High Accurate Positioning Technique for AUV

Transcription

1 High ccurate Positioning Technique or U TIN-SOU TSY Department o eronautical Engineering National Formosa University 64, Wen-Hua Road, Huwei, Yunlin, 68 TIWN tstsay@nu.edu.tw bstract: -In this paper, a high accurate positioning technique is proposed or autonomous underwater vehicle(u). It needs not position correction rom Global Position System (GPS) above the sea surace and short- or long-baseline acoustic positioning system(sbl or LBL) under the sea. Two long time experiments gave maximal and average deviations are less than.6m and 5.m respectively. Position deviations are veriied by tracking datum o a long-baseline acoustic position system with post navigation processing datum. These deviations are much less than the tracking range o sonar. High accurate positioning results let vehicles have less supporting rom launching vessel and give lexible and mobile operations. Key-Words: -Position estimation, Navigation and guidance, utonomous underwater vehicle. Introduction Two types o unmanned underwater vehicles are in use: Remotely Operated ehicle (RO) and utonomous Underwater ehicle (U). ROs are teleoperated through a cable, which supplies power to the vehicle. The drag on the cable and power transmission losses through the cable increase with increase in the operating range o the vehicle. Us do not have such limits, and have a wide scope o operation as they carry their power supply onboard. s there is no external communication or guidance, and power available is limited, mission planning and navigation are extremely critical or successul operation o Us. Unmanned underwater vehicles are used to perorm exploration, survey, monitoring and data collection task that reduce ship cost and human risks []. Generally navigation requirements or survey U [] are () mission programming to ollow a predetermined survey area (or survey grid) load to the U () mission positioning accuracy o to 4 meters () data positioning accuracy o 5 to meters (4) capable o using position updated rom acoustic positioning, e.g. short-baseline (SBL) or long-baseline (LBL) positioning systems [, 4] transmitted rom the support vessel, seabed beacons (5) preerably capable o using position updates orm global position system (GPS) when on the sea surace [5, 6]. The position o the U stated above plays a central role in guidance and control or engaging or searching underwater targets. This is due to the short-range detection o sonar in noisy environment or water clarity or imaging sensors(camera) and there is no position correction technique can be applied rom surace (e.g., GPS) or inertial navigation system (INS). The GPS is widely used or positioning above the sea surace. However, the strength o the electromagnetic wave rom GPS satellite is decayed rapidly in the water. Thereore, GPS is not applicable in the deep water. However, the initial position o the U can be corrected by GPS beore launch and give good mission plan positioning accuracy. Similar to the positioning techniques o the GPS, the LBL (or SBL) is normally used or submersed vehicles [, 6]. The sound wave replaces the electromagnetic wave or distance measurements. It needs one transponder in submersed vehicle and at least other three transponders mounted on the seabed. The distances between transponders are dependent on the power o the acoustic signal and may be up to 4m [4]. The accuracy o the LBL may up to 5m with positions o transponders are corrected by GPS. However, the LBL system is hard to install and maintain. It needs long time to install and recovery transponders on the new operating area. The operating time and range o transponders are limited rom the capacity o battery. Thereore, good position accuracy o the ISSN: Issue, olume 4, January 9

2 underwater vehicle without LBL is generally expected or lexible and mobile applications. Note that it is impossible to install the LBL system on the battleield or military applications. Position datum o the on-board INS is generally not applicable ater long-time operation (e.g., >hour). This is due to senor device alignment accuracy, gyro drit, and accelerometer accuracy. Maximal detection range o the on board active sonar or compact vehicle in deep water is about m. The detection range may be reduced to be about or less than m in the shallow water [7, 8]. Corresponding to m deviation in one hour, typical speciications o the INS[5] are: (a) Installation accuracy (σ ): rolling, pitching and yawing axes in.5deg (b) Gyro accuracy ( σ ): bias drit in.5deg/hr (c) accelerometer accuracy ( σ ):.mg. They are expensive. In this work, chipper components with accuracies reduced order one will be used. Since the vehicle depth can be measured by the depth meter, thereore much attention is paid or lateral deviations. Lateral deviations due to rolling gyro drit, rolling installing error, and accelerometer accuracy versus time t are unction o t,t,t respectively. Thereore, pure INS without correction becomes not applicable ater long-time operation. nother unpredictable parameter or positioning is the sea current. It is dependent on the moon and wind. For example, constant.5m/s (~knot) current gives ~8m position deviation ater one hour. It is usually greater than the detection range o the active sonar [8]. Thereore, other stable positioning techniques must be applied to get a non-diverging position datum or U operations. Rolling speed o the propelling motor, depth measurement o depth meter, estimated current inormation and low-cost rate gyros and accelerometers with state observers will be used to estimate the vehicle position. The attitude angles are low drit datum (e.g.,.5deg/hr). The accuracy o depth meter is between 5cm and 5cm. The vehicle steady-state speed is proportional to the rolling speed o the propelling motor. Depth measurement and motor rolling speed are two bounded data. Experiments or veriying the proposed positioning method are perormed. The operation time is 78sec. The vehicle was tracked by LBL. The proposed method gave maximal deviation is equal to.6m and average deviation is equal to 5.m with respect to LBL tracking datum. However, the INS gives 54m deviation. nother 76sec experiment gave maximal deviation is equal to 5.6m and average deviation is equal to.8m. These deviations are much less than the tracking range o the sonar. Thereore, the proposed method lets the U become a real autonomous vehicle system with less supporting rom launching vehicle. This paper is organized as ollows: Section describes the considered U, equations o motion, evaluates the small signal dynamic models and propelling model or 6-DOF simulations and autopilot designs Section perorms the adaptive autopilot designs Section 4 proposes the positioning techniques Section 5 gives the experimental and comparison results. System description and small signal dynamic modeling Fig. shows the coniguration and coordinate deinitions o the considered underwater vehicle. The physical dimension is compatible to that o the MK-48 torpedo (579cm long 5.cm diameter 545kg weight). The central o gravity (CG) is 5.4cm below the central o buoyancy (OB). Thereore, the rolling axis is inherent stable and major control eorts are paid or pitching/yawing controls. The ront propeller has seven leaves and rear propeller has ive leaves. They are actuated by two counter direction electric motors or rolling torque balance. Figure. Coordinate system o the underwater vehicle. Equations o motion are generally derived in the body coordinate rame. In this work, the mass, added mass and damping matrices are assumed be diagonal. Equations o motion o an underwater vehicle in six degree o reedom (6DOF) can be ISSN: Issue, olume 4, January 9

3 written as in the orm o [9] & η J ( η ) v & η J ( η ) v M v& C( v) v M v& C ( v ) v D ( v ) v C ( v ) v τ D ( v ) v g ( η ) τ () where η [ x y z] T, η [ φ θ ψ ] T, v [ u v w] T, v [ p q r] T. The symbols φ, θ, ψ p, q and r denote the roll, pitch and yaw angles and angular rates while x, y, z, u, v and w are the surge, sway and heave displacements and velocities respectively. The terms J ( η ), J ( η ), M, C ( v ), D ( v ), M, C ( v ), D ( v ) and g ( η ) denote the kinematical transormation, mass, Coriolis, damping matrices including the added mass eect, and the restoring vector, respectively. The kinematical transormation matrices in roll, pitch, and yaw are deined as cθcψ sφsθcψ cφsψ cφsθcψ sφsψ J ( η ) cθsψ cφcψ sφsθsψ cφsθsψ sφcψ () sθ sφsθ cφcθ sφtθ cφtθ J ( η ) cφ sφ () sφ / cθ cφ / cθ where c cos( ), s sin( ) and t tan( ). The mass matrices are M diag( m, m, m ). M diag( m m, ). (4), m where the positive constant terms m jj, j 6, denote the vehicle mass including added mass in surge(x), sway(y), heave(z), pitch and yaw. The Coriolis matrices are mw mv C ( v) mw mu (5) m v mu m66r m55q C ( v ) m66r m44 p (6) m 55q m44 p The damping matrices are i i D ( v ) diag d dui u, d dvi v, d d i i i i wi w i i D ( v) diag d44 d pi p, d55 dqi q, d66 d i i i i ri r (7) (8) where d jj,d ui,d vi,d wi,d pi,d qi, d and j 6, i,, represent the hydraulic-dynamic damping in surge, sway, heave, roll, pitch and yaw. The restoring orce vector is g η ) [ ρg GM sin( φ) ρg sin( ) ] T (9) ( T GM L θ where ρ, g,, GM T and GM L are the water density, gravity acceleration, displaced volume o water, transverse metacentric height and longitudinal metacentric height respectively. The available inputs are [ ] T τ, τ [ τ τ τ ] T τ u ri p q () r where τ u, τ p, τ q and τ r are the control orce in surge and torques in roll, pitch and yaw respectively. They are applied rom two counter direction propellers actuated by electric motors and our cruciorm tail ins( δ, δ, δ, δ ) at, 9, 4 8, 7. The relationship between rolling/pitching/ yawing channel actuating angles ( δ p, δq, δr ) and our in angles ( δ, δ, δ, δ ) is 4 δp / / δq / δr / / δ δ / δ δ 4 δ δ δ δ 4 δp δq δr () The small-signal perturbation models o three angular rates ( p,q, r ) and two accelerations ( w &, v& ) rom control eorts ( δ p, δq, δr ) or dierent operating speed ( m u v w in m/s) around trims ( α, β ) (, ) are given below: nm p p δp s p q δq s w& δq v& δq d m qn m s qnm r rn m s rn m qdm s qd δ m r s rd ms rd m 4 wnm s wn ms wnm s wdm s wd m 4 vnm s vn m s vnm s vd ms vd m () ll coeicients given in Eq.() are positive values. They give the considered system is an unstable open-loop system in pitching and yawing channels. Thereore, they need stable compensation and gain adaptation or autopilot according to the vehicle speed ( m ). ISSN: Issue, olume 4, January 9

4 The vehicle will approach to a steady-state speed ( ms ) ater the propelling orce and drag are balanced. That is, a rolling speed o propelling motor ( M spd ) corresponding to a steady-state vehicle speed ( ms ). The steadystate speed ( ms ) must be modiied by amplitudes o pitching and yawing angular rates or lager drag will be get or large angle o attack and sideslip( α, β ). It is in the orm o a a r a r a r (m/s) () ms where r r q and a i are unctions o M spd. They are evaluated rom theoretical calculations, 6-DOF simulations and corrected by real navigation experiments. Fig. shows relationships between M Spd, ms and r o the considered system. It shows the larger value o r, the less value o vehicle speed. Eq.() gives the steady-state conditions and can be used to ormulate the completely propelling dynamic model o vehicle speed orm motor speed command ( M TCmd ). Two dynamic models will be added to describe the motor speed response and the water compressibility. They are represented by two irst-order models: M Spd and total angular rate r. Control coniguration and adaptive autopilot designs The control coniguration o the considered autonomous underwater vehicle (U) is shown in Fig.. It is a rolling stabilized control with skid-to-turn maneuver[]. Control laws provide a stable controlled vehicle to be guided and variable control structures are ready to be selected or dierent guidance laws []. The yawing control law provides angular and angular rate controls to be selected. The pitching control law provides angular and depth controls to be selected. Note that the dashed-arrow lines represent gains: Kop, Kip, Kh, Koq, Kiq, Kor, Kir and angular rate/ angular limits: p lim, qlim, rlim, θ lim are adapted according to vehicle speed ( m ). The updating rate o them is Hz. The purpose o them is to keep angle o attack/sideslip within in eight degrees or small drag and vehicle stability. For instance, small values o p lim, qlim, rlim, θ lim will be used or low-speed to prevent large angle o attack/sideslip operation. M M spd TCmd (s).5s m ms (s).75s (4) Time constants (.5,.75) given in Eq. (4) are all evaluated and veriied by post data processing o navigation experiments. Eqs. ()- (4) describe the open-loop speed response rom motor speed command. In this work, open-loop speed control will be used or there is no speedometer in U. The time responses o the vehicle speed rom motor speed command will be illustrated in Section 5. Figure. daptive and variable structure autopilot coniguration. Design results o compensators, adaptive gains and rate limits shown in Fig. are all given below: (a) Rolling Channel gains and compensators: Figure. Steady-state relationships between ms,.z.65 5.z 4. Poc ( z) Pic ( z) z.87 z. Kop.9 m.5.79 m Kip. m p 45 / s. m lim (b) Yawing Channel gain and compensators:.5z z.9z 4.76 Roc ( z) Ric ( z) z.99 z.9z.79 Kor. m.5.47 m Kir.7 m m ISSN: Issue, olume 4, January 9

5 r lim m (c)depth, Pitching Channel gains and compensators:.84z.84 Hc ( z) z.78z H ( z) z.948.5z z.9z 4.76 Qoc ( z) Qic ( z) z.99 z.9z.79 Kh. m m θ. m lim m Koq. m.5.47 m Kiq.7 m m q lim.97 m 5. (d)fin actuating limits: δ 5, δ 5, δ 5, δ 5 c lim clim clim 4c lim They are evaluated rom the small-signal dynamic model described by Eq.() and veriied by 6-DOF simulations and navigation experiments. Note that the subtraction o yawing angular command ψ c and eedback ψ shown in Fig. is ormulated as in the orm o Δψ ψ c ψ i ( Δψ 8 ) Δψ Δψ 6 i ( Δψ 8 ) Δψ Δψ 6 (5) to get proper sign o yawing angular rate control or domains o ψ c and ψ are in (, 6 ). The perormances o depth and yawing angle controls will be illustrated by experimental results given in Section 5. 4 ehicle position estimation method 4. Positioning analyses o the INS For pure INS, lateral deviations ( Δ y gyro, Δ y Δφ _ ini, Δ y acc _ err ) due to rolling gyro drit ( φ drit ), rolling installing error( Δ φini ), and accelerometer accuracy( acc err ) versus time t are given below [5]: Δ y gyro (/6) 9.8 φ drit t /57.96 m Δ y Δφ _ ini (/) 9.8 Δ φini t /57.96 m Δ y acc _ err (/) acc err t m (6) The total lateral deviation is the root sum square o three deviation terms. For limited budget, the speciications o the INS used in the considered U are: (a) Installation accuracy ( σ ): in.5deg (b) Gyro accuracy (σ ): bias drit in.5deg/hr (c) accelerometer accuracy (σ ): in.5mg. For example: (a) Δ y gyro 88. 6m or φ drit.5deg/ hr and t 9sec (b) Δ y gyro 8, 47m or φ drit.5deg/ hr and t,6sec (c) Δ yacc_ err 595. m or.5mg and t 9sec (d) Δ yacc _ err 9, 55m or acc err. 5mg and t, 6 sec. They give the accelerometer accuracy gives larger lateral deviation than that o gyro accuracy and deviations become unacceptable ater time is greater than 9sec. Thereore, other positioning techniques must be applied or getting a nondiverging position datum or long-time underwater applications. 4. The proposed positioning method without state observers Two bounded datum and three low-drit attitude angles φ,θ, and ψ o INS can be used to improving positioning o the U. The bounded datum are the speed o the propelling motor ( M spd ) and the depth measurement rom depth meter ( d epth ). ssume that mest is the estimated vehicle speed with respect to sea current, and ( wes, t ψ w ) are estimated magnitude and course o the sea current with respect to ground. Then, the estimated vehicle speed [ ] t est, est, est with respect to ground along the inertial axes is in the orm o xest yest zest cθ cψ sφ sθ cψ cφ sψ cφ sθ cψ sφ sψ mest cθ sψ cφ cψ sφ sθ sψ cφ sθ sψ sφ cψ sθ sφ sθ cφ cθ cψ w mest west sψ w west J ( η ) J ( η w ) where η [ φ θ ψ ] T (7) and η [ ] T w ψ w The total velocity ( mt ) o the vehicle is deined as the root sum square o velocity components. Integrations o them give the estimated vehicle position [ X, Y, ] t. They are given below: est est est. x ( k ) T xest x X est x ( k ) y ( k ) T yest y Yest y ( k ) z ( k ) T zest z est z ( k ) (8) where x ( k), y ( k), z ( k) are state variables o integrations with initial states speciied. The computation period T ms. The estimated vehicle speed ( mest ) is derived ISSN: Issue, olume 4, January 9

6 rom steady-state speed ( est ) described by Eq. () plus the dynamics o the propelling motor and compress o seawater described by Eq. (4). They are transormed to -domain descriptions []. The motor speed command M TCmd (rpm) is the input and the output o the estimated result is mest (m/s). The relationships between M TCmd, est and mest are given below: est Scvm ( a a r a r a r ) () v ( k ).85 est.995 v mest v ( k ) () where r r q and r, q are yawing/ pitching angular rates measured by INS. S cvm is the correction actor. Deault value o S cvm is. and calibrated according the operating area. m ( k ).74 MTCmd.996 m( k) Mspd m( k ) (9) Figure 4. The proposed vehicle position estimation scheme. The sea current estimation is derived rom a constant-yawing angular rate, speed and depth motion. Note that circle motion can get the desired current datum with regardless the vehicle speed will be. The position deviation between start and end o the 6 degrees circle motion will give the current amplitude and course. The position datum ( X m, Ym, m ) is get rom INS or short-time inaccuracy is negligible. Equations or current estimation are (Δ where, Δ,, () x,δy z ) (X m,ym m ) (X T to m,ym m ) o to Δ Δ /T ψ a tan (Δ,Δ ) 57. () west x y o w y x t o is the starting time, c r is the yawing angular rate and period T o 6 / rc, west and ψ w is the estimated current speed and course with respect to the truth north( ). Once the estimation o sea current is obtained, the vehicle speed described by Eq. () can be urther calibrated by ollowing on-line adaptive law: G v ( k ) Gv ( k) [ γ mest west / min s ( γ ) ] Scvm Gv ( k ) (4) where v ( ) G, γ. 8 and mins xins yins zins is evaluated rom three axis velocity components measured by INS. The ratio o Gv ( k ) / Gv ( k) will be converged to be unity ater. min s mest west ISSN: Issue, olume 4, January 9

7 The calibrating process is perormed at beginning navigation ater current is estimated or position drit o INS is still acceptable. The positioning technique stated is shown in the lower part o Fig.4. It is an open-loop positioning process. 4. The proposed positioning method with state observers The open-loop positioning process can be urther improved by state observers [] shown in the upper part o Fig.4. The datum used or position accuracy improvement are accelerations o body-axis ( xb, yb, zb ), depth measurement ( d epth ), estimated velocity components ( xest, yest, zest ) described by Eq. (8). The dynamic model o the depth meter /(.s ) and vehicle speed dynamic model /(.5s ) are used in state observers or data synchronization. They are also transormed to -domain descriptions. K zv, K zz, K zv, K yv, K xv are observer gains. Equations o the position estimation with state observers are given below: xi yi zi J ) zb xb ( η yb (5) where η [ φ θ ψ ] T,, ( xb yb zb accelerations along the body axes, ) are,, are accelerations along the inertial axes. ( xi, yi, zi ) are corrected and double integrated to get the estimated position datum ( X est, Yest, est ) along the inertial axes. Certainly, better accuracy o ( X est, Yest, est ) is expected than that o ( X est, Yest, est ). The attitude angles ( φ, θ, ψ ) are evaluate rom the angular rates p, q, r ). They are in the orm o ( and & φ p & θ J ( η ) q ψ & r ( k ) T & φ φ ( k ) p ( k ) T & θ θ ( k ) q t p q p q xi yi (6) ( k ) T ψ& ψ ( k ) (7) r r where p ( k), q ( k), r ( k) are state variables o integrations with initial states speciied, and J ( ) is deined by Eq. (). The accelerations r zi ( xi yi, zi, ) are corrected by three velocity and one depth dierences as in the orm o xi yi zi xi yi zi K K xv K yv zv ( ( ( xest yest zest xins zins ) yins ) ) K zv ( d epth est ) (8) Integrations o ( xi, yi, zi ) gives ( xins, yins, zins ). Equations o integration are given below: vx vy vz ( k ) T ( k ) T ( k ) T xi yi zi vx vy vz xins yins zins vx vy vz ( k ) ( k ) ( k ) (9) where vx ( k), vy ( k), vz ( k) are state variables o integrations with initial states speciied. The terms ( xins, yins, zins, est ) given in Eq. (8) are evaluated as ollowing expressions: mx my ( k ).488 ( k ).488 mz( k ).488 ( k ).4 X dz x sin x sin x sin est mz.996 mx mx my xins xins xins est ( k ) ( k ) mz ( k ) ( k ) dz mx my () where mx ( k), my ( k), mz ( k), de ( k) are state variables with initial states speciied. The term is corrected by depth dierential. zins zins zins zz ( epth est K d ) () or only depth data can be used. Integrations o ) gives position ( X est, Yest, est ). ( xins, yins, zins x ( k ) T y ( k ) T ( k ) T z xins yins zins x z X Y y est ests est x ( k ) y ( k ) ( k ) z () where x ( k), y ( k), z ( k) are state variables o integrations with initial states speciied. The observer gains K, K, K, K, K are ound as zv zz zv yv xv yv., K xv K zv.5, K zz. 5, K zv., K.. 5 Experimental Results 5. Experimental planning The proposed positioning technique was veriied by two experiments. The average depth o the seabed is 78m. Fig.5 shows a testing plan o the navigation experiment with the launching point is located at ( E, 9 5 N). Six transponders (-F) at the seabed and one transponder in the vehicle are used or ISSN: Issue, olume 4, January 9

8 long-baseline acoustic positioning system (LBL). Positions o six transponders at the seabed are corrected by GPS in installation. ntennas are connected to the transponders by cables or transmitting distances between transponders to data processing center. The position error o the transponder is within 5m. Thereore, the best accuracy o the LBL is within 5m. Two sound sources or sonar tracking are installed at W p and W p with m depth. This experiment was planned or active and passive sonar target tracking. The passive target sound source was put at W p and the active target sound source was put at W p. The angle between tacking locus and line o sight (LOS) is 5degree or saety consideration o crew in the launching vehicle. The vehicle was navigated to and ro alternatively between waypoints W p and W p by locus tracking control law. The vehicle will change course at the situation o distance between vehicle and W p (or W p ) is equal to m. The vehicle course is determined by tracking locus described by W W or p p W p W. p The locus tracking control law is proposed and discussed in detail in ppendix. averages o them one can see the responses modeling o vehicle speed described by Eqs.() and (4) give good agreement with the LBL results. Fig.7 shows the vehicle depth responses and comparisons between depth command, depth meter and TBL. They give good agreements between them and good depth control perormance. Fig.8 shows the deviations (solid-line) between the estimated position ( X est, Yest ) and the tracked datum. It gives the maximal deviation is.6m and the average deviation is 5.m. They are much less than the detecting ranges o the sonar in the shallow water. The errors (doted- line) o proposed method without state observer are shown in Fig.8 also. It gives the maximal deviation is 6.m and the average deviation is 5.m. Figure 6. ehicle speed time responses. Figure 7. ehicle depth time responses. Figure 5. Mission Planning or U Navigation Testing. 5. Experimental results The circle motion or current estimation gives the estimated results was ( west, ψ w ) (.9m / s, 9deg) The calibration actor S cvm or the vehicle speed is.5. Fig.6 shows the vehicle speed responses and comparisons between proposed estimated and LBL results. The LBL datum is raw datum without low-pass iltering. Thereore, they are luctuating. However, rom Figure 8. Position errors with respect to LBL. ISSN: Issue, olume 4, January 9

9 Note that the position datum o the INS with the speciication stated in Section 4. It gives maximal deviation 54m rom the tracking locus. This deviation is greater than that o the detection range o sonar in the shallow water. Note that the launching vehicle is dangerous i the position datum o INS were used or locus tracking. Note also that greater deviation will be obtained or the operation time greater than mins. Eq. (6) gives the deviation will become unacceptable or one-hour operation. 5.. nother experimental results Fig.9 shows mission planning or large area underwater target searching and control perormance veriication. The current estimation gave ( west, ψ w ) (.4m / s, 5deg). The calibration actor S cvm or vehicle speed is.6. The position deviation with respect to LBL datum is shown in Fig.. The maximal deviation is 5.6m and the average deviation is.8m or 76sec(9.6mins) underwater operation. From comparison results shown in Figs. 8 and, one can see the proposed method gives good and non-diverging positioning and ready or longtime operation without correction rom LBL or GPS. The installation o LBL system was omitted in the next experiment. Figure 9. Mission planning or large area underwater target searching. Figure. Position errors o another experiment with respect to LBL. 6 Conclusions In this paper, an accurate positioning technique has been proposed or autonomous underwater vehicles (U). It needs not position correction rom GPS above the sea surace and SBL or LBL under the sea. Rolling speed o the propelling motor, depth measurement o depth meter, estimated current inormation and low cost rate gyros and accelerometers with state observers were used to estimate the vehicle position. It gave less than m deviations or minutes and 9.6 minutes underwater operations. The deviations were veriied by a long-baseline acoustic position system (LBL) with positioning accuracy less than 5m. High accurate position lets the vehicle have lexible and mobile applications and less supporting rom launching vessel. Reerences [] J. Yuh, Design and control o autonomous underwater robots: Survey, utonomous Robots, ol.8,, pp.7-4. [] D. Bingham, et al, The application o autonomous underwater vehicle (U) technology in oil industry-vision and experience, FIG, XXII International Congress, Washington DC,. [] W. H. Cheng, study o increasing the precision o navigation position or submerged body, Ocean Engineering ol., 4, pp [4] M. J. Morgan, Dynamic positioning o oshore vessels, Petroleum publishing Co. Tulsa, Oklahoma, 978. [5] J.. Farrell, The Global Positioning System & Inertial Navigation, McGraw-Hill Proessional, 998. [6] N. H. Kussat, C. D. Chadwell, immerman, R., bsolute positioning o an autonomous underwater vehicle using GPS and acoustic measurements, IEEE Journal o Oceanic Engineering, ol., 5, pp [7] W. S. Burdic, Underwater coustic System analysis, Prentice-Hall, 99. [8] R. J., Urick, Principles o Underwater Sound, McGraw-Hill, 99. [9] T. I. Fossen, Guidance and Control o Ocean ehicles, John Wiley & Sons, 994. []J. Garus, Design o Model Reerence daptive Control or Underwater Robotic ehicles, ISSN: Issue, olume 4, January 9

10 WSES Transactions on Systems, ol.5, No., 6, pp []W. Naeem, R. Sutton, hmad, S.M. and Burns, R.S., review o guidance laws applicable to unmanned underwater vehicles. Journal o Navigation, ol. 56,, pp.5-9. []K.Ogata,Discrete-time Control System, Prentice- Hall Inc. Englewood Clis, NJ, 994. []G. F. Franklin, Feedback Control o Dynamics, ddison-wesley Publishing Company, 986. ψ c ψ c ( LHc LH )... or LH < R LHc (5) ψ c ψ... c...or LH > R LHc (6) where R represents the minimal turning radius o the vehicle. ppendix : Locus Tracking Law The tracking locus connected with point # i ( X i, Yi ) and point # i ( X i, Yi ) and tracking deinition is ormulated as ollowing equations. The tracking locus is deined as a X b Y c () i i i with ai Yi Yi, bi X i X i and ci X iyi X i Yi, the normal displacement between vehicle( M YM and the tracking locus is X, ) Figure. The astest loci tracking concept with turning radius R. LH () ( ai X M bi Y M ci ) / ai bi Positive value o LH represents the vehicle is on the right-hand side o the tracking locus negative value o LH represents the vehicle is on the let-hand side o the tracking locus. The purpose o locus tracking is to keep LH be a wanted value (LHc) and moving rom point #i toward point # i. LHc represents the vehicle will moving on the tracking locus. The direction o the vehicle will move always rom way point #i to way point # i or controlled parameters are LHLHc and c ψ c ψ which is shown in Fig.. It shows the geometry relation o the vehicle and the tracking locus. For aster locus tracking purpose, variable structure control scheme is switched according to amplitude o LH. The vehicle will be guided toward to tracking locus orthogonally or LH > R, and toward to way point #i or LH < R. The selection o R is the minimal turning radius capability o the vehicle at high speed maneuvering. It will perorm smoothing tracking perormance and low water lowing noise. The guidance law is ormulated as ψ c a tan ( ai, bi ) () ψ c ψ c 9 sign( LH ) (4) ISSN: Issue, olume 4, January 9