Safety of Technical Processes September 2-4, 2015 Arts et Métiers ParisTech, Paris, France 9th IFAC Symposium on Fault Detection, Supervision Available online and at www.sciencedirect.com Safety of Technical Processes September 2-4, 2015 Arts et Métiers ParisTech, Paris, France ScienceDirect 48-21 (2015) 492–498 Strategy for an Autonomous Active Fault TolerantIFAC-PapersOnLine Decentralized Control 2WS4WD Electrical Vehicle Tracking Active Fault Tolerant Decentralized ControlPath Strategy for an Autonomous 2WS4WD Electrical Vehicle Path Tracking A HADDAD *’**, A AITOUCHE*’***, V COCQUEMPOT*’** A HADDAD *’**, A AITOUCHE*’***, V.M3, COCQUEMPOT*’** *CRIStAL Laboratory, UMR CNRS 9189, Building Cité Scientifique, 59655, Villeneuve d’Ascq, France *CRIStAL Laboratory, CNRS 9189, Building M3, Cité Scientifique, 59655, **Lille UMR University: Sciences and Technologies, Villeneuve d’Ascq, France Villeneuve d’Ascq Cedex 59655, France (e-mail: alain.haddad @ polytech-lille.fr or vincent.cocquempot@univ-lille1.fr ) **Lille 1Etudes University: Sciences13and ***Hautes d’Ingénieur, rueTechnologies, de Toul, 59046, Villeneuve d’Ascq Cedex 59655, France (e-mail: alain.haddad @ polytech-lille.fr or vincent.cocquempot@univ-lille1.fr ) Lille, France (e-mail: abdel.aitouche@hei.fr) ***Hautes Etudes d’Ingénieur, 13 rue de Toul, 59046, Lille, France (e-mail: abdel.aitouche@hei.fr) Abstract: This paper presents an active fault tolerant control (AFTC) strategy for preserving the path tracking for an autonomous wheel-steering wheel-driving (2WS4WD) electrical vehicle in the Abstract: paper presents anbased activeonfault tolerant control strategystrategy for preserving the path presence ofThis an actuator fault It is a decentralized fault (AFTC) tolerant control for overactuated tracking for an autonomous wheel-steering wheel-driving (2WS4WD) electrical vehicle the systems The strategy consists of generating new references for redundant actuators, which are onlyinused presence of an actuator fault It is based on a decentralized fault tolerant control strategy for overactuated when faults are detected, and tracking these references For a 2WS4WD vehicle, five actuators are used systems strategytoconsists newtracking: references redundant actuators, which are in normalThe situations ensure of thegenerating vehicle path theforfront-wheel steering actuator andonly the used four when faults are detected, andintracking these references For arear-wheel 2WS4WDsteering vehicle,actuator five actuators are used traction actuators However, faulty situations, the vehicle’s is controlled in in normal situations ensure the vehicle pathand tracking: the front-wheel actuator the four order to preserve thetosystem’s path tracking to ensure the desired steering performance Theand elaborated traction actuators faulty the situations, the vehicle’s actuator controlled in control law that isHowever, used to in control rear-wheels steeringrear-wheel system is steering composed of is interconnected order to preserve the system’s path tracking and to ensure the desired performance The elaborated control loops: an outer loop and an inner loop This decentralized control strategy tolerates the traction control law that is used to control the rear-wheels steering system is composed of interconnected and the front-wheel steering actuator faults The main advantage of the proposed fault tolerant strategy is control loop and an inner loop Thisonline decentralized control for strategy tolerates the traction that the loops: faults an canouter be compensated by computing new references the control loops without and the front-wheel steering actuator faults The main advantage of the proposed fault tolerant is changing the initial controllers This strategy provides the necessary time for a diagnosis strategy system to that the faults can be compensated by computing online new references for the control loops without precisely isolate the faulty actuator This method is tested and validated on a realistic vehicle dynamic changing the initial using controllers strategy providessoftwares the necessary time for a diagnosis system to model co-simulated CarSimThis and Matlab-Simulink precisely isolate the faulty actuator This method is tested and validated on a realistic vehicle dynamic Keywords: Autonomous trajectory path tracking, fault-tolerant systems, active control, dynamic © 2015,co-simulated IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd All rights reserved model usingvehicles, CarSim and Matlab-Simulink softwares reference generator Keywords: Autonomous vehicles, trajectory path tracking, fault-tolerant systems, active control, dynamic reference generator that is function of the state of the steering actuators, in order INTRODUCTION to tolerate actuator faults is function state fault of thetolerant steeringcentralized actuators, incontrol order When applying ofantheactive The control of autonomous 2WS4WD vehicles has been that INTRODUCTION toleratethe actuator faults strategy, system is viewed as a whole If a single the subject of intensive studies in recent years (Casavola, A to applying an active fault tolerant centralizedhascontrol control of R autonomous has2005) been When component is faulty, the system’s initial controller to be et alThe 2008, Wang, et al 2011,2WS4WD Zhou, Q.vehicles F., et al., the subject of intensive studies in recent years (Casavola, A strategy, the system is viewed as a whole If astep, single the Works show that this type of overactuated vehicles is redesigned in order to tolerate the fault During this has to be be component path is faulty, the system’s initial controller et al 2008, Wang, R et al.ones 2011, Zhou, Q.scenarios F., et al.,(Song 2005) tracking and performance cannot superior to the traditional in different J system’s redesigned in order to tolerate the fault During this step, the Works show that this type of overactuated vehicles is and al 2009, Potluri R et al, 2012) This is due to the guaranteed For dynamic systems as 2WS4WD vehicles, it is path and performance superior to they the traditional ones in front-wheel different scenarios J system’s necessary to reacttracking as soon as a fault is detected cannot in order be to possibility offer to combine steering(Song control guaranteed For dynamic systems as 2WS4WD vehicles, it is and al 2009, Potluri R et al, 2012) This is due to the with rear-wheel steering control, as well as active differential avoid accidents to react soonpresent as a fault detected in order to possibility they offer to combine front-wheel steering control necessary In this paper,as we an isactive fault tolerant control, in order to ensure better performances accidents with Existing rear-wheelstrategies steering control, as well as active differential decentralized control strategy that ensures the path tracking that deal with the control of avoid In this paper, presentvehicle an active fault control, in order to ensure betterbased performances of a we 2WS4WD as soon as a tolerant fault is 2WS4WD vehicles are mostly on centralized control and performance decentralized control strategy that ensures the path Existing strategies that deal with the control of control This type of control uses a single algorithm to compute detected It is designed using a decentralized tracking performance a 2WS4WD vehicle as soon as O a fault is 2WS4WD vehicles are mostly onMoriwaki, centralizedK., control approach, mainlyofused in aeronautics (Härkegård, et al., system inputs (Casavola, A et based al 2008, 2005, and detected It is designed using a decentralized control This type of control uses a single algorithm to compute Yang, H., et al 2010, Zhou et al., 2005) The computed 2005, Luo, Y et al 2004, Levine, W S., 2010) Compared to mainly used in aeronautics (Härkegård, et al., systemare inputs et al 2008, Moriwaki, K., 2005, existing centralized control strategies, faults are not O tolerated inputs then (Casavola, distributed A between redundant actuators using approach, 2005, Luo, Y et al 2004, Levine, W S., 2010) Compared to Yang, H., et al 2010, Zhou et al., 2005) The computed allocation strategies, which can be determined offline (Zhou, by modifying the initial controllers Instead, as soon as a fault existing centralized control strategies, faults are not tolerated inputs are then distributed between redundant actuators using is detected, new references are generated locally for the Q F., et al., 2005, Moriwaki, K., 2005), or online (Casavola, by modifying the initial controllers soonscenarios as a fault allocation strategies, determined offline (Zhou, redundant actuators, which are onlyInstead, used in as faulty A et al 2008, Yang,which H., etcan al be 2010) An offline allocation is detected, references locally for the the Q F., et is al.,presented 2005, Moriwaki, K.,Q 2005), or al., online (Casavola, trackingnew of these new are localgenerated references ensures strategy in (Zhou, F., et 2005), where The redundant actuators, which are only used in faulty scenarios A et al 2008, Yang, H., et al 2010) An offline allocation equal steering torques are computed for front-wheel and rear- compensation of the fault The global system’s path tracking tracking of are these local references ensures strategy is presented in (Zhou, Q F., A et et al.,al2005), and performance thennew recovered in the presence of the the wheel steering actuators In (Casavola, 2008, where Yang, The compensation of the fault The global system’s path tracking equal steering torques are computed for front-wheel and rearH., et al 2010), the authors use an online allocation strategy fault A fault isolation module can later be applied in order to wheel steering actuators In (Casavola, A et al 2008, Yang, and performance are then recovered in the presence of the H., et al 2010), the authors use an online allocation strategy fault A fault isolation module can later be applied in order to Copyright © 2015 IFAC 492 2405-8963 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd All rights reserved Peer review under responsibility of International Federation of Automatic Control Copyright © 2015 IFAC 492 10.1016/j.ifacol.2015.09.574 SAFEPROCESS 2015 September 2-4, 2015 Paris, France A HADDAD et al / IFAC-PapersOnLine 48-21 (2015) 492–498 identify precisely the fault, as in (Haddad, A., et al., 2013), which is necessary for the system’s reconfiguration This strategy, first presented in (Haddad, A., et al., 2014), is detailed in this article f ( X ) x y cos( ) ( x y )cos( ) The paper is organized as follows: Section describes the kinematic model of a 2WS4WD vehicle that is used for elaborating the presented control method Section describes the strategy used for controlling the rear-wheel steering system Section presents simulation results Conclusions and future work end the paper wf wr 493 x y sin( ) ( x y )sin( ) tan( wf ) tan( wr ) tan( wf ) tan( wr ) L x y (tan( wf ) tan( wr )) B f wf L B L f11 Fx1 R cos( wf ) Fy1 R sin( wf ) Jf Jr J1 r wr f 22 Fx R cos( wf ) Fy R sin( wf ) f11 Fx R cos( wr ) Fy R sin( wr ) J2 J3 f11 Fx R cos( wr ) Fy R sin( wr ) J4 T NONLINEAR VEHICLE MODEL g (U ) 0 0 0 In this section, the nonlinear model, which is used to elaborate the proposed decentralized control law, is described This model is presented in ((Dumont, P E et al., 2006, Sotelo, M A., 2003)) It is valid under the assumptions of planar motion, rigid body, non-slipping tires, and considering that the two front wheels (resp the two rear wheels) are oriented with the same angle These assumptions make it possible to determine the position of the rotation center using kinematic rules (as shown in Fig 1) uf Jf T ur Jr u1 J1 u2 J2 u3 J3 u4 J4 In these equations, L is the wheelbase, Bf and Br are respectively the front and rear tires rolling resistances, Jf and Jr are respectively the front and rear wheels steering inertia, R is the wheel radius, Ji and fi are respectively the inertia and the friction of the wheel i, and Fxi and Fyi are respectively the longitudinal and lateral forces applied on the wheel i Vehicle’s longitudinal and lateral positions and velocities are obtained from a GPS, orientation and yaw rate are measured via an inertial measurement unit (IMU), vehicle’s steering angles and velocities are obtained from absolute encoders, and wheels velocities are measured by incremental encoders FAULT TOLERANT CONTROL STRATEGY The vehicle’s lateral position y is monitored in order to detect undesirable deviations A residual is generated based on the difference between the reference trajectory and the vehicle’s lateral position measurement This residual is then compared to a threshold that may be a static one or a dynamic one (Haddad, A., et al., 2013) In normal situations, the path tracking is maintained by only using the front wheels steering system and the traction system As soon as an abnormal behaviour (i.e a lateral deviation from the vehicle’s trajectory) is detected, the rearwheel steering system is activated The control of the rearwheel steering system ensures that the trajectory tracking of the vehicle is preserved in the presence of the fault The decentralized control strategy used to control the rear-wheels steering system is elaborated using two interconnected control loops: an outer loop and an inner loop In the outer loop, a dynamic reference generator for rear-wheel steering is computed This generator calculates the rear-wheel steering references that have to be followed in order to ensure the desired performances In the inner loop, the control input is calculated in order to track the desired rear-wheel steering references, obtained in the outer loop (see Fig 2) Fig 2WS4WD vehicle model The state-space model of the nonlinear vehicle dynamics, in the frame OXYZ fixed to the ground, can be written as follows: (1) X f ( X ) g (U ) X x y x y wf U u f wf wr wr 1 2 3 4 ur u1 u2 u3 u4 T T (2) (3) x and y are respectively the vehicle’s longitudinal and lateral positions, x and y are respectively the vehicle’s longitudinal and lateral velocities, is the vehicle’s orientation, wf and wr are respectively the front and rear wheels steering angles, and are respectively the front and rear wheels wf wr steering velocities, i is the angular velocity of the wheel i with i 1, 2,3, 4 , ui is the traction torque applied on the wheel i , and uf and ur are respectively the torques applied on the front and rear steering actuators f ( X ) and g (U ) are expressed as 493 SAFEPROCESS 2015 494 September 2-4, 2015 Paris, France A HADDAD et al / IFAC-PapersOnLine 48-21 (2015) 492–498 Front-Wheels Steering Control Trajectory Reference + Alarm FD - Yref Y X ref X Outer Loop + Rear-Wheel Steering Reference Generator Inner Loop uf Vehicle Dynamics Rear-Wheel Steering Controller ur x y x y wf wf wr wr δwf Fig Global steering control system system f3 ( X1 , X , X , X ) To design the interconnected control loops, the vehicle lateral behaviour model derived from (1) is rewritten as interconnected submodels Then these submodels are used to elaborate independently each control loop This decentralized control approach gives the possibility of modifying independently control loops without having to redesign the global control law Initial controllers can then be maintained when faults are detected since these faults can be compensated by computing new local objectives in the outer loop to be followed in the inner loop Let us define X ( y y )T (4) X ( x x )T X ( ) X ( wr 1 X f ( X1 , X , X , X , X ) X f3 ( X1 , X , X , X ) X f ( X ,u ) 4 f X f5 ( X ,ur ) with f1 ( X , X , X , X , X ) L f5 ( X ,U r ) N1 X ) T B f N1 X u f Jf T N1 X ur Jr with N1 1 , and N2 1 0 (14) The initial control laws for the front-wheel steering system and the traction system are to be considered as designed previously The design of the interconnected control loops is presented in the following subsections (8) ( N1 X )2 ( N1 X )2 ( tan( N X ) tan( N X )) f ( X ,U f ) N1 X (7) A submodel from (1) may then be written as X f ( X , X , X , X , X ) ( (5) (6) wf )T wr )T X ( wf 3.1 Outer loop design In order to compute the desired rear-wheel steering angle wrdes , the condition that the vehicle’s yaw rate has to satisfy in order to obtain the desired vehicle tracking performances is determined Consider the following candidate Lyapunov function: (9) (10) (11) V1 ( X ) V1 X1ref X1 V1 ( yref y, yref y ) (12) If this function verifies the following conditions: C1: V1 ( yref y, y ref y ) (13) (15) for ( yref y, y ref y ) , and V1 (0, 0) dV1 ( yref y , y ref y ) C2: for ( yref y, y ref y ) dt ( N1 X )2 ( N1 X )2 sin( X ) ( yref y, y ref y ) (0, 0) is then a globally asymptotically ( tan( N X ) tan( N X )) 2 (( N1 X ) ( N1 X ) )cos( X ) stable equilibrium point This guarantees that ( y, y ) will L f2 ( X1 , X , X , X , X ) converge asymptotically to ( yref , y ref ) for any initial condition, thus ensuring the vehicle path tracking The ( N1 X )2 ( N1 X )2 cos( X ) condition that the vehicle’s yaw rate des has to satisfy for ( tan( N X ) tan( N X )) 2 (( N1 X ) ( N1 X ) )sin( X ) (15) to verify C1 and C2 is then determined Next, the rearL wheel steering angle, which is needed to obtain the vehicle’s desired yaw rate des , is computed by using the vehicle’s submodel (12) 494 SAFEPROCESS 2015 September 2-4, 2015 Paris, France A HADDAD et al / IFAC-PapersOnLine 48-21 (2015) 492–498 495 ( yref y ) (1 K1 )e1 ( K K1 )e1 (21) y in (21) can be expressed as in (9): y (( N1 X )2 ( N1 X ) ) cos( X ) (tan( N X ) tan( N X )) L x y cos( ) (22) Introducing (22) into (21), we can write ( yref x y cos( ) ) (1 K1 )e1 ( K0 K1 )e1 We then calculate the desired yaw rate des that has to be followed in order to verify (23) Let us define ( e1 ,e1 ) as Fig Outer loop control design Let us choose a positive definite function V1 (e1 , e1 ) as K (e1 )2 (e1 e1 ) 0 with e1 yref y , e1 y ref y and K0 V1 (e1 , e1 ) ( e1 ,e1 ) ( K1 )e1 ( K0 K1 )e1 (24) From (20) and (24) we have ( e1 ,e1 ) e1 If the vehicle’s yaw rate verifies the following equation: (16) If V1 (e1 , e1 ) verifies C1 and C2, then V1 (e1 , e1 ) is a Lyapunov function and (e1, e1) (0,0) is a globally asymptotically stable equilibrium point for the system Equation (15) shows that condition C1 is satisfied In order to satisfy C2, there must be dV1 (e1 , e1 ) K e1e1 (e1 e1 )(e1 e1 ) dt for (e1 , e1 ) e1 ( e1 ,e1 ) yref x y cos( ) (25) equation (19) is then satisfied and the trajectory tracking of the system is in this case guaranteed The yaw rate des verifying equation (25) can be expressed as yref (e1 , e1 ) des ( x y ) cos( ) (26) ( X , (e1 , e1 ), yref ) (17) One possible solution to obtain V1 (e1 , e1 ) is to impose e1 e1 K0 e1 K1 (e1 e1 ) (23) (18) The desired rear-wheel steering angle wrdes , which has to be followed in order to obtain des , is computed in the following From (11), vehicle’s yaw is expressed as yref y and K1 with e1 From equation (18), V (e1 , e1 ) in equation (17) can be written as V1 (e1 , e1 ) K e1e1 (e1 e1 )( K e1 K1 (e1 e1 )) (19) K e12 K1 (e1 e1 ) From equation (18), the following error equation can be obtained (20) e1 (1 K1 )e1 ( K0 K1 )e1 ( ( N1 X ) ( N1 X ) (tan( N X ) tan( N X )) L ) x y (tan( wf ) tan( wr )) (27) L Based on (27), the vehicle’s desired yaw rate des is expressed as x y (tan( wf ) tan( wrdes )) des L (28) From (28), the desired rear-wheel steering angle wrdes can be computed as L des tan( wf )) wrdes arctan( ( x y ) This error equation describes the free response of a nd order linear system The system’s overshoot Mp and settling time Ts within 2% can then be expressed as ( K1 1) M p exp( ) ( K1 1)2 ( K0 K1 ) 4( K K1 ) (21) ln(0.02) Ts ( K1 1) (22) K and K1 in equation (20) can then be chosen such as to obtain desired tracking dynamic performances In the following, the condition that the vehicle’s yaw rate has to satisfy in order to obtain equation (20) is presented In order to obtain this condition, equation (20) is firstly rewritten in function of Then, the desired yaw rate des that has to be followed in order to obtain (20) is calculated yref y , equation (20) can be rewritten as Since e1 ( X , des ) (29) Finally, equations (26) and (29) are used to rewrite the desired rear-wheel steering angle as L( yref (e1 , e1 )) wrdes arctan( tan( wf )) ( x y ) cos( ) ( X , ( X , (e1 , e1 ), yref )) ( X , (e1 , e1 ), yref ) y Knowing that arctan( ) , (29) can be expressed as x 495 (30) SAFEPROCESS 2015 496 September 2-4, 2015 Paris, France A HADDAD et al / IFAC-PapersOnLine 48-21 (2015) 492–498 L( K e1 K1e1 yref ) (31) tan( wf )) y 2 ( x y ) cos(arctan( )) x Singularities exist in equation (31) for As demonstrated in the previous section, that stabilizes X ( X 1ref X ) has to be equal to ( wrdes wrdes )T The wrdes arctan( subsystem (35) is then extended by adding (36) in order to calculate the input that ensures a global lateral trajectory tracking for the system The following equation is obtained X f1 ( X , X , X , X , ) (37) f5 ( ,ur ) Remark 1: Y arctan( ) These singularities can be avoided by X changing the vehicle’s frame, as in (Rajamani et al., 2003), when vehicle rotation angle does not verify C3: 3 Y 5 Y arctan( ) or C4: arctan( ) X 4 X The transition matrix can be expressed as 0 1 0 (32) T 1 0 0 1 By applying this transformation, the vehicle is controlled in the frame OYXZ instead of controlling it in the frame OXYZ In that case, the rear-wheel steering reference can be rewritten as follows: L wrdes arctan( ( K ( X ref X ) Y (33) 2 ( X Y )sin(arctan( )) X K ( X X ) X ) tan( )) ref ref For the extended subsystem (37), a positive definite function V2 (e1 , e1 , ) is defined as V2 (e1 , e1 , ) V1 (e1 , e1 ) T W (38) K ( wr wr ) V1 (e1 , e1 ) wr 2 with ( wrdes wrdes )T wr (t ) wrdes (t ) wr (t ) wrdes (t ) wr (t ) wr (t ) K 1 with K2 1 1 If V2 (e1 , e1 , ) verifies the following conditions: C7: V2 (e1 , e1 , ) for (e1 , e1 , ) , and V2 (0, 0, (0, 0)) dV2 (e1 , e1 , ) C8: for (e1 , e1 , ) dt (e , e , , ) 0, 0, 0, is then a wf and W Remark 2: It is clear that singularities exist also for Y Y arctan( ) and arctan( ) A transformation is also X X applied when vehicle rotation angle does not verify C5: Y 7 In Y 3 or C : 5 arctan( ) arctan( ) X 4 X this case, the transition matrix can be expressed as 0 (34) T 1 0 0 1 In other words, when conditions C5 or C6 are not verified, the vehicle is controlled in the initial frame OXYZ 1 wr wr globally asymptotically stable equilibrium point This guarantees that ( wr , wr ) converges asymptotically to (0,0), meaning that ( (t ), (t )) converges to ( (t ), (t )) wr wr wrdes wrdes Equation (38) shows that V2 (e1 , e1 , ) satisfies condition C7 3.2 Inner Loop design After computing the desired rear-wheel steering position δwrdes in the outer loop, the control input ur needed to track this reference is calculated For this purpose, the backstepping technique, which is a recursive control method, is used First, a subsystem from the considered vehicle’s lateral behavior model is used, for which a virtual control law is constructed The design is then extended in several steps by adding subsystems to the considered model until a control law for the entire system is obtained Along with the control law, Lyapunov functions are successively constructed in each step In the following, the rear-wheel steering control input necessary for satisfying condition C8 is computed dV2 (e1 , e1 , ) is expressed as dt dV2 (e1 , e1 , ) V1 (e1 , e1 ) T W T W dt V1 (e1 , e1 ) K wr wr ( )( ) wr wr wr wr ur (40) for (e1 , e1 , wr , wr ) , with wr wr wrdes Based on (40), C8 is satisfied if dV2 (e1 , e1 , ) V1 (e1 , e1 ) K wr wr (41) dt ( wr wr )( wr wr ) V (e , e ) expressed in (17), and used in (41), can be rewritten From (9) and (13), the following two subsystems are extracted (35) X f1( X1 , X , X , X , ) (36) f5 ( ,ur ) T with ( ) being the virtual input of the subsystem wr (39) as wr presented in (35) 496 1 SAFEPROCESS 2015 September 2-4, 2015 Paris, France A HADDAD et al / IFAC-PapersOnLine 48-21 (2015) 492–498 yref V1 (e1 , e1 ) K e1e1 (e1 e1 )(e1 wr f1 ( x1 , x2 , x3 , x4 , wr wrdes )) K e1e1 (e1 e1 )( K e1 K1 (e1 e1 ) ( )) 12 wr K e K1 (e1 e1 ) 12 (e1 e1 )( wr wr ) (42) wr with f1 ( x1 , x2 , x3 , x4 , wr wrdes ) f1 ( x1 , x2 , x3 , x4 , wrdes ) ( ) 12 wr wr (43) f1 ( x1 , x2 , x3 , x4 , wr ) f1 ( x1 , x2 , x3 , x4 , wrdes ) (44) Remark 3: If ( wrdes wrdes ) , then the expression f1 ( x1 , x2 , x3 , x4 , wr ) f1 ( x1 , x2 , x3 , x4 , wrdes ) in (44) becomes equal to zero This implies that, for this condition, we have 12 , and (42) becomes equal to equation (19) Using (42), equation (40) can be rewritten as V (e , e , ) V (e , e ) T W T W wr wr 1 1 T wr 1 wr wr wr wr (51) wr wr wr SIMULATION RESULTS The proposed strategy is tested using a co-simulation between CarSim, a professional simulator used by automobile manufacturers, and Matlab-Simulink software, as in (Haddad, A., et al., 2014) In this test, an overactuated autonomous vehicle is circulating with an initial constant speed of 60 km/h, and performing a double lane-change maneuver on a dry asphalt road (friction coefficient max = 1.2) At t=3.6s, a drop of wr (46) 1 efficiency is created at the front-wheel steering actuator Two scenarios are then considered In the first scenario, the vehicle is controlled using its frontwheel steering system only It can be seen in Fig that the front-wheel steering controller is not able to ensure alone the lateral stability of the vehicle The vehicle exceeds the limits of the road at t=4.58s 12 (e1 e1 )( wr wr ) K wr wr ( wr wr )( K wr K ( ) (e e )) wr 12 wr 1 (47) From (47), the following equation is finally obtained: V2 (e1 , e1 , ) K e12 K1 (e1 e1 ) K K ( ) 12 (e1 e1 ) wr with K3 This solution is verified by introducing the value of (wr wr ) expressed in (46) to equation (45) as V (e , e , ) K e K (e e ) 2 12 (e1 e1 ) asymptotically stable equilibrium point for the system K e12 K1 (e1 e1 ) 12 (e1 e1 )( wr wr ) K wr wr ( wr wr )(wr wr ) (45) A solution to obtain V2 (e1 , e1 , ) is to have K K ( ) wr (50) Using equations (50) and (51), we can write Br wr ur wrdes K wr K3 ( wr wr ) wr Jr 12 (e1 e1 ) (52) From (52), the rear-wheel steering control input ur is computed as ur J r ( K wr K ( wr wr ) wr (53) 12 (e1 e1 ) wrdes ) Br wr With u r computed as in (53), V2 (e1 , e1 , ) is a Lyapunov function and (e , e , , ) 0, 0, 0, is a global and 12 is expressed as 12 wr wrdes Br wr ur wrdes Jr From (49), wr in (50) can be expressed as K K ( ) wr 497 wr wr In the second scenario, fault detection (FD) system is used to monitor the lateral deviation When this deviation violates the acceptable security margins (determined based on the width of the road) at t=4.16s, the FD system activates the rear-wheel steering controller presented in section The rear-wheel steering system is then able to maintain the lateral stability of the global system in the presence of the component fault (see Fig 4) (48) wr Equation (48) shows that for (wr wr ) expressed as in (46), V2 (e1 , e1 , ) is a Lyapunov function since it satisfies C and C8 The control input ur that verifies (46) can now be computed From (13), we have N1 X ur Br wr ur wr Jr Jr Knowing that wr wr wrdes , we can write CONCLUSIONS In this paper, a fault tolerant control strategy is developed for a 2WS4WD autonomous vehicle It is demonstrated that this strategy can ensure the vehicle’s path tracking in the presence of an unknown actuator fault (49) 497 SAFEPROCESS 2015 498 September 2-4, 2015 Paris, France A HADDAD et al / IFAC-PapersOnLine 48-21 (2015) 492–498 14 12 Lateral position (m) 10 Vehicle lateral deviation detection Activation of the FTC strategy for controlling rear-wheel steering -2 Vehicle nominal behaviour Vehicle behaviour in presence of faulty actuator without using FTC system Vehicle behaviour in presence of faulty actuator and using FTC system Maximum threshold Minimum threshold Maximum security margin Minimum security margin 10 12 14 16 18 Time (s) Fig Vehicle lateral behaviour when performing a double lane-change maneuver Moriwaki, K (2005) Autonomous steering control for electric vehicles using nonlinear state feedback Hinfinity control Nonlinear Analysis, 63, 2257-2268, Potluri, R., and Singh, A K (2012) Path-tracking control of an autonomous 4WS4WD electric vehicle using driving motors' dynamics Proceedings of the 7th IEEE International Conference on Industrial and Information Systems, volume 63, number 5, pp 1-6 Rajamani, R., Zhu, C., and Alexander, L (2003) Lateral Control of a backward driven front-steering vehicle Control Engineering Practice , volume 11, number 5, pp 531-540 Song, J., and Che, W.S (2009) Comparison between braking and steering yaw moment controllers considering ABS control aspects Mechatronics, Special Issue on Hardware-in-the-loop simulation, volume 19, number 7, pp.1126-1133 Sotelo, M A (2003) Lateral control strategy for autonomous steering of Ackerman-like vehicles Robotics and Autonomous Systems, volume 45, number 3, pp 223233 Vermillion, C., Sun, J., and Butts, K (2007) Model Predictive Control Allocation for Overactuated Systems Stability and Performance Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, USA, pp 1251-1256 Wang, R., and Wang, J (2011) Fault-Tolerant Control with Active Fault Diagnosis for Four-Wheel IndependantlyDriven Electric Ground Vehicles American Control Conference, San Fransisco, CA, USA, pp.3954-3959 Yang, H., Cocquempot, V., and Jiang, B (2010) Optimal Fault-Tolerant Path-Tracking Control for 4WS4WD Electric Vehicles IEEE Trans On Intelligent Transportation Systems, volume 11, number 1, pp 237243 Zhou, Q., Wang, F., and Li, L (2005) Robust sliding mode control of 4WS vehicles for automatic path tracking Proceedings IEEE Intelligent Vehicles Symposium, pp 819-826 This strategy is developed using the backstepping technique, and consists of dividing the control strategy into two loops: the outer one and the inner one In the outer loop, the steering position needed in order to obtain the nominal vehicle performances is computed In the inner loop, the rear-wheel steering system is controlled in order to follow the desired reference calculated in the outer loop When a vehicle lateral deviation is detected, the elaborated algorithm is activated in order to maintain the global system’s lateral stability The efficiency of this strategy is illustrated using a co-simulation between Carsim and Matlab-Simulink softwares REFERENCES Casavola, A., and Garone, E (2008) Enhancing the Actuator Fault Tolerance in Autonomous Overactuated Vehicles via Adaptive Control Allocation 5th International Symposium on Mechatronics and Its Applications, pp 1-6 Dumont, P E., Aitouche, A., Merzouki, R., and Bayart, M (2006) Fault tolerant control on an electric vehicle., 2006 Proceedings of the IEEE International Conference on Industrial Technology, pp 2450-2455 Haddad, A., Aitouche, A and Cocquempot, V (2014) Fault Tolerant Control Strategy for an Overactuated Autonomous Vehicle Path Tracking The 19th World Congress of the International Federation of Automatic Control, volume 19, number 1, pp 8576-8582 Haddad, A., Aitouche A., and Cocquempot, V (2013) Hierarchical Diagnosis for an overactuated autonomous vehicle Proceedings of the IEEE Conference on Control and Fault-Tolerant systems, Nice, France, pp 613-618 Härkegård, O., and Glad, S T (2005) Resolvingactuator redundancy—optimal control vs control allocation Automatica, volume 41, number 1, pp 137-144 Levine, W S (2010) The Control Handbook, Second Edition: Control System Applications, Second Edition CRC Press Luo, Y., and Doman, D B (2004) Model Predictive Dynamic Control Allocation With Actuator Dynamics American Control Conference, Boston, Massachusetts, pp 1695-1700 498 ... we can write CONCLUSIONS In this paper, a fault tolerant control strategy is developed for a 2WS4WD autonomous vehicle It is demonstrated that this strategy can ensure the vehicle? ??s path tracking. .. (2011) Fault- Tolerant Control with Active Fault Diagnosis for Four-Wheel IndependantlyDriven Electric Ground Vehicles American Control Conference, San Fransisco, CA, USA, pp.3954-3959 Yang, H.,... V., and Jiang, B (2010) Optimal Fault- Tolerant Path- Tracking Control for 4WS4WD Electric Vehicles IEEE Trans On Intelligent Transportation Systems, volume 11, number 1, pp 237243 Zhou, Q., Wang,