Multiple Controller Switching Concept for Human

Multiple Controller Switching Concept for Human-Machine Shared Control of Lane Keeping Assist Systems Chouki Sentouh∗ , Anh-Tu Nguyen∗ , Jérôme Floris∗ , Jean-Christophe Popieul∗ ∗ LAMIH

Laboratory UMR CNRS 8201, University of Valenciennes, France E-mail: [email protected], [email protected]

Abstract—This paper is concerned with a new control method which can share the control authority between a human driver and a lane keeping assist system. Based on the concept of multiple controller switching, this shared control method is composed of two levels: operational and tactical. At the operational level, two local optimal-based controllers are designed to satisfy their own predefined control goals. At the tactical level, a supervisor is designed to orchestrate a smooth control authority transition between two local controllers. The closed-loop properties of the human-in-the-loop vehicle system are guaranteed via Lyapunov stability arguments. In particular, the design of both local controllers is recast as a convex optimization problem, easily solved with numerical solvers. The effectiveness of the proposed shared control method is experimentally validated with a human driver and a dynamic driving simulator. Index Terms—Shared control, driver assistance systems, vehicle control, human-in-the-loop control, control authority transition, Lyapunov stability.

I. I NTRODUCTION The performance failure of human drivers remains one of the most important causes of traffic accidents [1]. Therefore, advanced driver assistance systems (ADAS) have been intensively investigated in both academic and industrial contexts [2], [3]. Despite significant advances on the technology of ADAS, the shared control between an active safety system and a human driver is still widely open [4]–[7]. Most of existing works have mainly focused on the control of ADAS without taking into account the actions from the driver even these can destabilize the vehicle [8]. This paper addresses the shared steering control of a lane keeping assist (LKA) system of intelligent vehicles. Here, driver-automation shared control means that both driving actors can simultaneously control the vehicle via the steering wheel. Moreover, the human driver can fully either override the assistance action or conform to it [9]. The advantage of such a shared control scheme is to improve the driving performance while reducing the driver’s effort [10]. The need for an active coordination of driver-automation authority in shared control framework has been discussed in [4], [11]. However, shared steering control which can appropriately adapt the control authority allocation between human drivers and the LKA system in function of the driving situations This work was done within the AutoConduct project (ANR-16-CE22-0007).

still remains challenging due to the unpredictable humanmachine interaction involved in the control design. Shared control approaches have been developed in the framework of intelligent vehicles [12]–[14]. In these works, the degree of human-machine cooperation is quantified by some optimization criteria without considering the real-time activity of the driver in an open driving environment. Therefore, the driver-automation conflict issue seems hard to be solved for a general driving situation. In [15], the authors present a shared control method based on the combination of handwheel force feedback with a potential field path planning and path following approach for lane-keeping and collision avoidance assistance. However, only a fixed control authority allocation between the driver and the automation is considered which is not compatible for different driving contexts and the driver’s intention [13], [14]. Using the steer-by-wire technology, a model predictive control framework for shared control has been recently presented in [16] where the control objective of matching the driver’s steering angle is not compatible with other ones such as vehicle stability and obstacle avoidance. To overcome the above drawbacks, the information not only on the driving activity of the human driver (through modeling and measurements) but also on the vehicle environment perception is taken into account in the shared control design. We show that the consideration of this information is crucial to deal with the challenging human-machine conflict issue. Inspired from the concept of multiple controller switching [12], we propose a novel two-level shared control scheme, which is composed of two hierarchical levels: a tactical level and a operational level. The control supervisor at the tactical level is used to orchestrate a smooth control authority transition between human drivers and the LKA system. For the supervisor design, the information from the driver monitoring system [17], and the vehicle vision system is fully exploited. The operational level is composed of two local optimalbased controllers which are unified each other via a smooth transition signal provided by the tactical part. Using Lyapunov stability theorem, the feedback gains of both controllers are designed to guarantee the closed-loop properties of the whole human-in-the-loop vehicle (HiLV) system, constructed from a driver model and road-vehicle model. The control design is reformulated as an LMI (linear matrix inequality) optimization

which can be effectively solved with available numerical solvers [18]. This paper is a short version of our results in [12], in which formal proofs of technical statements and thoroughly experimental validations with human drivers and the SHERPA dynamic driving simulator are discussed in detail. Notation. For a matrix M , M > denotes its transpose. For a square matrix X, X > 0 means that X is positive definite, and He(X) = X+X > . I denotes the identity matrix of appropriate dimensions. ? stands for matrix blocks that can be deduced by symmetry. Arguments are omitted when their meaning is clear. II. D RIVER - IN - THE -L OOP V EHICLE M ODELING This section presents the modeling of the road-vehicle system and the driver model used for shared control design. The nomenclature is given in Table I.

 > where xv = β r ψL yL δd δ˙d is the vehicle state,  > is the disturbance vector, and the control w = fw ρr input uv is composed of both assistance and driver torques uv = Ta + Td . The state-space matrices in (1) are given by     a11 a12 0 0 b1 0 0 0  a21 a22 0 0 b2 0     0  0 1 0 0 0 0     , Bvu =  Av =  0  lp vx 0 0 0     vx 0  0 0 0 0 0 1  1 −Bu Js a61 a62 0 0 a65  Js e e2 0 0 0 0 > Bvw = 1 0 0 −vx 0 0 0 where 2(Cr +Cf ) 2(l Cr −lf Cf ) , a12 = r mv −1 2 mvx x 2(lr2 Cr +lf2 Cf ) 2(lr Cr −lf Cf ) a21 = , a22 = − Iz Iz vx 2C 2l C 1 b1 = mRsfvx , b2 = Rfs Izf , e1 = mv , e2 = lIwz x 2Cf ηt 2Cf lf ηt −2C η a61 = Rs Js , a62 = Rs vx Js , a65 = R2 Jfs t . s

a11 = −

TABLE I N OMENCLATURE . Notation m Cf /Cr Iz lf /lr lw lp fw vx /vy β r ψL yL δd Js Bs Rs ηt Ta /Td /Ts Tl /Ti Tn

Description mass of vehicle [kg] cornering stiffness of the front/rear tires [N/rad] moment inertia about the yaw axis [kgm2 ] distances of the front/rear tire from CG [m] lateral wind force impact distance [m] look-ahead distance [m] lateral wind force [N] vehicle longitudinal/lateral speed [m/s] vehicle sideslip angle [rad] vehicle yaw rate [rad/s] relative yaw angle [rad] lateral offset from the centerline [m] steering wheel angle at the column system [rad] moment of inertia of the steering system [kgm2 ] damping coefficient of the steering system [Nm/rad/s] reduction ratio of the steering system [-] width of the tire contact [m] assistance/driver/self-aligning torque [Nm] lead/lag time constant of the compensatory control [s] neuromuscular lag time of the driver [s]

B. Control-Based Driver Model For shared steering control design, the following two-level driver model is used [12]: x˙ d = Ad xd + Bd ud ,

yd = Cd xd

(2)

where    −1 x xd = d1 , Ad = T1i xd2 Tn Ti

0 −1 Tn

"

 , Bd =

(Tl −Ti )Kc Ti −Tl Kc Ti Tn

#

0 Ka Tn

.

The internal state xd1 can be interpreted as the driver’s perception of the steering wheel correction in a near future. The second state xd2 = Td is the driver torque, which is also the system output, i.e. yd = Td . The gains Ka and Kc represent respectively the visual anticipatory and compensatory controls. The input vector ud of (2) is defined as follows [12]:   0 0 φ1 φ2 0 0 ud = x (3) θ1 θ2 0 0 θ3 0 v l

where φ1 = 1 − vxpTp , φ2 = vx1Tp , θ1 = τa2 a21 , θ2 = τa + τa2 a22 and θ3 = τa2 b2 /Rs . Note that τa represents the driver anticipatory time w.r.t. the tangent point whereas Tp is the driver preview time [12]. C. Human-in-the-Loop Vehicle Model Gathering (1), (2) and (3), the control-based HiLV vehicle model can be rewritten in the following form: x˙ = Ax + Bu u + Bw w

(4)

Fig. 1. Lateral vehicle behavior modeling.

A. Road-Vehicle Control-Based Model The well-known bicycle model is used here to represent the vehicle lateral dynamics [18], [19], see Fig. 1. As a result, the road-vehicle model integrating the dynamics of the steering system can be represented as follows [3]: x˙ v = Av xv + Bvu uv + Bvw w

(1)

where the augmented and the control input are  state >vector > xd respectively x = x> and u = Ta . The system v matrices of (4) are given by       Av Bv Cd Bv Bvw A= , Bu = , Bw = . Bd C Ad 0 0 As shown later, the use of the HiLV vehicle model (4) for control design is crucial to define a performance index which aims to mange the human-machine conflict issue.

a) Driver Monitoring System: This provides the driver state monitoring variable DSM to manage the humanmachine control authority transition. In the case of driver hypovigilance, DSM tends to 1. Moreover, if there is no problem on driver hypovigilance, DSM tends to 0 with a predefined convergence rate (about 3s) to avoid a false alarm on distraction detection. b) Risk Evaluation: Taking into account the constraints related to the vehicle positioning and heading, this unit provides an evaluation on the risk of lane departure [20]. To this end, we define the limit of θnear as |θnear | ≤ θlim where   lf L − Sb + 1− |ψL lim | . θlim = 2vx Tp vx Tp Fig. 2. Diagram of the proposed two-level shared control scheme [12].

III. D RIVER -AUTOMATION S HARED C ONTROL S TRATEGY This section describes the proposed shared steering control.

where L is the lane width and Sb is the length of vehicle axles. Road accident data have shown that most of the run-off-road accidents start with ψL lim = 5◦ [20]. c) Conflict Detection: The indicator index representing the sharing quality in terms of conflict management between the driver and the LKA system can be defined by

A. Description of Shared Control Methodology The proposed shared control strategy for a LKA system satisfies the following closed-loop specifications. • •

The controller guarantees the stability of the HiLV vehicle system while minimizing the lane tracking error. The LKA system can share the control authority with human drivers according to their real-time driving activity to manage the conflict issue.

Using a single controller could be insufficient to guarantee the above conflicting requirements. To overcome that, we propose a new shared control method inspired from the concept of multiple controller switching [12]. The proposed shared control strategy is composed of two following levels, see Fig. 2. 1) Operational Level: This level consists of two local controllers: automatic lane keeping (ALK) controller and combined automation-driver (CAD) controller. These are respectively dedicated to two different control goals: lane tracking and management of conflict issue. Especially, the CAD controller allows the driver to have a full control authority when s/he desires to realize some specific driving maneuvers. 2) Tactical Level: This level aims to orchestrate the smooth control authority transition between two local controllers of the operational level to perform a given task. The tactical level is composed of two modules: driver monitoring system (DMS) and decision making algorithm (DMA). B. Supervisor Design for Shared Control Authority The supervisor aims to provide a weighting signal which represents the information not only on the driver’s state but also on the driving environment perception. Then, this signal is used to unify two local controllers at the operational level. 1) Decision Making Algorithm: This algorithm allows for a smooth transition between the ALK and the CAD controllers. It is designed from the information of three following units.

I = Td Ta

(5)

Note that a negative value of I in (5) indicates that the LKA system is in a conflicting situation with the human driver. 2) Smooth Control Authority Transition: Using the information from the DMA, the indicator signal orchestrating the smooth transition between two local controllers is designed as   0 1 σd = 

if (DSM = 1) ∨ ((|θnear | ≥ θlim ) ∧ (I ≥ λ)) if (DSM = 0)∧ (6) ((|θnear | < θlim ) ∨ ((|θnear | ≥ θlim ) ∧ (I < λ)))

Based on the hand stiffness feeling of the driver, the maximal level of negative interference λ = −2 is experimentally identified. Remark from (6) that σd = 0 (corresponding to ALK controller) when the driver’s distraction/drowsiness is detected by the DM S, or in the case where the risk from the driving environment is high. One has σd = 1 (corresponding to CAD controller) when the driver is not distracted and correctly steers the vehicle, or when a conflicting situation is detected. Note also that the ALK controller is systematically activated after 0.8s (i.e. the average reaction time of drivers) from the moment where the haptic interface system does not detect the presence of at least one driver’s hand on the steering wheel. Note that function (6) could result in undesirable chattering phenomena when the switching frequency between two local controllers is important. To overcome this drawback, the following low-pass filter is used: 1 σ(s) = σd (s) 1 + τσ s

(7)

where τσ = 0.8s is the driver’s response time. Assume that the ALK (respectively CAD) controller provides an assistance torque Ta1 (respectively Ta2 ). Using the smooth transition law (6)-(7), the unified assistance control can be defined as u = Ta = α1 Ta1 + α2 Ta2

(8)

where α1 = 1 − σ and α2 = σ, thus α1 + α2 = 1. Note that the input Ta of (4) is a convex combination of Ta1 and Ta2 . IV. LMI-BASED O PTIMAL C ONTROL D ESIGN This section presents the design of both ALK and CAD controllers of the operational level. A. Closed-loop Control Specifications Let us consider the HiLV vehicle model (4) with its performance vector of the following form: x˙ = Ax + Bu u + Bw w,

x(0) = x0

zα = Cα x + Dα u + Eα w

(9)

where the time-varying performance matrices are defined as zα = α1 z1 + α2 z2 ,

B. Optimal-based Control Design Hereafter, the design of two local controllers is presented. To this end, we consider the following performance index: Z ∞ Z ∞ Jα = zα (τ )> zα (τ )dτ = ξ(τ )> Qξ(τ )dτ (12) 0

  x ξ = u , w

Eα = α1 E1 + α2 E2 (10)

The performance matrices in (10) with the index 1 (respectively 2) corresponds to the ALK controller (respectively the CAD controller). To improve the human-machine shared control performance, zα can be defined as follows: zi = Wi y,

i = 1, 2

0

with

Cα = α1 C1 + α2 C2

Dα = α1 D1 + α2 D2 ,

2) Combined Automation-Driver Controller: This allows a shared control between the driver and the LKA system, and a full control resumption of the driver. Therefore, the weighting matrix W2 is parameterized (by tuning the parameters W2∆T and λc ) to promote the driver’s action w.r.t. that of the LKA system. Then, the driver can have more control authority to realize his/her intention and the LKA system assists him/her to achieve the steering maneuver without causing conflicts.

(11)



Qα Q =  Sα> Nα>

 Nα Mα  . Gα

Sα Rα Mα>

The weighting matrices of the performance index are given by Qα = Cα> Cα ,

Sα = Cα> Dα ,

Nα = Cα> Eα

Rα = Dα> Dα ,

Mα = Dα> Eα ,

Gα = Eα> Eα .

Let us rewrite (8) in the following state-feedback form:

where   Wi = diag Wiay , Wiψ˙ L , Wiθnear , Wiθf ar , Wiδ˙d , Wi∆T  > y = ay ψ˙ L θnear θf ar δ˙d Td − λc Ta . The form of the performance variable zi in (11) deserves particular attention. • The tracking performance is represented by θnear whereas θf ar provides the driver’s anticipatory behavior. • The driving comfort is represented by the lateral acceleration ay , the relative yaw rate ψ˙ L , and the steering rate δ˙d . • The human-machine conflict is characterized by Td − λc Ta . Note that all components of y in (11) can be expressed by those of x in (4). It follows that

u = (α1 K1 + α2 K2 )x = Kα x

where Ta1 = K1 x and Ta2 = K2 x. The following theorem provides the LMI conditions to design the control law (13) stabilizing the closed-loop system (9) while minimizing the performance index in (12). Theorem 1. Given system (9) and a positive scalar ζ. The control law (13) stabilizes the system (9) while minimizing the performance index (12) if there exist positive definite matrix X, matrices M1 , M2 , and a positive scalar γ satisfying the following convex optimization: min

X,M1 ,M2

γ

subject to

Ci = Wi Cx , Di = Wi Du , Ei = Wi Ew , i = 1, 2

Ψii < 0,

where

(13)

Ψij + Ψji < 0,

i, j ∈ {1, 2}, i < j

where 

0 vx 0 1  0 0 Cx =  θ1 θ2 0 0 0 0  Du = 0 0 0

0 0 φ1 0 0 0 0

0 0 φ2 0 0 0

0 0 0 θ3 0 0

0

−λc

0 0 0 0 1 0 >

0 0 0 0 0 0

  0 0 −vx 0   0  0 , Ew =  0   0  0 0 1 0

 0 0  0 0  0 0

.

The control task is now to parameterize W1 and W2 to achieve the predefined control goals of each local controller. 1) Automatic Lane Keeping Controller: This controller aims to ensure the lane tracking performance. For that, the controller assists the driver or fully takes care of the lane keeping task. To achieve this objective, the matrix W1 is parameterized to provide the best control performance in terms of lane tracking. Especially, W1∆T = 0 in this case.

 He(AX + Bu Mj + ζX) ? > Bw −γI Ψij =  Ci X + Di Mj Ei

 ? ? . −I

Moreover, the feedback gains can be computed as follows: Ki = Mi X −1 ,

i = 1, 2.

Proof. The proof of Theorem 1 and the details on the design of both ALK and CAD controllers can be found in [12]. V. I LLUSTRATIVE R ESULTS AND D ISCUSSIONS The interest of the proposed shared control approach is demonstrated with experimental results obtained from a human driver and a SHERPA dynamic driving simulator, see Fig. 3. The SHERPA simulator is equipped with a Continental driver monitoring system to measure the driver distraction.

Case 2: Shared control between driver and ALK controller, Case 3: Manual steering control. Observe that the amounts of both Ws+ and Ws− in Case 2 are much larger than those in Case 3. This means that a huge conflict between the driver and the LKA system has occurred in Case 2. However, the workload amounts in Case 1 are significantly reduced compared to those in Case 3. This means that the CAD controller yields a good comfort for shared lateral control with a better driver’s steering feeling. Fig. 5 shows also that Wd obtained in Case 1 is greatly improved compared to that in Case 3, which is in contrary to Case 2. • •

Fig. 3. SHERPA dynamic driving simulator.

Steering workload Ws (N2m2rad) and Satisfaction index Wd (N−2m−1)

A. Experimental Evaluation for Shared Control Quality

45

This test demonstrates the performance of the CAD controller in terms of conflict management. To this end, the driver performs a triple lane change at vx = 20 [m/s] to avoid successively three undetected obstacles, see Fig. 4. Let us

Manual control

40

Shared control with CAD

35

Shared control with ALK

30 25 20 15

6

10

5

Lateral position [m]

5

Case 1: shared control with CAD Case 2: shared control with ALK Case 3: manual control

4

0

Positive interference Ws+ Negative interference Ws−

Satisfaction criteria Wd

3

Fig. 5. Comparison of Ws and Wd between different control strategies corresponding to the experimental results presented in Fig. 4.

2 1 0

B. Shared Driving Control in Real-world Conditions 50

60

70 80 Time [s]

90

100

110

120

130

Fig. 4. Triple lane change maneuver with three different control cases.

define the following steering workload: Z ∆T Ws = Td (τ )Ta (τ )δ˙d (τ )dτ

(14)

0

The indicator Ws can be interpreted as the steering energy provided by the driver within a duration ∆T to perform a desirable steering maneuver [21]. For manual control, only Td and δ˙d are used to compute Ws . The product Ta Td involved in (14) aims to take into account the human-machine conflict situations. The driver performs some positive steering work Ws+ if s/he voluntarily steers the wheel to control the vehicle. However, the driver’s reactions performed on the steering wheel against unnatural fluctuations of the vehicle or the resistance of the LKA system in case of conflict result in unnecessary negative steering work Ws− . Hence, Ws+ and Ws− can be used to assess driver’s steering feel. We also define the following satisfaction criterion [12]: R ∆T yL (τ )dτ 0 . Wd = R ∆ T 2 dτ T (τ ) d 0 Fig. 5 depicts the comparison of the steering workload Ws and the satisfaction criterion Wd corresponding to the triple lane change maneuver of three following cases: • Case 1: Shared control between driver and CAD controller,

Using real-world driving situations, we now show the effectiveness of the proposed shared control method in terms of conflict management. To this end, assume that the driver desires to perform a lane keeping task with the Satory test track depicted in Fig. 6-a. Fig. 6-b shows the corresponding vehicle speed which is managed by the driver during the whole test. This scenario can be decomposed in three following phases according to the involvement of the driver in the driving task. • Phase 1: Shared driving control with an attentive driver. • Phase 2: Driving with a distracted driver. • Phase 3: Autonomous driving and driver takeover. 5

1.21

x 10

1.208

(a)

120

Phase 1 Phase 2 Phase 3 C2 C3

1.206 1.204 5.815

5

C4 C1

5.82 5.825 5.83 X position [m] x 105 (c) Driver Assistance

0 −5 0

Speed [km/h]

40

50 100 Time [s]

150

(b)

100 80 60 40 20 0

Smooth transition signal

30

Y position [m]

−2 20

Torque [Nm]

−1

1

50 100 Time [s] (d)

σ DSM

0.5

0 0

150

50 100 Time [s]

150

Fig. 6. Experimental results obtained with real-world Satory test track.

During Phase 1 (t < 50s which corresponds to the first four curves C1, C2, C3 and C4), the driver and the LKA system

(a) Near angle [deg]

20 θ

near

10

θlim

0 −10 departure risk detected

−20 0

50

100

150

Lat. deviation error [m]

jointly perform the lane keeping. Observe in Fig. 6-c that the driver shares the vehicle control with the CAD controller while taking the curves C1, C2 and C4. For the third curve taking, the driver purposely provides an insufficient driving effort, thus the ALK controller is activated to avoid the lane departure as shown in Fig. 6-d. Indeed, it can be seen in Fig. 7-a that the authority transition signal σ tends to 0 when θnear > θlim , i.e. the risk of lane departure is detected. For Phase 2, the driver simulates from t = 55s to t = 75s a distraction during curve taking by turning his head outside the driving visual field while applying some steering torque. We can see in Fig. 6-d that the variable DSM indicates a distraction problem. Therefore, the control authority is given to the ALK controller which counteracts the driver’s actions to prevent the lane departure. After the distraction period, DSM tends to 0 and the driver again performs the driving together with the CAD controller. During Phase 3, the driver releases both hands from the steering wheel from t = 105s to t = 120s. Then, the LKA system solely performs the driving using the ALK controller, see Fig. 6-c. After this autonomous curve taking, the driver regains the driving task and the LKA system smoothly gives him the control authority since σ tends again to 1 as shown in Fig. 6-d. Fig. 7 shows a good lane keeping performance with a reasonable lateral acceleration during the whole test. (b) 2 1 0 −1 −2 0

Veh. lat. position Lane edges

50

(c) 2

Lateral accel. [m/s ]

Yaw rate [deg/s]

20 10 0 −10 50

150

100

150

(d)

30

−20 0

100

100

150

6 4 2 0 −2 −4 0

50

Time [s]

Time [s]

Fig. 7. Vehicle response w.r.t. the results shown in Fig. 6.

VI. C ONCLUSIONS A new driver-automation shared control approach has been proposed for LKA systems. Based on the concept of multiple controller switching, the shared control scheme is composed of two levels: the tactical level with a control supervisor and the operational level with two local controllers. The supervisor manages the driver-automation control authority according to the driver monitoring and the risk of lane departure. Each local controller is designed with its specific driving goals. These controllers are unified by the supervisor via a smooth authority transition signal. Therefore, the assistance control is appropriately computed according to a given driving situation. Using Lyapunov stability theorem and LMI control framework, the feedback gains of both local controllers can be conveniently

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