# Personalised lane keeping assist strategy: adaptation to driving style

Jagat Jyoti Rath, Chouki Sentouh, Jean-Christophe Popieul

► To cite this version:

Jagat Jyoti Rath, Chouki Sentouh, Jean-Christophe Popieul. Personalised lane keeping assist strategy: adaptation to driving style. IET Control Theory and Applications, 2019, 13 (1), pp.106-115. 10.1049/iet-cta.2018.5941 . hal-03644349

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# Personalised lane keeping assist strategy: adaptation to driving style

ISSN 1751-8644
Received on 23rd August 2018
Revised 9th October 2018
Accepted on 5th November 2018
E-First on 6th December 2018
doi: 10.1049/iet-cta.2018.5941
www.ietdl.org

Jagat Jyoti Rath<fnref n="1" />, Chouki Senouth<fnref n="1" />, Jean Christophe Popieul<fnref n="1" />

**Abstract:** The research in advanced driver assistance systems (ADAS) has progressed to design architectures for driver specific performance. Personalised ADASs in this aspect have been developed with adaptation to driver attributes, state, style, behaviour, skill and so on. For the lane keeping task, the driver driving style while navigating a high/low curvature track plays an important part in the design of a lane keeping assist system. Considering this aspect, a robust co-operative control approach is formulated to design a personalised lane keeping assist with adaptation to driver style. Based on statistical analysis of lateral jerk and steer feel, a fuzzy rule based identification procedure for the classification of the driver style as clam, moderate, aggressive or very aggressive is designed. Using the identified driving style, a modulation function is proposed to adapt the assist torque. The assist torque is generated based on a robust higher order sliding mode approach as a feedback control for the driver-vehicle system. Closed-loop stability of the proposed driver-vehicle design in the presence of disturbances is established. Co-operative control between human driver-autonomous controller for the lane keeping task over the Satori test track with adaption to driver style is then shown for validation of the proposed architecture.

## 1 Introduction

The role of advanced driver assistance systems (ADAS) [1] has evolved over decades of research and commercialisation in assisting the human driver for tasks with focus on improvements in driving performance [2, 3] fuel efficient driving [4, 5], increased safety and comfort [6] and so on. Various ADAS architectures for lane keeping, collision avoidance, cruise control, braking assistance, parking assistance and so on [7, 8] have been developed. These advanced protocols are implemented in modern vehicles as semi-autonomous/fully autonomous features. The human-machine interaction (HMI) between drivers and automated vehicles for ADAS is dependent on variable factors which comprise of environmental, vehicular and human factors [2, 7]. Typically traffic, weather, road conditions, driving skill, fatigue, driver behaviour, driver driving style [2, 9] and so on are some factors which influence the performance [10]. To improve the HMI and the overall efficacy of the system, the objective is to design ADASs which can adapt to driver attributes such as behaviour, skill, style and so on, and hence be personalised.

Considering the case of semi-autonomous ADAS implementation and its subsequent interaction with the human driver, co-operative control between the human driver and the autonomous controller in the form of shared-authority based control, guidance based control, driver personalised control [9, 11, 12] and so on has gained prominence. Personalised ADAS for a specific driver with adaptation to driver attributes has been explored in many works such as [2, 3, 13] based on co-operative/ shared control. In the works of [2], control strategies based on adaptation to driver workloads, level of drowsiness and so on were proposed. Similarly in [13], the human arm properties were analysed and employed for the development of an assistance strategy. In other works, driver style (DS), behaviour, intent, response time to specific events [10] and so on have been studied for the development of assistance architectures. DS which classifies the driving response of the driver to different manoeuvres, events, scenarios and so on is a significant parameter that can be employed to design an assist system.

Driving style is a dynamic parameter that reflects how a typical driver operated a specific driving task. DS is affected by driving skill of the driver, environment, driving conditions, mood, fatigue

and so on [14, 15]. Further, the DS of a specific driver evolves continuously, i.e. a specific driver may have different DS for different manoeuvres. In [16], based on comprehensive analysis of driver decision-making capabilities, demographic background and character of the DS was categorised into dissociative, anxious, risky, angry, high-velocity, distress reduction, patient and careful styles. It was concluded that driver experience, training and familiarity with the vehicle and the environment further affected the DS of a driver. Similarly, in [17] the DS was classified on the basis of level of aggressiveness while driving over freeways with variable road, traffic and so on conditions. Consequently, calm, moderate/normal, aggressive and no speed driving styles for a group of drivers based on the analysis of lateral jerk signal were identified. In [18], the relationship between DS and driver characteristics such as somatic, behavioural and emotional conditions were exploited to develop a structural equation model for the classification of DS into various styles ranging from aggressive to cautious. Similarly, other approaches for DS classification based on levels of aggressiveness [19–21], based on vehicle dynamics such as headway time, jerk and so on [22], car pedal use and car following dynamics [23] among others have been developed. In these works, the DS was classified through rule based approach (fuzzy), model based approaches or machine learning based approaches (supervised/unsupervised) [10].

Integrating the information of DS, personalised ADAS systems for improved fuel consumption, collision avoidance, comfortable driving, safety and so on have been subsequently proposed. In [19], the information of identified DS was used to identify the ‘owner’ of a connected vehicle in case of theft. Similarly in [20], considering different driver models, i.e. aggressive, eco-driving and normal models, a personalised ADAS to minimise the fuel consumption in conjunction with a path planning algorithm was proposed. In [24], a personalised DS adapted active cruise control (ACC) was proposed. In this work, the proposed ACC was then able to mimic the human driving style for longitudinal control. The information of the classified DS was employed to plan the learning path for the driver for achieving fuel economy upgrades and improve driver behaviour in [5]. A fuzzy control based approach for the design of a driver advisory system to improve the fuel economy in hybrid electric vehicle was proposed in [4]. Other uses of DS adapted control have been exploited for car-following

<footnote n="1">¹Department of Automatic Control, LAMIH-UMR CNRS 8201, University of Valenciennes, Valenciennes, France</footnote>

<footnote>✉ E-mail: jagatjyoti.rath@gmail.com</footnote>
manoeuvre [25], driver steering control [26], driving safely along curved roads [27] and so on. Most of the works proposed for DS adaptation are for improving fuel consumption, safety and so on with focus on longitudinal motion control. In [28], a methodology was proposed for modelling individual driver behaviour for lane change manoeuvre. By integrating a sinusoidal lane change kinematic model and a Gaussian mixture model, the kinematic parameters were adjusted to individual driving styles. These parameters were then updated online for providing lane change w.r.t. individual driver/vehicle response. Similarly in [29] a driver model was used to detect unintentional lane change manoeuvres early and employ model predictive control action to prevent vehicle drifting through steering control. Using various vehicle state measurements, a switching logic was employed between the driver and the controller to detect the unintentional lane change and provide control accordingly. Further in [30], a DS personalised approach for driving on narrow roads was proposed. In this approach based on pre-recorded driving experience of the driver, reference trajectories are first established to classify driving styles. In real time, for any deviation from reference trajectory, a minimal assisting action is provided to keep the vehicle on the road. Along similar lines, we explore the possibilities of DS adaptation based personalised lane keeping assist (PLKA) for lateral motion control of vehicle in this work.

In this work, a DS adaptive lane keeping assist (LKA) system based on a co-operative control architecture is proposed. Initially, the bicycle model dynamics for lateral motion of a vehicle was integrated with the visual cues based human driver model [2] and the lane errors based road model, to establish a closed driver-vehicle dynamic model. For the developed model, the control objective was to design a PLKA system which could adapt to the DS. To develop the PLKA, the driving response of a group of drivers was first considered, i.e. the lateral jerk, mean speed, lateral acceleration, steer feel and so on [31] for analysis. Based on the statistical analysis of these measurements, lateral jerk and steer feel were considered as two measurements which could generate features for the classification of driving style into four classes, i.e. clam, moderate, aggressive and very aggressive [17, 27]. First, driving zones were identified based on the lateral acceleration and road map. Then specific to the driver zone, a fuzzy-rule based approach was proposed to identify the driving style as output. An adaptive activity function (AAF) for the driver considering the driver torque and DS was then formulated. Employing the AAF, an assistance modulation factor (AMF) was then formulated based on levels of assistance required [2, 3]. Subsequently, to minimise the lane errors, i.e. lateral deviation and heading error, a robust feedback controller based on the higher order sliding mode (HOSM) [32, 33] technique was designed to generate the assist torque. The co-operative control architecture was completed with the modulation of the assist torque with the developed AMF based on DS for driver-vehicle operation. The main contributions of the proposed work are:

* A fuzzy classification procedure for the identification of driving style based on levels of aggressiveness was proposed. First based on levels of lateral acceleration, driving zones are identified and mapped. Employing normalised values of lateral jerk and steer feel signals w.r.t. the identified driving zones, a fuzzy classifier is proposed to categorise driving style into four classes based on levels of aggressiveness.

* A robust state feedback controller based on HOSM approach is proposed to satisfy multiple objectives of (i) minimisation of lane deviation errors, (ii) improvement of driver comfort. Closed-loop stability in presence of disturbance and uncertainty is established.

* A dynamic function to represent the level of assistance required based on DS is proposed. Consequently, the co-operative architecture for lane keeping is developed with the DS modulated assisting torque and driver torque acting simultaneously to perform lane keeping.

The performance of the co-operative control approach is validated over the Satory test track for lane keeping thru numerical

simulations. For illustration, results of a single driver and generalised results for a group of drivers are shown. The subsequent analysis and discussions have been presented for the DS identification, HMI between the driver-autonomous controller and lane keeping performance for the proposed co-operative approach.

## 2 Driver-vehicle system: lateral motion

To improve HMI and the overall efficacy of an assistive driving system, the objective is to design ADASs which can adapt to driver attributes such as behaviour, skill, style and so on, and hence be personalised. In this aspect, we consider incorporating DS as a factor for analysing the HMI between human driver-autonomous system for a LKA system in this work. To design and implement the proposed co-operative control architecture, the integrated vehicle-driver-road dynamics for a driver-in-the loop LKA task is discussed.

### 2.1 Lateral motion: vehicle-road interaction

The lateral motion of vehicle can be replicated by the bicycle model which integrates the dynamics of lateral speed/slip and yaw motion. Under the effect of lateral friction forces and with assumptions of negligible longitudinal coupling, the non-linear lateral dynamics for a longitudinal vehicle velocity $v_x$ is given as [2, 7]

$$ \begin{cases} M v_x \dot{\beta} = F_r + F_f \cos(\delta_f) - M v_x \psi + F_w \\ I_z \dot{\psi} = l_f F_f \cos(\delta_f) - l_r F_r + M_w \end{cases} \quad (1) $$

where $M$ is the mass of the vehicle, $l_f$ and $l_r$ represent the distance from centre of gravity to the front and rear axles, respectively, and $I_z$ is the yaw moment of inertia. The yaw rate is denoted as $\psi$, the vehicle side slip angle as $\beta$, the tyre steering angle as $\delta_f$, the lateral aerodynamic force and moment as $F_w$ and $M_w$, respectively. The non-linear friction forces that excite the vehicle and are responsible for motion of the front and rear wheels are given as $F_f$ and $F_r$, respectively. The tyre-road interactive friction can be modelled using various static and dynamic models such as Dahl, LuGre, Brush-Tire and so on. Considering the non-linear Brush-Tire model, the dynamic friction between tyre-road is modelled in this work as [7]

$$ F_j = \begin{cases} 3\sigma_j[1 - |\gamma_j\zeta_j| + \frac{1}{3}(\gamma_j\zeta_j)^2]; & \forall \alpha_j \le \alpha_{sj} \\ \mu_f F_z \text{sign}(\alpha_j); & \forall \alpha_j > \alpha_{sj} \end{cases} \quad (2) $$

where $j = f, r$ denoting the front and rear tyres. The non-linear functions are given as $\gamma_j = (2C_p l_p^2 / 3\mu_f F_z)$, $\alpha_{sj} = \tan^{-1}(\gamma_j)$, $\sigma_j = \mu_f F_z \gamma_j \zeta_j$ and $\zeta_j = \tan(\alpha_j)$ with $C_p$ denoting the tyre stiffness coefficient, $l_p$ representing the tyre-road contact patch length, $\mu_f$ is the dynamic road-tyre friction coefficient and $F_z$ is vertical load on tyre. The front and rear tyre slip angles are given as

$$ \alpha_f = \delta_f - \frac{\beta v_x + l_f \psi}{v_x}; \quad \alpha_r = \frac{\beta v_x - l_r \psi}{v_x} \quad (3) $$

Based on the Brush-Tire model, the linear region of frictional forces, i.e. for low slip angles and saturated region, i.e. for high slip angles can be analysed. The tyre self-align moment as a function of the front tyre lateral force can be given as $T_{sn} = (K_p l_p^2 F_f) / R_s$, where $K_p$ is the level of assistance from the active steering system and $R_s$ denotes the steer gear ratio. For the vehicle, with above lateral dynamics undergoing a lane keeping task the objective is to keep the vehicle at the centre of the lane with appropriate orientation. Thus, the interaction of the vehicle with the road curvature $\rho_r$ for lane following can be depicted by the lateral deviation error $\gamma_l$ and the heading error $\Psi_l$ at a look ahead distance $l_s$. These entities
together represent the lane tracking error, with their dynamics given as [2, 3]

$$ \dot{y}_l = \beta v_x + l_s \psi + \Psi_l v_x; \quad \dot{\Psi}_l = \psi - \rho_v v_x \quad (4) $$

For a real vehicle, the lane tracking error measurements are available on a real-time basis from the vehicle perception unit [2]. Integrating the lateral motion dynamics (1) and the lane tracking error dynamics (4), a non-linear system can be formulated. In the absence of a human driver, the design of control focuses on generation of the steer angle $\delta_f$ for lane keeping system. In this work, with driver-in-the-loop considered, the dynamics of the steering column are hence introduced to depict the interaction between the human driver and the vehicle-road non-linear system. The steering column dynamics can be given as

$$ J_s \ddot{\delta}_f = R_s T_d + R_s T_c - R_s T_{sn} - R_s B_s \dot{\delta}_f \quad (5) $$

where $J_s$ is the steer column moment of inertia, $B_s$ is the viscous coefficient of steering system, $T_d$ is the torque from the driver and $T_c$ is torque from the assist system. With the driver considered, the driver steering angle can then be given as $\delta_d = R_s \delta_f$. For the lane keeping task, now the driver model mapping the torque $T_d$ based on visual cues is discussed.

## 2.2 Driver model: visual cues based

The human driver has been modelled in past researches based cognitive actions, neuromuscular actions, human arm dynamics and visual response. Considering the lane keeping objective of this work, a driver model as function of the visual angles, i.e. near visual angle $\theta_n$ and far visual angle $\theta_f$ is employed [2, 34]. The near and far visual angles represent the compensatory and anticipatory actions performed by a human driver while ensuring that vehicle remains in lane centre in the absence of any assistive action. Using an anticipatory behaviour, the driver visualises the road curvature at a far point of the road and generates and anticipated steering torque before entering the curve. Once the driver starts lane keeping by entering the curve, his/her compensatory behaviour enables him/her to generate the necessary compensatory steering torques. The integrating mapping of the anticipatory and compensatory steering motions of the driver can be then used to depict the total torque generated by the driver. The near and far angles are formulated as a function of the lane tracking errors, predicted road curvature, look ahead distance at the far point and given as [2]

$$ \theta_n = \frac{y_l}{v_x T_p} + \psi_l; \quad \theta_f = \rho_{tp} L_f \quad (6) $$

where $T_p$ is the driver preview time for the near point, $\rho_{tp}$ is predicted road curvature and $L_f$ is the look-ahead distance at the far point given as, $L_f = \tau_a v_x$ with $\tau_a$ representing time to the tangent of the far point tracked by the driver. When the vehicle is on a straight road, $L_f$ has a high value as $\rho_{tp} \to \infty$. In such a case, the far visual angle is zero. However, on a curved path the value of $L_f$ depends on the anticipation time of the driver and the driving velocity, becoming constant with the road curvature. The predicted road curvature can be approximated as [34, 35]

$$ \rho_{tp} = \frac{1}{v_x} \left[ \psi + L_f \frac{\dot{\psi}}{v_x} \right] $$

Based on these near and far angles, the following model of the driver is given:

$$ T_d = K_c \theta_n + K_a \theta_f \quad (7) $$

where $K_c$ is the compensatory gain and $K_a$ is the anticipatory gain. Integrating the above expressions for predicted road curvature, far visual angle and near visual angle, the driver torque can be easily

<figure><img src="image_2.png" /><figcaption>Fig. 1 Lane keeping task for a vehicle at a look-ahead distance</figcaption></figure>

represented in terms of the lane errors and the vehicle states. An illustration of the lane keeping task for a vehicle at a look-ahead distance $l_s$ is shown in Fig. 1.

## 2.3 Integrated model: vehicle-driver-road

The vehicle-driver model for a lane keeping/following task is then formulated by integrating the dynamics (1)–(7). This model can be represented as a generic non-linear system due to the effect of non-linear tyre-friction forces as

$$ \dot{x} = f(x, t) + g(x, t)U + \Delta \quad (8) $$

where $x$ denotes the states of the system, $f(x, t)$ represents the state transition dynamics, $g(x, t)$ the input-state dynamics, $U$ the control input and $\Delta$ the disturbances affecting the system. The states of the non-linear system are given as $x = [\beta \quad \psi \quad y_l \quad \Psi_l \quad \delta_d \quad \dot{\delta}_d]^T$. The non-linear functions $f(x)$, $g(x)$ can be obtained from the system dynamics discussed earlier and the control input is sum of the assistive torque $T_c$ and the driver torque $T_d$. For this non-linear system, the objective is then to design the assistive torque $T_c$ for ensuring lane keeping while traversing dynamic curves.

# 3 Proposed architecture

DS typically characterises the torque generating capability of a driver for a specific manoeuvre. The DS for a specific driver is influenced by various factors that can be based on psychological, physiological, environmental and vehicle responses such as driving conditions, traffic, weather, mood, driver skill, behaviour, fatigue and so on [10]. The use of DS recognition for active feedback in ADAS systems requires a trade-off between recognition efficiency, complexity, ease of implementation and improved comfort for the driver.

## 3.1 Driver style identification

In this work, the objective is to design a LKA system that assists the human driver while navigating variable road conditions. Specifically, the idea is to categorise the DS into various classes based on vehicle responses with focus on effective lane tracking and increased driver comfort. To classify the DS for the design of a LKA system, various measurements, i.e. lateral acceleration, lateral speed, jerk, steer rate, lateral quickness and so on can be considered. In this work, the following signals have been selected for the identification of different DSs.

**Lateral Jerk:** Lateral jerk is a third-order index representing the lateral vehicle motion. The lateral jerk signal has been extensively used for classification of DSs for lane keeping, lane change and so on driving tasks [10, 17, 20, 21, 27, 31]. For a driver following a track of variable road curvatures, the lateral acceleration has a significant variation w.r.t. to vehicle speeds. Consequently, the average jerk over different road segments also exhibits variations. In general, for a very sharp turn, the jerk magnitude would be significantly higher for an aggressive style of driving, in comparison to a calm style. This response is further dependent on the driver parameters and the driving velocity. The instantaneous lateral jerk at time instant $k$ can be given as
$$J_y(k) = \frac{1}{\Delta k} [a_y(k+1) - a_y(k)] \quad (9)$$

Steer feel: Its of note that while following a particular track with different road curvatures, its is quite feasible that one individual driver can have variable driving style. Thus, a particular driver may have an aggressive style of driving while manoeuvring a curved track, while on a straight track he/she might have an entirely different driving style [27, 31]. In such scenarios, the assisting action would involve high frequency switching as the driver switches between different driving styles. This in turn leads to severe discomfort for the driver and reduced the drive performance. To ensure that the DS identified takes into consideration the driver comfort, the steer feel factor (SFF) is introduced as follows:

$$SFF = v_x \dot{\delta}_d \quad (10)$$

The SFF indicates the steering feel for the driver for a typical driving velocity $v_x$ based on the driver comfort expressed as a measure of the steering rate. Thus, in the case of high driver comfort, the SFF has a low value while for a very low driver comfort, the SFF has a very high value. By the integrated analysis of the jerk signal and the SFF, the driving style can be categorised into multiple classes such as calm, moderate, aggressive and so on. It is of note that, to identify different driving styles of the same driver along various curves, the signals $J_y$ and SFF must be analysed w.r.t. the lateral acceleration of the vehicle while navigating the curve. The classified driving styles thus would be specific to the average lateral acceleration for the considered road segment. Consider that the vehicle is driven around a dynamic test track with the longitudinal velocity constrained as $|v_x| \le v_{mx}$. Accordingly, to preserve limits of stability across very sharp turns, the lateral acceleration is assumed to be constrained within $|a_y| \le a_{ymx}$. Incorporating the above effects of lateral acceleration, the following generic algorithm is proposed for detection of driving style:

* **STEP 1:** Based on the limits of lateral acceleration and road curvature map, partition the driving cycle into multiple driving zones. Each zone corresponds to an averaged lateral acceleration threshold.

* **STEP 2:** For each driving zone, compute the mean, variance (VAR), standard deviation (SD), root mean square (RMS) and peak value of signal (PK) for the signals $J_y$ and SFF. The data is analysed over an sliding window $s_w$ for smooth results. After analysis, the significant statistical values are then normalised w.r.t. particular driving zone.

* **STEP 3:** Employ the normalised statistical values of $J_y$ and SFF as inputs to a decision block for classification of driving style into four classes, i.e. calm, moderate, aggressive, very aggressive.

In this work, we employ fuzzy logic based decision algorithm to generate different driver classes based on the analysed jerk and steer feel signals. It is of note that other rule based approaches, look-up tables, supervised classification algorithms and so on can be employed to classify the driving style.

**Remark 1:** In this work, the signals lateral acceleration and driver steer rate are employed for identifying the DS. It is of note that other measurements such as lateral quickness, headway time and so on generate significant features when the objectives are lane change, lane departure, obstacle avoidance [21, 22, 31] and so on. In contrast, with the objective of lane keeping along dynamic curves considered in this work, the lateral jerk and steer feel are among the most significant signals used for DS classification based on aggressiveness levels with high accuracy [10, 17, 27].

## 3.2 Human-machine interaction: lane keeping w.r.t. driver driving style

The interaction between the human driver and the autonomous controller designed for lane keeping can be modulated to achieve various objectives such as lane keeping, obstacle avoidance, driver comfort improvement and so on. This modulation can be carried out by the design of an adaptive function that reflects the changes in driver attributes and lane keeping performance. In this work, the focus is on the design of an assistance architecture, where the assist torque generated by the driver is adapted to the driving style. To design such a function, the relationship between driver torque, DS and the level of assistance required similar to [2, 35] is explored. In accordance with that, an AAF is formulated as a function of the driver torque and the driving style as shown below:

$$AAF = 1 - e^{-p_1 T_{dn}^2 DS^{p_3}} \quad (11)$$

where, $p_1 = 2$, $p_2 = p_3 = 3$. The function $T_{dn}$ represents the normalised driver torque and given as $T_{dn} = |T_d/T_{dm}|$, with $T_{dm}$ denoting the maximum driver torque possible. The value of DS indicating driver has also been normalised w.r.t. various styles. The AFF replicates the activity of the driver in accordance with his driving style as an exponential function. To employ this information of the driver activity for modulating the assistance torque, the relationship between driver activity and level of assistance required [2] was exploited. Based on previous research, it can be established that the level of assistance required by the driver can be represented by a U-shaped function [2]. To replicate this curve, the following AMF is developed

$$\mu_{AF} = \frac{1}{1 + ((|AAF - q_1|/q_2)^{2q_3} + 0.2)} \quad (12)$$

where, $q_1 = 0.5$, $q_2 = 0.355$ and $q_3 = -2$, respectively. Employing the proposed AMF, the assistive control can be then generated as

$$T_c = \mu_{AF} U_{fb} \quad (13)$$

where $U_{fb}$ is a robust feedback control designed in the following section.

## 4 Lane keeping: a robust feedback approach

For the design of a LKA system, the control objective are formulated as follows: (i) minimisation of lane deviation errors, (ii) improvement in driver comfort. To ensure that the lane deviation errors, i.e. $y_l$ and $\Psi_l$ at a look ahead distance $l_s$ are minimised, the tracking error $e_l$ is defined as

$$e_l = y_l + l_s \Psi_l \quad (14)$$

The driver comfort can be analysed as a measure of the steering rate. Integrating the steering comfort with the lane tracking error, the integrated error surface can be hence formulated as

$$\sigma = \eta_1 e_l + \eta_2 \dot{e}_l + \eta_3 \dot{\delta}_d \quad (15)$$

where $\eta_1, \eta_2, \eta_3 > 0$ are positive constants to be designed. The dynamics of the error surface can be expressed as a function of the states of the integrated driver-vehicle model (8) as

$$\begin{aligned} \dot{\sigma} &= \eta_1 \dot{e}_l + \eta_2 \dot{e}_l + \eta_3 \dot{\delta}_d \\ &= \eta_1 [\dot{y}_l + l_s \dot{\Psi}_l] + \eta_2 [\dot{y}_l + l_s \dot{\Psi}_l] + \eta_3 \dot{\delta}_d \\ &= \eta_1 f_1(x) + \eta_2 f_2(x) + \eta_3 f_3(x) + \frac{\eta_3}{J_s} U_{fb} + \Delta \end{aligned} \quad (16)$$

where $f_1(x) = 2l_s\psi + v_x(\beta + \Psi_l)$, $f_2(x) = 2l_s\psi_n + v_x\psi\beta_n$ and $f_3(x) = (1/J_s)(T_d + T_{sn} + B_s\dot{\delta}_d)$ are functions of the states of the system. The non-linear functions $\psi_n, \beta_n$ represent the nominal
<figure><img src="image_3.png" /><figcaption>Fig. 2 Architecture of the proposed DS assisted co-operative control scheme</figcaption></figure>

dynamics of the yaw rate and side slip measurements, given as $\psi_n = (1/I_z)(l_f F_f \cos(\delta_f) - l_r F_r)$ and $\beta_n = (1/v_x)(l_f F_f \cos(\delta_f) + F_r) - \psi v_x$, respectively. The disturbance term $\Delta$ affecting the error dynamics is given as

$$ \Delta = -\frac{F_w}{M} - \frac{F_w l_w}{I_z} - (\eta_1 + \eta_2)l_s \rho_r v_x - \eta_2 l_s \dot{\rho}_r v_x \quad (17) $$

To ensure the convergence of the error dynamics, in the presence of the lumped disturbance $\Delta$, the following feedback control $U_{fb}$ is then designed as

$$ U_{fb} = \frac{J_s}{\eta_3} [-\eta_1 f_1(x) - \eta_2 f_2(x) - \eta_3 f_3(x) + \nu(\sigma)] \quad (18) $$

where $\nu(\sigma)$ is a robust control based on the HOSM approach and given as $\nu(\sigma) = -\alpha_1 \phi_1(\sigma) - \alpha_2 \phi_2(\sigma) dt$. The non-linear functions $\phi_1$, $\phi_2$ are given as $\phi_1 = \sigma + \alpha_3 |\sigma|^{0.5}$ sign($\sigma$), $\alpha_2 = \sigma + 0.5 \alpha_3^2$ sign($\sigma$) + $1.5 \alpha_3 |\sigma|^{0.5}$ sign($\sigma$), where $\alpha_1$, $\alpha_2$ and $\alpha_3$ are positive gains to be designed. Substituting for the proposed control (18), the error dynamics can be then expressed as

$$ \dot{\sigma} = \nu(t) + \Delta \quad (19) $$

Based on practical operating ranges and boundedness of the disturbances thereof, the bound on the perturbation $\Delta$ can be established as $|\dot{\Delta}| \le \rho_d$, where $\rho_d > 0$ is a positive constant. It can be shown that for appropriately designed gains $\alpha_1$, $\alpha_2$ and $\alpha_3$, the finite time convergence of the error surface ($\sigma = \dot{\sigma} = 0$) can be ensured. For details refer [32, 33]. The feedback control $U_{fb}$ designed to stabilise the tracking error dynamics represents the assistive torque to be generated by the actuator in the case of autonomous control. Integrating the information from the DS recognition unit, the feedback control is then modulated to generate the assist torque $T_c$ as shown in (13) to ensure co-operative control between the human driver and the autonomous system during shared control. The architecture of the proposed scheme is shown in Fig. 2.

# 5 Results and discussion

To evaluate the proposed approach, the parameters of the vehicle considered were $M = 2025$ kg, $I_z = 2800$ kgm², $l_f = 1.30$ m, $l_r = 1.60$ m, $t_p = 0.052$ m, $C_{pf} = 42500$ N/rad, $C_{pr} = 55690$ N/rad, $l_s = 5$ m, $B_u = 0.5$, $R_s = 16.3$, $J_s = 0.05$ kgm², $\tau_u = 1$ s and $T_p = 0.8$ s. The proposed co-operative control architecture was

validated on the Satory test track for different driving conditions. The Satory test track is a real-world test track composed of road sections with radii varying from 25 to 500 m [2]. The driver model (7) has been validated on the SHERPA simulator for various drivers [2, 34, 35]. Accordingly, real driver data validated on the simulator was used to determine the anticipatory and compensatory gains $K_c, K_a$, respectively, to represent various drivers [2, 34, 35]. The performance of the proposed approach was then validated thru numerical simulations carried out on Matlab/Simulink platform for the non-linear vehicle-driver model (8). It is considered that the vehicle traverses different sections of the track at a fixed velocity where $|v_x| \le 15$ m/s. The level of assist provided from the active steering system is fixed at $K_p = 0.65$. The road-tyre friction coefficient is a variable entity dependent on surface conditions. In this work, the results presented are for $\mu_f = 1$. However, the friction can vary in the $\mu_f \in [0, 1]$ based on the road surface and the proposed controller implemented accordingly with due modifications to the controller gains. For the above driving conditions it is considered that for effective lane keeping performance, the states of the non-linear system (8) are constrained as follows [2, 34, 35]:

$$ \begin{array}{l} |\psi| \le \psi_m, \quad |\Psi_l| \le \Psi_{lm}, \quad |y_l| \le y_{lm}, \quad |\delta_f| \le \delta_{fm}, \\ |\dot{\delta}_f| \le \dot{\delta}_{fm}, \quad |T_c| \le T_{cm} \end{array} $$

where the maximum value of each measurement is given as $\psi_m = 0.55$ rad/s, $\Psi_{lm} = 0.1$ rad, $y_{lm} = 1$ m, $\delta_{fm} = 0.18$ rad, $\dot{\delta}_{fm} = 0.11$ rad/s, and $T_{cm} = 10$ Nm. For the design of controller, the gains $\eta_1, \eta_2$ and $\eta_3$ were selected as $\eta_1 = \eta_2 = \eta_3 = 1$ for the sake of simplicity. These gains can also be elected based on design approaches such as pole placement, LMI and so on as discussed in [36]. Based on the maximum limits of the road curvature and the lateral aerodynamic forces, the bound of the perturbation $\Delta$ was computed posteriori as $\rho_d = 0.8$. Its of note that the procedure of computation of posteriori bounds is generally followed for HOSM approaches [32, 33]. Based on the bounds of the perturbation, the HOSM gains were selected as $\alpha_1 = 1.5$, $\alpha_2 = 15$ and $\alpha_3 = 4.5$ similar to [32, 33]. For the above considered driving scenarios, the proposed DS adapted co-operative driving architecture was then evaluated and the results are presented.

## 5.1 Driver style recognition

To identify and categorise the driving styles as discussed in Section 3.1, multiple runs on the Satory test track for different driving conditions and driver parameters were conducted. For different ranges of longitudinal velocity $|v_x| \le 15$ m/s, the entire track was
<figure><img src="image_4.png" /><figcaption>**Fig. 3 Driver zones identification**</figcaption></figure>

(a) Driving zones w.r.t. lateral acceleration and road curvature, (b) Driving zone identified for a single driver

<figure><img src="image_5.png" /><figcaption>**Fig. 4 Jerk profile of various drivers**</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 5 Steer feel of various drivers**</figcaption></figure>

divided into multiple zones of variable acceleration levels with peak acceleration during the entire test fixed at $|a_y|_{pk} = 5 \text{ m/s}^2$. Based on the road curvature map and the lateral acceleration, distinct driving zones can be mapped as shown in Fig. 3. The driving zones, DZ are normalised in the range $DZ \in [0, 1]$. With the increase in levels of acceleration and the road curvature the value for DZ increases as shown in Fig. 3a. Employing this mapping, the driving zones identified for a single driver are shown in Fig. 3b for illustration.

From the identified DZ, four distinct zones were considered as $DZ1 \in [0, 0.25]$, $DZ2 \in [0.25, 0.4]$, $DZ3 \in [0.4, 0.6]$ and $DZ4 \in [0.6, 1]$. For each driving zone identified, the lateral jerk and steer feel signal was then analysed to identify the DS as discussed in Section 3.1. Accordingly, the mean, variance (VAR), standard deviation (SD), root mean square (RMS) and peak value of signal (PK) was obtained for variable sliding window lengths. In this work, we considered three different sliding windows, i.e. $s_w = 15$, $s_w = 25$ and $s_w = 50$ for the data analysis. From the analysed data, it was found that the standard deviation from the mean value for each signal could best express the difference between different road zones. For illustration purposes, the mean SD of the lateral jerk signal ($J_{sd}$) computed over $s_w = 50$, for different driving zones and drivers is shown in Fig. 4.

It can be seen from Fig. 4 that for different driving zones, the jerk profiles of the drivers are different. Further, it is of note that a single driver can have an aggressive driving style during one zone while a calm style during another zone. Similarly, the illustration for the SD of steer feel ($SF_{sd}$) is shown in Fig. 5.

Employing the normalised values of $J_{sd} \in [0, 1]$ and $SF_{sd} \in [0, 1]$, a fuzzy inference logic as shown in Table 1 was then designed to identify DS. For the considered fuzzy system, the inputs were $J_{sd}$ and $SF_{sd}$, with the output as DS ($DS \in [0, 1]$). The $J_{sd}$ input was categorised into five normalised membership functions having labels $\in \{VL, L, M, H, VH\}$, i.e. very low to very high. The steer input $SF_{sd}$ was labelled based on comfort as $\in \{VS, S, C, R, VR\}$ where the labels are very smooth, smooth, comfortable, rough, very rough. The fuzzy output is the DS with labels $\in \{Calm, Moderate, Aggressive, VeryAggressive\}$. The fuzzy membership inputs have trapezoidal shapes while the output has a triangular shape as shown in Fig. 6.

For the above fuzzy inference system, 25 rules were formulated as shown in Table. 1. Based on the above fuzzy rules, the output DS is defuzzified as shown in Fig. 6b. Using the identified driver style DS, the driver assistance function DAF is then formulated as discussed in Section 3.1.
<figure><img src="image_7.png" /><figcaption>**Fig. 6 Fuzzy inference based driver style detection**</figcaption></figure>

(a) Fuzzy input for the Lateral jerk and Steer feel, (b) Output driver class, (c) Identified DS for the illustrated driver

<figure><img src="image_8.png" /><figcaption>**Fig. 7 Lane tracking performance**</figcaption></figure>

(a) Lateral deviation error, (b) Heading error

## 5.2 Lane keeping performance: satory test track

The designed co-operative control strategy was evaluated over the Satory test track for lane keeping performance. For illustration purposes, the performance of a single driver-autonomous system based co-operative system is discussed in detail first. Subsequently, the results are generalised for a group of drivers. Based on the statistical analysis of the jerk and the steer feel signals for the driver, the identified DS is shown in Fig. 6c. It can be deduced from Fig. 6c that the DS continuously evolves for the considered driver. It is dependent on the identified driver zone as discussed earlier.

<table><caption>**Table 1 Fuzzy rules for the DS identification**</caption><thead><tr><th rowspan="2">J<sub>sd</sub></th><th colspan="5">SF<sub>sd</sub></th></tr><tr><th>VS</th><th>S</th><th>C</th><th>R</th><th>VR</th></tr></thead><tbody><tr><td>VL</td><td>calm</td><td>calm</td><td>moderate</td><td>aggressive</td><td>aggressive</td></tr><tr><td>L</td><td>calm</td><td>moderate</td><td>moderate</td><td>aggressive</td><td>very aggressive</td></tr><tr><td>M</td><td>moderate</td><td>moderate</td><td>aggressive</td><td>aggressive</td><td>very aggressive</td></tr><tr><td>H</td><td>moderate</td><td>aggressive</td><td>aggressive</td><td>very aggressive</td><td>very aggressive</td></tr><tr><td>VH</td><td>aggressive</td><td>aggressive</td><td>aggressive</td><td>aggressive</td><td>very aggressive</td></tr></tbody></table>

For the identified driving style, the lane tracking errors $y_l$ and $\Psi_l$ are thus shown in Fig. 7. The lane errors employing the proposed control are minimised and within the limits established earlier. In Fig. 8, the controlled states, i.e. yaw rate, steer angle and steer angle velocity for the closed-loop system are shown to be within the prescribed limits. With the states of the controlled system shown to be within limits, the generated torques by the assisting $T_c$ and the driver $T_d$ are shown in Fig. 9a. Further, the torque generated by the driver while navigating the test track in the absence of any assisting torque is shown. It can be deduced from Fig. 9a, that for the co-operative controlled system, the torque generated by the driver is much lower, typically during high curvature regions. Consequently, the HMI between the human driver and the autonomous controller is shown in Fig. 9b by the illustrated plots of AAF and $\mu_{AF}$. It can be seen that typically during low driver activity regions, the automated system provides a high level of assistance to the driver, thus assisting it in lane keeping effectively.

The above results presented show the performance of the proposed DS adaptive co-operative control architecture in this paper achieves the control objectives of lane keeping and driver comfort. To generalise the performance, simulations were then conducted for various drivers to show the accuracy of the driver class recognition, lane keeping performance, level of assistance provided and so on. In Fig. 10a, the mapping of the DSs identified for various drivers over different driving zones is shown.
<figure><img src="image_9.png" /><figcaption>**Fig. 8 Controlled states of the system**</figcaption></figure>

(a) Yaw rate $\psi$, (b) Steer angle $\delta_f$, (c) Steer angle rate $\dot{\delta}_f$

<figure><img src="image_10.png" /><figcaption>**Fig. 9 Controlled system**</figcaption></figure>

(a) Assist torque $T_c$, driver torque $T_d$, (b) AAF and $\mu_{AF}$

<figure><img src="image_11.png" /><figcaption>**Fig. 10 DS identification and lane errors for drivers**</figcaption></figure>

(a) Identified DS w.r.t. driving zone for a group of drivers, (b) Modulation factor w.r.t. driving zone for a group of drivers, (c) Lateral deviation error $y_l$, (d) Heading error $\Psi_t$ over different driving zones

With the increase in the identified driver zones (DZ), the level of aggressiveness indicated by the DS increases. This behaviour is prevalent across the group of drivers considered as shown in Fig. 10a. It is also of note that for a single driver the driving style

increases towards a more aggressive driving with the increase in the zone of driving. The corresponding modulation provided under the proposed co-operative control scheme for the group of drivers
<figure><img src="image_12.png" /><figcaption>Fig. 11 Comparison of the lane keeping performance between DS assisted and no assist architectures</figcaption></figure>

is then shown in Fig. 10b. The modulation factor $\mu_{AF}$ and consequently the assistance provided by the autonomous controller is well distributed across the driving zones for all drivers. Under such levels of assistance, the lane keeping performance for the group of drivers is shown in Fig. 10c. For the four driving zones $DZ_1 \cdot DZ_4$, the RMS (root mean square) of the lane deviation error $y_l$ and heading error $\Psi_l$ was computed and is illustrated for different drivers. It can be seen that for all drivers, the lane errors are within the required limits thus establishing lane keeping performance of the proposed scheme across a group of drivers. Further in Fig. 11, a comparison between the proposed co-operative control scheme and the driver only system, i.e. no assist torque, is shown. It can be clearly seen that based on the DS adaptive design the lane error are reduced in comparison to a no assist case.

The proposed approach in this work used the information of identified DS for design of a LKA system. To increase the accuracy of the identification more signals such a lateral quickness, mean velocity, driver intent and so on can be employed for different driving scenarios. In such a scenario, use of a advanced learning approach for the classification would be viable. Having said that, the fuzzy DS recognition approach employed in this paper has less computation burden and is more efficient for being employed in a closed-loop control design as shown.

## 6 Conclusion

In this work, a DS adaptive co-operative control architecture was proposed. To identify the driving style lateral jerk and steer feel were used as inputs for a fuzzy-rule classifier with driving style as output. Based on identified driving style, i.e. calm, moderate, aggressive and very aggressive, a modulation factor for the assistance torque generated was then developed. To design the assistance torque for the closed driver-vehicle model, a robust HOSM controller was proposed and stability established. The proposed control framework was able to adapt to the driver driving style classified on levels of aggressiveness and consequently reduce lane tracking errors, i.e. lateral deviation/offset and heading error. Extensive results showing the driving style identification, lane keeping performance, HMI between driver and the autonomous controller were presented.

In future aspects, driving event, driver skill, behaviour and so on recognition in conjunction with the proposed DS identification would be explored for the development of the modulation factor to assist the driver.

## 7 Acknowledgments

This work has been done within the framework of the AutoConduct project (ANR-16-CE22-0007), funded by the Agence Nationale de la Recherche. This work was also supported by the International Campus on Safety and Intermodality in Transportation, the Hauts-de-France Region, the European Community, the Regional Delegation for Research and Technology, the Ministry of Higher Education and Research, and the French National Center for Scientific Research.

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