Dabic, S.

Marín Prades, Raúl

Sanz Valero, Pedro José

idUS. Depósito de Investigación Universidad de Sevilla

Using Symmetry Evaluation to Improve Robotic ManipulationPerformanceP. J. Sanz, R. Mar´ın and S. Dabic´Department of Computer Science & Engineering. Univ. Jaume I. Campus Riu Sec (12071-Castello´n)Key words: Vision based Robotic Manipulation; 2D Grasp Determination; Geometric Reasoning.PACS:1. IntroductionPresently, the robotics domain is increasing itsperformance possibilities mainly by using all kindof recent sensor based technology, jointly with veryefficient software and hardware to process the in-formation in a suitable manner. In particular, newrobotic applications in service context are startingto be available now (e.g. space and underwater ac-tivities, telesurgery, etc.), as can be observed in allthe most important conferences around the worldand in the real life scenarios. These emergent ac-tivities in robotics, outside the well structured andpredictable industrial domains, would be impossi-ble without the appropriate use of sensory infor-mation.In our case, after some years of previous researchin the robotic manipulation area, by using com-puter vision to guide the grasping actions of 2Dobjects [Sanz et al., 98], we have discovered the im-portance of implement some algorithms that makeeasier the underlying geometric reasoning neces-sary to improve the final robotic manipulation per-formance. In particular, the knowledge about sym-metry of planar shapes (i.e. 2D images of the ob-jects are available) has been successfully used bythe authors [Sanz et al., 99], and some other re-searchers before [Blake, 95], within the graspingdetermination domain.2. Problem Description and PreviousResultsAs it has been commented beforehand, in previ-ous works the geometric reasoning necessary to de-termine suitable regions of one object, in order tobe grasped, was supported by the symmetry knowl-edge associated to the contour of this object. Withthe aim to quantify this symmetry degree a newconcept was introduced by the authors [Sanz et al.,99] the .normalized global symmetric deficiency..In the following we clarify this concept. For a pla-nar shape two privileged directions exist related toits mass distribution (inertia), these directions areImin and Imax, and they represent the eigenvectorsof the moment of inertia covariance matrix. If mir-ror symmetry exists, these directions are the firstcandidates for that. As a result of that the nextobjective is evaluate the symmetry degree associ-ated with these two directions. From the curvaturedescription Kki, the symmetry degree is computedwith respect to the Imin associated with the con-tour, using the intersection points { C⋂Imin },computing ∆i, such as:∆i = Kk,P3−i −Kk,P3+i; i = 1,K,N2,where P3 ∈ {C⋂Imin } traversing the contourclockwise from the initial point, PI, between P 01andP 02 . That is to say, ∆i is computed as indicated,for each couple of points equidistant to P3, coveringall the contour. Using these quantities, we definethe normalized global symmetric deficiency as:Φ = 1N∑i= N2i=1 ∆iwhere N is the total number of points in the con-tour. The same process is utilized to compute Φfor the Imax direction, but now, instead of P3, wecompute∆i with P01 ∈ {C⋂Imax }, as introducedabove. Note that Φ = 0, i.e. perfect mirror symme-try with respect to the considered axis, exists onlyfor an ideal mirror symmetric object. Some resultsin relation with the usefulness of Φ are shown in20th EWCG Seville, Spain (2004)20th European Workshop on Computational GeometryTable 1Normalized global symmetric deficiency Φ computed fordifferent images in both directions Imin and Imax. It showsthe mean,νΦ, and the standard deviation, ρΦ, for each one.Table 1.The data shown in Table 1 are the mean andstandard deviation computed from four digitiza-tions for each object at different locations (positionand orientation) over the work area. From that ta-ble some empirical results can be observed:Imin direction. Looking at the table a gap be-tween ”pliers” and ”pincers” is observed, Φ =≤ 3.After many trials we have followed a mirror sym-metry approach for those images that present Φ <5, named Φc = 5 to this critical value.Imax direction. In this case the gap appear justbetween ”nut” and the rest of shapes. So a valueΦc = 3 represents a good critical value.A primary classification of the objects presentin Table 1 would be the following: ”mirror symme-try for Imin and Imax directions” {nut}; ”mirrorsymmetry in Imin direction” {nut..pincers}; and”without symmetry” {Allen wrench}. Note thatonly ”nut” has mirror symmetry in both directionsin correspondence with its inherent radial symme-try.These results were applied successfully to thegrasping determination domain [Sanz et al., 99],where the input were contours extracted from 2Dimages.Nevertheless, as it has been remarked above, aproblem was detected with some shapes, for in-stance, the pincers. The differences observed be-tween the hopped (i.e. mirror symmetry along theImin direction) and real results has been the start-ing point for the present research contribution. ToFig. 1. The performance analysis in the case of pincers.Marked with a circle is observed the bad situation betweenthe Imin axis and the external contour of this shape (i.e.P3).clarify this situation is convenient to observe theFig 1, in which an image of pincers is processed.When the curvature-symmetry fusion [Sanz et al.,99] diagram is used to analyze the performance, wefound that the intersection between one of the ex-tremes of the Imin axis, and the external contour(i.e.P3), is not well situated (i.e. see the circle inthis Fig.1). And when the computation to evalu-ate Φ is carried out, the final result is that shownin Table1, namely a higher value that the theoreti-cally hopped for this kind of shape, that as we canobserve it is symmetric in that direction.3. How to solve this problem?Well, looking at literature we find the Ley-ton’s Theorem [Leyton, 87], about ”symmetry-curvature duality”, were a local correspondencebetween a symmetry axis and a curvature pointcontour is established. Thus, if a symmetry axisexists in a shape, this axis intersect the shape al-ways in a local extreme of curvature. Our presentcontribution has been to implement this Theo-rem in our algorithms in order to solve the initialproblems found.And, as work in progress, we are now testingthe use of this new Φ, incorporating the Leyton.sTheorem, as a new descriptor in automatic objectrecognition.Finally, it is noticeable that with this improve-ment we have got a very robust solution to evaluatethe symmetry degree associated to a planar shapein a predefined direction, and in a very fast way,March 25-26, 2004 Seville (Spain)making feasible real applications in the roboticsdomain.References[1] [Sanz et al., 98] Sanz PJ, del Pobil AP, IestaJM, Recatal G. Vision-Guided Grasping of UnknownObjects for Service Robots . In IEEE Proc. on Roboticsand Automation (ICRA.98), pp. 3018-3025. Leuven,Belgium. May 1998.[2] [Sanz et al., 99] Sanz PJ, Iesta JM, del PobilAP. Planar Grasping Characterization Based onCurvature-Symmetry Fusion . Applied Intelligence 10,pp. 25-36. Kluwer Academic Pub. 1999.[3] [Blake, 95] Blake A. A Symmetry Theory of PlanarGrasp. The International Journal of RoboticsResearch, Vol.14, No. 5, pp. 425-444. October, 1995.[4] [Leyton, 87] Leyton M. Symmetry-Curvature Duality,Comput. Vision Graphics Image Process. 38, pp. 327-341. 1987

Using symmetry evaluation to improve robotic manipulation performance

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Using symmetry evaluation to improve robotic manipulation performance

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