Research on Longitudinal Tracking Control for a Simulated Intelligent Vehicle Platoon

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1 Research on Longitdinal Tracing Control for a imlated Intelligent Vehicle Platoon Ylin Ma Engineering Research Center of Transportation afety (Mintry of Edcation) Whan University of Technology Whan 4363 China Intelligent Transport ystem Research Center Whan University of Technology Whan 4363 China and Qing W 3 Ri Zhang 4 and Xinping Yan 3 chool of Logtics Engineering Whan University of Technology Whan 4363 China 4 chool of Atomation Whan University of Technology Whan 4363 China ABTRACT Intelligent vehicle platoon driving a process of flexible control based on the coordination between vehicle and highway in intelligent vehicle-highway system. It can improve the velocities and redce the spacing between vehicles in the platoon ths to improve road capacity and road safety. It the most important for developing intelligent vehicle-highway system to constrct intelligent vehicle platoon driving simlation experiment system by means of one tenth of model cars simlated road and the technology of intelligent control and wireless commnication. In order to simlate a platoon of intelligent vehicles traveling first the acceleration information has been added to control single vehicle and the controller for velocity tracing based on acceleration has been designed sing fzzy sliding mode control method then it designed a longitdinal tracing controller for doble vehicles by bilding a second-order plant model abot longitdinal relative dtance sing the acceleration and velocity as well as the dplacement information. Finally the good trac performance of the two controllers for both single vehicle and doble vehicles illstrated by simlation reslts which can promote the stdy in the intelligent vehicle platoon control nder the coordination between vehicle and highway. Keywords: Intelligent Vehicle-Highway ystem Platoon Fzzy liding Control Accelerator Longitdinal Relative Dtance Tracing Control. INTRODUCTION Intelligent vehicle-highway system throgh improving the intelligent control for single vehicle and the ability of information interaction between vehicle and highway can realize atonomos driving for vehicles simplify the complexity of traffic control adjst the traffic flow to the best ths redce the traffic problems cased by manal driving and improve road capacity and road safety [-]. Nowadays there are some of the developments in the main areas of atomatic control for single vehicle many intelligent control methods sch as PID control neral networ control fzzy control fzzy neral networ control are sed to atomatic vehicle control [3-4]. With the architectre of the intelligent vehicle-highway system perfect intelligent vehicle platoon control has become important to develop intelligent vehicle-highway system [5-6]. The platoon control can mae a grop of two or more closely spaced vehicles traveling with the same velocity along the same lane so that achieve the capacity expansion of ext roads meanwhile redce the control object increase traffic controllability and effectively slow down traffic congestion. The control system of a platoon of vehicles a nonlinear control system whose longitdinal control aims at eeping a certain relative dtance and maintains a relatively stable velocity between vehicles. o many relative stdy on the platoon control mainly focses on the design of nonlinear controller. Reference [7] proposes a mlti-mode hierarchical switching control method based on robst control theory. The method has designed a velocity and acceleration system which realizes fast and accrate control for velocity and acceleration withot the vehicle dynamics model. Reference [8] combines with system response and robstness charactertics adopts the sliding mode control method to design an acceleration controller of two-degree-of-freedom in vehiclar stop-and-go cre control system. The controller can effectively trac the acceleration according to the desired expectation of the dynamic charactertics. Reference [9] adopts a self-tning fzzy PID control method to design acceleration controller to eep spacing between doble vehicles. By adjsting the three parameters of PID to control the error range of longitdinal relative dtance and velocity between doble vehicles achieving the longitdinal control for doble

2 vehicles. A fzzy sliding mode control method adopted to design acceleration/speed controller for a platoon of vehicles []. The controller able to ensre the better stability of platoon withot specific vehicle dynamics model. An adaptive fzzy control algorithm applied to longitdinal control for a platoon of vehicles []. the controller designed can crb the spacing flctations and velocity flctations and effectively improve the stability of platoon. Th paper organized as follows. The following section presents a description of the strctre of intelligent vehicle platoon driving simlation experiment system. ection 3 begins by the intelligent control for single vehicle with its acceleration information added and designs a second-order velocity tracing controller based on acceleration adopting fzzy sliding mode control algorithm. ection 4 bilds a second-order plant model of longitdinal relative dtance sing the acceleration and velocity as well as the dplacement information to design longitdinal tracing controller for doble vehicles. imlation reslts are sed to demonstrate the effectiveness of the approach in ection 5. Finally we present conclsions and ftre wor in ection 6. Fig. The intelligent vehicle platoon simlation experiment system. TRUCTURE OF INTELLIGENT VEHICLE PLATOON DRIVING IMULATION EXPERIMENT YTEM The intelligent vehicle platoon simlation experiment system aims at simlating a platoon of vehicles traveling and the information interaction between vehicle and highway by the establhed vehiclar wireless networs. Th system strctre consts of three parts: road sand table sbsystem vehicle platoon simlation sbsystem and the road-side information gathering and monitoring sbsystem as shown in Fig.. The road sand table sbsystem shown in Fig. consts of : closed road of 7 centimeters wide two lanes and the height of bridge 5 centimeters the depth of tnnel centimeters which simlates varios freeway infrastrctres. The vehicle platoon simlation sbsystem shown in Fig. 3 inclding DP controller power conversion modle motor drive modle ZIGBEE wireless commnication modle CMO digital camera infrared obstacle sensors ltrasonic sensor and rotary encoder. Lateral information acqired by camera and infrared sensors sed to control the actator; velocity measred by rotary encoder and spacing of vehicles measred by ltrasonic sensor. In addition information interaction between vehicle and highway realized by ZIGBEE modles. The road-side information gathering and monitoring sbsystem selects high performance mode of information interaction between vehicle and highway to spport the platoon traveling. Fig. Road sand table Fig. 3 Configration of intelligent vehicle 3. CONTROLLER DEIGN FOR INGLE VEHICLE Intelligent vehicle traveling along the road sand table from Newton s second law the relationship between the acceleration of the vehicle proplsion force mechanical drag and aerodynamic drag can be derived as m = F v d m F denotes the proplsion force of the vehicle d v denotes the aerodynamic drag of the vehicle () m denotes the mechanical drag applied on the vehicle m denotes the mass of the vehicle.

3 The proplsion system which represents the engine dynamics of a vehicle can be modeled as a first-order nonlinear differential ation F & = ( F + ) τ ( v) τ (v) denotes the vehicle s engine time constant when the vehicle traveling with a speed al to v represents the controller otpt. In practice the vehicle control parameters are partially nown or completely nnown. In th paper we assme that the parameters of the vehicle mdm τ(v) are nnown bt satfied with the following inalities: m M ; d K D ; m K M ; τ (v) Γ. the parameters MK D K M Γ are constants. In addition with the acceleration added we assme that the pper bond of the vehicle s jer nown a & < K. K also a constant. Then we present the velocity error model regarded as a second-order nonlinear differential ation of velocity. It can be obtained by differentiating v & in Eq. () once: m = F& d v (3) Ptting Eq. () and Eq. () into Eq. (3) yields: v && = f ( v ) + d m d f ( v ) = ( + v + ) v τ ( v) m m m = mτ ( v). We define the velocity error as () (4) r = T (5) e [ e e& ] Among them e = vdes v e& = ades a v des a des denotes the desired reference velocity and acceleration respectively. Now we define a sliding srface as = C e = c e + e& (6) C= [c ] c> a constant to be chosen. Maing & = & = c e& + e&& = c e& + & = c e& + & yields: res res & f ( v ) = It clear that if we can choose the ivalent controller as Eq. (8) sch that lim ( t) = t then the control for velocity error can be achieved. ( c e& + & f ( v &)) res v (7) = (8) In order to satfy the sliding mode reaching condition (9) hitting control mst be sed. We define the hitting controller as Eq. (). & (9) h = ( e + β e& )sgn α () o according to fzzy control and sliding mode control principle we choose the fzzy sliding mode controller as The fzzy rles are shown as follows: If = + h () ZO then () If then + h (3) the fzzy sets ZO and denote zero and nonzero the inpt variable given in Eq. (6) and the ivalent control and hitting control h are given in Eq.(8) and Eq.() respectively. The rle () states that if the vale of zero then the fzzy sliding mode controller determined by the ivalent control. imilarly the rle (3) states that if the vale of nonzero then the hitting component h added to the controller to force the motion of the system states toward sliding srface. Fig. 4 shows the shape of the membership fnctions.

4 Degree of membership Degree of membership N Z B (a) N Z B (b) Fig. 4 The shape of membership fnctions: (a) inpt variable ; (b) otpt variable 4. LONGITUDINAL TRACKING CONTROL FOR DOUBLE VEHICLE For simlating a platoon of vehicles traveling the following vehicle rired to eep a safe dtance from its preceding vehicle. From the traffic capacity point of view the desired safe dtance shold be as small as possible. However th desired safe dtance not always constant and it has a relationship with the velocity of the following vehicle. In other words as the velocity of the following vehicle increases the desired dtance shold be increased to improve traffic safety; as the velocity decreases the desired dtance shold be redced to improve the road tilization. Therefore the safety dtance policy can be well defined by the velocity of the following vehicle. Assme that there a platoon of two vehicles traveling along the road sand table and let x (x respectively) v (v respectively) and a (a respectively) be the position velocity and acceleration of the following vehicle (the leading vehicle respectively). As shown in Fig.5 the longitdinal relative dtance for the following vehicle from the desired safety dtance e = x x L d (6) d the safety dtance and d = λ v + λ L the length of the following vehicle. By the defzzification method the control law of the fzzy sliding mode controller μ ZO + μ ( = μ ZO + μ = + μ sw + sw ) (4) Obviosly the membership fnctions of fzzy sets ZO and are selected overlap and symmetric to satfy μ μ ZO + μ = () = = +. In the case h of it seen that which similar to conventional sliding mode control; in the case μ () of the chattering phenomenon crbed by the changes of the membership fnction of fzzy set in the control laws. With the acceleration added the velocity at some time obtained by the following ations. a( ( ) = a( ) ) = a( ) + f [ v( ) ( )] + f [ v( )] ( ) v( = v( ) + a( the serial nmber of sampling time. (4) Fig. 5 Configration of the platoon of doble vehicles Here taing into accont the real-time platoon control system dynamic response as well as dynamic charactertics and variable conditions the plant model of longitdinal relative dtance shold reflect position velocity and acceleration information abot both two vehicles. o it regarded as a second-order plant model that can be obtained by differentiating e in Eq. (6) twice: e&& = && x && x && d = a a λ & (7) We se the acceleration soltion for single vehicle ptting Eq. (4) into Eq. (7) yields: e & = a a λ f ( v ) + f ( v ) ) (8) ( Now we define a sliding srface as

5 C e = c e + e& = C= [c ] c> a constant to be chosen. From Eq. (9) we obtain: & c e& + & e = (9) () In order to simplify the complexity of the platoon control system we design a fzzy sliding mode controller the strctre of which as follows: NB: negative big NM: negative medim N: negative small ZO: zero P: positive small PM: positive medim PB: positive big Inpt: and & Otpt: ΔU Fzzy rle: & If Degree of membership A and B then ΔU NB NM N Z P PM PB sdsd Fig. 6 The shape of membership fnctions In order to satfy the sliding mode reaching condition (9) the resltant fzzy control rles are shown in Fig. 7. The control rles state that if both and & are the positive big & which means the positive big then ΔU need a big positive variable to decrease & qicly; if & less than zero that the desired state; if both and & are the negative big which means & the positive big then ΔU & need a big negative variable to decrease qicly. The rles assre the stability of the fzzy sliding mode control system. C U & NB NM N ZO P PM PB PB ZO P PM PB PB PB PB PM N ZO P PM PB PB PB P NM N ZO P PM PB PB ZO NB NM N ZO P PM PB N NB NB NM N ZO P PM NM NB NB NB NM N ZO P NB NB NB NB NB NM N ZO Fig. 7 Fzzy control rles By the defzzification method the control law of the fzzy sliding mode controller Δ = f ( & ) = θ ( μ( ) μ( & )) i i= i= μ( ) μ( & ) () μ () μ( & ) the membership fnctions of normal dtribtion describing the fzzy sets of and θi the principal vales of corresponding fzzy set of ΔU. Therefore assming that both the leading vehicle and the following one have the same parameters charactertics that meet the conditions given for single vehicle at some time the longitdinal dplacement velocity and acceleration of the following vehicle are obtained by the following ations. a ( = a( ) λ ( f[ v( ) ( )] + f[ v( )] ( )) v( = v( ) + a( x( = x( ) + v( + a( () the serial nmber of sampling time. 5. IMULATION TET In order to test the proposed controller we perform a series of simlation tests. The control parameters are chosen as follows: m = 5 d =.3 m = 4 τ =. λ =. λ = 6 c & = In the first simlation we set abot velocity tracing control simlation for single vehicle nder variable conditions adopting PID control algorithm and FMC algorithm respectively. We assme that vehicle identical with the control parameters above. The vehicle assmed to accelerate from m/sec to m/s and then to m/sec. After the vehicle reaches m/sec it begins to decelerate to m/sec. The simlation reslts are shown in Fig een

6 from the simlation reslts the controller designed can well trac a desire reference velocity nder variable conditions and the range of acceleration rired from -m/s to m/s. Good velocity tracing are achieved for the single vehicle. Compared with PID control algorithm althogh the PID control algorithm responds qicly in the beginning as a reslt of the increasing overshoot the respond speed sbsently begins to slow down. o it taes a long time for the PID control algorithm to reach the steady velocity than for the fzzy sliding mode control algorithm. from Fig. - the controller designed has good performance of velocity and acceleration. Vehicle pacing m FMC PID time s v(m/s) Fig. pacing profiles of doble vehicles longitdinal tracing simlation nder variable conditions t(s) 5 Leader Follower Fig. 8 Velocity profiles of single vehicle longitdinal tracing simlation nder variable conditions peed m/s a(m /s) time s Fig. Velocity profiles of doble vehicles longitdinal tracing simlation nder variable conditions t(s) 3 Leader Follower Fig. 9 Acceleration profiles of single vehicle longitdinal tracing simlation nder variable conditions In simlation we go abot longitdinal tracing control simlation for doble vehicles nder variable conditions adopting FMC algorithm. We assme that two vehicles have the same control parameters given above. The leading vehicle assmed to accelerate from m/sec to m/s. After the vehicle reaches m/sec it begins to decelerate to m/sec. The simlation reslts are shown in Fig. -. een from Fig. when the velocity increases the corresponding longitdinal relative dtance between doble vehicles increases; on the contrary when the velocity decreases the corresponding longitdinal relative dtance between doble vehicles decreases. Besides seen Acceleration m/s time s Fig. Acceleration profiles of doble vehicles longitdinal tracing simlation nder variable conditions s

7 6. CONCLUION AND FUTURE WORK Intelligent vehicle platoon control based on the coordination between vehicle and highway one of the hotspots in the crrent research areas of intelligent transportation it very important to se the hardware-inthe-loop simlation technology. In th paper arond the intelligent vehicle platoon driving simlation experiment system bilt it carried ot longitdinal tracing control simlation experiment based on doble vehicles adopting fzzy sliding mode control algorithm. By bilding the velocity error model and the plant model of longitdinal relative dtance the corresponding controllers for both single vehicle and doble vehicles have been designed the good trac performance of which illstrated by simlation reslts achieving longitdinal tracing control for single vehicle and doble vehicles nder variable conditions. The next wor as follows: In information acqition improve the accracy of sensors and loo for efficient information fsion method to obtain more real-time accrate information to spport the platoon driving; In vehicle platoon control formation control shold be stdied the stability contines to be analyzed and the highfalt-tolerant control algorithm going to be explored. model Proceedings of the 4 American Control Conference Vol. 4 pp [8] Y. Bin K. Q. Li X. M. Lian H. Uawa M. Handa Longitdinal acceleration tracing control of Vehiclar top-and-go Cre Control ystem 4 IEEE International Conference on Networing ensing and Control Vol. 4 pp [9] Y. N. Li L. Zheng Y. J. Qiao Fzzy-PID Control Method on Vehicle Longitdinal Dynamics ystem China Mechanical Engineering Vol. 7 No. 6 pp [] G. D. Lee. W. Kim A longitdinal control system for a platoon of vehicles sing a fzzy-sliding mode algorithm Mechatronics Vol. No. pp [] Q. W Z. W. He. X. M. Ch and D. L An application of the adaptive fzzy control in the longitdinal control of the platoon 8 Pacific-Asia Worshop on Comptational Intelligence and Indstrial Application vol. 8 pp ACKNOWLEDGMENT The wor spported by the province natral science fondation of Hbei (No.7aba9) and the nation natral science fondation (No.68748). 8. REFERENCE [] X. J. Wang B. Li H. L. Gao and J.T. Zhang Overview of the th World Congress on IT and Dcssion abot the Developing Direction in China Jornal of Transportation ystems Engineering and Information Technology Vol. 4 No. 4 pp [] R. Horowitz P. Varaiya Control design of an atomated highway system Proceedings of the IEEE vol. 88 No. 7 pp [3]. A. Nobe F. Y. Wang An overview of recent developments in atomated lateral and longitdinal vehicle controls IEEE International Conference on ystems Man and Cybernetics Vol. 5 pp [4] Q. W Z. W. He X. M. Ch and C. Q. Zong Key Technologies Research Development of Vehicle Platoon Drive Control in Intelligent Vehicle-infrastrctre ystem Compter and Commnications vol. 6 No.4 8 pp [5]. Bengochea A Talamona and M. Parent A software framewor for vehicle-infrastrctre cooperative applications IEEE Proc. Intelligent Transportation ystems 5 pp [6] A. Göllü P. Varaiya mart AH: A simlation framewor for atomated vehicles and highway systems Mathematical and Compter Modelling Vol. 7 No pp [7] F. Gao; K. Q. Li J. Q. Wang and X. M. Lian Adaptive throttle controller design based on a nonlinear vehicle