UNIVERSITY OF PARMA, ITALY Dipartimento di Ingegneria dell’Informazione Robotics and Intelligent Machines Laboratory Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs Jacopo Aleotti aleotti@ce.unipr.it Stefano Caselli caselli@ce.unipr.it IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Outline Introduction and motivations Related work Overview of the approach Object decomposition Part-based planning of robot grasps Experiments Discussion IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Robot Grasping Advanced (service) robots require human like grasping capabilities grasping should be task-oriented • single hand • multifingered • point contacts with friction IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Part-based robot grasping • objects are usually grasped according to their affordances • affordances are the ways to grasp an object to perform a task • objects are composed of different parts • perception of (grasping) affordances is mediated by object parts IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Part-based robot grasping • affordances are shared among similar objects IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Related work (psychology) Psychological findings have shown that human perception of objects is based on part decomposition. D. D. Hoffman Parts of Recognition. Cognition, 18(1-3):65 – 96, 1984 shapes are perceived as an arrangement of simple components (naturally segmented into parts at negative curvature minima). IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Related work (psychology) I. Biederman Recognition-by-Components: A Theory of Human Image Understanding. Psychological Review, 94:115 – 147, 1987. Recognition-By-Components theory (RBC) Recognition is a bottom-up process where the visual system recognizes objects by separating them into interrelated geons (such as cubes, spheres, cylinders). E. Rivlin et al. E. Rivlin, S. J. Dickinson, and A. Rosenfeld. Recognition by Functional Parts. Computer Vision and Image Understanding, 62(2):164 – 176, Sept. 1995. explored the issue of functionality by combining functional primitives with shape primitives IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Related work (robotics) Part-based object decomposition for efficient grasp planning (no semantic) [Kyota et al., 2005] learning grasping positions (cylinder-likeness, NN) [K. Hsiao et al., 2006] learning whole body grasps from imitation by object morphing. Limited nuber of elementary primitives. [C. Goldfeder et al., 2007] Grasp Planning via Decomposition Trees (superquadrics) [K. Huebner et al., 2008] Minimum Volume Bounding Box Decomposition IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Related work (robotics) Part-based object decomposition, towards semantic grasping [G. Biegelbauer et al., 2007] 3D Object Detection by Fitting Superquadrics to Range Image Data [A. Sahbani et al., 2007-2009] Learning the Natural Grasping Component of an Unknown Object based on superquadrics. [ L. Montesano et al., 2009] Learning affordance visual descriptors for grasping through self-experimentation. IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Focus of this work Motivation: automatic object recognition and robot grasping should be guided by 3D shape segmentation. Method: an approach for planning robot grasps across similar objects by part correspondence. Novelty: topological decomposition enabling semantic grasp planning. Topological decomposition of a shape provides meaningful information about grasp affordances. IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
3D Object decomposition The approach is based on the Reeb graph theory • A Reeb graph is a data structure describing the evolution of a scalar function over a mesh. • Tracks topological changes of connected components and encodes them in the nodes of the graph. given a surface S and a real, continuous function f: S → R the Reeb graph is the quotient space of f in S × R by the equivalence relation (X 1 , f(X 1 ))~(X 2 , f(X 2 )) which holds if and only if f(X 1 ) = f(X 2 ) and if the two points X 1 and X 2 are in the same connected component of f -1 (f(X 1 )) IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
3D Object decomposition the Reeb graph depends on 1. the scalar function f 2. the number of quantization levels of f Human model ( ~25000 triangles ) • f is the height function computed along one axis (computationally efficient few milliseconds, Intel Core 2 quad @2.66Ghz ) • height functions are not invariant under rotation • a scalar function f that ensures invariance to rotation is the integral geodesic distance (computationally expensive, O(n 2 logn) ) • the annotated Reeb graph is used as input for height function integral geodesic the part-based grasp planner distance IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
3D Object decomposition Shape Segmentation with Reeb Graphs: ADVANTAGES • Provides a topological representation of the shape (skeleton) • Attempts to extract a semantic segmentation from a 3D shape • Enables grasp planning among similar objects • Provides a one-to-one mapping from the mesh vertices to the object parts • Can be augmented to include geometrical information T. Tung and F. Schmitt. Augmented Reeb Graphs for Content-Based Retrieval of 3D Mesh Models, 2004. IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Part-based grasp planning A method for grasp planning grounded on part decomposition • it computes the centroid of the part and plans around the principal axis • it naturally speeds up the planning process (plans in the neighborhood of a chosen part) IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Part-based grasp planning • Experiments have been performed with a simulated Barrett Hand • Principal axes of inertia of each part are computed by PCA • Random generation of both precision and power grasps • V-Clip is the adopted for collision detection • External obstacles may be included in the simulated environment. • The planner is scheduled for executing hundreds of trials. • It returns the force closure grasp with the highest quality value IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Experiments • The dataset consists of 15 object classes • Each class contains 20 similar models • large meshes ranging from 4K to 115K triangles with uniform density • dataset taken from the 2007 shape retrieval contest (SHREC) . IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Experiments • force closure grasps with the highest quality • three similar objects per class • corresponding parts have the same color IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Experiments IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Experiments • The best quality grasps are selected from three hundred trials • All the grasps have a good quality score which ranges from Q = 0.21 to Q = 0.49 (0<Q<1) • The simplest class of objects is the “cup” category, whose Reeb graph contains 4 nodes • The most complex class is the octopus category, whose Reeb graph contains 10 nodes • Segmentation is correct even with “strange” postures (e.g. sitting human model) • Objects of the same category may have a slightly different topology • All the 3D models are “ watertight ” • Automatic part annotation requires an “ ontological ” model, provided by the user IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
Grasp quality measure STANDARD QUALITY METRIC: • Q : radius of the largest sphere centered at the origin contained in the GWS (if Q<0 the grasp isn ’t force closed) Complexity: object segmentation ̴ 20s/1min grasp synthesis, evaluation and animation ̴ 3s IROS-2010 WORKSHOP on Grasp Planning and Task Learning by Imitation Grasp Synthesis by 3D Shape Segmentation Using Reeb Graphs
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