Task space trajectory tracking control of an underwater vehicle-manipulator system under ocean currents

Transcription

1 Indian Journal of Geo-Marine Sienes Vol. 4(6), Otober 013, pp ask spae trajetory traking ontrol of an underwater ehile-anipulator syste under oean urrents M Santhakuar Disipline of Mehanial Engineering, Shool of Engineering, Indian Institute of ehnology Indore, Madhya Pradesh, India [E-ail: santhakuar@iiti.a.in] Reeied 11 May 01; reised Septeber 01 his paper presents a new traking ontrol shee for an underwater ehile-anipulator syste (UVMS). he proposed task spae passiity based ontroller is not only used to trak the gien desired path but also allows the use of the self-otion of the ehile to perfor power effiient trajetory beause of its kineatially redundant nature. In the proposed shee, the priary task is to trak the gien end-effetor task spae trajetory despite of the syste assoiated with external disturbanes, syste unertainties and internal noises. he seondary task as the energy saings requireent, the ehile otion is ontrolled and to be aligned with the estiated underwater urrent orientation. he perforane and effetieness of the proposed oordinated ontrol otion of the UVMS is deonstrated nuerially and onfired with the speified UVMS tasks. Siulation results show that the required ontrol inputs for the gien traking task are redued, and the UVMS an suessfully trak the gien desired spatial trajetory. eywords: Underwater ehile-anipulator syste; raking ontrol; Passiity based ontrol; Coordination ontrol; ineatially redundant syste; Underwater urrent Introdution In the present senario, underwater robotis has huge ipat on the exploration of the oean's resoures and deep-sea anipulation issions and the underwater anipulator, as an iportant piee of equipent for underwater roboti ehiles, plays a ruial role in underwater appliations. Underwater ehileanipulator syste (UVMS) is an underwater ehile syste ounted one or ore anipulators to oplete ertain underwater task. With the inreased interest in the deelopent of undersea interention tehnology in the fields of offshore oil, ilitary, and oean sientifi inestigation, any approahes hae been presented to iproe undersea interention apability of UVMS 1-4. Currently, the state of art of the underwater anipulator is represented by reotely operated ehiles with anipulators through aster/slae shees by huan pilots 1. his huanpiloted shee auses seeral operational diffiulties, inaurate trajetory traking and fore ontrol, tie delay in the an-ahine ontrol loop, and fatigue and perforane of the huan operator. Soe of the aboe entioned diffiulties an be oeroe by the use of autonoous anipulation, whih onsidered the nonlinear and oupled dynais between the underwater ehile and anipulator systes. A suary of the reent deelopents and researhes of odelling and ontrol of an UVMS an be found in the literature 1-5. Seeral ontrol strategies based on perfet opensation of the UVMS dynais hae been proposed 5-6. A nonlinear odelbased ontrol shee that ontrolled the ehile and anipulator siultaneously was deeloped and inestigated 6, and feedbak linearization along with PID ontrol was deeloped and inestigated 5. Howeer, these shees required the exat knowledge of the UVMS dynais whose hydrodynai paraeters generally hae large unertainties. Considering these unertainties, adaptie ontrol shees were proposed in soe of the preious literature 7-9. In referene 9, an adaptie traking ontroller was introdued with irtual deoposition along with regressor atrix with respet to the paraeter etor. But this work requires a regressor atrix with respet to the paraeter etor, as well as a proper update rule. Larger unertainties are diffiult to adapt in this shee. he adaptie ontrol based on the iro-aro anipulator onept has been proposed for the UVMS whih an be applied only to non-redundant anipulators with full-rank Jaobian 10. he appliation of an adaptie disturbane obserer based

2 676 INDIAN J. MAR. SCI., VOL. 4, NO. 6, OCOBER 013 on the non-regressor atrix ontrol shee was also proposed for the UVMS 11. In referene 1, authors hae suggested a disrete-tie resoled aeleration ontrol based on diret obserer tehnique and this tehnique is further iproed with the added opensation disturbane loop 13. A oordinated ontrol shee for the UVMS using a disrete-tie approxiation dynai odel was deeloped for opensating the traking errors of the anipulator during ehile otion 14, and otion planning and oordination ontrol of UVMS Robust oordinated otion ontrol of an UVMS was deeloped through iniizing restoring oents along with the H-infinity ontrol 16. In general, odel-based adaptie approahes for UVMSs are generally based on Lagrangian forulation whih leads to oputationally intensie ontrol shees. Moreoer, ost of these shees required the exat knowledge of the UVMS dynais. Hene in pratie, siple ontrol shees (e.g., proportional-integral-deriatie (PID) ontrol) hae been adapted. hey are oputationally effiient; howeer often offer inadequate traking perforane of the ontrol syste. In fat, the UVMS operations typially inole anipulation tasks in the presene of paraeter unertainties, sensor noises and external disturbanes (e.g., underwater urrent). his requires the syste ontrol to be ore robust in ters of opensating external disturbanes and adaptie to the syste unertainties. For the underwater anipulation tasks, it is not always effiient to use ehile thrusters to oe anipulator end effet or due to oplexity of ontrolling the ehile in ertial and lateral diretions (due to under atuation). Moreoer, due to the different inertias between the ehile and the anipulator, oeent of the anipulator is energetially ore effiient. hus, it is energetially effiient to keep the ehile at rest during the task. Howeer, to aintain the ehile at rest in the presene of external disturbanes suh as underwater urrent requires the usage of the ehile's thrusters whih are expensie in ters of power onsuption. herefore, the ehile an be aligned to the oean urrent in order to iniize the energy onsuption of the thrusters. In this paper, it presents a new oordination ontrol shee for an UVMS where the proposed ontroller is not only used to trak the gien desired path but also allows the use of the self-otion of the ehile to perfor power effiient trajetory beause of its kineatially redundant nature (i.e., the total nuber of ontrollable degrees of freedo or the nuber of onfiguration spae ariables are ore than the task spae oordinates). he proposed ontroller siple in struture and does not require the exat knowledge of the syste. he effetieness of the proposed ontrol shee is deonstrated using nuerial siulations. he reainder of this paper is organized as follows. he dynai odelling of a general UVMS is deried in Se.. In Se. 3, a passiity based traking ontroller for the UVMS is disussed and the detailed perforane analysis of the UVMS is presented in Se. 4. Finally, Se. 5 holds the onlusions. Dynai odelling of an UVMS In this work, dynai odelling of an UVMS is deried using Newton - Euler and reursie Newton - Euler forulation shees he frae assignent of the UVMS is presented in Fig. 1. he dynai equations of otion of the UVMS an be expressed as follows 19 : M( ) C(, ) D(, ) G( ) F(, ) d... (1) where M ( ) H ( ) M ( ), C(, ) H ( ) M ( ) C (, ) 0 0 (, ) C D (, ) 0 g ( ) D(, ), ( ), 0 (, ) G ( ) D g F (, ) F(, ),.... () F (, ), x y z φ θ ψ is the etor of absolute positions and Euler angles (roll, pith and yaw). x-surge position, y-sway position, z-heae position, -roll angle, -pith angle, -yaw angle. M () is the etor of inertial fores and oents of the ehile (inluding added ass effets). C (, ) is the etor of Coriolis and entripetal effets of the ehile (inluding added ass effets). D (, ) is the etor of daping effets of the ehile (both linear and quadrati daping ters). g () is the etor of restoring effets of the ehile

3 SANHAUMAR: AS SPACE RAJECORY RACING CONROL OF AN UNDERWAER VEHICLE 677 Fig. 1 Coordinate frae arrangeent of an underwater ehile-anipulator syste (both buoyany and graity effets). ] Bf is the resultant input [ x y z (fores and oents) etor of thrusters. f [ f1 f... f n ] is the etor of thruster input fores. B is the thruster input atrix. [ 1... n ] is the etor of joint ariables and,, 1... n are the joint positions of the orresponding underwater anipulator links, n is the nuber of the anipulator joints (axes). M ( ) is the etor of inertial fores and oents of the anipulator (inluding added ass effets). C (, ) is the etor of Coriolis and entripetal effets of the anipulator (inluding added ass effets). D (, ) is the etor of daping effets of the anipulator (both linear and quadrati daping ters). g ( ) is the restoring etor (both buoyany and graity effets) of the anipulator. H ( ) and H ( ) are the etors of reation fores and oents between the ehile and the anipulator due to the anipulator and the ehile inertial effets, respetiely. F (, ) and F (, ) are the etors of the oupling dynai effets due to the anipulator inlusion and its otion on the ehile, and interation effets due to the ehile otion on the anipulator, respetiely.... is the etor of anipulator [ ] 1 n ontrol inputs and,,... are the joint torques 1 n of the orresponding anipulator links. d is the etor of external disturbanes (e.g., due to underwater urrent, payload, et.). he UVMS (for the analysis) onsists of an 3-DOF anipulator and a 6-DOF ehile, whih eans the syste, has ore degrees of freedo (onfiguration spae) than the diension of the task spae, required to perfor gien task. he task oordinates are related with the syste states is gien as: f ()... (3) where, [ xt yt zt ] is the etor of task spae oordinates (suh as end effetor position) and f () is the etor representing the forward kineatis. Differentiating (3) with respet to tie gies: J... (4) where, J is the Jaobian atrix, apping syste (joint and body-fixed) eloities to task eloities. he general solution of (4) is gien as: J N... (5) J is the generalised inerse of J and N is the null spae projetion atrix whih projets to the null spae of J. A general for of N is gien by: N ( I J J)... (6) he first ter of the (5) is the partiular solution of the equation of otion in (4), whih enables to

4 678 INDIAN J. MAR. SCI., VOL. 4, NO. 6, OCOBER 013 Fig. Establishing link oordinate systes of the anipulator alulate syste eloities neessary to perfor gien task. he seond ter is the hoogenous solution of the aboe equation, whih ontributes to a otion in the null spae only, without affeting the task spae otion. his otion is the self otion of the kineatially redundant syste. In general, there are an infinite nuber of redundant syste onfigurations whih satisfy the desired task oordinates. he proposed approah is based on splitting the syste otion proble into a task spae otion and a onfiguration spae otion. Forward kineatis of the end effetor position of the UVMS he anipulator is equipped with three joint axes whih onsist of indiidual joint atuators. he atheatial relations of the end effetor position with the known syste states (the ehile states and the anipulator joint angles) are deried here. he atheatial (kineati) desriptions of the underwater anipulator are deeloped based on the Denait- Hartenberg (D-H) paraeter notation 18. he establishent of the link oordinate syste as shown in Fig.. Based on the UVMS paraeters the forward kineati solutions of the UVMS end effetor are obtained as follows: x xb os os yb (os sin os sin sin ) xt zb (sin sin os os sin ) os1l1 L os L3 os( 3) y xb sin os yb (os os sin sin sin ) yt zb (os sin os sin sin ) sin 1L1 L os L3 os( 3) z xb sin yb os sin zb os os zt d1 L sin L3 sin( 3)... (7) UVMS Controller he dynai odel of the UVMS in (1) inoles nonlinear funtions of state ariables and haraterizes the behaiour of the anipulator states. he proposed ontrol shee is apable of fulfilling the traking ontrol objetie is proposed in this study (refer appendix: Proposition 1 for detailed stability analysis of the proposed approah). he blok diagra that orresponds to the proposed ontroller is shown in Fig. 3. he passiity ontroller will get inputs fro trajetory planner and different sensor inputs (UVMS onfiguration states and urrent diretions). he proposed task spae passiity ontrol law with self-otion is presented as gien: J G( )... (8) 1 3

5 SANHAUMAR: AS SPACE RAJECORY RACING CONROL OF AN UNDERWAER VEHICLE 679 able 1 he UVMS Paraeters Fig. 3 Blok diagra of the proposed ontrol shee Syste eleents Vehile Manipulator Details Length = 1.1, width = 0.7, depth = 0.7 and ass (): 40 kg Inertia(s): I xx = 19.5 kg, I yy = 18.1 kg and I zz =37.5 kg Centre of graity (CG)=0, 0, 5) Centre of buoyany (CB)=(5, 0, 15) Link 1: Mass ( 1 )=0.8 kg, link length (L 1 ) = 0.1 Offset (d 1 ) = 01 and radius = 0.08 Link : Mass ( ) = 3.5 kg, link length (L )=0.4 and radius = 0.05 where 1 33 is the syetri positie definite atrix. d is the task spae error etor. d is the etor of task spae referene oordinates. 6 n6 n is the syetri positie definite design atrix. diag(( k k 0 0 0) ) is 3 the syetri positie definite atrix. ( ˆ ˆ 0 0 0) is the ehile orientation error etor. ˆ and ˆ are the estiated oean urrent diretions. and are the ehile pith and yaw angles, respetiely. Perforane Analysis Desription of the siulated syste and the task o explore and inestigate the perforane of the proposed ontrol shee, nuerial siulations are arried out on the UVMS and its paraeters (for the nuerial siulations) are gien in able 1. he ontroller perforane and effetieness are deonstrated with the help of the following task. he end effetor is oanded to trak a spatial spiral trajetory. During this task, an unknown oean urrent is added in the siulation by properly onsidering the relatie eloity of the syste in the dynai odel. It is assued as an irrotational urrent, slowly arying (rando walk) in the inertial frae and the initial alue of the urrent is onsidered as follows: /s, the syste paraeters unertainties are assued to be 15% and the UVMS assued to be positiely buoyant (the net positie buoyany of the ehile is assued to be 5 kg and the anipulator buoyany is assued to be 10% of the total anipulator ass). he proposed shee is opared with that of traditional PID ontroller with restoring opensation, and is gien by, dt G( )... (9) P I D where, P, I, and D are the proportional, integral and deriatie gain atries of the UVMS, respetiely. Siilarly, the proposed shee is opared with that of indiret adaptie ontroller based on feedbak linearization (oputed torque ontrol) as well, and is gien by 19, M ( ˆ)( ) ( ˆ, ˆ) ˆ ( ˆ, ˆ) ˆ r P D C D G( ˆ) F( ˆ, ˆ) dˆ...(10) where, P and D are the proportional and deriatie gain atries of the ontroller and hosen as syetri positie definite atries, respetiely. he sybol '^' denotes the estiated alues obtained using the extended alan filter (EF). Results and Disussions In this setion, nuerial siulation results are presented and disussed to inestigate the effetieness and robustness of the proposed ontrol shee. Coparatie ontroller perforane results are presented in Figs 4 to 7. In Fig. 4, the gien desired and atual task spae trajetories of four different ases are plotted (ase 1 is the PID ontroller with restoring opensation, ase is the perforane of the indiret adaptie ontrol shee based on feedbak linearization shee and extended alan filter, and both of these (ases 1 and ) are based on independent ontrol shees (i.e., the ehile and the anipulator ontrolled independently).

6 680 INDIAN J. MAR. SCI., VOL. 4, NO. 6, OCOBER 013 Fig. 4 Coparatie task spae (xyz) trajetories of the end effetor Fig. 6 ie trajetories of the ehile ontrol inputs during the desired task Fig. 5 raking errors of the end effetor position trajetory Cases 3 and 4 are the perforanes of the proposed ontrol shee without and with ehile orientation, i.e., in ase 4, the ehile to be aligned with the estiated urrent diretion. It is noted that the atual trajetories of the end effetor are alost super iposed on the desired-trajetories and suh good traking perforane is to be expeted when the desired trajetories lie within syste apabilities. ie histories of the task spae traking errors are presented in Fig. 5. It an be seen that exept for the PID ontrol, the task spae trajetory traking errors for all other ases are sall. ie histories of the ontrol inputs of the ehile and the anipulator are plotted in Figs. 6 and 7, respetiely. It is obsered that the atuator ontrol inputs are low in the proposed ontrol shee. In all these siulation Fig. 7 ie trajetories of the anipulator ontrol inputs during the desired task exaples, the ontrol inputs are within the liits of the atual atuators of the UVMS. Fro the obtained results, it is obsered that the proposed ontroller is good in adapting the unertainties and external disturbanes. Howeer, the power onsuption analysis is perfored in order to opare the ontroller perforanes in ters of power onsuption. he details of the total power onsuption of the atuators during the gien task (duration of 50 s) in the presene of oean urrent for different ontrol shees are gien in able. here is little differene in ters of traking perforane,

7 SANHAUMAR: AS SPACE RAJECORY RACING CONROL OF AN UNDERWAER VEHICLE 681 able Power onsuption of the UVMS during the gien desired trajetory Control shees PID ontrol Indiret adaptie ontrol Proposed ontroller and without the ehile orientation Proposed ontroller and with the ehile orientation otal power onsuption (for 50 s) 11.7 kw 11.8 kw 11.3 kw 4.8 kw howeer a notieable differene in power onsuption (ore than 50%) was obsered. his is due to that the ehile is aligned on the estiated oean urrent diretions, where oean urrent effets opensated only with the help of surge thrusters. herefore the total power onsuption of the syste is redued signifiantly and this an be noted fro Figs 6 and 7. Fro the siulation results, the alidity of the proposed approah is onfired and the perforane is better with other ases. hough, the proposed shee required the oean urrent diretions as an additional requireent for orienting the ehile along the urrent diretions, as a power saing task. he proposed approah an be perfored well een without orienting the ehile along the urrent diretions. hese results illustrate the apabilities for siultaneously ontrolling the otion of the ehile and the anipulator with the interation effets between the ehile and the anipulator, and the enironental interation effets. It is also deonstrate the ability of the proposed ontrol shee to siultaneously follow oplex end effetor and ehile trajetories with a natural preferene gien to end effetor traking perforane. hese results are intuitie, proising and point out the prospetie of the proposed approah. On the other hand, these results based on nuerial siulations, therefore it is iportant that extensie real-tie experients need to be onduted to alidate the adantages of the proposed shee whih will be aailable in near future. Conlusions his paper proposed a task spae ontrol approah for an UVMS to perfor underwater anipulation tasks. he priary task of this approah is to trak the gien end-effetor task spae trajetory despite of the syste assoiated with external disturbanes, syste unertainties and internal noises, and the seondary task of the approah as the power saing purpose the ehile is aligned with the estiated oean urrent orientation. he effetieness of the proposed shee deonstrated and erified using extensie nuerial siulations, and the results onfired the effetieness and robustness of the proposed shee in ters of traking errors in the presene of an unknown oean urrent. he siple struture, robustness and ease of oputation of the proposed ontroller ake it ery attratie for real tie ipleentation for ontrolling UVMSs. his work an be extended by onsidering the anipulator workspae in order to iproe the dexterity and anipulability of the UVMS. his researh proides a generalized fraework of the passiity based ontrol for ontrolling (oordinated otion) of an UVMS onsidering the dynai oupling between the ehile and the anipulator whih is ruial for ahieing underwater anipulation tasks for a ariety of sientifi, industrial and ilitary issions using unanned underwater robots. Referenes 1 Cui Y & Sarkar N, A unified fore ontrol approah to autonoous underwater anipulation. Robotia, 19 (001) Antonelli G, Underwater Robots Motion and Fore Control of Vehile-Manipulator Systes, (Springer, Berlin) Marani G, Choi S & Yuh J, Underwater autonoous anipulation for interention issions AUVs, Oean Engineering, 36 (009) Yuh J, Underwater Roboti Vehiles: Design and Control, (SI Press, North West United States of Aeria) Shjolberg & Fossen I, Modelling and ontrol of underwater ehile-anipulator systes, In: Proeedings of the 3rd onferene on Marine-raft Maneuering and Control, Southapton, (1994) De Wit C C, Diaz O & Perrier M, Nonlinear ontrol of an underwater ehile/anipulator with oposite dynais, IEEE ransations on Control Systes ehnology, 8 (000) Mahesh H, Yuh J & Lakshi R, A oordinated ontrol of an underwater ehile and robot anipulator, Journal of Roboti Systes, 8 (1991) MLain W, Rok S M & Lee M J, Experients in the oordinated ontrol of an underwater ar/ehile syste, Autonoous Robots, 3 (1996) Antonelli G, Caaale F & Chiaerini S, Adaptie traking ontrol of underwater ehile-anipulator systes based on the irtual deoposition approah, IEEE ransations on Robotis and Autoation, 0 (004) Fossen I, Adaptie aro iro ontrol of nonlinear underwater roboti systes, In: Proeedings of the 5th

8 68 INDIAN J. MAR. SCI., VOL. 4, NO. 6, OCOBER 013 International Conferene on Adaned Robotis, Italy, (1991) Yuh J, Zhao S & Lee P M, Appliation of adaptie disturbane obserer ontrol to an underwater anipulator, In: Proeedings IEEE International Conferene on Robotis and Autoation, Seoul, orea, (001) Sagara S, aura M, Yatoh & Shibuya, Digital RAC for underwater ehile-anipulator systes onsidering singular onfiguration, Artifiial Life and Robotis, 10 (006) Yatoh, Sagara S & aura M, Digital type disturbane opensation ontrol of a floating underwater robot with link anipulator, Artifiial Life and Robotis, 13 (008) Shepf H & Yoerger D, Coordinated ehile/anipulator design and ontrol issues for underwater tele-anipulation, In: Proeedings of the IFAC Control Appliations in Marine Syste, Italy, (199) Sarkar N & Podder, Coordinated otion planning and ontrol of autonoous underwater ehile-anipulator systes subjet to drag optiization, IEEE Journal of Oeani Engineering, 6 (001) Han J, Park J & Chung W, Robust oordinated otion ontrol of an underwater ehile-anipulator syste with iniizing restoring oents, Oean Engineering, 38 (011) Fossen I, Guidane and Control of Oean Vehiles, (Wiley, Chihester) Craig J J, Introdution to Robotis: Mehanis and Control, (Addison Wesley, Boston, MA, USA) Santhakuar M & i J W, Indiret adaptie ontrol of an autonoous underwater ehile-anipulator syste for underwater anipulation tasks, Oean Engineering, 54 (01) elly, R., Santibanez, V., and Loria, A., Control of Robot Manipulators in Joint Spae, (Springer-Verlag, London, U) 005. Appendix: Proposition 1 Consider the syste whose goerning equations are gien by (1). Let us define a positie definite Lyapuno funtion as : 1 1 V, ( ) M 1... (11) where is the syetri positie definite atrix. d d is the task spae error etor. is the etor of task spae referene oordinates. M () is the positie definite atrix by property of the syste herefore, V, is the positie definite funtion on and. Choosing the ontrol input etor and the obserer input etor of the fors based on bakstepping ontrol and proportional deriatie shees are as gien by (1), as presented below: J G( )... (1) 1 will lead to the UVMS task spae traking errors tending to zero asyptotially. i.e., the UVMS will follow the gien desired task 6n6n spae trajetory. Here, is the syetri positie definite design atrix. Proof he stability analysis of the losed-loop equation is analysed using Lyapuno s diret ethod 0. For proing the asyptotially stable nature of the proposed syste and errors onergene, the Lyapuno funtion V, is differentiated with respet to tie along the state trajetories, it yields, 1 ( ) V, M ( ) M 1... (13) Howeer, fro (1) the ter M ( ) an be expressed as: M ( ) C D G F (, ) (, ) ( ) (, ) d... (14) And based on the property of skew-syetri the following expression is true for the UVMS M ( ) C(, ) 0... (15) he ter an be rewritten as follows: J 1 J 1... (16) Substituting the aboe relations (15-16) in to the (13), it yields: V, D(, ) G( ) F(, ) J 1 d... (17) Substituting the ontrol etor fro (1), it beoes: V, (, ) D Ft... (18) F F d where, t (, ) is the su of interation effets and external disturbanes. If there are no external disturbane and F 0 interations inoled in the syste, then t. herefore, the aboe expression redued as:, V D(, )... (19) 0 where, the ontroller gain atrix is a syetri positie definite atrix by design and D(, ) is a positie definite atrix by syste property herefore, the Lyapuno funtion deriatie V, is positie definite on. Howeer, fro (19), it an be obsered that the Lyapuno funtion deriatie is only sei-positie definite funtion on and. It an be obsered that the traking errors onerge to zero asyptotially as well 0. herefore, the syste loally asyptotially nature an be obtained using the Barbalat's and odified LaSalle's leas 0. 0, then the syste ust also hold Based on these leas, if that 0 fro the losed loop equation that, for all t 0. aking this into aount, it an show 0 C(, ) D(, ) G( )... (0) Substituting the ontrol etor fro (1) and 0, the equation beoes: 0 J 1... (1)

9 SANHAUMAR: AS SPACE RAJECORY RACING CONROL OF AN UNDERWAER VEHICLE 683 Moreoer, the gain atrix 1 33 definite atrix by design, and the ter 1 0 is a syetri positie J. Hene, 0 for all t 0 is its unique solution and it an be obsered that the task spae traking errors also onerge to zero asyptotially 0. hat is, (t) li 0 t (t)... () (t) 0 0 li t li t he sae approah an be extended for the UVMS with onsidering the interation effets and external disturbane, and the stability of the syste an be assured by hoosing the ontroller gain atries in the following for 0 : in in 1 Ft Ft... (3) herefore, the traking errors of the task spae oordinates onerge to zero asyptotially 0. For the underwater anipulation tasks, it is not always effiient to use ehile thrusters to oe anipulator end effetors due to oplexity of ontrolling the ehile in hoering and lateral diretions. Moreoer, due to the different inertias between the ehile and the anipulator, oeent of the anipulator is energetially ore effiient. hus, it is energetially effiient to keep the ehile at rest during the task. Howeer, to aintain the ehile at rest (or soe station point) in the presene of external disturbanes suh as oean urrent exhibits the ehile and its thrusters should reat whih onsues ore energy. herefore, the ehile an be aligned to the oean urrent in order to iniize the energy onsuption of the thrusters. In the proposed shee, the priary task is to trak the gien end-effetor task spae trajetory despite of external disturbanes, syste unertainties and internal noises. As the energy saings requireent, the ehile otion is ontrolled to be aligned with the estiated oean urrent orientation. herefore, the ontrol etor an be reised by onsidering the aboe entioned task and expressed as gien: J 1 3 G( )... (4) where diag k is the 3 syetri positie definite atrix ˆ ˆ is the ehile ˆ orientation error etor. and are the estiated oean urrent diretions. and are the ehile pith and yaw angles, respetiely. he sae losed-loop syste stability is guaranteed and the syste traking errors are onerging to zero asyptotially, if the ontroller gain atries are hosen in suh a way that 0, in 3 in 1 3 ˆ k ψ... (5) herefore, the UVMS follows the gien desired task spae (end effetor) trajetory and the ehile aligns with the oean urrent orientation.