Using symmetry evaluation to improve robotic manipulation performance

Using Symme y E alua ion o Imp o e Robo ic Manipula ion Pe o mance P. J. Sanz, R. Ma ´ın and S. Dabi´c Depa men o Compu e Science & Enginee ing. Uni . Jaume I. Campus Riu Sec (12071-Cas ell´on) Key wo ds: Vision based Robo ic Manipula ion; 2D G asp De e mina ion; Geome ic Reasoning. PACS: 1. In oduc ion P esen ly, he obo ics domain is inc easing i s pe o mance possibili ies mainly by using all kind o ecen senso based echnology, join ly wi h e y e icien so wa e and ha dwa e o p ocess he in- o ma ion in a sui able manne . In pa icula , new obo ic applica ions in se ice con ex a e s a ing o be a ailable now (e.g. space and unde wa e ac- i i ies, elesu ge y, e c.), as can be obse ed in all he mos impo an con e ences a ound he wo ld and in he eal li e scena ios. These eme gen ac- i i ies in obo ics, ou side he well s uc u ed and p edic able indus ial domains, would be impossi- ble wi hou he app op ia e use o senso y in o - ma ion. In ou case, a e some yea s o p e ious esea ch in he obo ic manipula ion a ea, by using com- pu e ision o guide he g asping ac ions o 2D objec s [Sanz e al., 98], we ha e disco e ed he im- po ance o implemen some algo i hms ha make easie he unde lying geome ic easoning neces- sa y o imp o e he inal obo ic manipula ion pe - o mance. In pa icula , he knowledge abou sym- me y o plana shapes (i.e. 2D images o he ob- jec s a e a ailable) has been success ully used by he au ho s [Sanz e al., 99], and some o he e- sea che s be o e [Blake, 95], wi hin he g asping de e mina ion domain. 2. P oblem Desc ip ion and P e ious Resul s As i has been commen ed be o ehand, in p e i- ous wo ks he geome ic easoning necessa y o de- e mine sui able egions o one objec , in o de o be g asped, was suppo ed by he symme y knowl- edge associa ed o he con ou o his objec . Wi h he aim o quan i y his symme y deg ee a new concep was in oduced by he au ho s [Sanz e al., 99] he .no malized global symme ic de iciency.. In he ollowing we cla i y his concep . Fo a pla- na shape wo p i ileged di ec ions exis ela ed o i s mass dis ibu ion (ine ia), hese di ec ions a e Imin and Imax, and hey ep esen he eigen ec o s o he momen o ine ia co a iance ma ix. I mi - o symme y exis s, hese di ec ions a e he i s candida es o ha . As a esul o ha he nex objec i e is e alua e he symme y deg ee associ- a ed wi h hese wo di ec ions. F om he cu a u e desc ip ion Kki, he symme y deg ee is compu ed wi h espec o he Imin associa ed wi h he con- ou , using he in e sec ion poin s {CTImin }, compu ing ∆i, such as: ∆i=Kk,P3−i−Kk,P3+i;i= 1, K, N 2, whe e P3∈ {CTImin } a e sing he con ou clockwise om he ini ial poin , PI, be ween P0 1 and P0 2. Tha is o say, ∆iis compu ed as indica ed, o each couple o poin s equidis an o P3, co e ing all he con ou . Using hese quan i ies, we de ine he no malized global symme ic de iciency as: Φ = 1 NPi=N 2 i=1 ∆i whe e N is he o al numbe o poin s in he con- ou . The same p ocess is u ilized o compu e Φ o he Imax di ec ion, bu now, ins ead o P3, we compu e ∆iwi h P0 1∈ { CTImax }, as in oduced abo e. No e ha Φ = 0, i.e. pe ec mi o symme- y wi h espec o he conside ed axis, exis s only o an ideal mi o symme ic objec . Some esul s in ela ion wi h he use ulness o Φ a e shown in 20 h EWCG Se ille, Spain (2004) 20 h Eu opean Wo kshop on Compu a ional Geome y Table 1 No malized global symme ic de iciency Φ compu ed o di e en images in bo h di ec ions Imin and Imax. I shows he mean,νΦ, and he s anda d de ia ion, ρΦ, o each one. Table 1. The da a shown in Table 1 a e he mean and s anda d de ia ion compu ed om ou digi iza- ions o each objec a di e en loca ions (posi ion and o ien a ion) o e he wo k a ea. F om ha a- ble some empi ical esul s can be obse ed: Imin di ec ion. Looking a he able a gap be- ween ”plie s” and ”pince s” is obse ed, Φ =≤3. A e many ials we ha e ollowed a mi o sym- me y app oach o hose images ha p esen Φ < 5, named Φc= 5 o his c i ical alue. Imax di ec ion. In his case he gap appea jus be ween ”nu ” and he es o shapes. So a alue Φc= 3 ep esen s a good c i ical alue. A p ima y classi ica ion o he objec s p esen in Table 1 would be he ollowing: ”mi o symme- y o Imin and Imax di ec ions” {nu }; ”mi o symme y in Imin di ec ion” {nu ..pince s}; and ”wi hou symme y” {Allen w ench}. No e ha only ”nu ” has mi o symme y in bo h di ec ions in co espondence wi h i s inhe en adial symme- y. These esul s we e applied success ully o he g asping de e mina ion domain [Sanz e al., 99], whe e he inpu we e con ou s ex ac ed om 2D images. Ne e heless, as i has been ema ked abo e, a p oblem was de ec ed wi h some shapes, o in- s ance, he pince s. The di e ences obse ed be- ween he hopped (i.e. mi o symme y along he Imin di ec ion) and eal esul s has been he s a - ing poin o he p esen esea ch con ibu ion. To Fig. 1. The pe o mance analysis in he case o pince s. Ma ked wi h a ci cle is obse ed he bad si ua ion be ween he Imin axis and he ex e nal con ou o his shape (i.e. P3). cla i y his si ua ion is con enien o obse e he Fig 1, in which an image o pince s is p ocessed. When he cu a u e-symme y usion [Sanz e al., 99] diag am is used o analyze he pe o mance, we ound ha he in e sec ion be ween one o he ex- emes o he Imin axis, and he ex e nal con ou (i.e.P3), is no well si ua ed (i.e. see he ci cle in his Fig.1). And when he compu a ion o e alu- a e Φ is ca ied ou , he inal esul is ha shown in Table1, namely a highe alue ha he heo e i- cally hopped o his kind o shape, ha as we can obse e i is symme ic in ha di ec ion. 3. How o sol e his p oblem? Well, looking a li e a u e we ind he Ley- on’s Theo em [Ley on, 87], abou ”symme y- cu a u e duali y”, we e a local co espondence be ween a symme y axis and a cu a u e poin con ou is es ablished. Thus, i a symme y axis exis s in a shape, his axis in e sec he shape al- ways in a local ex eme o cu a u e. Ou p esen con ibu ion has been o implemen his Theo- em in ou algo i hms in o de o sol e he ini ial p oblems ound. And, as wo k in p og ess, we a e now es ing he use o his new Φ, inco po a ing he Ley on.s Theo em, as a new desc ip o in au oma ic objec ecogni ion. Finally, i is no iceable ha wi h his imp o e- men we ha e go a e y obus solu ion o e alua e he symme y deg ee associa ed o a plana shape in a p ede ined di ec ion, and in a e y as way, Ma ch 25-26, 2004 Se ille (Spain) making easible eal applica ions in he obo ics domain. Re e ences [1] [Sanz e al., 98] Sanz PJ, del Pobil AP, Ies a JM, Reca al G. Vision-Guided G asping o Unknown Objec s o Se ice Robo s . In IEEE P oc. on Robo ics and Au oma ion (ICRA.98), pp. 3018-3025. Leu en, Belgium. May 1998. [2] [Sanz e al., 99] Sanz PJ, Ies a JM, del Pobil AP. Plana G asping Cha ac e iza ion Based on Cu a u e-Symme y Fusion . Applied In elligence 10, pp. 25-36. Kluwe Academic Pub. 1999. [3] [Blake, 95] Blake A. A Symme y Theo y o Plana G asp. The In e na ional Jou nal o Robo ics Resea ch, Vol.14, No. 5, pp. 425-444. Oc obe , 1995. [4] [Ley on, 87] Ley on M. Symme y-Cu a u e Duali y, Compu . Vision G aphics Image P ocess. 38, pp. 327- 341. 1987