MANIPULATION OF LARGE FLEXIBLE STRUCTURAL MODULES BY SPACE ROBOTS MOUNTED ON FLEXIBLE STRUCTURES

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1 MANIPULAION O LARGE LEXIBLE SRUCURAL MODULES BY SPACE ROBOS MOUNED ON LEXIBLE SRUCURES Dmtro zeran 1, Yohyuk Ihjma 2, Steven Dubowky 1 (1) MI, 77 Maachuett Avenue #3469, Cambrdge, MA 2139, USA, {tzeran,dubowky}@mt.edu (2) Japan Aeropace Exploraton Agency, 211, Sengen, ukuba, Ibarak, 35855, Japan, hjma.yohyuk@jaxa.jp ABSRAC uture large pace tructure (LSS) wll be contructed on orbt by aemblng large ubaemble ung team o robot. Here, the challengng tak o the control and plannng o the cooperatve manpulaton o large lexble tructural module by uch team addreed. he robot are mounted on the complant LSS whle movng a module to t preaembly poton. he objectve to poton the module accurately and to mnmze the nduced vbraton n the large tructure and the module. A method developed to control the orce appled by the robot to the module and ther upport tructure, whch explot robot cooperaton and redundancy. he method evaluated ung mulaton. 1. INRODUCION uture pace olar power taton (SSPS) are expected to be an mportant power ource [1]. Due to ther large ze, they wll need to be contructed on orbt by pace robot nce human extravehcle actvty (EVA) expenve and dangerou [2]. Stude o the robotc contructon o LSS have largely ocued on the aembly o tru tructure by mall mple tructural element and on the degn o pace tructure component [3, 4]. However, the problem o ung robot to manpulate and aemble large lexble ubtructure ha not been well addreed. Related work can be ound n the cooperatve manpulaton o lexble object and n the plannng and control o robot on complant bae [5, 6, 7]. Here, the problem o cooperatve manpulaton o a large lexble object by a team o robot mounted on the LSS under contructon condered. he objectve to degn a plannng and control algorthm that permt robot to manpulate the tructural module precely whle nducng low level o vbraton n the module and the robot complant bae tructure, g 1. he propoed approach ue meaurement o the orce/torque appled by the robot to the module and the LSS and explot robot cooperaton and redundancy to plan and control the orce appled by the robot to the module and the LSS. Smulaton reult how the eectvene o the approach n potonng the module precely whle mantanng low level o redual vbraton n the module and the large tructure. he analy alo provde gudelne or the robot degn that enhance t ablty to apply the propoed method. Large lexble Structural Module Space Manpulator LSS under contructon g. 1 : Concept pcture or the contructon o LSS by pace robot mounted on lexble tructure. 2. PROBLEM DEINIION 2.1 ak Decrpton uture LSS wll be contructed by aemblng large tructural module on orbt [1]. Every module need to be potoned nto t prece preaembly poton o that t can be aembled nto the LSS probably ung automatc connecton mechanm [4]. h manpulaton tak wll be carred out by pace manpulator mounted on the LSS. h a challengng cooperatve manpulaton tak due to the ze and lexblty o the LSS module and the lexblty o the LSS that upport the robot. A mple planar model o uch a ytem hown n g. 2. wo rgd lnk redundant robot (etmated ze 2m) maneuver a long (etmated ze 1 to 2 m) lexble tructural module rom ome ntal poton (about 8m Proc. o 'he 8th Internatonal Sympoum on Artcal Intellgence, Robotc and Automaton n Space SAIRAS, Munch, Germany. 58 September 25, (ESA SP63, Augut 25)

2 rom the LSS) to t preaembly poton (le than 1m rom the LSS). he robot are mounted on the LSS under contructon. he drawng not to cale a the module lkely to be an order o magntude larger than the robot. he objectve to ue robot to poton the module precely nto t dered poton, n gven tme (about 36 econd), whle nducng mnmal level o vbraton to the module and the robot bae tructure. Whle the example condered n th paper are planar, the approach can be extended to the more general threedmenonal cae. g. 3b how an example LSS concept conguraton condered n th tudy. he tructure dameter approxmately two klometre. or uch a planarlke tructure, the tructure tne n the plane o the tructure much larger than the tne normal to th plane. Robot 1 orce/orque enor Bae LSS 2.2 Sytem Model LSS Module r e1 Y Z X r G y x r e2 è g. 2. Sytem model Reacton Wheel Robot 2 Each robot aumed to have N rgd lnk and a reacton wheel whoe ax parallel to the Z ax, g 2. It aumed that each robot ha at leat three lnk and that t grap the beam rmly at t end. Each robot apple orce to the module but not torque (the connecton act a a pnned jont). he tate o each robot decrbed by t jont angle vector θ, where =1 reer to the let robot and =2 to the rght robot. denote the torque appled at the jont o robot, the orce appled by robot to the module and J e the Jacoban or the poton r o robot endeector: e J e e r& = & θ (1) he robot dynamc wrtten n operaton pace (concde wth the nertal rame XYZ) are [8]: B & r η D r& = γ (2) A e A where η are nonlnear term and B A A, D A are the manpulator nerta and dampng matrce wth repect to t operaton pace. he vector γ the contrbuton o the endeector orce due to jont actuaton e A e : = J γ (3) he reacton orce and moment b µ exerted to b the LSS by the robot are (aumng low bae moton): b d L = (4) µ dt H r Ge r Gb b b where L, H are the robot lnear and angular momentum and r Ge, r Gb are vector tartng rom the robot centre o ma and endng at t endeector and bae repectvely. he module aumed to be contructed rom lender rod and cable and can be modelled a a long Euler Bernoull beam, g. 3a. he beam rgd body moton decrbed by t orentaton θ and the nertal poton r G o t centre o ma, g 2. Gven the nature o the tak condered here, θ and & θ are aumed to be relatvely mall. It alo aumed that the eect o orbtal mechanc neglgble, that the knematc and dynamc parameter o the module are relatvely well known and that ntally the beam ha no vbraton. he beam vbraton dplacement u approxmated by the rgd body moton and the rt N mode o the reeree beam through the aumed mode method [9]. he correpondng equaton or the dynamc o the reeree beam are: M & x = W (5) r [ ] 1 2 h1 ( t) 2 1 q& 2Z Ωq& Ω q = W =... (6) v 2 h ( t) N where [ ] x = θ the beam rgd body tate, r G M the beam ma matrx, Z and Ω are the beam modal dampng and natural requency matrce, and W r, W v are grap matrce [1]. g. 3. Sample LSS tructural module (a) and LSS under contructon (b) 3. APPROACH OVERVIEW In the propoed approach, called Vbraton Mnmzaton ung Redundancy (VMR), robot plan

3 and control the orce they apply to the module and the LSS through cloed loop orce controller, g. 4. he robot plan and control the orce they apply to the module cooperatvely o that the module potoned accurately and wth low level o redual vbraton. Each robot explot t redundancy to plan and control the reacton orce and torque b µ t apple to b the LSS o that the vbraton nduced to the LSS mnmzed whle t avod collon or underable conguraton. orce Plannng d Endpont orce Controller Bae orce & Moment Controller b, ì b ô E ô B è ô g. 4. Overvew o the VMR algorthm Plant Dynamc or the cae condered here, the plannng and control algorthm or the orce appled to the module and to the LSS are omewhat derent. he endpont orce controller or the orce calculate jont torque E or all robot ung orce meaurement rom all robot. h orm o robot cooperaton mprove the ablty o the robot to control the orce compared to the cae where each robot control the orce t apple to the module ndependently. he dered orce d or each robot are planned o that the module placed accurately, wth low redual vbraton and the load dtrbuted evenly among the robot. Each robot plan and control ndependently the reacton orce and moment µ t apple to the b b LSS whle multaneouly avod underable conguraton. he dered reacton and bd µ bd mnmze the exctaton o vbraton n the LSS. h acheved through a varaton o the parallel orce/poton control cheme n combnaton wth robot moton plannng and ue o reacton wheel [11]. he total actuaton or the robot jont : = E B = J eγ E B (7) where E and B are the jont torque or the th robot rom the endpont orce controller and the bae reacton orce/moment controller repectvely. 4. ORCE PLANNING h ecton decrbe a mple algorthm or the calculaton o the dered orce that robot are to d apply to the module o that t potoned accurately and wth low level o redual vbraton. he ntal beam poton and orentaton are r G ( ) = and θ ( ) =. he dered module poton and orentaton are r G ( t), θ, where t the maneuver duraton. he jth component o d expreed a a um o M nuod: jd M ( t) = { a n( ω t)} (8) k= 1 jk where =1,2 and j = X,Y. he requence ω p are choen to be wthn the bandwdth o the endpont orce controller. he value o the parameter a jk are ound by mpong the ollowng contrant: 1. he orce are alway mooth. d 2. he orce caue the beam to tranlate by d r G and rotate by θ. 3. he orce nduce mnmum redual d vbraton n the beam ater the maneuver. h acheved by mpong the ollowng condton or each one o the beam mode that domnate t vbraton repone [12]: L{ h } t h ( t) e p t dt = (9) where h dened n Eq. 6 and the pole o beam mode. he condton or robut redual vbraton elmnaton at th mode : t dl{ h} t = th ( t) e dt = (1) d he mode that domnate the beam vbraton repone when the beam excted at t end by the orce are elected a the mode wth the hghet Hankel ngular value [13]. or mall angle θ, the mpoed condton orm a lnear ytem A p a = b p where A p, b p are coecent matrce and a contan the unknown parameter a jk. he oluton o th ytem obtaned by ung the peudonvere o A [1]. p

4 h orce plannng approach computatonally ecent and provde mooth orce prole. Redual vbraton elmnaton can alo be acheved by nput hapng [14]. he method decrbed n th ecton omewhat more general than nput hapng becaue t can deal wth nonzero ntal vbraton condton. It alo can be run onlne to provde updated orce command wthout nducng tme delay. 5. ORCE CONROL DESIGN 5.1 Endpont orce Controller h ecton decrbe the degn o the endpont orce controller that control the orce robot apply to the module n order to track the command. he d degn baed on a lnearzed nomnal model o the robotbeam dynamc, obtaned or ome robot conguraton (where B A and D A are contant): γ 1 x& = A x B γ 2 (11) 1 = C x 2 where x the ytem tate. he vector γ are dened n Eq. 2 and 3. he plant zero are the pole o the reeree beam. he plant pole are the pole o the total robotbeam ytem. Snce pace tructure have poor modal dampng, the ytem pole and zero are located very cloe to the magnary ax. I each robot control ndependently t nteracton orce by a PI controller (orce controller uually contan P and I term to avod the derentaton o noy orce gnal) the cloed loop perormance poor becaue controller gan mut be kept too mall to avod makng the cloed loop ytem untable. h problem overcome by the controller degn hown n g. 5. he endpont orce controller cont o a tate eedback controller (centralzed controller) combned wth the ndvdual PI controller that each robot ue to control t. he centralzed control acton ue meaurement o rom all robot to calculate jont torque or all robot: C C γ γ = K x (12) [ ] E1 E 2 C γ the part o γ (ee Eq. 7) that E E where correpond to the centralzed part o the controller. he ytem tate x etmated rom meaurement o. he centralzed part o the controller explot robot cooperaton to mody the dynamc o the robotmodule ytem. h allow the applcaton o larger gan n the PI controller o each robot that mprove cloed loop perormance. 1d 2d 1 2 Robot 1 PI orce controller Robot 2 PI orce controller Decentralzed Control Acton ã E1 ã E2 J e1 J e2 ô ô Centralzed Control Acton E1 E2 tate eedback controller g. 5. Endpont orce controller Plant Dynamc 2 1 he robutne o the cloed loop perormance to the conguraton dependent nertal properte o the robot acheved n two way. he rt the applcaton o an actve dampng term: damp = J e D Ad J & eθ (13) where D Ad the dered dampng or robot, ee Eq. 2. he econd to mnmze the robot nerta een by the beam. h acheved by a multlnk robot degn where the majorty o t weght concentrated n t mddle lnk and by explotng robot redundancy to avod certan robot conguraton (or example ngular one). 5.2 Bae Reacton orce/moment Controller h ecton decrbe the cloed loop controller or the reacton orce and torque b µ appled by each b robot to the LSS. It aumed that the LSS ntally ha neglgble vbraton. It dered to keep the vbraton mall by elmnatng the reacton and µ n the b b drecton that nduce gncant vbraton n the LSS. or the cae condered here, th the drecton normal to the plane o the LSS, ee g. 3b. he degn o the bae reacton orce controller derent than the degn o the endpont orce controller (ecton 5.1). Each robot apple a cloed loop cheme to control t own reacton orce and to avod underable jont conguraton. he controller hown n g 6, and a varaton o the parallel orce/poton control cheme [11]. Each robot control the moton o t redundant jont θ and t reacton wheel ψ by mple jont PD controller. Snce each robot control already the two

5 component o, t ha the reedom to control the N 2 remanng jont. he cloed loop orce/moment acton acheved by tranlatng the error between the dered and the actual bae reacton orce and moment nto a change n the dered jont acceleraton & θ d through a PI controller. d Module Dynamc Model Robot Momentum Plannng Robot Moton Plannng r e.. L, H PrortyBaed Robot Invere Knematc è d ø d Robot Jont Controller PI Controller è, ø ô B Sytem Dynamc b, ì b bd, ì bd gure 6: Bae reacton orce/moment controller he command or the robot jont moton θ d and the robot reacton wheel moton ψ are calculated through d a prortybaed nvere knematc algorthm [1]. he algorthm prorte are: 1. he robot endeector velocty matche the etmated moton rˆ e o the correpondng beam end that nduced by the planned orce. d rˆ & e = J & e θ d (14) 2. he momentum o the robotmodule ytem reman contant. he momentum o each robot approxmated through a Jacoban J R a: L & θ = J R (15) H ψ& hen θ, ψ are planned o that the dervatve d d o robot momentum equal the eectve orce and moment at the robot CM due to the orce appled by the module to the robot : && θ d BCL d = J R (16) r Ge µ d BCL & ψ d where, µ are the output o the bae BCL BCL reacton orce/moment PI controller. 3. he robot avod underable conguraton. Each robot can control the orce whle elmnatng bae reacton orce t able to vary t lnear b momentum accordng to Eq. 16. Aumng low robot bae moton, the robot momentum expreed a: L = m & r& ) (17) ( Gb d h ablty lmted by the ze o the locu o reachable locaton or the robot CM (CMworkpace) r Gb. he ze o the CMworkpace larger or robot that have many lnk and concentrate ther weght n a ngle heavy mddle lnk. he elmnaton o bae reacton moment µ mproved by ung reacton b wheel that do not have workpace contrant although they can be lmted by actuator torque and peed lmt. 6. SIMULAION RESULS 6.1 Sytem Decrpton he perormance o the VMR controller evaluated by mulatng a planar manpulaton o a beamlke lexble module by two robot, ee g. 2. he properte o each robot are hown n able 1. Each robot ha orce/torque enor n both endeector and a reacton wheel at t mddle lnk, ee g. 7. Heavy robot body Reacton wheel Z Y X è 13 è 14 è 12 Bae LSS m b è 15 è 16 orce/orque enor è 11 kb è 17 LSS Module (ntal poton) LSS Module (nal poton) g. 7. he planar ytem ued n mulaton. Only one o the two robot that manpulate the beam hown. able 1: Robot properte Number o lnk: 7 Lnk length [m]: [3, 3, 3, 2, 3, 3, 3] Lnk ma [kg]: [18,18,18,242,18,18,18] Reacton wheel nerta [kg m 2 ] 2 he module modelled a an EulerBernoull beam. he properte o the beam condered n the mulaton are hown n able 2. able 2: Beam properte Length [m]: 2 Young modulu [GPa].159 Lnear denty [kg/m]: 3 Lowet vbraton mode [Hz] 1 =.197, 2 =.539, 3 =1.42 he robot bae tructure condered rgd n the X drecton and complant n the Y drecton. he bae dynamc n the Y drecton are modelled by a ma m o 2 kg and a prng rate k o 2 N/m, g. 7. B B

6 he robot manpulate the beam rom t ntal poton r G (), θ () to t nal dered poton r G ( t),. he parameter o the θ wthn tme t mulated manpulaton tak are hown n able 3. he degn o the robot controller baed on the peccaton hown n able 4. able 3: Manpulaton parameter Beam ntal poton r G () [m] [,] Beam dered poton r G ( t) [m] [,6] Beam ntal orentaton θ () [deg] Beam dered orentaton θ [deg] Manpulaton duraton t [ec] 4 able 4: Controller degn peccaton Poton error o r G ( t) [m] ±.1 Orentaton error o θ [deg] ±.5 Redual vbraton at beam end [m] ±.1 Redual vbraton at robot bae [m] ± VMR Controller Degn he VMR algorthm, g. 4, cont o an endpont orce controller or the orce appled by the robot to the module, and a bae reacton controller or the robot bae reacton orce/moment and jont moton. able 5 provde the pole that are ued to calculate the gan K or the centralzed part o the endpont orce controller. able 5 alo provde the poton o the correpondng pole o the reeree beam. able 5: Dered pole o the robotmodule dynamc reeree Beam Pole Dered pole or the degn o the gan K 1 =.116 ± =.6 ± j 2 = =.5 ± 2.9j he nput o the centralzed orce controller ltered by a lowpa lter to avod pllover eect [15]. he cutto requency o the lter ω = 4.5 rad/ec: he decentralzed part o the endpont orce controller cont o PI controller or each component o. he beam condered rgd along the X drecton and lexble along the Y drecton. hereore, derent PI controller G CX, G were ued to control the X and CY Y component o :.88.8 G CX = 2 b.75.5 G CY = 2 he actve dampng added by each robot to the ytem, Eq 13, correpond to the dampng matrx: 5 D Ad = 2 he parallel orce/poton controller or the bae reacton orce and torque cont o jont PD controller or the robot redundant degree o reedom and a PI controller or each component o bae reacton, g 6. he PD jont controller gan or the rt jont o the robot are K = 1[ ] K DM and = 1[ ]. he PD gan or the reacton wheel control are k Pw = 2 and k Dw = 5. he PI controller or each component o the bae reacton orce and moment are: G CB ( ) = Smulaton Reult he robot degn ued n the mulaton ha a large number o jont and the majorty o t weght concentrated n a ngle mddle lnk, the robot body. h degn ha two derable eect. he rt that the beam eel a very lght robot a long a the robot avod conguraton where t lat two jont are concurrently maller than 3 degree. h make the robot able to control ater command. he econd that the CMworkpace o the robot relatvely large, roughly a crcle wth radu 9m. h make eaer or the robot to elmnate t bae reacton orce whle controllng the orce t apple to the module, ee Secton 5.2. g. 8 how the calculated orce that each robot d commanded to apply to the module. Each orce component planned a a um o M=2 nuod. he obtaned orce command mooth and a d expected reult n acceleratng and then deceleratng the beam. g. 8 alo how the mulaton reult or the orce ung the VMR algorthm. he delay between the command and the repone d generally le than 1 ec. PM

7 orce [N] repone Y command Yd repone X In th cae, where the bae aumed to be rgd along the X drecton, each robot need to control only the Y component o t bae reacton orce. he dered command byd =. Each robot ue t reacton wheel to reduce the magntude o the torque t apple to the LSS. In the general three dmenonal cae robot could control all the component o and µ. b b 1 15 command Xd tme [ec] g. 8. orce command d ung the VMR method. and actual orce repone he endpont controller track the commanded orce well enough to poton the beam wthn the d requred poton accuracy. g. 9 how the repone o the beam moton ung the VMR method and the repone o the beam when the beam drven by deal orce equal to. g. 9a how the repone o the d beam CM moton. g. 9b how the repone o vbraton delecton at the beam end. he derence between the deal cae and the reult ung the VMR algorthm mall. beam CM Y poton [m] vbraton dplacement [m] repone ung VMR beam drven by orce d tme [ec] beam drven by orce d repone ung VMR tme [ec] (A) (B) g. 9. a)poton repone o the beam CM and b) vbraton delecton at the let beam end. g. 1 and 11 how the eectvene o the VMR algorthm n elmnatng bae reacton orce and moment. hey how mulaton reult ung the VMR algorthm when the whole algorthm ued and when the bae reacton controller not ued. g. 1 how mulaton reult or the Y component o robot 1 bae reacton orce b 1 Y. I no bae orce control appled, the magntude o the bae reacton orce omehow larger than the magntude o the command or th d robot. g. 11 how mulaton reult or the bae reacton torque o robot 1. g. 1 and 11 how that the VMR algorthm elmnate the Y component o the reacton orce and reduce the magntude o the torque appled to the bae. orce [N] wthout bae reacton orce control wth bae reacton orce control tme [ec] g. 1. Reacton orce appled to robot 1 by the LSS torque [Nm] wthout plannng acton wth plannng acton tme [ec] g. 11. Reacton torque appled to robot 1 by the LSS

8 g. 12 how mulaton reult or the poton repone o robot 1 bae wth and wthout bae orce control. When the bae reacton orce are not controlled they caue large dplacement n the complant LSS. hee dplacement may orce the robot to get nto underable conguraton that deterorate gncantly the perormance o the endpont orce controller, g. 13. In th cae robot al to poton the beam accurately. he bae reacton orce controller o the MVR algorthm reult n mall bae reacton orce/moment that nduce mall vbraton n the robot bae, g. 12. h allow the ucceul control o the orce that robot apply to the module, ee g. 8. bae dplacement [m] 1.5 wthout bae reacton 1 orce control wth bae reacton orce control tme [ec] g. 12. Bae dplacement repone o robot 1 wth and wthout bae reacton orce control orce [N] repone 1Y 15 command 1Yd tme [ec] 4 5 g. 13. Command orce 1 Yd and repone 1 Y when the bae reacton orce are not controlled. 7. SUMMARY h paper decrbe an algorthm or the manpulaton o large lexble tructural module by a team o redundant robot that are mounted on lexble bae tructure. he algorthm plan and control cooperatvely the orce appled by the robot to the module n order to maneuver the module accurately and wth low redual vbraton. he algorthm alo mnmze vbraton exctaton n the complant robot bae tructure by ung a cloed loop controller and explotng robot redundancy. 8. ACKNOWLEDGEMENS h work ponored at MI by the Japanee Aeropace Exploraton Agency (JAXA). he author would lke to thank Dr. Matt Lchter and Peggy Bonng or ther helpul comment. 9. REERENCES 1. M. Oda et all, Study o the Solar Power Satellte n NASDA, Proc. o SAIRAS 23, Nara, Japan, May W. Whttaker et all, Robotc or Aembly, Inpecton, and Mantenance o Space Macroaclte, AIAA Space 2 Conerence, Reton VA, September 2 3. Senda K. et all, Hardware Experment o Space ru Aembly by Autonomou Space Robot, AIAA Gudance, Navgaton and Control Conerence, Denver CO, Augut 2 4. Doggert W., Robotc Aembly o ru Structure or Space Sytem and uture Reearch Plan, IEEE Aeropace Conerence 22, Vol. 7, March 22, pp Yakawa. et all, Stablty o Control Sytem n Handlng o a lexble Object by Rgd Arm Robot, 1996 IEEE Internatonal Conerence on Robotc and Automaton, Mnneapol MN, pp , Aprl orre, M. and Dubowky, S., Path Plannng or Elatcally Contraned Space Manpulator Sytem, 1993 IEEE Internatonal Conerence on Robotc and Automaton, Atlanta GA, Vol. 1, pp , May Yohda et all, Vbraton Suppreon and Zero Reacton Maneuver o lexble Space Structure Mounted Manpulator, Smart Mater. Struct., 8, 1999, pp Khatb O., Inertal Properte n Robotc Manpulaton: An ObjectLevel ramework, he Internatonal Journal o Robotc Reearch, Vol. 13, No. 1, ebruary 1995, pp Merovch L., Method o Analytcal Dynamc, Dover Publcaton, Nakamura Y., Advanced Robotc; Redundancy and Optmzaton, AddonWeley Publhng, Chavern S., Sclano B., he Parallel Approach to orce/poton Control o Robotc Manpulator, IEEE ran. Automatc Control 1993, 39, pp Bhat S. and Mu D., Prece PonttoPont Potonng Control o lexble Structure, ASME Journal o Dynamc Sytem, Meaurement and Control, December 199, Vol. 112, pp Gawronk W., Dynamc and Control o Structure; a Modal Approach, Sprnger, Snger N.C., Seerng W.P., Prehapng Command Input to Reduce Sytem Vbraton, ASME Journal o Dynamc Sytem, Meaurement and Control, March 199, Vol. 112, pp Bala M., eedback Control o lexble Sytem, IEEE ranacton on Automatc Control, Vol. 23, No. 4, Augut 1978