally, the stability proof and corresponding stable boundaries which are not mentioned in this paper will be carried out in future research.