Shared Control of Highly Automated Vehicles Using Steer-By-Wire Systems

Ⅰ. INTRODUCTION

AUTONOMOUS vehicles have a promising future of making transportation effortless and free the driver to engage in other activities. Many major global corporations are investing heavily into the development and implementation of autonomous vehicles. However, there are concerns expressed by various research groups on the practicability of high level automation. The literature on human factors in automation has widely reported on the disadvantages of improper automation [1], [2]. High automation may increase boredom in the operator, decrease vigilance and undermine the ability of the operator to regain control [3]. Overreliance on automation may lead degradation of the operator's skill or loss of situation awareness [4]. This in turn can result in demand for a higher level of automation [5], ultimately adversely influencing the overall safety and performance of system [6].

In light of the potential problems caused by driver-less technology, there is an increasing interest to keep the driver in the control loop, and to have the final authority in controlling the car. In the concept of shared control proposed by Sheridan in 1992 [7], the human operator and the intelligent machine work in parallel to perform a specific task. The human-machine shared control is widely studied in serial cars and trucks [7] and is considered as a promising approach in automotive applications [8]. In shared control of a vehicle, the control of the vehicle is shared between the driver and the intelligent controller [9], [10]. Some examples are HAVEit (Highly automated vehicle for intelligent transport) and Nissan's haptic gas pedal system [11], developed for safer, more efficient and easier-to-use transportation. In HAVEit, the human operator shares the control of the vehicle with an automatic controller in three modes of low automated (or assisted), semi-automated and high automated [12]. In low automated mode such as LKAS (Lane keeping assistant systems), due to sensor/environment degradation, the automatic control only partly assists with the driving and the driver has full control authority [13]. In semi-automated mode such as ACC (Adaptive cruise control), the driver collaborates with the automatic control that aims at reducing the driver workload [14]. In high automated mode, the automatic control takes over the control of the vehicle, particularly in an emergency situation [15]. Examples of emergency situations are when the driver falls asleep or is impaired, or in a near-crash situation where the driver has a long reaction time. In high automated mode, the driver still has the authority to regain the control of the car [16].

In order to successfully apply the shared control concept of vehicle to production, many issues need to be addressed. First, the human driver and the automatic system must understand each other's intent in complex systems [4], [17]. In [18], a given trajectory is used to represent the driver intent and nonlinear model predictive control (NMPC) based shared control is designed for path planning. Saleh et al. [19] uses a driver-vehicle road (DVR) model to model the driver's behaviour and intention. References [20] and [21] incorporate the driver's steer command directly as one of the control objectives of the optimization problem to match the driver's command.

Second, the degree of the authority given to the human operator and the automatic system in the driving should be well defined in order to improve the quality of cooperation between the human driver and the automated system [22]. In system proposed in [23], the driver is able to determine degree of the authority of the driver and the automatic system by for example pressing a button to inform the automatic system to exert more control. However there may not be sufficient time for the driver to issue such notification, and this approach can place a heavy burden on the driver if the request for higher authority of the automatic system is too frequent.

Third, a new human machine interface is needed to enhance situation awareness like traffic information. Different types of human machine interface like knobs, switches, buttons or touch-screens like windshield display have been designed and tested in [24]-[27]. Forth, transition in authority and control initiated by changes in the ability of the human operator or automatic system should be smooth and smart [28]. Transition between skills can be either mandatory or discretionary. Mandatory transition is deployed when one of the actors, the driver or the automatic system (human or automation) loses its ability to control the vehicle and the other actor should take over control in time before the system reaches an undesirable state [9]. An example of mandatory transition is when a sudden change in the driving environment or traffic condition is not detected and managed by the automatic system, requiring the driver to take over the control of the vehicle. A discretionary transition occurs when in a specific situation one actor is perceived to have skills that are more expedient and/or more safe [29].

In contrast to conventional steering system with mechanical links, the mechanical connection in steer-by-wire (SbW) system between the steering wheel and the front wheels consisting of the steering column and shaft is removed. The signals are transmitted electronically by wires. Therefore, availability of steer-by-wire augmentation and electronic stability programmes can enable the vehicle to perform under the guidance of the automatic system and various forms of shared control as the driver's steering input can be implemented without physical interaction. The electronic control unit (ECU), which includes hardware and software components, monitors the driver and vehicle status and executes the authority based on the driver's intention, driving environment and vehicle status.

For reliability and safety requirements, the software failure detection of the automatic system including component failure, communication failure and electric control unit (ECU) failure must be addressed during human-machine operation to prevent failures that can lead to a catastrophic event. Inaccurate or noisy sensors may impair the reliability of the system and therefore influence the driver's trust in the automatic system [30]. It is necessary to design a control system which can detect and implement any potential fault, in order to improve the system reliability and maintain an acceptable driving performance [31].

In addition, the human failure such as taking incorrect action may lead to dangerous outcomes [32]. Some examples of human failure are the inability of the drive to react to a sudden change in driving condition fast enough, drowsiness caused by long time driving, limited steering skill, injury, falling asleep or any driving action that may destabilise the vehicle and lead to accidents like rollover, head-collision or lane boundaries crossing. Road danger is a man-made crisis, with human error accounting for over 90 $\%$ of accidents, said Bob Joop Goos, chairman of the International Organization for Road Accident Prevention. Rollover occurs due to a sudden and large steering input by the driver, while harsh braking can result in rear-end collision [30]. In such situations, the automatic system should compensate for the driver's fault. For example, if the driver's behaviour such as braking, acceleration and steering manoeuvre is perceived to be unsafe, the automatic system should intervene immediately and take over the control of the vehicle, take prompt actions or make an emergency stop [33]. Some studies show that an automatic system has potential to reduce the impact of human error in changing lane [33], [34] on the motorway, or providing cooperative adaptive cruise control (CACC) [35] to avoid head-on collision, pedestrian detection [36], lane departure warning [37], traffic jam assistant [38], valet parking [39], electronic stability program (ESP) [40], traffic sign detection [41] and anti-lock braking system (ABS) [42]. These systems ensure stability in critical situations, maintain a safe distance to the vehicle and pedestrian in front to avoid collisions and accidents, and support the driver while parking by offering technologies that alert the driver, implement safeguard or take over the control of the vehicle.

Although some shared control methods have been proposed, there are still much room to improve. In aforementioned methods, the shared control strategy is designed based on either matching the driver's command or the vehicle's stability requirement. However, it is reasonable to consider the factor of a human driver, vehicle, environment and comfort of passengers simultaneously. Moreover, differing from a given desired trajectory to fed into the shared control algorithm, a model predictive (MP)-based trajectory generation is designed in this paper to obtain the desired manoeuvres. Therefore, leveraging the advancements in sensing technologies in steer-by-wire systems and fault detection capability of fault detection (FD) system, a shared control of highly automated system tolerating the driver's inappropriate steering behaviours intersection crossing and lane change is reported. First, a FD system is designed to detect the fault. The observer-based FD schemes are proposed to describe the fault information perfectly. It is noted that many observer-based FD methods have been proposed in the literature. The main feature of sliding mode observer is its robustness to uncertainty or external disturbance signal in estimating the state variables and failures [43]. The data driven fault detection system is based on residual signals by using evaluation method to make a final decision [44]. A proportional integral observer (PIO) [45] is designed to estimate both of the faults and the faulty VTOL aircraft system states. Based on Lyapunov theory and $\mathcal{L}_2$ optimization, the observer gain can be easily and effectively calculated. A descriptor observer [46] is designed and used to estimate jointly vehicle dynamic states and time-varying sensor faults to improve tracking performance of the vehicle motion.

A mandatory transition from driver to the automatic system is then performed to compensate for the driver's fault and to achieve an optimal driving performance. The optimal driving path is generated by MP algorithm aiming at smooth turning of the vehicle and maximizing the distance between the position of the wheel and boundaries, simultaneously.

The remainder of this paper is organised as follows. The framework of fault-tolerant shared control of SbW system including SbW model and the driver model is described in Section Ⅱ. In Section Ⅲ, the formulation of the trajectory planning and fault detection system is described. The fault tolerant control algorithm is introduced in Section Ⅳ. The validation of the effectiveness of the proposed control method is reported in Section Ⅴ. Some conclusion is provided in Section Ⅵ and the future work is discussed.

Ⅱ. SYSTEM DESCRIPTION

A General Framework

Fault tolerant control (FTC) system can significantly enhance safety and convenience of the driver and passengers, and prevent injuries or death [47]. The direct and common way is to use hardware redundancy method [48]. The basic idea is to add one or more modules to a specific module, usually in parallel so that the duplicated output signals can be compared as a method to diagnose and identify the fault. This technology has some obvious advantages like it can offer high reliability and is simple to control. However, a complex system is required, likely to consist of not only redundant actuators, sensors and micro-controllers, but also other elements such as control and power amplifier. The complexity may led to design errors as well as unexpected interactions among components, making high level of reliability more difficult and expensive to achieve. The analytical redundancy technology is then developed with the aims to reduce the numbers of redundant components without compromising reliability and reduce the overall cost [49]. In analytical redundancy approach, the FD system is used to detect and identify the occurrence and type of the component failure. After the fault is detected, the fault information is then passed to the fault tolerant controller to adapt to the fault by switch the authority of the vehicle to the automation in order to maintain stability and desired dynamic performance.

The framework of the proposed fault tolerant shared control of SbW system is shown in Fig. 1. It is assumed that the driver uses visual information to identify the upcoming road bending, as well as the position, speed and the direction of the vehicle ride relative to the road. After the driver rotates the steering wheel through the steering wheel system, the steering wheel angle which reflect the driver's steering intention is generated as the output signal of driver system. The trajectory plan scheme based on MP algorithm generates an optimal and feasible trajectory which minimises the distance from the road centreline and maximizes the distance from the road boundary and moving obstacles. The aim of the scheme is to identify the driver's intentions and abnormal steering action. By calculating the difference between the real trajectory and reference trajectory, a threshold is defined and designed to detect the occurrence of driver's steering failure. The fault tolerant controller can maintain stability of the overall vehicle system and obtain an optimal steering performance by increasing the authority of the automatic system in the presence of driver's abnormal steering behavior.

Figure  1.  Block diagram of shared control of SbW system.

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Figure  2.  Block diagram of driver system.

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B Driver Model

The shared control law is designed based on the driver model. It is assumed that the driver detects the upcoming road curvature, as well as the position, speed and heading direction of the vehicle relative to the road using visual information. The driver's intention is considered as the desired steering wheel angle ($\delta_{dd}$). Through the neuromuscular system, the driver's intention is converted to the driver's torque and applied to the steering wheel subsystem to control the vehicle direction. By taking the self-aligning torque into account, the actual steering wheel angle ($\delta_{dr}$) is obtained through the steering wheel subsystem.

We assume that the driver learns about the road through the visual field of view and accordingly generate a desired steering wheel angle for steering. The desired steering wheel angle is calculated by

where $\delta_{fref}(t)$ is the desired front wheel angle which will be discussed in Section Ⅲ and $N_\theta$ is the ratio between the steering wheel rotational angle and the front-wheel steering angle. Through the neuromuscular system, the driver's intention is converted to the torque command $\tau_d (t)$. The steering torque generated by the neuromuscular system is proportional to the desired steering wheel and the vehicle speed ($K_r v_x$). $K_r$ is the angle-to-torque coefficient and $v_x$ is the vehicle forward speed. It is also assumed that the actual steering wheel angle is applied to the steering wheel has a simple gain $K_t$, a closed-loop reflex gain which represents the neuromuscular reflex rejecting any disturbance torque on the steering wheel caused by an external source such as a gust of wind. This gain minimizes the difference between the actual steering wheel angle and the desired steering wheel angle. $G_{nm}$ as a simplified model of arm dynamics and can be expressed as

C Steering Wheel Subsystem

The steering wheel subsystem contains the steering wheel, steering column, steering angle sensor and steering wheel feedback motor. The inputs of steering wheel subsystem are driver's torque $\tau_d (t)$ and self-aligning torque $\tau_a (t)$. The steering wheel subsystem dynamics can be described by the following equation:

where $J_h$, $B_h$ and $C_h$ are the moment of inertia, the viscous friction coefficient, and the torsional stiffness of the steering wheel shaft, respectively. $\delta_{fd} (t)$ is the actual steering wheel angle. The self-aligning torque, $\tau_a (t)$, is generated by the steering wheel feedback motor. In this work, the steering wheel feedback motor is controlled by a PD regulator of the tracking error between the actual steering wheel angle and front wheel angle to provide the driver with the true feeling of the steering effort.

Ⅲ. TRAJECTORY PLAN

A Vehicle Dynamics Model

A four degree of freedom vehicle model is utilised to describe the dynamic motion of the vehicle with a steer-by-wire system. Based on this vehicle dynamic model, the steering angle of front wheels can be predicted and optimised in real time. It is assumed that the vehicle is front wheel drive and has a constant forward speed ($\dot{v}_x=0$). The equations of motion of can be described by

where $\dot{v}_y$, $r=\psi$ are the vehicle lateral velocity, yaw angle and yaw rate, respectively. $i=fl, fr, rl, rr$, which represents the front left, front right, rear left and rear right wheel, respectively. $F_{xi}$ and $F_{yi}$ are longitudinal tyre force and lateral tyre force, respectively. $l_f$ and $l_r$ are the front and rear wheel base lengths, while $b_f$ and $b_r$ are the front and rear track widths. $I_z$ and $m$ are the moment of vehicle inertia in terms of yaw axis and vehicle mass.

The tyre traction or brake force and side force are defined as $F_{ti}$ and $F_{si}$, respectively. It is assumed that the traction or brake force of front wheel $F_{tf}$ is zero. Thus, $F_{ti}$ and $F_{si}$ can be related to the longitudinal and the lateral tyre forces by the front wheel angle $\delta_f$ ($\delta_f=\delta_{fl}=\delta_{fr}$) as follows:

The $F_si$, can be simplified as

$C_a$ is the lateral cornering stiffness. $α_i$ is the lateral slip angle which can be calculated as followings [50]:

B Trajectory Generation Based on MP Algorithm

As shown in Fig. 3, the vehicle body axis system is a right-hand orthogonal coordinate frame with origin at the vehicle centre of mass with positive $X$ axis is defined along the centre-line of the vehicle and positive $Y$ is defined to the right. This coordinator frame can be used to describe the orientation and location of the car as well its velocity along each axis ($v_x$, $v_y$, $v_z$). A world coordinate frame ($X^\oplus$, $Y^\oplus$, $Z^\oplus$) coinciding with the vehicle coordinate frame at $t=0$ is defined. The subsequent rotation angle of the vehicle coordinate frame relative to earth coordinate frame about $Z^\oplus$ axis is the vehicle heading angle, $\psi$.

Figure  3.  World and vehicle coordinate frames.

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The velocity and acceleration vectors of the vehicle relative to the world coordinate system can be obtained from:

The objectives are to minimize the yaw acceleration of the vehicle throughout the length of the manoeuvre, minimize the distance between the current vehicle position and road centreline, and maximize the distance between the position of the wheel and boundaries.

Based on the vehicle model (4)-(8), the cost function of the optimization trajectory can be presented as:

s.t.

where $X_d^\oplus$ and $Y_d^\oplus$ are the longitudinal and lateral position of road centreline. $X_U^\oplus$ and $Y_U^\oplus$ are the longitudinal and lateral positions of road upper boundary and $X_L^\oplus$ and $Y_L^\oplus$ are the longitudinal and lateral positions of road lower boundary. $\hat{X}^\oplus_p$ and $\hat{Y}^\oplus_p$ are the predicted trajectory optimised by this model predictive (MP) algorithm. $a_1$, $a_2$, $a_3$, $a_4$ are scaling factors of each optimization term. $a_1$ is relating to the term of minimizing the distance between the current vehicle position and road centreline. $a_2$ and $a_3$ are relating to the term of maximizing the distance between the current vehicle position and road boundaries. The term $a_4$ is used to minimise the yaw acceleration of the vehicle throughout the path.

$\hat{X}^\oplus_p$ and $\hat{Y}^\oplus_p$ can be presented by the following discrete dynamics model:

where $X^\oplus (k-1)$ and $Y^\oplus (k-1)$ are feedback values of vehicle longitudinal and lateral position relative to the world coordinate system in the previous time step, $t_{k-1}$. $\hat{v}^\oplus_x(k)$ and $\hat{v}^\oplus_y(k)$ are predicted vehicle longitudinal and lateral velocities relative to the world coordinate frame in the current time step, $t_k$, which can be presented by:

where $\hat{v}_x (k)$ is constant and $\hat{v}_y (k)$ is the predicted lateral velocity relative to the world coordinate frame in the current time step and $\hat{\psi}(k)$ is the predicted vehicle yaw angle in the current time step with $\hat{\psi}(k)=\hat{\psi}(k-1)+r(k-1)(t_k-t_{k-1})$. $\hat{v}_y (k)$ and $r(k)$ can be estimated at each time step by (14).

where

$F_{sfi} (k)$ and $F_{sri} (k)$ are predicted tyre front wheel side force, rear wheel side force and rear wheel traction in the previous time step.

The relationship given in (10) defines constraints on the steering angle. In the conventional steering system, the limitations of the front wheel angle is $\pm 35^\circ$ but in the electric vehicle, the practical limitation of the steering angle is considered between $-90$ degrees and $90$ degrees ($\delta_{\max}=90^\circ$). The inequality (11) defines the constraint on the sideslip angle of front wheel. It can be assumed that the maximum value of sideslip angle $\beta_{\max}$ is 6 degrees [51].

Based on the assumptions made so far, an optimal travel path that is smooth, near the midline and does not cross the boundary is generated. The front wheel angle and the positions and velocities $[\delta_{fref}, X_{ref}^\oplus, Y_{ref}^\oplus, X_{ref}^\oplus, Y_{ref}^\oplus]$ are obtained by the MP algorithms.

C Fault Detection

To detect the driver's steering intention and modify the driver error due to limited steering skill or sleep, a trajectory tracking error is defined. According to Fig. 4, the trajectory tracking error is the difference between the real position of vehicle and the reference position relative to the world coordinate. The trajectory tracking error is

Figure  4.  Trajectory tracking error.

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When the driver is steering the steering wheel to make the vehicle driving near the road centreline this error is small and may fluctuate in a small value range. But when the driver suddenly steers the steering wheel due to distraction or drowsiness to deviate the vehicle from the centreline and drive over to the kerb or guardrail or over-correct the vehicle when the driver finds him veering off out of the lane, the trajectory error is increased rapidly.

In this paper, a threshold is designed and the occurrence of faults can be detected by comparing the following logic rule:

where $E_{\max}$ is the non-exceeding limit. When $E_n(k)$ is greater than $E_{\max}$, the vehicle dynamics may be disables leading to rollover or head-on collision.

Once the driver steering behaviour failure occurs, the automatic system takes over the control of vehicle to prevent an undesirable state. The automatic system sets the front wheel angle according to the reference steering angle and ensures the vehicle smoothly follows the desired trajectory in a safe normal driving situation.

Ⅳ. FAULT TOLERANT CONTROL

Once the automatic system takes over the control of the vehicle, the SbW control reconfigures the MPC fault tolerant controller for a good steering performance.

A SbW System Modelling

The dynamic equation of the front wheel subsystem is described by the following equations [52]:

where $\delta_f$ is the steering angle, $J_w$ is the moment of inertia of the steering system at the road wheels, $b_w$ is the damping of the steering system at the road wheels, $r_s$ is the steering ratio, $\tau_f$ represents the coulomb friction, $\tau_M$ is the steering actuator torque, $u_u(t)$ is the motor voltage, $k_M$ is the motor constant. $\tau_a$ is seen as self-aligning torque; $C_{\alpha, f}$ is the front tyre cornering stiffness coefficient, $t_p$ is the pneumatic trail (the distance between the resultant point of application of lateral force and the center of the tyre). $t_m$ is the mechanical trail (the distance between the tyre center and the point on the ground about which the tyre pivots as a result of the wheel caster angle), $V$ is the longitudinal component of the center of gravity (CG) velocity, $r(t)$ is the yaw rate at the center, $a$ is the distance of the front axle to the CG, $\beta$ is side slip angle, $F_w$ is the Coulomb friction constant, and $sgn (\dot{\delta}_f(t))$ is the sign function defined as

Rewriting Equation (18) in state space form yields:

where $x(t)\in \mathbb{R}^{n}$ denotes the SbW systems state vector and can be expressed as

where

The inputs of the front wheel subsystem is the voltage supplied to the front wheel motor $u (t)$ and the self-aligning torque which represents the resistance offered by the road and coulomb friction $\tau(t)=[\tau_a (t)\ \ \tau_f (t)]^T$. Moreover, we take the saturation effects of the steering system into account in the control design. This means that the motor voltage and rate of change of the voltage need to be limited.

Let us consider a SbW system with system uncertainty as

where $w(t)=B_\tau \tau(t)+w_1(t) \in \mathbb{R}^n$, $B_{m}\in \mathbb{R}^{n\times m}$ is the control input matrix for $u(t)$. $B_\tau \tau(t)$ can be defined as system disturbance and $w_1(t)$ denotes the system matched uncertainties.

The matched uncertainty $w_1 (t)$ can be defined as

Assumption 1: $w_m(t)$ is bounded and smooth, which satisfies

$\delta_m$ is the maximum value of $w_m(t)$ and known a priori. $\varepsilon$ is a small positive quantity. It is also assumed that the system is controllable.

Using a sampling time $T$, the continuous-time system model (22) can be discretized as

where

with

B MPC Fault Tolerant Controller Design

MPC has made a significant impact on control engineering and has a highly efficient approach to perform failure accommodation. An important advantage of MPC is its ability to handle hard system constraints. Constraint handling is a necessity as constraints can limit the actions of controllers and reduce system functionality. The core principle of MPC is to deploy an explicit SbW model to predict the system output. At each control interval, the MPC algorithm optimizes the future control trajectory by minimizing the error between the reference front wheel angle and predicted system output, i.e., front wheel angle.

In this work, the objective of the MPC fault tolerant controller design is to take over the control of the vehicle and track the reference trajectory path smoothly under the precondition of vehicle stability and controllability in order to accommodate the driver's abnormal steering behaviour (Fig. 5). In the normal driving with driver having full authority, the driver rotates the steering wheel according to the road information and steering intention. The aim of the MPC controller is to minimize the desired front wheel angle error $e_r(t)$ expressed as

Figure  5.  MPC fault tolerant control.

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$\delta_{fn} (t)$ is the desired front wheel angle in the normal driving situation, $\delta_{fd} (t)$ is the actual steering wheel angle and $N_\theta$ is the steering ratio. Once the driver's steering behaviour is identified as abnormal, the steering wheel is disconnected from ECU. The automatic system is given higher authority, taking over the control of the vehicle ensuring that the front wheel angle follows the reference front wheel angle produced by the trajectory generation algorithm. The aim of the fault tolerant MPC controller is then to minimize the tracking error between the reference front wheel angle produced by the trajectory generation algorithm and actual front wheel angle.

The MPC is defined by the state-space model (26). The system augmented model which is used in the design of predictive control is defined by [53]

where

and $\Delta u_u (k)=u_u (k)-u_u (k-1)$. $N_y$ is the prediction horizon (number of predictions) and $N_u$ is the control horizon (number of control moves). The following cost function is defined for the MPC steering controller

s.t.

where $r$ is the reference signal as mentioned before. In the normal driving situation, $r=[\delta_{fn}^T (k), \ldots, \delta_{fn}^T (k+N_y)]^T$ while in the faulty driving situation, $r_f=[\delta_{ref}^T (k), \ldots, \delta_{ref}^T (k+N_y)]^T$. At each time step, the MPC controller chooses an input sequence which minimises the predicted trajectory error estimated based on the reference model and the FD model. If the driver's fault is detected by the FD scheme, the $r_f$ is updated as the reference model for MPC controller to track. The inequalities given by (30) and (31) define the constraints on the motor voltage. The battery pack of front wheel motor is the heart of an electric vehicle and its power is limited. This means that, the voltage and the rate of change of the voltage should be bounded. Otherwise, the controller may skew the amount of the actual turning of the vehicle with undesirable consequence. The computation complexity of FTC algorithm is mainly based on the SbW model and system constraints of MPC optimization problem. The SbW model should describe the most significant dynamics of the system and also simple enough for solving the optimization problem. In addition, the constraint horizon, prediction and control horizons have the impact on computation time and MPC region. The larger the horizon, the larger the number of regions in the state space partition.

C Optimization

In addition, to make the transitions smooth and smart in order to improve the comfort of passengers, a new optimization problem by taking the yaw acceleration in account is designed. The optimization problem is based on linear vehicle model. The state equation of linear vehicle model yields:

where $C_{\alpha f}$ and $C_{\alpha r}$ are the cornering stiffness of front and rear tires (N/rad). Then we can combine the state equation of SbW system model and state equation of linear vehicle model into the following state space model:

where $x_v (t)\in \mathbb{R}^n$ denotes the SbW systems state vector and vehicle status which can be expressed as

where

Similar to SbW system modelling, we consider the $\eta(t)=B_{v\tau} \tau_f (t)$ as system disturbance and using a sampling time $T$, the continuous-time system model (34) can be discretised as

where

By defining the difference of the state variable and the difference of the control variable as

the system augmented model in a compact matrix form is defined as

where

A new cost function is defined by considering the yaw acceleration as one of the optimisation objectives

s.t.

with

The new optimization objective is to minimise the predicted trajectory error and the yaw acceleration of the vehicle throughout the length of the manoeuvre in the faulty driving situation. It guarantees the authority of vehicle is smoothly and reasonably transferred from manual to automated driving back so that the driver can react in a usual way and no negatively influence happened on driving performance.

It is noted that MPC incorporates constraints explicitly and is easy to formulate as a constrained optimization problem. Its main disadvantage is its strong dependence on the model. Compared with MPC, PID algorithm requires lesser measurement and it can reach higher control speed. In addition, In classical PID control, it is difficult to guarantee closed-loop stability when there are parametric uncertainties to deal with. MPC employs a receding horizon concept in establishing a control sequence in order to assure that closed-loop stability is generally guaranteed. Furthermore, the sliding mode control (SMC) shows strong robustness in the presence of disturbance compared with MPC. However, SMC has a heavier computational burden than MPC.

Ⅴ. SIMULATION RESULTS

In this section, the proposed controller designed is validated by a series of simulations. It is shown that developed algorithm reduces the impact of human steering error.

A Parameters of the SbW System and Vehicle Dynamics

The parameters of the vehicle used in the simulation are given in Table Ⅰ [54].

Table  Ⅰ.  VEHICLE PARAMETERS

Symbol	Description	Values and Unites
$m$	Mass	1298.9 kg
$l_f$	Distance of CG from the front axle	1 m
$l_r$	Distance of CG from the rear axle	1.454 m
$b_f$	Front track width	1.436 m
$b_r$	Rear track width	1.436 m
$C_s$	Longitudinal stiffness of the tyre	50 000 N/unit slip
$I_z$	Vehicle moment of inertial about yaw axle	1627 kg$\cdot {\rm m}^2$
$C_\alpha$	Cornering stiffness of the tyre	30 000 N/unit slip

 | Show Table

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The parameters of the SbW systems used in the simulation are given in Table Ⅱ [55].

Table  Ⅱ.  SBW SYSTEM PARAMETERS

Symbol	Values and Unites
$b_w$	12 ${\rm Nm/rad}$
$J_w$	2.6 ${\rm kg\cdot m^2}$
$r_s$	16.1
$r_p$	12
$k_M$	250
$l$	0.17 m
$N_\theta$	12

 | Show Table

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In this paper, the front wheel angle is between $-45 \sim 45$ degrees. Any degree outside of this range will not be acknowledged by the vehicle controller. In addition, the saturation effects of the steering system are considered. The limits of $\delta_f(k), \Delta u_u(k)$ and $u_u(k)$ are

B Scenario of the Intersection

1) Scenario of intersection: The first set of simulations is based on an intersection scenario in which the controlled vehicle makes a right turn (Fig. 6).

Figure  6.  Scenario in the intersection.

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The centreline ($X_d^\oplus, Y_d^\oplus$) is calculated using the geometric method [56] consisting of circular arcs and straight line segments. The radius $R$ of the circular trajectory is calculated as

where $\mu$ is the friction coefficient and $g$ is the gravity acceleration. In the scenario of the intersection, $v_x=40$ km/h and $\mu=1$. Therefore, $R=12$ m. The guided centreline ($X_d^\oplus, Y_d^\oplus$) is presented in Fig. 7.

Figure  7.  Intersection.

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The reference trajectory obtained by (9) is shown in Fig. 8. It is a smooth, feasible and highly appropriate path for driver to turn in the presence of road boundaries. The wheels do not hit the boundaries in the crossing.

Figure  8.  Guided centreline in the intersection.

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It is assumed that the driver makes a mistake in steering due to limited driving skills or drowsiness. This implies that the desired steering wheel angle is assumed as

It can be seen from Fig. 9 that a large steering wheel angle drives the car close to the adjacent lane and takes a long time to steer the vehicle near the centreline of the lane (Red solid line). This oversteering increases the the chance of head on collision. Based on the fault detection rule introduced in (16), the driver's steering faults can be detected effectively and quickly. In the scenario of intersection, the threshold of fault detection is set to 0.2 m. After the detection of the steering fault, the automatic system takes over the control of the vehicle and deploys the MPC controller to track the reference trajectory. Initially, there is some oscillation in the trajectory generated by the MPC that is dampened after 2 minutes.

Figure  9.  Fault tolerant control in scenario of intersection based on understeering.

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2) Scenario of lane change: In the second set of simulations, the controlled vehicle is driven in a double lane road. It overtakes the vehicle on the right by moving swiftly into the right lane and then goes back to left lane as it detects another vehicle in the front.

In the scenario of the lane change, $v_x=60$ km/h and $\mu=1$. Therefore, $R=28$ m. The guided centreline for lane change ($X_d^\oplus, Y_d^\oplus$) is shown in Fig. 11. Geometric method is used to generate the guided centreline which consists of circular arcs and straight line segments.

Figure  10.  Scenario of lane change.

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Figure  11.  Guided centreline in the lane change.

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The lane change operation needs higher levels of driving skill. The driver needs precise estimation of the relative location and speed of the head vehicle, checking the vehicle's blind spot, paying attention to the vehicles in the adjacent lane during the driving manoeuvre in order to safely pass other vehicles. Errors made when changing lanes are some of the most common causes of car accidents. In the scenario of the lane change, we simulate the driver's two common errors. One is to drive the vehicle too close to the adjacent lane after first lane change and the other error is not keeping sufficient distance behind the head vehicle before the second lane change.

The reference trajectory obtained by (9) is smoother and feasible based on the position of vehicles and the road boundaries (Fig. 12). The vehicle which follows the reference trajectory can easily avoid the other vehicles.

Figure  12.  Reference trajectory in the lane change scenario.

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In Fig. 13, the driver successfully changes the lane by overtaking the other vehicles. However, the vehicle is too close to the white line on the road after entering a new lane. This is due to the driver's eagerness to drive back to the first lane, miscalculating the relative location of the white line on the road or not checking the position of the vehicle relative to other vehicles through side and rear mirrors. This results in an abrupt or sharp steering which is dangerous for both the driver and the other driver of other cars. The driver of blue vehicle does not notice the lane changing signal and does not provide the necessary space. Based on the fault detection system, a smooth transition is applied from manual driving to automatic to drive the vehicle to the middle of the road. Furthermore, a smooth drive into the original lane is obtained.

Figure  13.  Fault tolerant control in scenario of lane change 1.

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Another common mistake is to overestimate the amount of space available in front of the green car and to underestimate its speed (Fig. 14). This can expose drivers of both cars to danger and increase the possibility of rear-end collision.

Figure  14.  Fault tolerant control in scenario of lane change 2.

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It can be seen that the automatic system can take over the control of the vehicle before a potential collision occurs. Once the driver's fault is detected by the FD scheme, the automatic system takes over the control of the vehicle immediately and takes only 1-2 s to follow the optimal trajectory. However, there is a sharp steering and small fluctuations before the steering performance becomes stable.

3) Scenario of intersection with optimised fault tolerant controller: Fig. 15 shows that the automation can take over the control of vehicle smoothly without sharp steering and drive the vehicle quickly and correctly follows the reference trajectory when a driver's inappropriate steering behaviour is detected and defined.

Figure  15.  Optimised fault tolerant control in scenario of intersection.

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4) Scenario of lane change with optimised fault tolerant controller: In the scenario of lane change, the the automation can steer the vehicle more smoothly and safety while being minimally invasive to the driver by taking the yaw acceleration into account. The driver therefore can easily adapt to the automation (Fig. 16).

Figure  16.  Optimised fault tolerant control in scenario of lane change.

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Ⅵ. CONCLUSION

In this paper, the driver's steering fault in a shared human-vehicle system was studied. Similar to component failures, the driver's steering fault was identified by a FD scheme. Based on the faulty information applied by the threshold, a fault tolerant MPC controller is designed to tolerant driver's failure by using the automatic driving replace the manual driving. The proposed algorithm was validated by considering driver's oversteering and understeering in common driving situations. These simulation and experimental results demonstrate the smooth integration of the controller's and driver's commands. The automatic system can take over the control of the vehicle successfully after detection of the driver's inappropriate steering behaviour and the vehicle can be automatically driven along an optimal trajectory generated by the MP controller. Sensor is an important component in electric or electric-mechatronic system. In addition, when the sensor is faulty or damaged, the information it reads and sends (angle, torque, position) to the vehicle's ECU is inaccurate, the controller then cannot have the accurate measured variable and may not generate an optimal control effect. An interesting direction for future research would be take the sensor fault into account in the shared controller design and apply the obtained results to the experimental test rig to further verify the shared control problem.