Minimising Energy Consumption for Robot Arm Movement

Transcription

1 Mnmsng Enegy Consumpton fo obot Am Movement Abdullah Mohammed, Benad Schmdt, Lhu Wang, Lang Gao KH oyal Insttute of echnology, Bnellvägen 8, Stockholm, SE- Sweden, E-Mal: Unvesty of Skövde, Högskolevägen, Skövde, SE- 8 Sweden, E-Mal: benad.schmdt@hs.se Huazhong Unvesty of Scence and echnology, 7 Luoyu oad, Wuhan, 7 Hube, Chna, E-Mal: gaolang@mal.hust.edu.cn Abstact obots ae wdely used n ndusty due to the effcency and hgh pefomance. Many of them ae opeatng n the manufactung stage of the poducton lne whee the hghest pecentage of enegy s consumed. heefoe, the enegy consumpton became a majo focus fo many obots manufactues and academc eseach goups. Nevetheless, the optmsaton of that consumpton s stll a challengng task whch eques a deep undestandng of the obot s knematc and dynamc behavous. hs pape poposes an appoach to develop an optmsaton module usng Matlab to mnmse the enegy consumptons of the obot s movement. Wth the help of Denavt-Hatenbeg notaton, the appoach stats fst by solvng the nvese knematcs of the obot to fnd a set of feasble jont confguatons equed to pefom the task, solvng the nvese knematcs s usually a challengng step whch eques n-depth analyses of the obot. he module then solves the nvese dynamcs of the obot to analyse the foces and toques appled on each jont and lnk n the obot. Futhemoe, a calculaton fo the enegy consumpton s pefomed fo each confguaton. he fnal step of the pocess epesents the optmsaton of the calculated confguatons by choosng the one wth the lowest powe consumpton and sends the esults to the obot contolle. hee case studes ae used to evaluate the pefomance of the module. he expemental esults demonstate the developed module as a successful tool fo enegy effcent obot path plannng. Futhe analyses fo the esults have been done by compang them wth the ones fom commecal smulaton softwae. he case studes show that the optmsaton of the locaton fo the taget path could educe the enegy consumpton effectvely. Keywods: enegy consumpton, path plannng, obot dynamcs. INODUCION Many ndustal countes wtnessed an ncease n pces of both electcty and fuel dung the last decade. Accodng to the ecent statstcs one of the lage consumes of enegy s manufactung ndusty. he majoty of the enegy s usually consumed by obots used n the manufactung ndusty. In addton, the optmal usage of enegy n obots plays an mpotant ole n mnmsng CO emsson n the poducton stage of a poduct s lfecycle. Industal obots ae often seen as unsustanable equpment that demand a hgh level of enegy consumpton. On the othe hand, those obots povde pecson; stength and sensng capabltes whch can poduce hgh qualty end poducts []. Consequently the obotc enegy consumpton became a majo objectve fo many eseach goups and obot manufactues. Seveal eseaches focused on defnng tools to measue and analyse the obot s enegy consumpton. Fo example the wok epoted by [] contbutes to dentfyng enegy effcent stateges n obotc applcatons. Othes lke [] summased dffeent methods fo enegy-effcent use of common ndustal obots. At the same tme, many eseaches pesented obotc tajectoy plannng appoaches that have the ablty to optmse tme and enegy consumptons [- 7]. Howeve, these appoaches put a hgh poty on mnmsng the movement tme of a obot, whch may not necessaly povde a mnmsaton of the enegy consumpton. he total enegy consumed by the obot s usually affected by the equed toque on each jont and neta tensos of each lnk. Othe eseaches focused on optmsng a obotc manufactung system as a whole [8, 9]. Despte the afoementoned effots, mnmsng obotc enegy consumpton emans a challenge and eques futhe nvestgatons. In ths pape we ntoduce an appoach to mnmsng the enegy consumpton of an ndustal obot s movements. It s acheved by developng a module that optmses the obot s jont confguaton to follow a cetan tajectoy defned by an opeato. We evaluated the pefomance of the system by compang the esults of the optmsaton module wth those of commecal smulaton softwae of the obot. hee scenaos have been used to study the esults of the developed module; wth and wthout a payload at the obot s end-effecto. Futhe expements have been pefomed n dffeent locatons of the obot s wokspace to dentfy the aeas wth the lowest level of enegy consumpton. SYSEM OVEVIEW he developed system conssts of modules: the fst one s esponsble fo pepang the desed tajectoy of the obot wth the desed velocty and acceleaton. he second module s dedcated to solve the nvese knematcs of the tajectoy. he thd module calculates the fowad and backwad ecusons to solve the nvese dynamcs of the desed task. he enegy consumpton s calculated by the fouth module, ntoducng a set of obot s jonts confguatons to be optmsed n the ffth module. Fgue llustates the developed modules whch ae mplemented n MALAB softwae. he 8th Intenatonal Confeence on Dgtal Entepse echnology (DE), Stuttgat, Gemany

2 Fgue : Ovevew of the developed system. MEHODOLOGY he mplementaton of the system stats by buldng the mathematcal model of the obot to solve the knematcs and dynamcs ssues and calculate the obot s feasble jont confguatons. he system then optmses the obot s jonts confguatons to fnd the best one based on enegy consumpton. Both the knematc and dynamc models of the obot have been developed to analyse the foces and toques on the obot s jonts dung the moton of the obot. As an example the ABB IB ndustal obot has been chosen.. Denatv-Hatenbeg notaton hs development eques fst establshng the knematc paametes of the obot and assgnng the jonts fames. he defntons of the paametes ae qute cucal fo the knematcs and dynamcs calculatons n the fothcomng steps. he descptons of the obot jont s fames wee based on the Denavt-Hatenbeg (D- H) notaton. Statng fom the base of the obot, the fames have been assgned fo each jont. It s acheved by takng nto account that the jont s otaton s always aound the z-axs of the assgned fame. Fgue shows applcaton of the D-H notaton on the obot model. Fame maked as s assgned to the obot base (lnk ) and s used as global/wold fame. Fames,, ceate the obot wst and the ogn s located n the same place, called wst cente P w =[P xw P yw P zw ]. Paametes a -a, d and d ae used to descbe tanslaton between fames n appled D-H notaton. Fgue : obot's fames assgnments.

3 . Fowad knematcs he fowad knematcs s pefomed to calculate the tansfomaton matx that descbes the locaton and oentaton of the end-effecto of the obot wth espect to ts base. Wth the help of the defned D-H paametes, the matx s found by fst calculatng the tansfomaton matces of each jont wth espect to the pevous ones, and then multplyng eq. () those matces. he esult s a tansfomaton matx that descbes the elatonshp between the end-effecto and the base of the obot. ( ) ( ) ( ) ( ) ( ) ( CP ) ( ) CP P ( ) CP CP () Fgue : he fst jont angle pojecton on the x-y plane. j s tansfomaton matx between lnk and j, s whee: CP tansfomaton appled by tool attached to lnk of the obot. CP and P ae espectvely otaton matx and tanslaton vecto. In fowad knematcs, tansfomatons ae functons of jont values.. Invese knematcs Solvng the nvese knematcs of the obot s an mpotant step fo calculatng the nvese dynamcs of the obot n the fothcomng steps. It s achved unde the assumpton that the fst thee jonts ae esponsble fo the end-effecto s poston and the last thee ae esponsble fo ts oentaton. Wth gven poston and oentaton of the taget locaton, the poston of the wst s calculated. he pevous assumpton povdes a smplfcaton fo the calculatons theefoe t s wdely used fo solvng the nvese knematcs of the seal-chan manpulatos. he calculaton of the fst thee jonts (,, ) s made geometcally, wheeas the last thee jonts (,, ) ae calculated analytcally. he pocess stats by solvng the confguaton of the fst jont n eq. (). It s acheved by lookng at the obot fom the top vew as seen n Fgue ; whch clealy shows that the angle changes the obot s wst poston n the x-y plane. heefoe, s calculated usng atan functon defned by eq. () and the esults s angle value wthn a ange: [-:]. Fo jont thee ae two possble values, that coespond to the confguatons that obot am s eachng the taget towad o backwad. Havng moe than one value fo some of the obot s jonts povdes nvese knematc solutons wth multple confguatons. a tan ( P yw,p xw ) () a tan ( P, P ) yw xw Fgue : he second jont and thd jont angles pojecton. hen the values of the next two angles ae calculated by lookng at the plane Z-XY fomed by lnk and lnk of the obot n Fgue. It stats by calculatng cos value usng equaton () whch s used late to calculate jont value by mplementng equaton (). wo values coespond to two obot am confguatons, as shown n Fgue. d cos a a P zw d a a d P a cos P a sn xw yw atan cos,cos () atan cos,cos () a tan ( y, x ) actan( y / x ) actan( y / x ) actan( y / x ) undefned x y, x y, x y, x y, x y, x () he pocess then contnues to calculate jont value accodng to equaton () fo each value of. β α P zw d β atan a α atan d a sn a a cos ()

4 When the fst thee jont values ae obtaned n all confguatons, wth fowad knematcs the oentaton of the wst can be calculated (7) and the otaton that have to be appled n the wst (8). (,, ) (7) W zxz,, W CP CP Z X Z α β γ When Eule angles,, n confguaton ZXZ ae used to expess otaton ZXZ, the dependency between these angles and jont values s gven n (9). o obtan Eule angles fom known otaton matx calculatons follow (-). (8) veloctes and acceleatons fo all possble confguatons. Afte that, fowad-backwad ecuson algothm s appled. Fowad ecuson hs pocess s used to obtan the lnea and angula moton of each lnk of the obot. It stats fom the fst lnk to the last one N=, and wth assumpton that obot base (lnk) s not movng, the ntal condtons; angula velocty and acceleaton togethe wth lnea acceleatons a, a c ae all set to be. hen the angula velocty and acceleaton fo each lnk as well as lnea acceleatons at the end a and the gavty cente a c of the lnk ae also calculated usng equatons (). ω α a a c ω z α z ω z a ω, ω ω, a ω,c ω ω,c () α, β, γ (9) atan, β () atan, Backwad ecuson he foces and toques affectng the jonts of the obot ae calculated n ths step. he pocess stats fom the last lnk N and ends at the fst lnk. he angula velocty and acceleaton values whch ae obtaned n the pevous step ae used n the cuent stage. Fst, the gavty vecto g s expessed n fame fo each lnk usng equaton (). g g () α atan, sn β sn β γ atan, sn β sn β () Fo each confguaton of the fst jonts, two possble confguatons () n the wst can be obtaned. hat gves n total eght possble confguatons of jont values fom nvese knematcs. Havng at least one confguaton means that the taget s eachable by the obot.. Invese dynamcs Due to ts effcency ecusve Newton-Eule Algothm (NEA) [] s used to calculate the necessay paametes fo the enegy consumpton calculaton. Wth a gven set of jont acceleaton the algothm s able to calculate the toque and foce value of each jont. o stat usng the method, the netal tenso matxes values need to be obtaned fst. heefoe the D CAD model of the obot s used wth the help of SoldWoks softwae to calculate the netal data. Calculatons have been made wth assumpton that the mass of each obot lnk s dstbuted equally though the volume of the lnk. aget path s ntepolated wth small tme ntevals. Fo each pont on the path nvese knematcs s pefomed to obtan jont postons, hen the foces f and toques ae calculated fo each lnk usng equatons (). At ths stage, nputs ae extenal foces and toques f N+, N+ appled to the obot end effecto. f m a c g τ f,c f,c ω f τ I ω I a (). Enegy consumpton calculatng he calculaton of the powe consumpton s pefomed by two steps. Fst, the powe consumed n each jont dung a specfc tme nteval k s found, and then the total powe consumpton at that nteval s calculated by summng all jonts powe consumptons as shown n equaton (). Fo shot tme ntevals, t can be assumed that toque and angula velocty ae constant. P k τ k k n ) P k P( k ()

5 he enegy consumpton s then calculated n equaton (), whee d tk s the length of kth tme nteval of the path dvded nto M ntevals. t M E t M P( t )dt k ) k P( dt k (). Enegy optmsaton he developed system s desgned to choose the jont confguaton that eques the lowest enegy consumpton. Snce the numbe of possble confguatons s lmted to a few solutons; an optmsaton algothm s mplemented to analyse the consumpton n each confguaton n teatve way though the whole taget path and chooses the best one. CASE SUDIES he valdty of the optmsaton module was examned usng thee scenaos: staght lne, squae path and dffeent locatons. hese scenaos ae explaned n detal n the followng sectons.. Staght lne scenao In ths case, a staght lne path begnnng at (9,, ), and endng at (9, -, 8) mm was used as a desed tajectoy fo the end-effecto of the obot. Stat conf. Stat jont values End conf (,,,x) (-,,,x).9 End jont values Enegy consumpton [J] Module obotstudo Payload kg kg able : Staght lne scenao esults fom the optmsaton module. wo expements have been done to evaluate the pefomance of the module, wth and wthout payload; both n the obot smulaton softwae (obotstudo ) and n ou optmsaton module. able shows the esults fom the optmsaton module compaed wth the obotstudo ones.. Squae path scenao A squae shaped path s used as anothe case to evaluate the developed system. he system s agan tested wthout and wth payload. Optmal tajectoy fo the case wth payload s pesented on Fgue, whee jont values ae obtaned though nvese knematcs, jont velocty and acceleaton ae calculated by dffeentaton and toques ae obtaned wth nvese dynamcs calculatons. able and able show the esults fom the optmsaton module and the ones fom obotstudo, espectvely. he dffeences n enegy consumpton calculated by ou mplemented module and obotstudo ae caused by the smplfcaton of used dynamc model. Cones jont values Enegy consumpton [J] wthout load wth load Optmal confguaton (-,,,x) able : Squae path scenao esults fom the optmsaton module. Jont values [ad] Velocty [ad/s] Acceleaton [ad/s] oque [Nm] theta theta theta theta theta theta.... me [s] me [s] me [s] me [s] Fgue : esults obtaned fom the second case.

6 Enegy consumpton [J] Jont confguaton wthout load wth load (-,,,x) (,,,x). 8. (-,-,,x).9. able : Squae path scenao esults fom obotstudo. Enegy consumpton [J] dynamc model whch s affected by the techncal specfcatons and the task equements. Ou futue wok wll focus on the dynamc model of the obot, as t needs to be expanded to consde fcton and the dynamcs of the actuatos that nclude motos, geas and couplngs. he cuent mplementaton has a modula stuctue, and t can be easly updated wth moe accuate model as well as extended fo othe types of obots. Moeove, valdaton of enegy consumpton model wth actual enegy consumpton though eal expement and measuements need to be pefomed. Futhemoe, the developed enegy optmsaton module can be extended n the futue to consde the oentaton of the taget path x [m]...8 Fgue : Enegy consumpton fo task pefomed n dffeent locatons n obot wokspace.. Dffeent locatons scenao In ths scenao squae hozontal path s placed n dffeent locatons n obot wokspace. Fo each locaton the mnmal enegy consumpton fo optmal confguaton s calculated. Fgue pesents how the enegy consumpton depends on the locaton of the taget path n the obotc space. Data ae vsualsed fo slces x=, y= and z=.he colou n the fgue ndcates the level of the powe consumpton. Whte ponts epesent the locatons whee the task cannot be pefomed. It could be notced that enegy needed to pefom the task vaes sgnfcantly and s stctly elated to the locaton of the taget path. hs scenao povdes a tool fo the obot cell desgne to place the wokpece n the sutable locaton. he ed ponts n the fgue gve ndcaton to the desgne to avod the aeas that consumes the hghest level of enegy. CONCLUSIONS It s mpotant to optmse the enegy consumpton fo the economc aspect as well as to mnmse the potental envonmental mpact. he same taget can be eached by the obot am wth dffeent confguatons and each confguaton needs dffeent powe consumpton. Ou module addesses ths ssue by selectng the optmal confguaton to pefom the task. As pesented n the last case, the enegy consumpton fo pefomng the task depends also on the locaton whee the taget path s defned. In ths case the optmsaton of the locaton of the path to mnmse the enegy consumpton seems to be equed to ensue enegy savng. he optmal locaton depends on the obot s..... y [m]. ACKNOWLEDGMENS hs wok s suppoted by GEENet poject. he authos of ths pape would lke to thank Andea Azamend Moñux and Men Matcoena Lzaso fo the patal contbutons. 7 EFEENCES [] Bugmann, G., Segel, M. Bucn,. (): A ole fo obotcs n Sustanable Development, In: Poceedngs of the IEEE Afcon, p. -. [] Chemntz, M., Scheck, G., Kuge, J. (), Analyzng enegy consumpton of ndustal obots, In: Poceedngs of the IEEE EFA'. [] Meke, D., bcks, L. (): Enegy Effcent Use of obotcs n the Automoble Industy, In: Poceedngs of the th Intenatonal Confeence on Advanced obotcs, p. 7-. [] Hansen, C., Oltjen, J., Meke, D., Otmae,. (): Enhanced Appoach fo Enegy-Effcent ajectoy Geneaton of Industal obots, In: Poceedngs of 8th IEEE Intenatonal Confeence on Automaton Scence and Engneeng. [] Meke, D., bcks, L. (): Industal obot Path Optmzaton Appoach wth Asynchonous FLY-BY n Jont Space, IEEE Intenatonal Symposum on Industal Electoncs (ISIE), p.9-9. [] We, Y., Mnxu, K., Lnng, S.(): Optmal moton geneaton fo heavy duty ndustal obots-contol scheme and algothm, In: Poceedngs of the IEEE Intenatonal Confeence on Mechatoncs, p. 8-. [7] Vescheue, D., Demeulenaee, B., Sweves, J., De Schutte, J., Dehl, M. (8): me-enegy Optmal Path ackng fo obots: a Numecally Effcent Optmzaton Appoach, AMC '8. th IEEE Intenatonal Wokshop on Advanced Moton Contol, p [8] Vegnano, A., hostensson, C., Lennatson, B., Falkman, P., Pellcca, M., Leal, F., Blle, S. (): Modelng and Optmzaton of Enegy Consumpton n Coopeatve Mult- obot Systems, IEEE ansactons on Automaton Scence and Engneeng, 9:. [9] Meke, D., bcks, L. (): ecupeated Enegy Savngs Potental and Appoaches n Industal obotcs, In: Poceedngs of IEEE Intenatonal Confeence on Automaton Scence and Engneeng, p [] Luh, J.Y.S., Walke, M.W., Paul,.P.C. (98): On-lne Computatonal Scheme fo Mechancal Manpulatos, Jounal of Dynamc Systems, Measuement and Contol, ansactons of the ASME, :, p. 9-7.