Intelligent Parking Method for Truck and Trailer in Presence of Fixed and Moving Obstacles

Transcription

1 Autralian Journal of Baic and Applied Science, 5(11): , 11 ISSN Intelligent Parking Method for Truck and Trailer in Preence of Fixed and Moving Obtacle 1 Morteza Sharafi, 2 A.Zare and Khalil Alizadeh 1 Ilamic Azad Univerity Gonabad-Branch Member of Young Reearcher Club. 2 Aitant Profeor of Ilamic Azad Univerity - Gonabad Branch Gonabad, Iran. Ilamic Azad Univerity Gonabad Branch, Iran. Abtract: A Fuzzy approach to backward movement control for truck and trailer in a dynamic environment i preented in thi paper. The approach i then extended and employed for condition where obtacle are placed on the truck and trailer pathway. In the firt cae, obtacle are aumed to be fixed, while the econd condition include moving obtacle through which the truck and trailer hould be directed toward the parking dock. The method i deigned in a way to be ued in condition with infinite number of obtacle at arbitrary place. In any cae, to find the parking dock, the truck and trailer movement mut be adapted to that of obtacle. In the preent paper, two eparate fuzzy controller are ued for directing the truck and trailer: one for finding the target, and the other for avoiding the obtacle. While there i no obtacle around, the target finder controller i in ue; and in the cae where the truck and trailer get cloe to obtacle the obtacle avoider controller i activated. The propoed method i employed for parking a truck and trailer model through fixed and moving obtacle. Key word: Fuzzy Control - Avoiding Obtacle Truck and trailer Parking - Routing - Fixed and Moving Obtacle. INTRODUCTION In 19, Nguyen and Widrow applied a elf-learning neural network to the truck backer-upper problem. The latter ha become an acknowledged benchmark in non-linear control ince and numerou other technique have been tried, including genetic programming (Koza, 1992) neurogenetic (Schoenauer and Ronald, 1999), implified neural network olution through problem decompoition (Jenkin and Yuha, 199), etc.1. Computational overhead i uually very high in uch application, e.g. in (Kong and Koko, 19) it i hown that about of back-up cycle are needed before neural network learn and even then, the back propagation algorithm may not converge for ome et of training ample. A implified verion of the control problem (coniting of the cab part only), on the other hand, ha been heavily exploited in the field of fuzzy control (Wang and Mendel, 1992; Ramamoorthy and Huang, 1991; Shann and Fu, 1995; Imail and Abu-Khoua, 1996; Kim, 1998; Kong and Koko, 1992; Dumitrache and Katalin, 1999; Su and Chang, ). Apparently, it eem to be one of thee cae where the traditional application area of fuzzy logic - knowledge-baed control - would be an appropriate olution. Ability to drive a car i a very common kill among people thu it hould not be too difficult to find an expert whoe verbal intruction would then contitute the core of the control ytem. Car driving kill, however, i uually learned to a degree where it rarely intrude on concioune (the occaion when it doe are unuual circumtance like a potential accident or a ituation the driver i not ued to (i.e. he/he ha not yet learnt it). Conequently, it i difficult to extract appropriate rule from the expert becaue of one inability to explain how the action behind the teering wheel i exactly related to car poitioning and further difficultie in putting it down in term of fuzzy logic. The deign of knowledge baed controller therefore become much more difficult than wa aumed in the firt place. Though the computational load i low, controller deign procedure i ill-defined and plagued with the cure of dimenionality that often lead to ubpar performance. In [15] i hown how the decompoition of the control problem can make controller deign very natural and ubtantially implify expert knowledge acquiition. In the decompoed view we focu on information concerning car optimal orientation in two-dimenional pace (much eaier to explain and undertand than the minute action on the teering wheel), which ultimately lead to the efficient olution of the problem. The decompoition principle, according to [16], alo help to tackle the truck and trailer problem. Problem Definition: Deigning an optimal pathway for backward movement of a truck and trailer through a number of fixed and moving obtacle i among mot complicated problem in engineering. Factor uch a type, hape, and rate of Correponding Author: Morteza Sharafi, Ilamic Azad Univerity, Gonabad Branch, Member of Young Reearcher Club. mortezaharafi@gmail.com Tel:

2 Aut. J. Baic & Appl. Sci., 5(11): , 11 movement a well a time limitation for achieving the target dock may introduce further complication into the problem. Backward movement of a truck and trailer on a dock i a nonlinear control problem. Uing the conventional control method, a mathematical model for the ytem can be obtained, and then nonlinear control theory may be employed to deign of the controller. An alternative to thi i to deign a controller which imulate human behavior. The latter i ued in the preent paper. We aume that an experience truck and trailer driver i available; in addition, we can meaure different poition of the truck and trailer and correponding driver action to move the truck and trailer backward. Figure 1 how the truck and trailer and the loading (parking) dock. x 1 x x, (,, ) 1 (b) x x x (a) Fig. 1: A chematic of the truck and trailer and parking dock; the poition of the truck and trailer i determined by the three tate variable x, y, and φ. ( x, y) c y t x Fig. 2: State variable involved in intelligent backward movement of the truck and trailer. For truck: θ: the angle formed between wheel direction and horizontal axi. φ: the angle formed between the truck direction and vertical axi. x, y: current poition. The truck i controlled by changing θ. Only backward movement i allowed here. In each tep, the truck move backward with a contant change in poition. We aume that a ufficient pace i preent between the truck and parking pot, and therefore, the vertical poition y i not required a a tate variable for our purpoe. The objective here i to deign a controlled with (x, φ) a input and a θ output in order to move the truck to the final tate a (x f, φ f )=(5, ). Furthermore, we aume that: x [,], [,27 ], [ 4,4 ] which mean: V [ 4,4 ], U [,] [,27 ] 99

3 Aut. J. Baic & Appl. Sci., 5(11): , 11 Problem Contraint: The truck ha a contant velocity of V. The length of the truck i L. L v Fig. : Contraint of the truck parking problem. In order to imulate the control ytem, we have to obtain the mathematical model for the truck. Here, we ue the following approximate model (Wang and Mendel, 1992; Ramamoorthy and Huang, 1991; Shann and Fu, 1995; Imail and Abu-Khoua, 1996; Kim, 1998; Kong and Koko, 1992; Dumitrache and Katalin, 1999; Su and Chang, ): x( t 1) x( t) co[ ( t) ( t)] in[ ( t)]in[ ( t)] (1) y( t 1) y( t) in[ ( t) ( t)] in[ ( t)]co[ ( t)] ( t 1) ( t) in 2in( l 1 ( t)) For more convenient calculation in MATLAB, we can convert the above equation into complex form: p x jy dp V (co ) e dt d V in dt L j 2 (2) The length and velocity of the truck may alo be changed in the imulation program. For trailer: The trailer i controlled by changing θ. Only backward movement i allowed here. In each tep, the trailer move backward with a contant change in poition. We aume that a ufficient pace i preent between the trailer and parking pot, and therefore, the vertical poition y i not required a a tate variable for our purpoe. t c t c c t t t t Fig. 4: Relationhip between trailer angle. Problem Contraint: The trailer ha a contant velocity of V. The length of the trailer i Lc L. 4

4 Aut. J. Baic & Appl. Sci., 5(11): , 11 v Fig. 5: Contraint of the trailer parking problem. L c L State Control Contraint Equation of Motion Parameter x, y t c x Detail of Plant Coordinate of the center rear of the trailer Angle of trailer with x-axi Angle of the cab with x-axi Steering angle of the front wheel relative to cab orientation The loading dock i at x t The angle between the cab and trailer can't exceed 7 7 Limit of teering of the front wheel A r co( ) r L L c c[ t 1] m 14m 6m B A co( [ t] [ t]) c x[ t 1] x[ t] B co( [ t]) y[ t 1] y[ t] B in( [ t]) r in( ) c[ t 1] c[ t] arcin( ) L L t A in( c[ t] t[ t]) t[ t 1] t[ t] arcin( ) L t t c I then adjuted to repect the contraint on ditance front wheel move per time tep length of the trailer, from rear to pivot length of the cab, from pivot to axle t Defining the Fuzzy Set: In thi ection, we decribe how to define the fuzzy et for the problem in MATLAB. The fuzzy et in thi problem are: Fuzzy et for horizontal poition of the truck: Very right, right, middle, left, and very left Fuzzy et for the angle φ (degree), 6, 1, 18, 24,, and 6 Fuzzy et for the angle θ Hard right, right, oft right, traight, oft left, left, hard left. Figure 6 through 8 how the memberhip function defined in MATLAB: Fig. 6: Memberhip function for poition of the truck. 41

5 Aut. J. Baic & Appl. Sci., 5(11): , 11 Fig. 7: Memberhip function for the angle φ (degree). Fig. 8: Memberhip function for the angle θ. Overall, 5 fuzzy rule are defined a follow: Far Left:1 Left:2 Center: Right:4 Far Right:5 : 1 Soft Right:5 Right:6 Right:6 Hard Right:7 Hard Right:7 6 : 2 Soft Right: Soft Right:5 Right: 6 Hard Right:7 Hard Right:7 1 : Soft Left: Soft Left: Right: 6 Right: 6 Hard Right:7 18 : 4 Left: 2 Left: 2 Straight:4 Right: 6 Right: 6 24 : 5 Hard Left:1 Left: 2 Left: 2 Soft Right:5 Soft Right:5 : 6 Hard Left:1 Hard Left:1 Left: 2 Soft Left: Soft Left: 6 :7 Hard Left:1 Hard Left:1 Left: 2 Left: 2 Soft Left: Fig. 9: Fuzzy rule defined for the control problem. The program will run until the truck i parked at the deired dock or hit the wall in which cae the program will top running. The 5 fuzzy rule provided here uccefully generate a trajectory for truck movement from any initial tate to the final tate. The following are the output of the program for ome arbitrary initial tate: 42

6 Aut. J. Baic & Appl. Sci., 5(11): , 11 DOCK Start Point DOCK Start Point (a) (c) DOCK Start Point (b) DOCK Start Point (d) Fig. : Trajectorie determined by fuzzy controller for different initial tate (x,y,φ); a) (,,27); b) (5,,18); c) (,,2); d) (,4,-). And for trailer: Table 1: Fuzzy rule defined for the control problem. c t NE Negative RB Right below ZR Zero RU Right Upper PO poitive RV Right Vertical VE Vertical LV Left Vertical LU Left Upper LB Left Below LE LC CE RC RI x Left Left Center Center Right Center Right ZE Negative Big Negative Medium Negative Small Zero Poitive Small Poitive Medium Poitive Big Figure 11 through 14 how the memberhip function defined in MATLAB: Fig. 11: Memberhip function for poition of the trailer. 4

7 Aut. J. Baic & Appl. Sci., 5(11): , 11 Fig. 12: Memberhip function for the angle (degree). t Fig. 1: Memberhip function for the angle. c Fig. 14: Memberhip function for the angle. Overall,5 fuzzy rule are defined a follow: Talbe 2: Fuzzy rule defined for the control problem. t c NE ZR PO RB RU RV VE x LE LV LU LB 44

8 Aut. J. Baic & Appl. Sci., 5(11): , 11 t c NE ZR PO RB RU ZE RV VE x LC LV LU LB t c NE ZR PO RB RU RV VE ZE ZE ZE x CE LV LU LB t c NE ZR PO RB RU RV VE x RC LV LU ZE LB t c NE ZR PO RB RU RV VE x RI LV LU LB 45

9 Aut. J. Baic & Appl. Sci., 5(11): , 11 Fig. 15: Control urface for the fuzzy controller. The program will run until the trailer i parked at the deired dock or hit the wall in which cae the program will top running. The5 fuzzy rule provided here uccefully generate a trajectory for trailer movement from any initial tate to the final tate. The following are the output of the program for ome arbitrary initial tate: Fig. 16: Trajectorie determined by fuzzy controller for different initial tate. Deign of Fuzzy Controller for Backward Movement Through Moving and Fixed Obtacle: The procedure ued to detect the obtacle i explained in thi ection. Suppoe that two poition enor are intalled at the back of the truck a hown in the figure below. The green circle repreent the field of view for thee enor. Left and right enor are ued to detect the poition of obtacle relative to the truck poition. Figure 17 how the procedure ued for obtacle detection. A hown in figure 17: dc1<dc2 mean the obtacle i een at the left ide if the truck by the driver, and dc1>dc2 how an obtacle at the right ide (a een by the driver). The enor are able to detect any obtacle on their field of view. In practice, enor for ditance meaurement are ued for uch purpoe. dc1 dc2 dc1 dc2 Fig. 17: Senor placement and meaurement of the ditance and relative poition for obtacle. 46

10 Aut. J. Baic & Appl. Sci., 5(11): , 11 The two enor can detect the relative poition of the obtacle (e.g. whether the obtacle i placed at the right ide or left ide). For improving the accuracy, in fact, 8 enor are intalled on the vehicle. Figure 18 how the poition of thee enor: Fig. 18: Senor poition on the truck and trailer In practice, only four enor are activated in each tep baed on the relative poition of the obtacle (e.g. four enor are activated for right obtacle and four for left one). Let u denote the enor a follow. S 1 -S 2 : back enor placed at right and left ide, repectively; S -S 4 -S 5 - S 6 : enor placed at the right and left ide of the truck; and finally, S 7 -S 8 : enor intalled on the front of the truck at right and left, repectively. Thee enor meaure the ditance d 1 to d 8, repectively. Colliion avoidance in backward driving mode work on the following principle: if an obtacle i detected in truck way (either d1 or d2 i maller than predetermined detection limit ddet), firt, the turning direction (left or right) i determined the on the bai of d1-d4 (Fig.19). Fig. 19: Turning deciion making. Baed on thi deciion and orientation of the obtacle (that will be identified according to rear ditance enor reading) a temporary gate i projected onto the bounding wall in car turning direction (Fig. ). Note that preently, turning direction i choen according to rear enor reading only, a there are no relevant obtacle in car ide direction. Alo note that the oppoite turning deciion would reult in the temporary gate projected onto oppoite (upper) bounding wall. Fig. : Temporary driving goal. In forward driving mode the algorithm i baically the ame, only we are uing enor 5-8 intead of 4,, 2 and 1, repectively and the obtacle orientation angle β mut be corrected by 18 degree. 47

11 Aut. J. Baic & Appl. Sci., 5(11): , 11 Performance of the colliion avoidance ytem i ubject to the following parameter ddet - obtacle detection limit dexcl - rear enor reading larger than dexcl will be emulated by d + w, where d i the rear enor reading reponible for obtacle detection. dide - determine if ide enor information will be ued in turning direction determination (Fig.21). wr - the ditance by which the temporary gate i hifted from the obtacle projected line (Fig.21). State Tranition Control: We can peak of two tate in car control - normally car move toward (xf, yf, Φf) according to the tmupecified profile (tate ), however, when an obtacle i detected by ditance enor, colliion avoidance ytem (previou ection) take over and witche the temporary gate (tate 1). Thi temporary goal remain valid until it i afe to return to the normal tate. For overall good performance tate tranition control mut be mooth and effective. Thi i done in three tep a explained below. Fig. 21: State tranition diagram (backward driving mode). Truck Backward Movement Through Fixed and Moving Obtacle: If fixed obtacle are placed at the backward pathway of the truck, the truck mut adapt itelf with the contraint in order to reach the parking pot. What happen in practical cae, however, i that moving obtacle are alo preent on the pathway and the truck i required to take appropriate action while facing the obtacle whether fixed or moving. In the automatic parking mode, the truck not only hould be able to identify the environment, but alo hould avoid the obtacle. In a dynamic model, moving obtacle (uch a people or other object) change the environment. In order to follow an identified path, the truck hould be equipped with ome type of real time identification of it urrounding environment in order to meet the requet received from navigation ytem. An intelligent method i propoed here for navigating the truck in a dynamic environment uing fuzzy logic. Such ytem alo enable the truck to avoid obtacle. In [17] a controller wa ued for finding the path through fixed obtacle; here, two eparate fuzzy controller are ued a target finder and obtacle avoider which enable the truck to avoid moving obtacle a well. While no obtacle i cloe to the truck, the target finder determine the path toward the target (parking pot). A oon a an obtacle i detected, the obtacle avoider come to act. In the propoed method, when an obtacle i faced (a ituation which i called emergency here), the high-level controller determine the path in order to avoid obtacle. When the truck i far enough from obtacle, the control action i reduced to low level. Thi procedure repeat until the truck reache the target. The overall procedure i baed on the algorithm ued for fixed obtacle cae; however, few change are made in the avoiding procedure. Unlike other method, in the method propoed here the ingle controller i replaced by two controller at two level: one controller act at high-level a the upervior, while the other control the ytem at low level. In normal cae, the low-level control generate the command ignal and the upervior ha no role in the control proce. However, the latter i activated in emergency, cauing the former going back to inactive tate. When the condition are back to the normal tate, the low-level controller become activated and the upervior i inactive. Figure 22 how the block diagram for the propoed control method. 48

12 Aut. J. Baic & Appl. Sci., 5(11): , 11 Here, the target finder i defined a low-level controller, while the obtacle avoider act a high-level controller or upervior. A a reult, when no obtacle i detected (normal condition), the low-level controller direct the truck toward the target. Obtacle poition target poition Obtacle Avoider Target finder Vehicle ytem Vehicle poition Fig. 22: Block diagram for the propoed control method. A oon a an obtacle i detected (emergency), the obtacle avoider come to act in order to avoid colliion with the obtacle. When the truck i far enough from obtacle, the control action i reduced to low level. Thi procedure repeat until the truck reache the target. Contraint: There are everal contraint preent in the problem facing which the truck hould adopt the appropriate deciion in order to find the path toward parking pot. Obtacle Size: The ize of obtacle on the pathway could be different: The obtacle may be big enough to cover the whole pathway toward the target and given the initial tate, it i not poible to avoid the obtacle. In thi cae, the truck mut be topped. The obtacle may be mall enough to allow the truck to run it over! In thi cae, controller mut direct the truck to run over the obtacle. The ize of obtacle may be in a range that allow the truck to pa it by change in the direction and to make it way toward the parking pot. Poition of Obtacle: The poition of obtacle on the pathway i alo of great importance, ince the obtacle can: Be placed on the pathway in a way that do not provide the pace enough for the paage of the truck; in thi cae, it i not poible to avoid the obtacle. Be placed on the pathway in a way that allow the truck to pa through them by changing it direction and to reach the target. Low-Level Control: A mentioned earlier, target finder i defined a low-level controller. The low-level controller i the ame a the fuzzy controller ued for parking in the normal condition. target eeking Fig. 2: Fuzzy tructure for low-level controller for truck. phi theta Fig. 24: Fuzzy tructure for low-level controller for trailer. 49

13 Aut. J. Baic & Appl. Sci., 5(11): , 11 The tructure decribed above wa tudied in detail. High-Level Controller (Supervior): The obtacle avoider i deigned baed on a three-input two-output mamdani fuzzy ytem. The input are direct ditance between the truck and the nearet obtacle, the angle formed by the enor intalled on the truck front and the nearet obtacle, and the peed of the nearet obtacle relative to the truck peed. The output are rotation angle with repect to the truck axel and the truck peed. Figure 25 through 28 how the fuzzy tructure, and input and output memberhip function for the high-level controller. Fi.g 25: High-level fuzzy ytem. Fig. 26: The ditance between the truck and the nearet obtacle. Fig. 27: The angle formed between the truck and the nearet obtacle. Fig. 28: Relative peed of the nearet obtacle with repect to the truck. 4

14 Aut. J. Baic & Appl. Sci., 5(11): , 11 A hown in the figure above, memberhip function are defined a follow: Three memberhip function near, middle, and far are defined for the firt input to the fuzzy ytem (the ditance between the truck and the nearet obtacle) over the range [ m, 6 m] Seven memberhip function right -back (rb), right (r), right-front (rf), front (f), left-front (lf), left (l), and left - back (lb) for the econd input to the fuzzy ytem (the angle formed between the truck and the nearet obtacle), over the range [-18, 18 ]. Four memberhip function negative (n) (for the cae where the truck move away from obtacle), zero (z), poitive (p) (for the cae where the truck move toward obtacle), and very poitive (vp) for the third input to the fuzzy controller (the peed of obtacle relative to truck peed). And for upervior output: Fig. 29: The truck rotation angle. Fig. : Truck peed. Five memberhip function very right (vr), right (r), traight (z), left (l), and very left (vl) for the firt output from the fuzzy ytem (truck rotation angle) over the range [-45, 45 ] Five memberhip function low (), middle low (m), middle (m), middle quick (mq), and quick (q) for the econd output from the controller (truck peed) over the range [ cm/, cm/] If the truck i far from the nearet obtacle in front of the truck (farther than 6 m), or the truck i very near to the target (nearer than 1m), the truck will be controlled by the low-level controller. Otherwie, when the truck i near to obtacle, the upervior come to act to avoid the obtacle, change the direction, and reduce the peed to pa the obtacle. Once the obtacle i paed by, the peed increae again. Figure 1 decribe the angle and ditance between the truck and the obtacle. Direction Angel obtacle Ditance to the obtacle Direction Angle obtacle Ditance to the obtacle Fig. 1: Decription of the angle and ditance between the truck and the obtacle. 411

15 Aut. J. Baic & Appl. Sci., 5(11): , Simulation and Reult: To tet the propoed navigation method, imulation i performed uing MATLAB in different condition for the poition of the truck and moving and fixed obtacle. We tried to improve the truck movement through changing or weighting the fuzzy rule. Due to the low noie in the intalled enor in comparion to the minimum range of control input (maximum of 1 to 2 cm compared to 1 m), there i no need to conider the meaurement noie while modeling the controller. In the following line, the movement of the truck while facing obtacle moving with contant velocity i reviewed. The ign () i ued to denote the movement and peed of the truck. The pace between the tar repreent the change in the truck peed. The propoed algorithm i applied for a ituation coniting of two fixed obtacle and one moving with contant peed (however, there i no limitation on the number of fixed and moving obtacle). The algorithm may be applied for a greater number of obtacle moving with different velocitie. A it can be een, the fuzzy controller operate well in variety of condition. The following how the program reult for different condition. Number of moving and fixed can be increaed in the imulation. Figure 2 through 5 how the reult obtained from MATLAB imulation. Demo I - Fixed Obtacle: DOCK + Start Point 1 2 Fig. 2: Truck movement through fixed obtacle with different normal ize. Demo II -Fixed and Moving Obtacle: DOCK + Start Point 1 2 Fig. : Truck movement through two fixed obtacle with different normal ize and one moving obtacle.

16 Aut. J. Baic & Appl. Sci., 5(11): , 11 Demo III-Fixed and Moving Obtacle: Fig. 4: Trailer movement through two fixed obtacle with different normal ize and one moving obtacle. Demo IV-Moving Obtacle: Fig. 5: Trailer movement through nine moving obtacle. A New Approach for Parking the Truck: In thi tage, a tranmiion i being tated from one mode to another in different form. So far the main concern in olving the problem i that in deigning the feaibility of the problem be in oppoition with the optimality of the anwer, therefore, from now on, we focu on an anwer which, a far a poible, i optimum. Meeting the optimal condition call for a perfect invetigation of the mode pace, alo involve the calculation of contant function. Feedback plan are very powerful in gaining the path in typical pace, therefore optimality in feedback plan i conidered tage by tage and alternatively, but it i alo important that how, and by which action and reaction the contant problem turn to a dicrete one in the tatement of the problem. Depending upon the poition of the truck, parking in a pecific pace in ome place, i abolutely impoible Fig. 6: Firt it move forward to reach the appropriate point, and then it park. 41

17 Aut. J. Baic & Appl. Sci., 5(11): , 11 Conidering the exiting limitation in the path a crah with the wall, i inevitable. For example, in the following picture if the truck want a merely backward movement, with it big dimenion, it certainly cannot be located in the deired area. In the following the imulated output by MATLAB oftware could be oberved Fig. 7: Truck' failure in parking and it topping by the dimenion and limitation. In reality, locating the truck in thi poition doe not occur much. In thi mode, conidering truck' dimenion and limitation, a olution mut be found to olve the problem which could be called the Blind Point. Here the program and fuzzy rule were reformed in a way that firt the truck doe not regard one of it limitation (obligatory backward movement) and move forward to the point that it can come back to the parking area from the new point. Conidering it dimenion and the locating angel, the truck in normal condition cannot be placed in the parking area, therefore to olve the problem, firt it move forward to reach the appropriate point, and then it park Fig. 8: Conidering it dimenion and the locating angel, the truck in normal condition cannot be placed in the parking area, therefore to olve the problem, firt it move forward to reach the appropriate point, and then it park. A it could be een from the reult of the imulation, the truck firt pae the path forward and after reaching the deired area, i located in the parking (loading) point; In cae thi proce doe not occur, parking i impoible. In thi ection a fuzzy controller i alo ued. Thi controller meaure it ditance from the wall. If the meaured ditance by the related enor, two time exceed the truck' length, the firt controller i not ued and the operation i hifted to the econd fuzzy controller. The function of the econd and the third controller were invetigated thoroughly. 414

18 Aut. J. Baic & Appl. Sci., 5(11): , 11 A it could be een, in the following picture firt the truck take ditance from the wall, and then pae among the fixed obtacle. Filg: 9: Reult obtained from MATLAB imulation. Concluion: Uing earch table method, an appropriate fuzzy controller wa deigned to find a trajectory for parking a truck on a pathway with no obtacle. Then, a number of fixed and moving obtacle were added on the path. Baed on it adaptive performance, the fuzzy controller find an appropriate movement path through the fixed and moving obtacle. Simulation how a deired mooth movement of the truck. It may be uggeted then that if the ytem input are meaured with mall error and applied to the fuzzy controller, the propoed method can be applied in practice. Appendix: θ: the angle formed between wheel direction and horizontal axi φ: the angle formed between the truck direction and vertical axi x, y: current poition V: The truck ha a contant velocity of V. L: The length of the truck i L. t : Angle of trailer with x-axi : Angle of the cab with x-axi c x : The loading dock i at x t : The angle between the cab and trailer can't exceed 7 7 : Limit of teering of the front wheel c [ t 1] : I then adjuted to repect the contraint on t r : ditance front wheel move per time tep L : length of the trailer, from rear to pivot L c : length of the cab, from pivot to axl REFERENCES Dumitrache, I. and B. Catalin, Genetic learning of fuzzy controller, Mathematic and Computer in Simulation, 49: Imail, A. and E.A.G. Abu-Khoua, A Comparative Study of Fuzzy Logic and Neural Network Control of the Truck Backer-Upper Sytem, Proc. IEEE Int. Symp. On Intelligent Control, Dearborn, pp: Jenkin R.E. and B.P. Yuha, 199. "A Simplified Neural Network Solution Through Problem Decompoition: The Cae of the Truck Backer-Upper", IEEE Tran. Neural Network, 4(4): Kim, D., Improving the fuzzy ytem performance by fuzzy ytem enemble, FuzzySet and Sytem, 98:

19 Aut. J. Baic & Appl. Sci., 5(11): , 11 Kong S. and B. Koko, 19. "Comparion of fuzzy and neural truck backer-upper control ytem". Proc. IJCNN, : Kong, S.G., B. Koko, "Adaptive Fuzzy Sytem for Backing up a Truck-and-Trailer," IEEE Tran. on Neural Network, (5): Koza, J.R., "A genetic approach to the truck backer upper problem and the intertwined piral problem". Proc. Int. Joint Conf. Neural Network, Picataway, NJ, 4: -18. Nguyen, D. and B. Widrow, 19. "The truck backer-upper: An example of elf-learning in neural network," IEEE Contr. Syt. Mag., (2): Ramamoorthy, P.A. and S. Huang, Fuzzy Expert Sytem v. Neural Network - Truck Backer- Upper Control Reviited, Proc. IEEE, pp: Schoenauer M. and E. Ronald, "Neuro-genetic truck backer-upper controller. Proc.Firt Int. Conf. Evolutionary Comp., Orlando, FL, USA, pp: Shann, J.J. and H.C. Fu, A fuzzy neural network for rule acquiring on fuzzy control ytem, Fuzzy Set and Sytem, 71: Su, M.C. and H.T. Chang,. Application of neural network incorporated with realvalued genetic algorithm in knowledge acquiition, Fuzzy Set and Sytem, 112: Tanaka, K., T. Koaki and H.O. Wang, "Backing Control Problem of a Mobile Robot with Multiple Trailer: Fuzzy Modeling and LMI-Baed Deign". IEEE Tran. Syt.,Man, Cybern. Part C., 28(): Wang, L.X. and J.M. Mendel, "Generating fuzzy rule by learning from example," IEEE Tran. on Sytem, Man, and Cybernetic, 22(6):