Ship Steering Autopilot Based on ANFIS Framework and Conditional Tuning Scheme

Transcription

1 Marine Engineering Frontiers (MEF) Volme Isse 3, Agst 23 Shi Steering Atoilot Based on ANFIS Framework and Conditional Tning Scheme Sin-Der Lee *, Ching-Yaw Tzeng 2, Wen-Wei Hang 3 Deartment of Transortation Science, National Taiwan Ocean University Deartment of Commnications, Navigation and Control Engineering, National Taiwan Ocean University No.2 Pei-Ning Road, Keelng 2224,Taiwan R.O.C. * leesd@nto.ed.tw; 2 b2@nto.ed.tw; 3 M9767@nto.ed.tw Abstract The ever changing sea condition makes it difficlt to se a single mathematical model to describe the nonlinear dynamic behavior of a vessel. Hence, the erformance of model-based atoilots is generally inferior to that of modelfree designs sch as fzzy controllers or neral networks. This stdy combines the robstness roerty of fzzy logic controllers and the learning caability of artificial neral networks to create an ANFIS (Adative Network-based Fzzy Inference System) shi steering atoilot. In addition, a conditional tning scheme is resented to increase the resonse seed of the roosed atoilot, while simltaneosly redcing the overshoot. The erformance of the roosed atoilot is evalated by erforming a series of corse-changing and track-keeing simlations. The simlation reslts show that the roosed atoilot rovides a more adative and robst control erformance than a traditional PD fzzy controller nder tyical sea conditions. Keywords Fzzy Control; Adative Network-based Fzzy Inference System; Atoilot; Track-keeing Introdction The atomatic steering of shis dates back as far as the invention of the gyrocomass. One of the earliest gyro ilots was resented by Minorsky in the early 92s, in which a gyrocomass was sed to rovide heading measrements in order to enable the corse correction of atomatically steered bodies (Minorsky, 922; Skjetne, 23). Broadly seaking, modern atoilot control systems can be categorized as model-based, model-free or hybrid, deending on their mode of oeration. Amongst the model-based schemes, the linear-qadratic-gassian (LQG) atoilot resented by Holzhüter (997), the adative control scheme demonstrated by Åström and Wittenmark (989), the Internal Model Control (IMC) aroach roosed by Tzeng (999), and the H control system develoed by Morawski and Pomirski (998) are the most well known examles. Meanwhile, tyical examles of model-free atoilot systems inclde the fzzy control scheme roosed by Vaneck (997), the genetic algorithm-based shi steering control system develoed by McGookin et al. (2), the artificial neral network (ANN) berthing system resented by Zhang et al. (997), the sliding-mode tracking control of srface model vessel rosed by Ashrafion et al. (28) and the SISO and SIMO neral control schemes roosed by Hearn et al. (997). Finally, tyical examles of hybrid-tye atoilots inclde the IMC- ANN system resented by Tzeng and L (23), the fzzy-sliding mode control scheme roosed by Chen and Hs (23), the ANFIS (Adative Network-based Fzzy Inference System) scheme develoed by Stton et al. ( 997) and a vessel collision avoidance system sing ANFIS method resented by Ahn et al.(22). In ractice, it is virtally imossible to describe the nonlinear dynamic motion of a vessel in wavy conditions sing a single mathematical model. Hence, the erformance of traditional model-based atoilots is inevitably constrained by the effects of model ncertainty. However, fzzy controllers and ANN control schemes do not reqire an exlicit modeling of the lant and therefore roviding a better robstness and adative erformance than model-based methods. In fzzy control systems, the ott resonse is determined by a set of fzzy rles and membershi fnctions. In ractice, the design of the membershi fnction has a significant effect on the ott resonse of the fzzy controller. Ths, in imlementing fzzybased control schemes, it is essential that the membershi fnctions are roerly defined. Accordingly, the athors in (Jang, 993) resented an ANFIS (Adative Network-based Nero-Fzzy Inference System) framework, in which the fzzy logic controller was integrated with an ANN in order to learn the most aroriate membershi fnction arameters. 53

2 Marine Engineering Frontiers (MEF) Volme Isse 3, Agst 23 In the resent stdy, the ANFIS framework roosed in (Jang, 993) is alied to realize a fzzy-based shi steering atoilot. The erformance of the roosed atoilot is enhanced by means of a conditional tning scheme, designed to increase the resonse seed, while simltaneosly redcing the amont of overshoot via an aroriate tning of the int and ott gains of the fzzy controller. The effectiveness of the roosed atoilot is evalated by erforming a series of corse-changing and track-keeing simlations in a Matlab/Simlink environment. It is evident that the roosed ANFIS framework rovides a more adative and robst shi steering caability than a traditional PD fzzy controller. Track-keeing Gidance Method Figre illstrates the basic strctre of the shi steering atoilot develoed in the resent stdy. As shown, the track-keeing mission is accomlished throgh a series of corse-changing manevers, in which the conventional line-of-sight (LOS) gidance scheme is sed to calclate the reqired reference heading in each case. way-oints LOS Algorithm x,y ψ r + - Atoilot Control System δ Wind, Waves, Ocean Crrents Shi x,y ψ where (xk, yk) are the coordinates of the way-oint and (x(t), y(t)) are the ositional coordinates of the vessel. In erforming the track-keeing mission, the aim is to steer the vessel in sch a way that it enters the target zone at each way-oint along the reference ath. In accordance with the recommendations of Fossen (22), the radis of the target zone, R, is secified as aroximately two shi lengths. Once the vessel has entered the target zone, i.e., ( xk x( t)) + ( yk y( t)) R (2) the track-keeing atoilot atomatically selects the next way-oint ( x, y k+ k+ ) along the reference ath and resets the reference heading angle accordingly. Fzzy Control Aroach for Shi Steering Atoilot Fzzy systems have been widely alied in many fields, inclding signal rocessing, commnications, control and exert systems, and so on. Fzzy systems can be sed as either oen-loo controllers or closedloo controllers. Figre 3 shows a tyical closed-loo system. int + Fzzy Rle Base Fzzifier Fzzy Inference Engine Defzzifier Fzzy Controller Plant ott FIG. CONFIGURATION OF PROPOSED TRACK-KEEPING AUTOPILOT SYSTEM X x k x(t) y(t) ψ ref y k Target zone R Way-oint FIG. 2 LOS GUIDANCE CONCEPT Figre 2 resents a schematic illstration of the LOS concet. Basically, the LOS is an imaginary line stretching between the vessel and the target (a wayoint marker in the resent case). To reach this wayoint, the vessel mst adjst its heading via a reference heading angle ψ, given by ψ ref yt () k ( t) = tan ( ) ref x xt () k y Y () FIG. 3 BASIC CONFIGURATION OF CLOSED-LOOP FUZZY CONTROL SYSTEM In imlementing a fzzy control system, the realvaled int is fzzified by a fzzifier and rocessed by the fzzy inference engine in accordance with a set of fzzy rles. The ott of the fzzy interference engine is then defzzified and slied as a control signal to the lant. As discssed in Section (Introdction), the erformance of a fzzy system is deendent not only on the fzzy IF-THEN rles, bt also on the design of the membershi fnctions, e.g., Trianglar, Gassian (Pi), S-fnction, and so on (Wang, 25). Having rocessed the fzzified int, the ott of the fzzy inference engine is defzzified sing one of several different methods, inclding Max Grade, Maximm, Center of Area, Center of Average, or Height and Center of Sms (Wang, 25). Throgh these rocesses, there is an imortant advantage that the fzzy systems theory is rovided a systematic rocedre for transformation of the knowledge base into a nonlinear maing. 54

3 Marine Engineering Frontiers (MEF) Volme Isse 3, Agst 23 ψ + r e e K K2e E de Fzzy K X C Shi ψ FIG.4 PD-TYPE FUZZY CONTROLLER STRUCTURE The atoilot system develoed in the resent stdy is based on the PD-tye fzzy controller strctre shown in Fig. 4. Note that ψ r is the reference heading angle calclated sing the LOS gidance scheme, e is the heading error signal, E and de are the int heading error and yaw error, resectively, is the defzzified control signal, Xc is the ott command, and ψ is the system ott. As shown, the controller has two int gains ( Ke and Ke 2 ) and one ott gain ( K). The int gains ma the ints of the fzzy system to the int niverse of discorse, while the ott gain scales the ott of the controller to the ott niverse of discorse. It is noted that for all three gains, the niverses of discorse are normalized in the range of [-, ]. For the shi steering controller develoed in the resent stdy, the niverse of discorse for the int heading error is secified as [-6, 6 ], while that for the int yaw error is set as [-4 /s, 4 /s] and that for the ott rdder command is chosen as [-35, 35 ]. In addition, the widths of the niverses of discorse for the int heading error and yaw error are both set as [-6, 6], while that of the niverse of discorse of the ott rdder command is set as [-7, 7]. As a reslt, the defalt settings for the two int (normalizing) gains are K = 6/6 =. and K2 = 6/4 =.5, resectively, while that for the ott gain (scale factor) is K = 35/7 = 5. Finally, the fzzy controller is imlemented sing the Max-Min Comosition fzzy inference method and the Center of Gravity defzzifier (Wang, 25). Figres 5 ~ 7 illstrate tyical membershi fnctions for the heading error, yaw error, and rdder command, resectively. Meanwhile, Table shows the fzzy rles sed by the fzzy controller in determining the rdder commands reqired to accomlish the corsechanging and track-keeing manever. FIG.5 MEMBERSHIP FUNCTIONS OF HEADING ERROR E FIG.6 MEMBERSHIP FUNCTIONS OF YAW ERROR de FIG.7 MEMBERSHIP FUNCTIONS OF RUDDER COMMAND TABLE. FUZZY CONTROL RULES de E NB NM NS ZE PS PM PB NB NB NB NB NB NM NS ZE NM NB NB NB NM NS ZE PS NS NB NB NM NS ZE PS PM ZE NB NM NS ZE PS PM PB PS NM NS ZE PS PM PB PB PM NS ZE PS PM PB PB PB PB ZE PS PM PB PB PB PB ANFIS Aroach for Shi Steering Atoilot The ANFIS method is the main research of Jang s PhD thesis (Jang, 992). These techniqes rovide a tool to learn information from reared data bank for the fzzy modelling rocess. The otimization and adatation of many arameters in fzzy inference system rles can be imlemented throgh the learning rocess of artificial neral network. In this section, the erformance of the fzzy-based shi steering atoilot described in Section III is enhanced by means of an ANFIS (Adative Network-based Fzzy Inference System) framework, in which the membershi fnctions of the fzzy inference engine are otimized by an artificial neral network (ANN). In this stdy, ANFIS ses a hybrid learning algorithm to identify the membershi fnction arameters of two ints with single-ott, the fzzy conseqences of first-order Sgeno tye rles of the form: If x is A and x2 is B then δ = x + qx2 + r (3) where x and x2 are the int vector, δ is the ott vector and {, q, r} are the conseqent arameters of this rle. The membershi fnction arameters will be tned by sing the ANFIS method. Figre 8 illstrates the first order Sgeno fzzy model with corresonding ANFIS layer architectre. A total five layers strctre was adoted in the ANFIS design rocess. Note that O,ij denotes the ott of the i-th 55

4 Marine Engineering Frontiers (MEF) Volme Isse 3, Agst 23 node with j-th member set in the first layer. as the conseqent arameters. Layer 5 The single node in this layer calclates the overall otts as the smmation of all incoming signals: O 5, P = = P = w f = P = w f The constrcted adative network in Fig. 8 is fnctionally eqivalent to a fzzy inference system. w (8) FIG.8 LAYER STRUCTURE OF ANFIS Layer Each node in this layer will generate a membershi grade of a lingistic label. For examle, the node fnction of the i-th node may be a generalized bell membershi fnction as follow: O, ji = µ j ( xi ) = x 2 ji i c b ji + a ji (4) for i =, 2,..., N; j =, 2,..., M i where xi is the int to node I; µ ( x ) is the lingistic label (small, large, etc.) associated with this node; {aji, bji, cji} is the arameter set. Parameters in this layer are referred to as remise arameters. Layer 2 Each node in this layer labelled Π which mltilies the income signals and sends the rodct ot. For examle, N O2, = w = µ j ( x ) i i i= (5) for ji =,..., Mi; =,..., P where w reresents the firing strength; T-norm oerators that erform generalized AND can be sed as the node fnction in this layer. Layer 3 Each node of this layer comtes the roortion of the rle s firing strength to the sm of all rles firing strengths: w O3, = w = P w (6) = Layer 4 Each node in this layer has the following fnction: 4, = = O wf w x + qx 2 + r (7) where w is the ott of layer 3, {, q, r} is the arameter set. Parameters in this layer are referred to j i Figre 9 illstrates the basic configration of the ANFIS atoilot. As shown in Fig., the ANN comrises two ints (corresonding to the heading error and yaw error, resectively) and one ott (corresonding to the rdder command). The ANFIS arameters otimization method otions available for Fzzy Inference System training are hybrid and backroagation. Error tolerance is sed to create a training stoing criterion, which is related to the error size. ψ + r e e K K2e E ANFIS K de X C Shi ψ FIG. 9 BASIC CONFIGURATION OF ANFIS SHIP STEERING AUTOPILOT FIG. ANN USED TO TRAIN MEMBERSHIP FUNCTIONS OF ANFIS SHIP STEERING AUTOPILOT Three membershi fnctions are assigned to each int, and ths a total of nine fzzy rles are reqired (as indicated by the ble circles in Fig. ). Note that for both the int nodes and the ott node, the membershi fnctions have the form of a generalized bell shae. In otimizing the arameters of the membershi fnctions sing the ANFIS framework, it is desirable to se heading and rdder command data obtained from real-world track-keeing manevers. However, for reasons of cost and racticality, the int and 56

5 Marine Engineering Frontiers (MEF) Volme Isse 3, Agst 23 ott data sed in the resent stdy were obtained from nmerical simlations erformed sing the fzzy shi steering atoilot described in reviosly Section. The otimal vales of the membershi fnction arameters were determined via a training rocess erformed sing a back-roagation (BP) algorithm based on the gradient steeest descent method. Dring the training rocess, the error was qantified sing a least-sqares metric. Note that the error was defined as the difference between the training data (ott rdder command) and the ANFIS ott command. The training rocess terminated once the error redced to a vale less than.. The training rocedre was erformed sing 75% of the data generated in the fzzy controller simlations. Having trained the ANFIS framework, it was tested sing the remaining 25% of the simlation data Fzzy Corse Controller Vessel simlation trajectory Initial osition range of heading changes and rdder commands, the fzzy controller simlations rerodced the ±4 zigzag trajectory shown in Fig.. The corresonding heading angle and rdder commands issed by the fzzy atoilot are shown in Fig. 2. The total simlation time was set as seconds, while the samling rate was set as. seconds; giving a total of airs of I/O data for training and testing roses. It is to be noted that the training data was withot wave distrbance. The main rose is to show the ANFIS system robstness of distrbance rejection. Figres 3 and 4 show the ntrained membershi fnctions of the heading angle error and yaw error, resectively. Figres 5 and 6 show the eqivalent membershi fnctions following the training rocess. Finally, Fig. 7 shows the overall int-ott contor lot of the ANFIS controller. In another way, the Fig.7 reresents the control srface, the widely sed the center of area method strategy generates the center of gravity of the ossibility distribtion of a control action FIG.3 UNTRAINED MEMBERSHIP FUNCTION OF E FIG. SIMULATED VESSEL TRAJECTORY (±4 ZIG-ZAG) 5 4 Fzzy Corse Controller 4 deg Zig-Zag Simlation FIG.4 UNTRAINED MEMBERSHIP FUNCTION OF de 3 2 Rdder command FIG.5 ANFIS TRAINED MEMBERSHIP FUNCTION OF E Time (sec) FIG.2 HEADING ANGLE AND RUDDER COMMAND RESPONSE DURING SIMULATED ±4 ZIG-ZAG TRACK- KEEPING TASK In order to train the ANFIS controller over a wide FIG.6 ANFIS TRAINED MEMBERSHIP FUNCTION OF de 57

6 Marine Engineering Frontiers (MEF) Volme Isse 3, Agst Fzzy Corse Controller 7 6 ANFIS Corse Controller Degree(deg) 3 Degree(deg) Time(s) Time(s) FIG.7 I/O CONTOUR PLOT OF ANFIS CONTROLLER Simlation Trials and Reslts The steering caabilities of the fzzy-based atoilot (Section 3) and trained ANFIS atoilot (Section 4) were evalated by erforming a series of simlated corse-changing and track-keeing tasks sing a Nomoto shi model with a length of 5 m and breadth of 22 m. In accordance with the shi model, the rdder gain was secified as k=.32 (sec - ) and the time constant was set as T= 34.2 (sec). In erforming the simlations, it was assmed that the vessel was ertrbed by the following wave distrbance, generated by assing a white noise throght a second order shaing filter given by Fossen (22) as follows: K ( ws do = )* ws ( ) 2 s + 2ξ ws e + w (9) e in which do reresents the ott distrbance, ξ is the daming coefficient; we is the wave enconter freqency; and K w is a wave intensity constant, and deends on the dominant wave freqency, the forward seed of the shi, and the angle between the heading of the shi and the direction of the waves. This aroach has an advantage as its simlicity for simlation roses. In the crrent simlations, ξ, w e and K w were assigned vales of.5,.6 and 2.5, resectively, which reslted in a narrow band tye of distrbance to the vessel and indced abot ±8 heading error of distrbance. It gave a good qalited descrition of irreglar waves. However, additional research is reqired to find a general exression between the sea-state arameters, the vessel dynamics and the distrbance model arameters. Corse-Changing Task Withot Wave Distrbance Figre 8 shows the simlation reslts obtained for the heading angle and rdder resonse of the fzzy and ANFIS atoilots when erforming a simle 6 corse-changing manever in the absence of environmental distrbances. As discssed in Section 3, the niverse of discorse for the int heading error of the fzzy controller was secified as [-6, 6 ]. FIG.8 HEADING ANGLE AND RUDDER RESPONSE OF FUZZY AUTOPILOT (LEFT) AND ANFIS AUTOPILOT (RIGHT) WHEN PERFORMING 6 COURSE-CHANGING TASK IN ABSENCE OF WAVE DISTURBANCE Moreover, the ANFIS atoilot was trained sing the I/O data obtained from the fzzy atoilot. Ths, as shown in Fig. 8, the heading angles and rdder resonses of the two atoilots are very similar Fzzy Corse Controller FIG.9 HEADING ANGLE AND RUDDER RESPONSE OF FUZZY AUTOPILOT WHEN PERFORMING 2 COURSE-CHANGING TASK IN ABSENCE OF WAVE DISTURBANCE ANFIS Corse Controller FIG.2 HEADING ANGLE AND RUDDER RESPONSE OF ANFIS AUTOPILOT WHEN PERFORMING 2 COURSE-CHANGING TASK IN ABSENCE OF WAVE DISTURBANCE Figres 9 and 2 show the heading angle and rdder resonse of the fzzy atoilot and ANFIS atoilot, resectively, when erforming a 2 corse-changing task (Note that the effects of environmental distrbances are once again neglected). It is observed that the heading resonse of the fzzy atoilot exhibits a greater overshoot than that of the ANFIS atoilot and takes a longer time to reach steady-state conditions. This reslt is to be exected since the int heading error (2 ) lies otside of the original 58

7 Marine Engineering Frontiers (MEF) Volme Isse 3, Agst 23 niverse of discorse [-6, 6 ], and ths the fzzy controller rovides a less recise and slower resonse. In general, the reslts resented in Figs. 9 and 2 show that the ANFIS atoilot rovides a more robst and efficient erformance than the fzzy control system de to the overshot angle in Fig.2 less than which shown in Fig. 9 and even the steady state erformance of ANFIS better than it shown in Fig.9. Conditional Tning of ANFIS system X: 64.4 Y: 9.37 ANFIS Controller (K2=.) FIG.2 HEADING ANGLE AND RUDDER RESPONSE OF ANFIS AUTOPILOT WHEN PERFORMING 8 COURSE-CHANGING TASK GIVEN K 2= X: 7.3 Y: 86.9 ANFIS Controller (K2=.5) FIG.22 HEADING ANGLE AND RUDDER RESPONSE OF ANFIS AUTOPILOT WHEN PERFORMING 8 COURSE-CHANGING TASK GIVEN K 2= ANFIS Controller (K2=.4) demonstrated that the ANFIS controller rovides a better control erformance than the traditional PDtye fzzy controller. The resent section rooses a conditional tning scheme for frther imroving the resonse seed of the ANFIS controller, while simltaneosly redcing the overshoot. The normalizing gains K, K2 and the scale factor K have been shown in the Fig.4 (Fzzy) and Fig.9 (ANFIS) which have the caability to change the int and ott niverse of discorse ranges. If this advantage can be flly tilized, then the erfect controller may be achievable. To evalate the effect of the yaw error gain on the resonse time and overshoot of the ANFIS controller, the int heading error gain and rdder command gain were assigned constant vales of K=.75 and K=5, resectively, while the yaw error gain was assigned vales of K2=.,.5 and.4. The corresonding simlation reslts for an 8 corsechanging task are resented in Figs. 2 ~ 23, resectively. Comaring the three figres, it is seen that the system overshoot redces with an increasing vale of K2, bt the resonse time increases. Accordingly, the erformance of the ANFIS atoilot roosed in Section IV has been enhanced by means of the conditional tning strctre shown in Fig. 24; designed to atomatically switch the normalizing gains and scale factor by re-testing the resonse effect. This is the main idea to design the conditional tning of ANFIS system in which the better erformance can be achieved simlataneosely both increasing the resonse seed and redcing the system overshoot. ψ r + e K e K e 2 E de ANFIS K Main Controller K 2 e K e 22 E de ANFIS 2 K 2 Condition Controller Switch Box Shi ψ FIG.23 HEADING ANGLE AND RUDDER RESPONSE OF ANFIS AUTOPILOT WHEN PERFORMING 8 COURSE-CHANGING TASK GIVEN K2=.4 Ideally, any controller shold rovide a raid resonse and no overshoot. The revios section has FIG.24 BASIC STRUCTURE OF CONDITIONAL TUNING ANFIS CONTROLLER As shown in Fig. 24, the conditional tning ANFIS atoilot has a arallel strctre. In other words, only a single ott command is issed to the control lant. It is also noted that the switch box is connected to the int error signal. That is, the controller resonse deends on the magnitde of the error signal. In the 59

8 Marine Engineering Frontiers (MEF) Volme Isse 3, Agst 23 resent simlations, an error signal range of ± was taken as a trigger in activating ANFIS 2 in Fig. 24. Secifically, if the absolte vale of the error signal was less than, the original gains of the ANFIS atoilot (i.e., ANFIS ) ket nchanged. However, if the absolte vale of the error signal was greater than (i.e., the system resonse needs to work harder than before), so the critical condition can be sed to seed the system resonse and sacrifice some system erformance sch as overshoot. In other words, the normalized and scaling gains of the ANFIS atoilot were conditioned in sch a way as to accelerate the system resonse at the exense of a slightly higher overshoot Conditional tning ANFIS controller Time s) FIG. 26 HEADING ANGLE AND RUDDER RESPONSE OF CONDITIONAL TUNING ANFIS CONTROLLER WHEN PERFORMING 8 COURSE-CHANGING TASK IN PRESENCE OF EXTERNAL DISTURBANCES X: 55.7 Y: 83.3 Conditional tning ANFIS controller 6 4 Conditional Tning ANFIS Controller FIG.25 HEADING ANGLE AND RUDDER RESPONSE OF CONDITIONAL TUNING ANFIS CONTROLLER WHEN PERFORMING 8 COURSE-CHANGING TASK IN ABSENCE OF WAVE DISTURBANCE Figre 25 illstrates the simlated resonse of the conditional tning ANFIS atoilot when erforming an 8 corse-keeing task in the absence of wave distrbances. It can be seen that the controller achieves both a raid resonse time and a redced overshoot. Based on insection, the total overshoot angle is jst 3.3, while the resonse time is less than 5 seconds. By contrast, nder the original ANFIS control scheme, the overshoot angle and resonse time are.3 degree (see Fig.2) and more than 5 sec (see Fig. 23), resectively. Ths, the serior erformance of the conditional tning ANFIS framework is confirmed. Figre 26 shows the resonse of the conditional tning ANFIS controller when erforming the 8 corsechanging task in the resence of wave distrbances. Meanwhile, Fig. 27 shows the resonse of the conditional tning ANFIS controller when erforming the ±4 zig-zag track-keeing task in the resence of wave distrbances. It is evident that the heading resonses of both corse keeing (in Fig. 26) and zigzag track-keeing missions (in Fig. 27) were fitted to the task nder the wave distrbances FIG. 27 RESPONSE OF CONDITIONAL TUNING ANFIS CONTROLLER DURING ±4 ZIG-ZAG TRACK-KEEPING TASK Finally, the erformance of the conditional tning ANFIS controller was evalated by simlating the track-keeing mission shown in Fig. 28 in the resence of external distrbances. The corresonding heading angle and rdder resonse are shown in Fig Conditional Tning ANFIS Controller Track-Keeing Manever with Distrbance wayoint 4 Vessel Trajectory Initial Position Wayoints wayoint 5 wayoint 8 wayoint 3 wayoint 9 wayoint 6 wayoint 7 wayoint 2 wayoint FIG. 28 TRACK-KEEPING MISSION VESSEL TRAJECTORY Figre 3 shows the overla track-keeing mission vessel trajectories with three different kinds of controller. Figre 3 illstrates the ath deviation distribtion for the 3 way-oints track-keeing mission. It is observed that the deviation made by the 6

9 Marine Engineering Frontiers (MEF) Volme Isse 3, Agst 23 conditional tning ANFIS oterforms the others Conditional Tning ANFIS Controller Track-Keeing Manever with Distrbance FIG.29 RESPONSE OF CONDITIONAL TUNING ANFIS CONTROLLER DURING TRACK-KEEPING TASK IN PRESENCE OF EXTERNAL DISTURBANCES The simlation reslts reveal that the roosed concet has the better robstness than the original ANFIS system, and secifically, confirm that the tracking erformance, resonse seed and overshoot angle are all satisfactory. In other words, the robstness and efficiency of the roosed conditional tning ANFIS atoilot are confirmed. 3Kinds of Controller Track-Keeing Manever with 3 Wayoints ANFIS Fzzy Conditional Tning ANFIS wayoint 3 wayoint wayoint FIG.3 TRACK-KEEPING MISSION VESSEL TRAJECTORIES OF DIFFERENT KINDS OF CONTROLLER Deviation Conclsions Vessel Trajectory Deviation Fzzy ANFIS Conditional Tning ANFIS Time (sec) FIG.3 THE PATH DEVIATION DISTRIBUTION This stdy has develoed a shi steering atoilot based on an ANFIS (Adative Network-based Fzzy Inference System) control scheme. The atoilot reqires two ints, namely the heading angle error and the yaw angle error, and rovides one ott, namely the rdder command. In designing the ANFIS atoilot, the membershi fnctions are otimized by an Artificial Neral Network (ANN) sing the int and ott data obtained from a series of corsechanging simlations erformed sing a traditional PD-tye fzzy atoilot. The erformance of the roosed atoilot has been evalated by erforming a series of corse-changing and track-keeing simlations. It has been shown that the ANFIS atoilot oterforms the conventional PD fzzy atoilot in terms of both a lower overshoot and a more raid resonse. In addition, it has been shown that the erformance of the ANFIS atoilot can be frther imroved by means of a conditional tning scheme, in which the gains of the atoilot are adjsted adatively in accordance with the magnitde of the int error signal. The roosed conditional tning scheme can increase the resonse seed of the roosed atoilot and redce the overshoot simltaneosly. In a ftre stdy, the ractical feasibility and robstness of the roosed conditional tning ANFIS atoilot will be verified by erforming a series of track-keeing manevers sing a small boat in a real-world harbor setting. REFERENCES Ahn, J.H., Rhee, K.P. and Uo, Y.J. A stdy on the collision avoidance of a shi sing neral networks and fzzy logic, Alied Ocean Reserch, Vol , 22. Ashrafion, H., Mske, K.R., McNinch, L.C. and Soltan, R.A. Sliding-mode tracking control of srface vessels, IEEE Transactions on Indstrial Electronics, Vol. 55, Isse,.44-42, 28. Åström, K.J. and Wittenmark, B., Adative Control, Addison-Wesley, Massachsetts, 989. Chen, S.L., and Hs, W.C. Fzzy-sliding mode control for shi roll stabilization, Asian Jornal of Control, Vol. 5, Isse. 2,.87-94, 23. Fossen,T.I., Marine Control Systems: Gidance, Navigation, and Control of Shis, Rigs and Underwater Vehicles, Marine Cybernatics, Trondheim, Norway..5, 22. Hearn, G.E., Zhang, Y., and Sen, P. Comarison of SISO and SIMO neral control strategies for shi track keeing, IEE Proceedings-Control Theory Alications, 6

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