Vibration and Speedy Transportation

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1 Research Paper EAEF (3) : 8-5, 9 Path Plag of Tomato Cluster Harvestg Robot for Realzg Low Vbrato ad Speedy Trasportato Naosh KONDO *, Koch TANIHARA *, Tomowo SHIIGI *, Hrosh SHIMIZU *, Mtsutaka KURITA *3,Mtsuyosh TSUTSUMI *, Vu Kog CHONG *, Shgemue TANIWAKI * Abstract A mapulator cotrol method was developed to realze the harvestg of operato for tomato clusters at hgh speeds. I robot harvestg, both speedy trasportato ad vbrato dampg are requred whe a tomato cluster s trasported to a box or a basket by usg a mapulator. A put shapg method (ISM) s oe of the typcal cotrol methods for such cotrol problems. Although the ISM requres accurate atural frequeces of the cotrolled object, the atural frequeces are dfferet for each tomato cluster. The, the detfcato of the atural frequecy was combed wth the ISM our method. Ths detfcato s based o the data obtaed real tme usg a mache vso system, a force sesor, ad a database o the physcal propertes of tomato clusters. A umercal smulato study ad expermets were coducted ad t was verfed that the proposed method was applcable to the tomato harvestg robot moto. [Keywords] harvestg robot, tomato, frut cluster, mapulator, moto ad vbrato cotrol. I Itroducto I recet years, the large-scale tomato producto a large-szed greehouse facltes has bee creasg, ad the cotrol of evrometal codtos ad varous operato procedures are hghly automated such facltes. However, a harvestg operato that requres huma volvemet s ot automated yet, ad ths fact preveted the mprovemet of operatg effcecy (Kodo ad Tg, 998; Kodo et al., 4). (),() I Japa, t s commo to harvest each tomato frut. O the other had, tomato cluster harvestg s popular Europe ad the Uted States because the operato effcecy s hgher ad frut freshess ca be mataed better by ths method. It s thought that tomato cluster harvestg becomes mastream large-szed tomato facltes. Therefore, ths project, a method of trajectory plag whe a robot arm trasports tomato clusters as elemetal techology for the automatc harvestg of a tomato cluster was studed. Trasportato ths paper s defed as the movemet from the posto where a tomato peducle of a tomato cluster s cut wth a ed effector to a basket for storg. It s requred to crease the trasportato speed for mprovg the workg effcecy. Moreover, the dampg vbrato of a tomato cluster s also desred for prevetg the frut from spolg. I geeral, speedg up ad dampg vbrato are coflctg requests, however, both speedg up ad dampg vbrato ca be smultaeously carred out by coductg the feedforward cotrol of a accelerato patter of a ed effector. Whe ths model-based feedforward cotrol method s appled to a trajectory for the trasportato of a tomato cluster, the atural frequecy of the tomato buch becomes determate ad such a techcal problem must be dealt wth. Therefore, the objectves of ths project were to develop a method for estmatg the atural frequecy of a tomato cluster real tme by usg the formato obtaed from a load cell ad a mache vso system that ca be easly stalled o the harvestg robot, ad to propose a method o how to adjust a cotrolled parameter of a put shapg method (Sger et al., 99; Blackbum et al., 6), whch s oe of the feedforward cotrol methods. II Modelg of tomato cluster ad cotrol method * JSAM Member, Correspodg author, Graduate School of Agrculture, Kyoto Uversty, Ktashrakawa-Owakecho, Sakyo-ku, Kyoto 66-85, Japa : [email protected] * Graduate School of Scece ad Egeerg, Ehme Uversty, 3, Bukyo-cho, Matsuyama, Ehme , Japa *3 Techology developmet departmet, S.I.Seko Co.Ltd, Matsuyama Sh Takaoka cho 66, Ehme, Japa

2 KONDO, TANIHARA, SHIIGI, SHIMIZU, KURITA, TSUTSUMI, CHONG, TANIWAKI : Path Plag of Tomato Cluster Harvestg Robot for Realzg Low Vbrato ad Speedy Trasportato 9. Outle of cotrol method A put shapg method (Sger et al., 99; Blackbum et al., 6) s oe of the methods of trajectory geerato for realzg both hgh-speed movemet ad dampg vbrato uder the kematc cotrol of a adaptable body (addedum cosultato). I ths method, t s premsed that the atural frequecy of the target object s kow, ad the feedfoward cotrol of the accelerato s performed such that the atural frequecy of the vbrato formed by put accelerato s deed by the vbrato that forms by aother put accelerato, as show Fg.. Arrows A ad A represet the accelerato of body ad A Respose ad A Respose represet the vbrato by the accelerato of A ad A. Total Respose expresses the sum of vbrato of the body. Vbrato arose from A ad t was caceled by A. However, t s dffcult to apply ths method drectly to a tomato cluster whe the dvdual dfferece of atural frequecy s large because ths method s used, robustess agast the varato of character frequecy of the cotrolled object s small ths method. Therefore, ths research, the cotrol parameters were adjusted by employg the character frequecy that was estmated from the mass ad the mass ceter of the dvdual frut cluster that were measured wth a load cell ad mache vso system. The bed test of actual tomato peducle was coducted to costruct a model for descrbg the relato betwee the cofgurato ad character frequecy of the tomato cluster, ad the relatoshp betwee the dameter of the tomato peducle ad bedg rgdty was derved. The character frequecy of the etre tomato cluster was calculated usg the sze of the etre frut cluster ad the estmated mass. Swg agle(deg) A A Tme(s) A Respose A Respose Total Respose Fg. Iput shapg method. Bed test of peducle The bed test was coducted as show Fg.. The dsplacemet of peducle was measured usg a laser dsplacemet sesor whe the same load was added o the peducle durg the defte perod. Oe ed of the tomato peducle was fxed ad a weght was loaded at the other ed; the tme course of the dsplacemet chage caused by bedg was measured. The bedg rgdty was approxmated by four elemet models (Phyto-techology, ; JSAM, 979), whch were ofte used for modelg the vscoelastc property of each part of plats, as show Fg.3. Each parameter was detfed by usg the expermetal results. The expermetal result of bed test of a peducle ad the umercal soluto of the detfed model were show Fg.4. The red crcle represets the actual measured values ad the black le represets the approxmate curve. It was clear that the vscoelastc property of the tomato s peducle ca be modeled as four elemet model wells. I the rage wth a small bed agle, the effect of k was domated as the resttuto force, ad ths s the major parameter for determg the atural frequecy whe a tomato cluster s trasported by a mapulator. The expermets were coducted usg te tomato peducles, ad the followg equato that descrbes the relato betwee the dameter of a peducle ad parameter k was obtaed. k = 33d.6 () 3. Vbrato expermet of tomato cluster A accelerato sesor was attached at the very ear mass ceter of a tomato cluster, ad oly oe ed of the tomato cluster was fxed ad the other ed was dsplaced. Free decay was determed ad the atural frequecy f l of the etre tomato cluster was calculated by aalyzg the obtaed accelerato waveform. The atural frequeces of eght tomato clusters are calculated ad the maxmum value, the average value, ad the mmum value are show Table. The atural frequecy of the frst mode s show ths table. I the actual stuato of vbratory cotrol for trasferrg the tomato cluster, the varato the atural frequecy should be cosdered. tomato peducle dsplacemet sesor weght Fg. Bedg test cofgurato

3 Egeerg Agrculture, Evromet ad Food Vol., No. 3 (9) D s p l a c e me t ( mm).5 k F k c c Fg. 3 Four elemet models Fg. 4 Deformato profle Table Natural frequecy Frequecy [Hz] Max.93 Average.7 M Estmato method of atural frequecy actual tme The parameters of each tomato cluster obtaed real tme durg the harvestg operato are mass m obtaed by usg the load cell attached to the ed effector, the dameter of peducle, ad the posto of mass ceter that s acqured by processg the captured mage by mache vso. The dstace l was defed as the dstace betwee the posto where the ed effector held the tomato peducle ad the mass ceter. The costat of sprg k was calculated by substtutg the dameter of the tomato peducle obtaed real-tme measuremet to Eq.(), whch was the model that descrbed the relato betwee peducle dameter ad bedg rgdty advace. Assumg that mass m was cocetrated at oe ed of a beam wth legth l whe the other ed of the beam was fxed uder the codto that the rate of sprg agast bedg s k, the atural frequecy of the etre frut cluster, f e, ca be formulated as Eq.(). k mgl = () π ml + f e Tme(s) Expermatal result Approxmate curve 5 5 Here, g s the accelerato of gravty. I ths maer, fe for each tomato cluster was calculated real tme. To evaluate the estmated error of f e, the relato betwee fe ad f l was plotted, as show Fg.5. The horzotal axs represets the estmated atural frequecy based o the theoretcal value (Eq.()) ad the vertcal axs represets the actual measuremet value of atural frequecy calculated by usg the accelerato sesor ad FFT aalyss. The correlato betwee f e ad f l was ot equal to because the model for fe was too smple. However, the relato betwee f e ad f l s showed as a lear fucto of Eq.(3) by the least square method. f.7 f +.34 (3) l = e Therefore, frst, m ad l were measured usg the sesors attached to the harvestg robot ad k was calculated by Eq.(). Secod, f e was calculated by assgg m, l,ad k to Eq.(). Fally, the estmated atural frequecy of the etre frut cluster, f l, uder the codto whe the peducle was held by the harvest robot was estmated. The error betwee the true value of atural frequecy ad the estmated atural frequecy usg the above-metoed method was show Table. Further, the error betwee the true value ad.7hz, whch s average of the atural frequecy of eght frut clusters, was demostrated the same table. It was foud that both the maxmum error ad the average error by the proposed method were smaller tha those by the method usg.7hz. Fg.5 Estmato of atural frequeces Table Frequecy estmato error Maxmum error [%] Average error [%] Proposed method Mea value Ⅲ Aalyss of umercal smulato. Model of umercal smulato Robustess of vbrato cotrol ablty for the estmated error of atural frequecy was tested by umercal smulato.

4 KONDO, TANIHARA, SHIIGI, SHIMIZU, KURITA, TSUTSUMI, CHONG, TANIWAKI : Path Plag of Tomato Cluster Harvestg Robot for Realzg Low Vbrato ad Speedy Trasportato Frst, the followg symbols were defed ths paper. A :Ed effector B ( =,,3 ):Compoets of tomato cluster J ( =,,3 ):Jots for coectg each elemet ( =,,3 ):Base vector of ertal coordate system a ( =,,3 ):Base vector of fxed coordate system of A system =,,3, j =,,3 :Base vector of fxed coordate b ( ) j B system of g :Vector of gravty accelerato 3 g A Ed-effector J B a 3 J a b 3 B b Trasportato drecto (Horzotal drecto) b 3 b J 3 Tomato cluster Fg. 6 Smulato model The state whch the tomato cluster was held by the ed effector was modeled by lks of a ormal cha rgd body, as show Fg.6. Here, t was cosdered that the flexblty of a tomato cluster was modeled as a adjacet rgd lk wth sgle-degree-of-freedom; ths lk had a spg sprg ad damper. The dyamcs equato of ths model was derved usg Kae s method (Kae et al., 983), also kow as the formulato method of the may-body dyamcs system. Resolvg ths equato, the state quattes of pose ad posto of the ed effector were gve as put varable ad vbrato of frut cluster,.e., the state quatty of the jot agle was resolved by usg umercal tegrato. The ed effector ad tomato cluster were assembled ad t was cosdered as a rgd body four-lk system ths study. Each axs of rotato was take as the drecto of B axs. All axs of rotato of each jot was take as the drecto of b axs (vertcal drecto of page space Fg.6). I addto, t was assumed that the move of the ed effector was cofed to a flat sgle-axs drecto (drecto of ) ad had o postural fluctuato. O the bass of the above expermet, the mass of a frut cluster was approxmately.3kg. The atural frequecy ad the dampg rato that were obtaed by chagg to the mode coordate system B 3 b 3 b 33 helped determg the sprg costat ad the vscous costat of each jot; the values of atural frequecy ad dampg rato are lsted Table 3. Table 3 Model parameters mode Frequecy [Hz] Dampg rato st.7.6 d rd Result of calculato It was aalyzed for the case where -4 to 4% of a error s gve to the estmated atural frequecy used by the put shapg method, ad the robustess over the estmated error was checked. The results of calculato whe there s o estmated error of atural frequecy were show Fgs.7 to. Fgs.7, 8, ad 9 show the accelerato, the velocty, ad the locato of the ed effector, respectvely. The ed effector was accelerated by puttg pulsed accelerato three tmes betwee s ad.6 s, ad the was mataed at a fxed velocty; the ed effector was slowed dow by the putted pulsed accelerato three tmes whose code was opposte to the accelerato betwee. s ad.8 s. The ed effector moved for.5m approxmately.8 s. Ths s the dstace betwee the locato of harvestg a frut cluster ad the locato of the basket for stockg the frut cluster. Fg. shows the jot agle of the cluster model. Although vbrato was excted by the frst pulse whe the cluster was accelerated, t was damped by the secod or thrd pulse ad was damped wth. whe the ed effecter moved wth a costat speed. I the same way, vbrato was also damped whe the ed effecter slowed dow to complete the trasportato of the cluster. Fg. shows the trajectory of the etre cluster that was plotted o the ertal coordate system every.5 s, the top ed shows the locato of the ed effecter, ad the bottom ed shows locato of bottom cluster. At the tme of accelerato, the bottom ed was left o ertal coordate system by ertal force; however, the vbrato was mostly damped after the speed was fxed. At the tme of slowdow, although the tedecy for the bottom ed to mata the erta movemet accordg to the force of erta aga was observed, t was cofrmed that the tomato cluster was stopped wthout cotuous vbrato. The, Fgs. to 6 show the results of calculato case -3% of the error s cluded the estmated atural frequecy It was clear that the effect of dampg vbrato deterorates remarkably ad the vbrato was mataed after the completo of trasportato.

5 Egeerg Agrculture, Evromet ad Food Vol., No. 3 (9) vertcal drecto [m] accelerato [m/s ] velocty [m/s] dsplacemet [m] agle [deg] Fg. 7 Ed effector accelerato (error %) Fg. 8 Ed effector velocty (error %) Fg. 9 Ed effector posto (error %) Fg. Jot agle (error %) holzotal drecto [m] Fg. Moto of tomato cluster (error: %) J J J vertcal drecto [m] accelerato [m/s ] velocty [m/s] dsplacemet [m] agle [deg] Fg. Ed effector accelerato (error: -3%) Fg. 3 Ed effector velocty (error: -3%) Fg. 4 Ed effector posto (error: -3%) Fg. 5 Jot agle (error: -3%) holzotal drecto [m] Fg. 6 Moto of tomato cluster (error: -3%) J J J

6 KONDO, TANIHARA, SHIIGI, SHIMIZU, KURITA, TSUTSUMI, CHONG, TANIWAKI : Path Plag of Tomato Cluster Harvestg Robot for Realzg Low Vbrato ad Speedy Trasportato 3 Fg.7 shows the maxmum of vbrato before trasportato case -4 to 4% of the error was cluded the estmated atural frequecy, ad Fg.8 shows the maxmum of the remag vbrato after the completo of trasportato. It was observed that both the vbrato durg the trasportato ad the resdual vbrato after the completo of trasportato creased wth the error. Whe applyg the put shapg method, the peak ad bottom of the peak are combed ad the vbrato s removed; therefore, f oly the prmary mode of vbrato of a lear system s take to cosderato, the vbrato s removed completely whe there s o error the atural frequecy. However, vbrato may crease wth error creased. The effect of dampg cotrol may be lost at about 5% of the error, ad vbrato may be coversely amplfed by more tha 5%. The vbrato of the tomato cluster volves complcated moto because the actual tomato cluster s a olear system ad the model used by our umercal smulato was a olear system, as show Fg.6. The results show Fgs.7 ad 8 qualtatvely agreed wth the results by aalyzg the lear system. Fg.7 shows the maxmum value of vbrato before the trasportato of the tomato cluster ad Fg.8 dcates the maxmum value of vbrato after the trasportato of the tomato cluster (after stoppg mapulator). The st, d ad 3 rd sgfes each jot part (J, J, ad J3). The estmated error of the atural frequecy usg the proposed method was 3.5% or less o a average ad 8.69% or less at the maxmum, as show Table. Therefore, t may be sad that ths error rage was effectve for the put shapg method. st 8 d 6 3rd maxmum agle error [%] Fg. 7 Maxmum jot agle durg trasportato maxmum agle st d 3rd error [%] Fg. 8 Maxmum jot agle after trasportato Ⅳ Expermetal aalyss. Expermetal codto A smple expermetal setup was costructed as show Fg.9. The slde servo system coductg the traslato moto of uaxal drecto was attached to the ed effector ad ths ed effector held the tomato cluster. cotrol PC slde drecto tomato tomato peducle cluster ed-effector Fg.9 Expermet system DOF mapulator vdeo camera A expermet was coducted usg the actual tomato cluster to aalyze the effect of delay o the servo system ad the effect of modelg error o the mathematcal model of cluster, as show Fg.6. The ed effector has a 34-Nm grp force ad hold top of cluster. I ths expermet, the mass of the cluster ad the mass ceter was measured maually ad the atural frequecy was calculated based o the bass of the measuremet data. The parameters of the put shapg method were adjusted o the bass of the acqured atural frequecy, ad were set the servo system. However, the ampltude value was chaged three steps, -.5,, ad.5 m/s because a ampltude resoluto of the accelerato commad was coarse, ad the trajectory cotrol of the ed effector was performed by adjustg the pulse wdth (tme legth) of accelerato. The ed effector ad the state of the tomato cluster were recorded wth a vdeo camera, ad the vbrato of the tomato cluster was evaluated from these pctures.

7 4 Egeerg Agrculture, Evromet ad Food Vol., No. 3 (9). Result of aalyss Oe of the typcal results was show Fg.. I ths expermet, the trasportato tme was approxmately.5 s ad the trasportato dstace was.5 m. Fg.(a) shows the result of the put shapg method usg the estmated atural frequecy, ad Fg.(b) shows the result that was ot used the put shapg method but gvg commad value of velocty of trapezod wave for acqurg the same trasportato dstace at same trasportato tme. The expermets were coducted usg fve tomato clusters ad the rato of the peak magtude of the put shapg method for the peak magtude of the expermetal result of a trapezod wave put was summarzed Table 4. I each case, t was foud that the effect of dampg vbrato was greater usg the put shapg method tha the trapezod wave. The effect of the dampg cotrol was dfferet because of the dvdual specfcty of the physcal propertes of the tomato cluster, the slght vbrato at the begg of the trasportato, ad the varato at the a tal phase agle. However, the suffcet effect of dampg vbrato was acqured by combg the proposed atural frequecy estmato method wth the put shapg method. Swg agle[deg] Tme [s] Swg agle[deg] Tme [s] (a) Iput shapg (b) Trapezum velocty put Fg. Expermet results Table 4 Expermet results Specme No. Reducto rato [%] Ⅴ Cocluso I ths study, the applcato of the put shapg method for the trajectory plag of the ed effector for hgh speed trasportato ad low vbrato of tomato cluster by harvestg robot s studed. The techque of estmatg the atural frequecy of a each object was proposed by combg the physcalty value acqured real tme wth sesors attached to the harvestg robot ad the compesatory model of atural frequecy costructed advace. By usg umercal smulato ad expermetal aalyss, t was cofrmed that the hgh effect of dampg vbrato was acqured by adjustg the accelerato patter of the put shapg method for each tomato cluster based o the estmated atural frequecy. The proposed method s applcable for realzg the hgh speed ad less damage durg tomato cluster robot harvestg. Refereces Blackbur, D. Sghose, W. Ktche, J. Patragearu, V. Lawrece, J. 6. Advaced commad shapg algorthm for olear tower crae dyamcs, Proceedgs for the 8th Iteratoal Coferece o Moto ad Vbrato Cotrol, TD3-5, Kae, T.R. Lks, P.W. Levso, D.A Spacecraft dyamcs, McGraq-Hll, Ic., Kodo, N. Tg, K.C Robotcs for Boproducto systems, The Socety for Egeerg Agrcultural, Food, ad Bologcal Systems, ASABE, St Joseph, MI, USA. Kodo, N. Mota, M. Noguch, N. 4. Agr-Rob(I) Fudametals ad Theory, CORONA publshg Co.,Ltd, Tokyo, Japa. Japaese Socety of Agrcultural Machery, 979. Research of physcal propertes of plats (Frst collecto) sythetc research of physcal property of plats ad measuremet method, Japaese Socety of Agrcultural Machery: 49-5 ( Japaese). Phyto-techology,. Phyto-techology How to see, lste, ad measure, Yokedo, Tokyo, Japa: ( Japaese). Sger. N.C. Seerg, W.P. 99. Preshapg commad puts to reduce system vbrato, ASME Joural of Dyamcs Systems, Measuremet ad Cotrol, Vol., (Receved :. September. 8, Accepted : 9. Jue. 9) Addedum: Iput shapg method The put shapg method s a techque of performg the feed-forward cotrol of accelerato by takg the atural frequecy of vbrato to cosderato so that t may be deed by vbrato whch vbrato produced by a certa accelerato put produces by aother accelerato put. For example, the appled research s coducted as a method of cotrollg a crae for hagg o a wre ad coveyg a object, ad the hgh precso posto cotrol techque of the robot arm wth hgh flexblty. Although the put pulses of accelerato s two tmes, as show Fg., the umber of tmes ca be specfed by regulato of the value of ampltude, or the tmg of a pulse. Whe pulse umber s, the ampltude of resdual vbrato V s gve by ζω V = e t C( ω, ζ ) + S( ω, ζ ) (4)

8 KONDO, TANIHARA, SHIIGI, SHIMIZU, KURITA, TSUTSUMI, CHONG, TANIWAKI : Path Plag of Tomato Cluster Harvestg Robot for Realzg Low Vbrato ad Speedy Trasportato 5 where C( ω, ζ ) = A e cos( ω ζ t ) = ζω t S( ω, ζ ) = A e s( ω ζ t ) = ζω t A s the tal ampltude of vbrato wave for the th mpulse, t s the elapsed tme,ω s the atural agular frequecy, ζ s the dampg rate. The put shapg method gves A ad t for mmzg V by settg whe there are kow ω ad ζ. The put shapg method s the techque of gvg A ad t that specfy certa ad mmze V whe ω adζ are kow. The followg equato ca be used ths method. C ( ω, ζ ) = S( ω, ζ ) = (7) ω ω A t e cos( w ζ t ) = = ζω t A t e s( w ζ t ) = = A = ζω t (5) (6) (8) (9) = () I ths study, equals to 3. Ths techque s called the Zero Vbrato Dervatve Shaper method (the ZVD method) amog the put shapg method, ad t s kow that the robustess over the error of the atural frequecy s hgher tha the case where the umber of tmes of a mpulse s two. A ad t satsfed the codtos from Eqs.(7) to () are wrtte as A = + k + k () k A = + k + k () k A3 = + k + k (3) ζπ k = exp ζ (4) t = (5) π t = ω ζ (6) π t 3 = (7) ω ζ