Automation-driver cooperative driving in presence of undetected obstacles

Control Engineering Practice 24 (2014) 106–119

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Automation-driver cooperative driving in presence of undetected obstacles B. Soualmi n, C. Sentouh, J.C. Popieul, S. Debernard LAMIH, CNRS, UMR 8201, Campus du Mont Houy, F-59313 Valenciennes, France

art ic l e i nf o

a b s t r a c t

Article history: Received 13 December 2012 Accepted 17 November 2013 Available online 20 December 2013

The work presented in this paper describes and discusses the principles of a haptic shared control between a human driver and an Electronic copilot (E-copilot) for a vehicle. The aim of the sharing control is to allow the driver to momentarily take control over the E-copilot without deactivating it nor being constrained, in order to deal with a specific situation such as avoiding an obstacle that has not been detected by the E-copilot. As the E-copilot acts simultaneously on the steering system with the driver, both have to be aware of one another's actions, which means bi-directional communication is essential. In this work, to achieve this goal, we consider the haptical interactions through the steering wheel. The torque applied by the driver on the steering system is used by the E-copilot to take into account the driver's actions while the E-copilot assistance torque is felt by the driver and used by him to understand the system's behavior. This low communication level strongly improves the cooperation between the driver and the E-copilot. The system takes into account the drivers actions thanks to a driver lane keeping model that is added to the road vehicle one in the controller synthesis step. This allows to introduce driver's interaction control variables in such a way that the E-copilot can consider conflicting objectives between the driver and the lane keeping task, and thus handle them. In order to highlight the assets of the approach, a comparison of the behaviors of a simple lane keeping E-copilot to that of a cooperative proposed here is given at the end of this paper. This comparison is achieved through computer simulations and experimental tests with a human driver carried out in the SHERPA-LAMIH interactive dynamic driving simulator. The results of these tests confirm the improvement of the level of cooperation between the human driver and the E-copilot and show that the cooperative E-copilot gives more authority to the human driver especially in hazardous situations. & 2013 Elsevier Ltd. All rights reserved.

Keywords: Advanced driver assistance systems Human–machine cooperation Fuzzy logic Optimal control

1. Introduction Automobiles are essential in our modern society; more than 82% of people (in France) use their cars for their everyday travels. Nevertheless, the car remains a common cause of death and disability (67 288 accidents in 2010 in France causing about 4000 deaths, where in 90% of the cases the driver is responsible, O.N.I.S.R., 2010). A way of proceeding to remedy for this situation is to introduce assistance systems that can help the driver in normal and hazardous situations. The present technical advancements of automatic control, data processing and telecommunications as well as the reduction in cost of electronic components and their miniaturization, offer the n

Corresponding author. Tel.: þ 33 3 27 51 14 98. E-mail addresses: [email protected], [email protected] (B. Soualmi), [email protected] (C. Sentouh). 0967-0661/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conengprac.2013.11.015

ability to develop Advanced Driver Assistance Systems (ADASs). ADAS can assist the driver in safely navigating the vehicle, which reduces the workload of driving and road accidents (Isermann, 2008; Rajamani, 2006). Mammar et al. (2005) classified the driver assistance systems into three groups according to their action levels. In the first group there are systems that try to stabilize the vehicle by acting at a low control level so that the vehicle remains more stable and controllable by the driver. This is the case of ABS and ESP that are integrated in most new vehicles. The common feature of such systems is their restriction to only the information (measurements) on the vehicle's state. Second group there are systems that alert the driver if a risk is detected (possible lane crossing: Lane Departure Warning Systems, too close to an obstacle, unadapted speed before a curve, etc.) and no action is being taken to avoid the hazards (Lee, 2002; Sentouh, 2007). These systems can be quite ineffective if the driver is inattentive. This group also includes systems that act if the warning does not have an effect, but exclude

B. Soualmi et al. / Control Engineering Practice 24 (2014) 106–119

the driver in the driving process (Enache, Mammar, Netto, & Lusetti, 2010). The last group concerns the systems that can take action and modify the vehicle's dynamics and/or trajectory or those which perform a part of the driving task, like ACC (Adaptive Cruise Control) for longitudinal control. Several solutions using different control strategies and technics to the lane tracking problem were proposed in the literature in order to cover human errors (El Hajjaji, Ciocan, & Hamad, 2005; Enache et al., 2010; Naranjo, González, García, de Pedro, & Haber, 2005; Netto, Chaib, & Mammar, 2004; Shimakage, Satoh, Uenuma, & Mouri, 2002; Tanaka & Sano, 1995). In Tanaka and Sano (1995) the authors have proposed a Takagi–Sugeno controller that stabilizes a car for a trajectory tracking. Naranjo et al. (2005) have proposed a two layer controller combining a high level fuzzy logic controller with a PID controller at a low level for an autonomous steering car. The proposed controller is implemented and successfully tested within real vehicle. Most of works dealing with the lateral control (so lane keeping) use the steering angle as a control signal in the framework of autonomous vehicles (El Hajjaji et al., 2005; Naranjo et al., 2005; Netto et al., 2004; Tanaka & Sano, 1995). Through this the driver is neglected in the driving process or his actions are considered as perturbations! But when the system is in a situation that it cannot cope with, full control is restored to the driver. This can generate a serious accident risk because these situations are generally complex (that is why the system cannot handle them) and the driver might not be ready to perform the right maneuver (since he has not had control of the vehicle for a long time, he is certainly not aware of the situation or not attentive to it). So, while the reliability level of autonomous vehicles is not yet sufficient to introduce them to a real environment, an efficient solution is certainly cooperative control. This will keep the driver in the loop in order to sustain his attentiveness level and contribute to a better confidence in the system allowing the driver to handle complex situations in cooperation with the system (Biester, 2005; Flemisch et al., 2003). Nagai, Mouri, and Raksincharoensak (2003) suggest that a way to allow the driver in the driving process of a vehicle equipped with an E-copilot is the use of the steering torque as a control signal. The authors have made a comparative study between a steering angle control and a steering torque one and suggest that the steering torque control is more appropriate to permit the driver's steering actions. The steering angle control provides good robustness, however, it does not permit the driver's actions during the steering process. It considers them to be disturbances and therefore does not allow them (Shimakage et al., 2002). The level of cooperation between the driver and an E-copilot can be improved considering the driver in the loop through the

107

integration of a driver (driving process) model to vehicle–road one that allows the integration of a priori information about the driver steering behavior (Louay, 2012; Sentouh, Debernard, Popieul, & Vanderhaegen, 2010). Works concerning driver modelling have begun since the 1960s (Pilutti & Ulsoy, 1999; Sentouh, Chevrel, Mars, & Claveau, 2009; Wohl, 1961) but until now few works in driver assistance systems have taken into account the driver in the controller synthesis step. Sentouh et al. (2010) have proposed an approach where the vehicle–road model is augmented with the driver lane following model, and with this, the obtained controller takes into account the driver's actions. To avoid unresolved conflict situations an authority managing algorithm is proposed. With regards to Human–Machine interaction viewpoint, the introduction of automatic steering in a vehicle with a human driver involves the crucial study of the interaction between the two agents. However up now few works have dealt with this question (Flemisch et al., 2003; Flemisch et al., 2008; Griffiths & Gillespie, 2004; Steele & Gillespie, 2001). One of the efficient means of communication between the automation and the driver is the haptic interface via the steering-wheel (Griffiths & Gillespie, 2004). Flemisch et al. (2003) and after Flemisch et al. (2008) introduce the concept of H-metaphor as a guideline for driver assistance system conception. The authors argue that in the state of technical progress achieved today the full autonomous vehicle is not the best solution. They refer to the image of a rider and his/her horse to inspire the conception of an intelligent vehicle where the interactions between the human driver and his vehicle via the steering system are incorporated in the same manner as those between the rider and his/her horse through the reigns: The horse is able to navigate alone but responds to the rider's commands by use of reigns. Fig. 1 gives the global shared driving task scheme. The cooperation between the driver and the E-copilot occurs at two levels. The first one is called High Level of Cooperation (HLC). HLC can be seen as the cooperation at the navigation level. The state of the global system (environment–vehicle–driver–automation) is taken into account at this level of processing the information provided by the trajectory planning unit, the driver monitoring unit (driver state), the traffic and the vehicle's state. Depending on the state of each component of the system, decisions are taken to choose the mode in which the system can run: full automatic, cooperative or manual as well as the vehicle trajectory choice. This paper does not deal with this level of cooperation, we only consider the cooperative mode in which the driver and the E-copilot together assume control of the vehicle. The second level of interaction is called Low Level of Cooperation (LLC). The LLC concerns the interactions between the driver and the E-copilot in the steering system (action). The communication means

HLC Target position

Fig. 1. Global sharing control scheme.

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at this level is the torque exerted by each participant. The driver feels the E-copilot's action and can immediately understand if the controller's actions are appropriate to a given situation or not. In this work, we focus on this level of interaction and discuss the proposed solution to resolve conflict situations. Keeping in mind the H-metaphor, this paper expands the work presented in Soualmi, Sentouh, Popieul, and Debernard (2011) for a lane keeping assistance system that shares vehicle lateral control using T–S controller with a human driver which considers the case where obstacles undetected by the E-copilot are present on the lane. In the proposed approach, a lane keeping driver model is introduced in the controller synthesis step by adding it to road– vehicle model. This allows for consideration of the driving style of the driver in the design process of the E-copilot. Much more, the difference between the driver's and the controller's torque is included in the objectives to be minimized as the driver's torque appear as a stat variable of the system. The obtained controller has the driver's torque as input, in addition to vehicle guidance error. Which can be interpreted as a communication channel from the driver to the controller. The cooperation degree between the driver and the E-copilot is quantified by objective indicators that use the driver's and E-copilot's torque. Finally, a comparative study with an E-copilot obtained without considering a driver model illustrates the advantages of the proposed approach. As longitudinal speed of the vehicle appears as a varying parameter in the lateral dynamics, we introduce T–S control approach to take into account this variation. This allows to maintain lateral lane keeping performances under longitudinal speed variation and a better coordination with the driver during acceleration or deceleration phases. This paper is organized as follows. Section 2 introduces T–S fuzzy modeling and its interest in the control of nonlinear systems. The vehicle model and the driver lane keeping one are presented in Section 3, the associated T–S controller of the nonlinear model is given in Section 4. Section 5 resumes tested scenarios. Numerical simulation and interactive experimental results are shown in Sections 6 and 7. Section 9 concludes the results of this work and gives a guideline of future works.

where hi ðρÞ ¼ wi ðρÞ=∑ri ¼ 1 wi ðρÞ and wi ðρÞ ¼ ∏lj ¼ 1 μj ðM ij ðρj ÞÞ A ½0; 1 is the degree of validity of the ith rule. It is easy to verify that hi ðρÞ Z 0 8 i ¼ 1; …; r

and ∑ri ¼ 1 hi ðρÞ ¼ 1:

The stability of (2) is derived using Lyapunov's approach (Tanaka, Ikeda, & Wang, 1996; Wang, Tanaka, & Griffin, 1996). Theorem 1 (Wang et al., 1996). The system (2) for u¼ 0 is asymptotically stable if there exists a common positive definite matrix P 4 0 such that P ¼ PT ;

P 4 0;

ATi P þ PAi o 0; i ¼ 1; …; r

ð3Þ

In the case r ¼1 the stability condition represents the one of linear system driven from Lyapunov's theorem. The representation of the nonlinear system in (2) form is a weighted convex sum (∑ri ¼ 1 hi ðρÞ ¼ 1) of local linear subsystems. Therefore, to control the global system, the problem can be solved by finding appropriate controllers for each subsystem while ensuring the global stability. Parallel Distributed Compensation (PDC) is a simple and natural design technique for T–S fuzzy model described by (2) (Guerra & Vermeiren, 2004; Tanaka, Ikeda, & Wang, 1998; Wang et al., 1996). In the PDC concept, each controller is distributively designed for the corresponding rule of T–S fuzzy model (Tanaka et al., 1998; Wang et al., 1996). Thus linear control theory can be used to design the consequences of fuzzy control rules because the consequences of T–S fuzzy models are described by linear state equations. The fuzzy controller shares the same fuzzy sets with the fuzzy model in the premises. Let us denote by Ki the linear state feedback corresponding to the ith linear subsystem in the corresponding rule. Then the expression of the T–S corresponding controller is Rulei: IF ρ1 ðtÞ is Mi1 … and ρl is Mil THEN uðtÞ ¼ K i xðtÞ

ð4Þ

The overall fuzzy controller is represented by r

uðtÞ ¼  ∑ hi ðρÞK i xðtÞ

ð5Þ

i¼1

So the global dynamics of the closed loop system is r

2. T–S modeling and PDC control

r

_ ¼ ∑ ∑ hi ðρÞhj ðρÞðAi Bi K j ÞxðtÞ xðtÞ

ð6Þ

i¼1j¼1

T–S modeling has been proposed by Takagi and Sugeno (1985) as a tool to represent nonlinear, parameter varying and uncertain systems in the form of a finite set of fuzzy IF … THEN rules. Each rule has the following form: Rulei: IF ρ1 ðtÞ is Mi1 … and ρl is Mil THEN ( _ ¼ Ai xðtÞ þ Bi uðtÞ xðtÞ ð1Þ yðtÞ ¼ C i xðtÞ þ Di uðtÞ i ¼ 1; …; r where xðtÞ A Rn , uðtÞ A Rm and yðtÞ A R p represent, respectively, the state vector, input and output signals. Ai A Rnn , Bi A R nm , C i A Rpn and Di A R pm represent the ith local model matrix of the fuzzy system. The vector ρ contains the varying parameters which can be function (or not) of the state variables or external disturbances and must be known or measurable (Li, Wang, Niemann, & Tanaka, 2000). Mij are the input fuzzy terms. Using the center-average defuzzifier, the following global dynamic model can be obtained: 8 r > _ ¼ ∑ hi ðρÞðAi xðtÞ þ Bi uðtÞÞ > xðtÞ > < i¼1

r > > > : yðtÞ ¼ ∑ hi ðρÞðC i xðtÞ þ Di uðtÞÞ i¼1

ð2Þ

The design conditions for the stability and performance of the system (6) are stated in terms of the feasibility of a set of Linear Matrix Inequalities (LMIs) (Gahinet, Nemirovskii, Laub, & Chilali, 1994) given in the following theorem. Theorem 2 (Tanaka et al., 1998; Wang et al., 1996). The system (6) with the PDC control law (5) is asymptotically stable if there exists a common positive definite matrix P such that the following LMI constraints are satisfied: ( Γ ii o0; i ¼ 1; …; r ð7Þ Γ ij þ Γ ji o 0; 1 ri o j rr where

Γ ij ¼ ðAi  Bi K j ÞT P þ PðAi Bi K j Þ In the particular case when all subsystems have a common input matrix (B ¼ Bi ; i ¼ 1; …; r), the stability condition of (7) can be simplified as follows. Corollary 1 ((Tanaka et al., 1998)). Assuming B ¼ Bi ; i ¼ 1; …; r, the system (6) is asymptotically stable if there exists a common positive

B. Soualmi et al. / Control Engineering Practice 24 (2014) 106–119

109

3.2. Linear road–vehicle model synthesis The model used for T–S controller synthesis considers a constant longitudinal velocity at different operating points (vx ¼ V, v_ x ¼ 0). So assuming small angles (δ, βf and βr), the lateral tire forces can be approximated as   vy þ lf r F yf ¼ 2C f βf ¼ 2C f δ  V F yr ¼ 2C r β r ¼ 2C r

definite matrix P such that i ¼ 1; …; r

3.1. Nonlinear road–vehicle model In our work, we focus on a driver assistance system that helps the driver in the lane keeping task. So we are concerned with lateral vehicle dynamics and the most commonly used model, which in this case, is the single track or bicycle model (Fig. 2) (Rajamani, 2006). Neglecting roll, pitch, vertical movements and throttle and brake actuators dynamics, the corresponding simplified nonlinear dynamic model is obtained by writing the translational and rotational equations in the vehicle fixed frame (Swaroop & Yoon):

ð9Þ

where vx, vy and r ¼ ψ_ represent, respectively, the longitudinal velocity, the lateral velocity and the yaw rate. δ is the steering angle, lf and lr are, respectively, the distances of the front and rear axles from the vehicle's center of gravity, cx and cy are the longitudinal and lateral aerodynamic drag coefficients, m, and Iz are, respectively, the vehicle mass and the moment of inertia of the yaw axis passing through the vehicle center of gravity. Teng is the engine torque, F yf , F yr are the lateral forces given by the Pacejka, Bakker, and Nyborg formula (known as magic formula): F yk ðβk Þ ¼ Dk sin ½ck arctanðbk ð1 ek Þβ k þ ek arctanðbk βk ÞÞ k A ff ; rg



ð8Þ

3. Road–vehicle and driver models

8 T eng  cx v2x > > þ vy r > v_ x ¼ > m > > > < F yf cos ðδÞ þ F yr  cy v2y  vx r v_ y ¼ > m > > > > lf F yf cos ðδÞ  lr F yr > > : r_ ¼ Iz

vy  lr r V

where Cf and Cr are the linear cornering stiffness coefficients of the front and rear tires respectively. Neglecting aerodynamic forces (cy ¼0) in (9), the vehicle lateral dynamics model can be written as 2 3 2 C 3 C þC l C l C    2 rmV f  V þ 2 r rmV f f  vy  2 f v_ y 6 7 4 m 5δ 2 2 ð11Þ þ ¼ 4 l C l C 5 l C l Cr þ l C r r_ 2 fI z f 2 r rIz V f f  2 r Iz V f f

Fig. 2. Lateral vehicle behavior modeling.

ðAi  BK i ÞT P þ PðAi  BK i Þ o 0;



3.2.1. Road vehicle positioning Since we deal with lane keeping assistance, the vehicle positioning on the road is studied (Fig. 2). This concerns two supplementary variables: the lateral offset from the road centerline at a lookahead distance ls (yL) and the heading error (ψ L ) so that ( yL ¼ yc þ ls sin ðψ L Þ ð12Þ ψ L ¼ ψ v  ψ des where yc is the lateral offset at the vehicle center of gravity, ψv is the vehicle heading and ψdes is the road heading (Fig. 2). Considering small heading errors ( y_ L ¼ vy þ ls r þ ψ L V ð13Þ ψ_ L ¼ r  κ V where κ is the road curvature. In real application, these two supplementary variables (yL and ψ L ) can be given by a vehicle perception system (McCall & Trivedi, 2006).

3.2.2. Steering system model To consider the driver's feeling of the steering torque feedback (self-aligning and E-copilot torques) and to study the haptical driver E-copilot interaction, the steering system (Fig. 3) is modeled and added to vehicle–road one.

ð10Þ

The side slip angles (βk, k ¼ f ; r) for the front and rear tires are

βf ¼ δ  arctan

βr ¼ arctan

  vy þ lf r vx

  vy lr r vx

Fig. 3. Vehicle steering system.

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B. Soualmi et al. / Control Engineering Practice 24 (2014) 106–119

As the dynamics of the two variables yd and ψ L are similar to that of (12), the driver model torque dynamic is

Table 1 Vehicle parameters. Parameter

Value

Parameter

Value

T_ d ¼  k1 vy  ðk1 τV þk2 Þr  k1 V ψ L þ k2 V κ

m lf Cf Js Rs

1500 (kg) 1.0065 (m) 47 135 (N/rad) 0.05 (kg m2) 16

Iz lr Cr Bs ηt

2454 (kg m2) 1.4625 (m) 56 636 (N/rad) 0.5 (N/rad/s) 0.13 (m)

The driver model used in simulation is the one developed by Sentouh et al. (2009).

ð17Þ

4. T–S controllers The simplified steering linear dynamic system is given as   ðvy þlf rÞ  Rs Bs δ_ J s δ€ ¼ Rs T d þ Rs Ra T m  2C f ηt δ  ð14Þ |fflffl{zfflffl} V |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Tc

In this section T–S controllers corresponding to the modeled systems are presented.

T al

where Js is the equivalent steering system inertia, Bs is the equivalent steering system damping coefficient, Rs is the steering column-wheels gear ratio, ηt is the trail length, Tal is the selfaligning torque and Tm is the electric motor torque. To simplify notation we note the E-copilot torque as T c ¼ Ra T m . Thus the global dynamic of road–vehicle system has the following state vector: xv ¼ ½vy r ψ l yL δ δ_ T and the system equations are ( x_ vau ¼ Av xv þ Bu u þ Bw κ ð15Þ yv ¼ C v xv The dynamic matrices are given as 0 1 a11 a12 0 0 b1 0 B C 0 C B a21 a22 0 0 b2 B C B 0 1 0 0 0 0 C B C Av ¼ B C; V 0 0 0 C ls B 1 B C B 0 0 0 0 0 1 C @ A T s1 T s2 0 0 T s3 T s4

In this section the T–S representation of the nonlinear vehicle model (9) is obtained considering different operating points of the longitudinal velocity varying in [5, 25] m/s range. The fuzzy membership functions used for the longitudinal velocity variable vx are triangular (see Fig. 4). The T–S model obtained is written as Rulei: IF vx is Mi THEN ( x_ v ¼ Avi xv þ Bu u þ Bw κ ð18Þ yv ¼ C vi xv i ¼ 1; …; 5 where Avi, Bu, Bw and Ci (i¼1,…, 5) are the local dynamic matrices of the five linear subsystems (15) developed in the last section and a PDC (19) is driven to control the nonlinear system (9). The main goal of the reached controller is to keep the vehicle in the lane center, i.e, keeping the lateral offset (yc) and heading error (ψ L ) in an admissible interval, without resisting the driver when he wants to take control of the vehicle. The driver comfort is integrated by minimizing the lateral acceleration (ay) and steering wheel speed (δ_ ). To achieve this goal, we propose the use of the T–S optimal controller:

0 1 0 B0C B C B C B0C B C Bu ¼ B 0 C B C B C B0C @ A 1 Js

Bw ¼ ð0 0 V 0 0 0ÞT : where

5

Cr þ Cf ; a11 ¼  2 mV a21 ¼ 2

4.1. Without considering the driver model (WCDM)

lr C r  lf C f ; Iz V

C f ηt ; T s1 ¼ 2 J s Rs V

lr C r  lf C f a12 ¼  V þ 2 ; mV a22 ¼  2

T s2 ¼

2C f lf ηt ; J s Rs V

2 2 lr C r þ lf C f

Iz V T s3 ¼ 

;

Cf b1 ¼ 2 ; m

b2 ¼ 2

2C f ηt ; J s Rs

ð19Þ

That minimizes the LQ criteria given as Z 1 ðzT Wz þ uT RuÞ dt J¼

ð20Þ

i¼1

lf C f ; Iz

T s4 ¼ 

uðtÞ ¼  ∑ hi ðvx ÞK i xv ðtÞ

0

Bs : Js

Now the input of the system is u ¼ T c þ T d is the controller's torque (Tc) added to the driver's torque (Td). Table 1 summarizes the values of different parameters.

3.3. Driver lane keeping model The driver model used in the controller synthesis is a simple proportional to the lateral deviation error at a look ahead distance (ld) and the heading error (yd, ψ L ), so T d ¼  k1 yd  k2 ψ L

ð16Þ

The driver look ahead distance is given as ld ¼ τV which depends on the vehicle's speed times the driver's time anticipation (considered here τ ¼ 0:8 s). So the expression of lateral offset observed by the driver is the same as the one of the perception system with a difference of velocity dependance.

Fig. 4. Membership functions of the vehicle longitudinal velocity.

B. Soualmi et al. / Control Engineering Practice 24 (2014) 106–119

with z ¼ C 2i xv ¼ ½ay ; ψ L ; 0 a11 a12 þ V 0 B 0 0 1 B C 2i ¼ B @ 0 0 0 0

0

0

yL ; δ_ T . 0

part (K Γ i ) amplifies the driver torque (action), so the control signal is

1

0

b1

0

0

1

0

0C C C; 0A

0

0

1

5

u ¼  ∑ hi ðvx ÞðK εi xv þ K Γ i T d Þ

The weights qi ¼ 1=maxðzi Þ represent the inverse of the maximum tolerated errors of each variable. As the feedback gains Ki share the same premisses as the T–S representation (18), the problem of global optimization can be resolved by finding the feedback gains Ki that minimize J criteria under the dynamics (Ai ; i ¼ 1; …; 5; B ) and the weighing matrices W and R for each corresponding subsystem (Wu & Lin, 2000). This is solved by resolving the associated Riccati equations: i ¼ 1; …; 5

ð21Þ

So K i ¼ Ri 1 BT P i ;

i ¼ 1…; 5

ð22Þ

The global stability of the closed loop system is verified by Lyapunov's approach (Theorem 2) and we find P ¼ 10  3 0 203:71 B 9:49 B B B 46:88 B B 11:86 B B @  18:24 0:04

ð24Þ

i¼1

W ¼ diag½qay ; qψ L ; qyl ; qδ_ 

ATi P i þ P i Ai  P i BR  1 BT P i þ C T2i WC 2i ¼ 0;

111

In the absence of the driver's torque (Td ¼0), the E-copilot is a lane keeping system as in the case of WCDM. In the case of the presence of a driver's torque the controller, the E-copilot, assists the driver to do what he wants as the vehicle error positioning in the lane is small. However, when the vehicle drifts from the center of the lane the controller counteracts the driver in order to bring the vehicle back to the center of the lane. The global stability of the closed loop system is, as in the first case, verified using (Theorem 2) and we find the common positive matrix: P ¼ 10  3 0 75:7 B 24:3 B B B 27:3 B B B 24:5 B B  5:8 B B @ 0:3  8:3

24:3 159:3

27:3 139:8

24:5 59:0

 5:8 3:4

0:3 0:6

139:8

3062:6

194:3

50:0

0:4

59:0

194:3

107:7

13:4

0:3

3:4

50:0

13:4

13:1

0:1

0:6

0:4

0:3

0:1

0:01

 20:1

70:3

 12:8

 4:5

 0:1

1  8:3  20:1 C C C 70:3 C C  12:8 C C C  4:5 C C C  0:1 A 16:3

1

9:49

46:88

11:86

18:24

0:05

7:18

9:89

1:77

 2:07

9:89

205:13

6:82

87:04

1:78

6:82

6:69

20:72

2:07

87:04

20:72

281:89

0:02 C C C 0:04 C C40 C 0:005 C C 0:02 A

0:017

0:03

0:005

0:02

0:01

4.2. Considering the driver model (CDM) Adding the driver model (17) to the road–vehicle one (15), the state space representation of the global system road–vehicle– driver is written as " # " #" #   " # x_ v xv Bw Bu Av Bu u þ κ ð23Þ ¼ þ T_ d Td a61 a62 a63 014 k2 V 0 where a61 ¼  k1 , a62 ¼  ðk1 τV þ k2 Þ, a63 ¼  k1 V and xv is the vehicle–road vector state (15). The procedure of the T–S controller synthesis is the same as the one discussed in Section 4.1 considering the road–vehicle–driver model (23). When including the driver model, the driver's torque and the difference between the driver's torque and that of the E-copilot's are included in the performance vector, so z ¼ ½ay ; yL ; ψ L ; δ_ ; Td ; ðTd Tc ÞT . The performance vector contains three components as follows:

 Lane keeping performances expressed by yL and ψ L .  Driving comfort expressed by ay and δ_ .  Driver/controller conflict degree expressed by Td and (Td  Tc ). With this, by choosing the appropriate weights qi of the new matrix W ¼ diag½qay ; qψ L ; qyL ; qδ_ ; qT d ; qðT d  T c Þ  the minimization of the performance criteria J (20) results in a degree of conflict reduction between the driver and the controller. The obtained feedback gains Ki can be interpreted in two parts: the first part (K εi ) that ensures the lane keeping and the second

5. Environment and scenarios tests In all numerical simulations, carried out on Matlab/Simulink, presented here, the nonlinear vehicle model described in Eq. (9) is used and the driver model is the one proposed by Sentouh et al. (2009). The longitudinal speed is regulated with a sliding mode controller similar to the one developed in Swaroop and Yoon. The evaluation of the proposed approaches (E-copilot WCDM and E-copilot CDM) with a human driver is made with the dynamic simulator of the LAMIH laboratory: SHERPA.1 The simulator is equipped with a force feedback steering wheel that reproduces the self-aligning torque (Tal) provided by the nonlinear vehicle dynamics model and allows for the addition of an external torque signal: the E-copilot one (Tc) in this work (Fig. 5). The driver's torque is measured by a torque sensor mounted just behind the steering wheel (see C.T. GmbH, 2010 for technical details). While driving, the vehicle longitudinal speed is given by the path planning system and managed by the sliding mode controller. All the tests are made on the test track presented in Fig. 6. Three scenarios are tested: 1. Autonomous lane keeping where the lateral control is ensured only by the developed controller and no action is taken by the driver. This scenario shows the performances of lane keeping of the E-copilot working in ideal conditions. 2. Shared control for lane keeping: both the driver and the E-copilot participate in the driving task with the same goal which is lane keeping. This scenario gives a overview of the driver behavior in the presence of the E-copilot that acts in the steering system with him. 3. Shared control with obstacle avoidance by the driver: an undetected obstacle is present in the lane and the driver tries 1 Simulateur Hybride d'Etude et de Recherche de PSA pour l'Automobile http:// www.univ-valenciennes.fr/simulateur_sherpa.

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to avoid it. The driver has to steer the vehicle in order to reach the center of the left-hand lane (lateral offset of 3.5 m).

6. Numerical simulations in Matlab/Simulink 6.1. Driver model validation

We assume that the path planing system of the vehicle gives right lane center as a reference to the controller in all scenarios to be tested and the full state of the vehicle is measurable.

With the values k1 ¼ 4 and k2 ¼ 0:5  180=π , the achieved performances by the driver model are reported in Fig. 7. Fig. 8(I) reports numerical simulations of an obstacle avoidance manoeuvre achieved by the used driver model and Fig. 8(II) that of a human driver carried out on the SHERPA simulator. In the numerical simulation the obstacle avoidance is simulated by a double lane change by the used driver model. It can be pointed out that the driver model behaves like the human driver. This behavior will be used to compare the driver behavior when he drives with an E-copilot.

6.2. Case without considering the driver model (WCDM) Fig. 5. SHERPA force feedback steering wheel dynamics scheme.

Fig. 6. SATORY test track and its curvature (κ).

6.2.1. Automatic driving In this test, only the proposed E-copilot ensures the lateral control of the vehicle and the main goal to be achieved is to keep the vehicle in the center of the right lane i.e. minimizing yL and ψ L . As reported in Fig. 9, the proposed E-copilot ensures a good lane keeping with maintaining the lateral offset and heading errors in admissible intervals (jyc j o 23:51 cm and jψ L jo 2:471) in spite of the vehicle velocity variations (from 7 to 16 m/s). The front wheel steering angle is performed smoothly by the E-copilot and the lateral acceleration is maintained below 2.5 m s  2 which is a comfortable acceleration for a human passenger (see Fig. 10). It can be noticed that the obtained results meet our assumptions of small angles (δ and ψ L ).

6.2.2. Shared control driving In this scenario both the driver model proposed in Sentouh et al. (2009) and the E-copilot (WCDM) participate in the driving process. During the first 105 s, the driver and the controller ensure, together, the lane following task (the two agents have the same

Fig. 7. Lane tracking performances achieved by the proposed driver model, (a) vehicle speed (vx), (b) lateral offset (yc), (c) driver model torque (Td) and (d) heading error (ψ L ).

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Fig. 8. Obstacle avoidance performed by (I) used driver model, (II) human driver. (a) Lateral deviation error (yc), (b) driver's torque (Td).

Fig. 9. Performances achieved by the autonomous vehicle: (a) vehicle velocity (vx), (b) lateral offset (yc), (c) E-copilot torque (Tc) and (d) heading error (ψ L ); case WCDM.

goal). At t¼105 s the driver tries to avoid an obstacle on the lane that is not detected by the vehicle sensors. As reported in Fig. 11, in the fist step (t o 105 s), both E-copilot and driver's torque have the same sign: the driver and the E-copilot drive cooperatively. The maximum lateral offset is about

24.85 cm and the heading error is under 2.561 as can be seen in Fig. 11b and d. From t¼ 105 s the driver tries to perform a lane change maneuver to avoid an obstacle undetected by the vehicle perception system, thus he acts differently than the E-copilot does: the controller remains on the first goal that is lane keeping.

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The E-copilot counteracts the driver as soon as the vehicle goes away from the center of the lane by delivering a recovery torque. This results in a conflict situation between the driver and the E-copilot as can be seen in Fig. 11c, where the driver and E-copilot torques are opposite. The driver's torque reached 10 N m.

6.3. Case considering a driver model (CDM): shared control As in the previous section, where no driver model is considered in the E-copilot design, the test protocol below includes both cooperative driving (same objectives for the driver and the assistance) and a conflict situation. The obtained results are reported in Fig. 12. It can be noticed that the lane keeping performances achieved are similar to the case where the driver is not considered (jyc j o29:75 cm and jψ L jo 2:571) during the first 105 s. However the major difference appears when the driver tries to avoid an undetected obstacle. As it is reported in Fig. 12c, zoom on when this event occurs, the

torque produced by the driver to achieve the obstacle avoidance manoeuvres is much lower than that when the E-copilot WCDM is used. Moreover, initially (t A ½105; 105:5 s) the controller provides a torque that assists the driver to achieve his goal (T d  T c 40). However when the vehicle drift away from the lane center the controller smoothly counteracts the driver with a small amount of torque. This behavior can be interpreted as the E-copilot accepts the authority of the driver but communicates to him that the vehicle has to return to the center of the right lane which is the normal driving situation. The cooperative assistance behavior can also be observed after passing the obstacle: the driver initiates the manoeuvre to come back to the right lane and the E-copilot helps him to do it perfectly in comparison to the results obtained by the driver model alone (Fig. 8). Fig. 13 shows the obtained vehicle trajectory during the obstacle avoidance maneuver for the case where the driver drives with the E-copilot WCDM and when he drives with the E-copilot CDM. Contrary to the first case where the vehicle hardly passes the obstacle, in the second case, the vehicle completely avoids it.

7. Interactive simulation on LAMIH-SHERPA vehicle dynamic simulator As described above, the goal of our work is to develop a driver assistance that keeps the vehicle in the center of the lane while allowing for the driver's manoeuvres (lane changing for obstacles avoidance, if any). 7.1. Case without considering a driver model (WCDM)

Fig. 10. Performances achieved by the autonomous vehicle. Top: front well steering angle (δ), bottom: vehicle lateral acceleration (ay) (case WCDM).

In the case of WCDM, in order to allow lane changes by the driver, the controller is adjusted to make it less sensitive to the lateral deviation (yL). As reported in Fig. 14 the proposed approach ensures a good lane keeping with a little intervention of the driver on the steering-wheel (T d C 0) around the first bends. The lateral offset (yc) is kept under 49 cm and ψ L under 4.551 despite vehicle speed

Fig. 11. Results of numerical simulation of a shared driving with obstacle avoidance: (a) vehicle velocity (vx), (b) lateral offset (yc), (c) E-copilot and driver's torque (T c ; T d ) and (d) heading error (ψ L ); case WCDM.

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Fig. 12. Numerical simulation results in a shared driving with obstacle avoidance: (a) vehicle velocity (vx), (b) lateral offset (yc), (c) E-copilot and driver's torque (T c ; T d ) and (d) heading error (ψ L ); case CDM.

when the vehicle drifts far from the center of the lane, the E-copilot reacts to recover the original vehicle position: which gives a considerable recovery torque. In order to achieve the obstacle avoidance, the driver produces a torque of about T d ¼ 3:85 N m which is half as much as in the case of the WCDM, where the driver's torque is about T d ¼ 8:5 N m.

8. Performance evaluation

Fig. 13. Vehicle trajectory in the undetected obstacle avoidance maneuver: Dashed line: case WCDM and slid line: case CDM.

variations from 5 to 20 m/s (18 to 70 km/h). When the driver and the controller have different objectives, as it is reported when the driver is attempting to avoid an obstacle (t A ½76; 80 s), the E-copilot tries to prevent the driver's maneuver to achieve his own objective which is to keep the vehicle in the right center of the lane. The maximum measured torque delivered by the driver at this maneuver to supersede the controller and steer the vehicle is T d C8:5 N m comparable to the one obtained in numerical simulations in the last section. 7.2. Case considering a driver model (CDM) Fig. 15 shows the performed test results. It can be noticed that the lane keeping performances achieved are similar to those obtained in WCDM jyc j o 50:1 cm and ψ L o 5:151. The major difference is in the E-copilot torque when the human driver performs the obstacle avoidance (t A ½90; 96 s). As in the numerical simulations, initially (t A ½90:5;  91 s), the E-copilot provides a torque that goes in the same direction as that of the driver and

In this part, we provide a synthesis of the performance evaluation of the proposed assistance systems regarding two criteria: the lane keeping aspect and the degree of cooperation with the driver. As a major indicator of lane keeping performances, we consider the maximum absolute value of the lateral offset and the heading error, respectively, jyc jm and jψ L jm . For characterizing the cooperation between the driver and the E-copilot we use two indicators:

1. The effort used by the driver and the E-copilot to perform the driving task in some time interval ½t 1 ; t 2  that represents the energy of the driver's and the E-copilot torque signal (Louay, 2012): Z t2 Efc;dg ¼ T 2fc;dg ðtÞ dt t1

2. As we consider conflict situations, we focus on the instances where the driver and the E-copilot have different objectives (obstacle avoidance vs lane keeping) and calculate the degree of the driver's goal achievement. For that, the ratio of the lateral displacement to avoid the obstacle by the effort devoted by the driver is measured by R t2 t yc dt W d ¼ R t12 2 t 1 T d dt

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Fig. 14. Interactive results carried out on LAMIH-SHERPA simulator: (a) vehicle velocity (vx), (b) lateral offset (yc), (b) E-copilot and driver's torque (T c ; T d ) and (d) heading error (ψ L ); case WCDM.

Fig. 15. Interactive results carried out on LAMIH-SHERPA simulator: vehicle velocity (vx), lateral offset (yc), assistance and driver's torque (T c ; T d ) and heading error (ψ L ) (case CDM).

with ½t 1 ; t 2  is the time interval where the driver tries to avoid an obstacle. A comparison of lane keeping performance of two E-copilot and the sharing quality of the tests performed in the first four turns of SATORY test track (Fig. 6) is summarized in Table 2. In numerical simulation, the lane keeping performances (jyc jm and jψ L jm ) achieved with the E-copilot WCDM are better than the ones of the driver alone (used model) and of the DM with the E-copilot CDM. This is an expected results because the objective of the first E-copilot is focused on the lane keeping while the second includes the driver's action as the second objective. When this E-copilot drives with the driver, the vehicle trajectory is performed in the inner side of the bends, which is the result of an oversteering behavior because the E-copilot does not take into account the torque delivered by the driver. The driver's effort is (Ed ¼ 34:57 ðN mÞ2 ) and the E-copilot one is (Ec ¼ 115:72 ðN mÞ2 ).

The oversteering steering behavior is not observed with the E-copilot CDM, where the maximum lateral offset is about (22 cm) with (Ed ¼ 18:20 ðN mÞ2 and Ec ¼ 154:07 ðNmÞ2 ). In the interactive simulation the lane keeping performances are similar when the driver drives with both E-copilots and are better than ones of the human driver alone. As the E-copilots (WCDM and CDM) ensure a good lane keeping, the human driver does not participate, practically, in the driving process, so the low values of Ed for the two cases. With these results, we can say that the automation (E-copilot) can substitute the driver because it has better performances and it can solve the problem of road accidents due to road departure. But this result is conditioned by a perfect working of all sub-systems before the controller (sensors, image processing and data fusion, path planning, etc.) and after it (actuators). For this reasons, we have proposed the E-copilot CDM that keeps the driver in the loop of the driving task to sustain his attention and his vigilance level

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and contribute to a better confidence in the system letting the driver handle complex situations like what is shown for undetected obstacle avoidance. Fig. 16 reports a comparison of the driver's torque, E-copilot one, driver's and E-copilot torques difference (T d  T c ) and the lateral offset achieved in interactive tests during the obstacle avoidance maneuver. The first important remark concerns the E-copilot torque signal during this maneuver: in the case of the E-copilot WCDM, it counters the driver immediately to prevent that the vehicle goes from the center of the lane. The driver succeeds partially in achieving his goal (going to the left-hand lane with a lateral offset of 2.49 m instead of 3.5 m) through providing a considerable torque (8.5 N m). This situation results in a maximum driver's E-copilot torque difference of about (15 N m). With the CDM E-copilot, the torque signal goes the same as the driver's one for a little time. Then, to avoid a vehicle lateral

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position overshoot if the E-copilot is deactivated (as observed by Hoc, Mars, & Milleville-Pennel, 2006), in our system, the E-copilot stays active thus adding a damping in the steering system. This phenomena can be interpreted as an “impedance” adaptation of the steering system (Abbink, Mulder, & Boer, 2012). With this CDM E-copilot reaction, the driver also feels that the E-copilot is still participating in the driving process, keeping the driver's situation awareness (Biester & Bosch, 2005). According to Fig. 16, the driver has only to deliver a maximum torque of 3.85 N m (lower than when he drives alone) to fully achieve his goal (reach the left-hand lane). Thus we can say that the degree of conflict is reduced by more then 50% when driving with CDM E-copilot. Table 3 summarizes the different calculated indicators characterizing the human driver – E-copilot cooperation in hazardous situation. As a first remark, the effort made by the driver (Ed) to perform an obstacle avoidance is strongly reduced when using the

Table 2 Comparison of the lane keeping performance. Test

Table 3 Comparison of cooperation degrees.

Indicator jyc jm (cm)

jψ L jm (1)

Ec (N m)2

Ed (N m)2

Numerical simulation Driver model only E-copilot only (WCDM) Shared control WCDM E-copilot Shared control CDM E-copilot

47.72 23.51 24.85 29.75

2.56 2.47 2.56 2.57

– 324.19 142.73 215.67

321.87 – 37.70 18.20

Interactive simulation Human driver only E-copilot only Shared control WCDM E-copilot Shared control CDM E-copilot

56.73 50.04 49.01 50.1

5.53 4.23 4.55 5.16

– 229.13 186.26 206.95

227.63 – 16.34 15.08

Test

Numerical simulation Driver only WCDM Matlab/Simulink CDM Matlab/Simulink Interactive simulation Human driver WCDM on SHERPA CDM on SHERPA

Indicator Ed (N m)2

Ec (N m)2

jyc jm (m)

Wd

36.83 196.70 17.39

0 228.18 38.07

4.07 1.43 2.63

0.44 0.02 0.36

30.02 48.86 10.22

0 90.92 35.87

4.06 2.49 3.58

0.47 0.1 0.38

Fig. 16. Obstacle avoidance maneuver comparison (left: WCDM, right: CDM), top: driver's, E-copilot and the driver–E-copilot torque difference, bottom: lateral offset (yc).

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E-copilot integrating a driver model: in numerical simulation 17.39 (N m)2 when CDM vs 196.70 (N m)2 when WCDM comparing to 10.22 (N m)2 vs 48.86 (N m)2 in interactive simulation. This means that the E-copilot helps the driver to perform his maneuver as to go left-hand lane to avoid the obstacle as to recover the original vehicle trajectory (see Fig. 16). The second and important remark is the E-copilot effort reduction during this maneuver through the use of the driver model. Using the E-copilot WCDM, as it counters the driver immediately when he tries to avoid the obstacle in a brutal way, the value of Ec is 228.18 (N m)2 in simulations and 90.92 (N m)2 in interactive test, while in case of CDM this value are strongly reduced (38.07 and 35.87 (N m)2). As a consequence the values of Wd are much greater when using the E-copilot CDM.

9. Conclusions In this work a preliminary study of the contribution that may bring a driver model in the design of an E-copilot that assists the driver in the driving task in both normal situations and in hazardous ones is performed. The proposed approach uses the haptical interaction between the driver and the E-copilot in order to improve their cooperation. The use of T–S approach allows lateral and longitudinal dynamics decoupling and thus maintains lateral performances and guarantees the global stability of the closed loop system within vehicle longitudinal speed variations. The proposed approach is firstly tested in numerical simulations and then with a human driver in the LAMIH SHERPA dynamic simulator. As illustrated in the obtained results, the use of steering torque, as the control signal, permits the driver's actions in the steering process. However the driver has to apply a height effort to take the control of his vehicle if he want to do other than the E-copilot WCDM. By adding a driver model in the conception of an E-copilot, the degree of cooperation between the driver and the obtained E-copilot is largely increased and more authority is given to the driver. The quantification of the cooperation is illustrated by introducing objective indicators. Future works will concern, first, the elaboration of states observer of both the vehicle and driver one in order to reduce the cost of the needed sensors (torque sensor and vehicle lateral speed one). Also, a higher driver–E-copilot cooperation at the strategic level is required. This concerns the path planning system that can integrate the driver's intentions via the steering well to modify the E-copilot reference.

Acknowledgments The present research work has been supported by International Campus on Safety and Intermodality in Transportation, the Nord-Pas-de-Calais Region, the European Community, the Regional Delegation for Research and Technology, the French National Research Agency, the Ministry of Higher Education and Research and the National Center for Scientific Research. The authors gratefully acknowledge the support of these institutions.

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