Unions of Balls for Shape Approximation in Robot Grasping Markus Przybylski, Tamim Asfour and R¨ udiger Dillmann Abstract— Typical tasks of future service robots involve grasping and manipulating a large variety of objects differing in size and shape. Generating stable grasps on 3D objects is considered to be a hard problem, since many parameters such as hand kinematics, object geometry, material properties and forces have to be taken into account. This results in a high- dimensional space of possible grasps that cannot be searched exhaustively. We believe that the key to find stable grasps in an efficient manner is to use a special representation of the object geometry that can be easily analyzed. In this paper, we present a novel grasp planning method that evaluates local symmetry properties of objects to generate only candidate grasps that are likely to be of good quality. We achieve this by computing the medial axis which represents a 3D object as a union of balls. We analyze the symmetry information contained in the medial axis and use a set of heuristics to generate geometrically and kinematically reasonable candidate grasps. These candidate grasps are tested for force-closure. We present the algorithm and show experimental results on various object models using an anthropomorphic hand of a humanoid robot in simulation. I. INTRODUCTION AND RELATED WORK The increasingly aging society will benefit from intelligent domestic robots that are able to assist human beings in their homes. The ability to grasp objects is crucial to many supporting activities a service robot might perform, such as serving a drink, tidying up or giving water to the flowers, for example. Human beings perform grasps intuitively on almost any kind of object. In contrast, grasping is a challenging problem for robots. Knowledge of hand kinematics, object geometry, physical and material properties is necessary to find a good grasp, making the space of possible candidate grasps intractibly large to search in a brute-force manner. This is especially the case for modern dexterous robot hands with an increasing number of degrees of freedom. A. Grasp Planning Many approaches for grasp planning have been developed in the past. Grasp synthesis on the contact level concen- trates primarily on finding a predefined number of contact points without considering hand geometry [1]. Some work on automatic grasp synthesis focusses especially on object manipulation tasks ([2],[3]). Shimoga [2] presents a survey on measures for dexterity, equilibrium, stability, dynamic behavior and algorithms to synthesize grasps with these properties. Li et al. [4] recorded grasps for basic objects using motion capturing and used this information to perform shape matching between the inner surface of the hand and This work was supported by EU through the project GRASP. All authors are with the Institute for Anthropomatics, Karlsruhe In- stitute of Technology, Karlsruhe, Germany {markus.przybylski, asfour, dillmann}@kit.edu novel objects. The resulting candidate grasps were clustered and pruned depending on the task. Since simulators such as GraspIt! [5], OpenRAVE [6] and Simox [7] have become available it is possible to simulate candidate grasps with robot hand models on object models, where hand kinematics, hand and object geometries as well as physical and material properties and environmental obstacles can be taken into account. In the recent past, many researchers developed grasp planning methods based on these simulation environments. Berenson et al. (see [8],[9]) developed a grasp scoring function that considers not only grasp stability but takes also environmental obstacles and kinematic reachability into account. In [10] an integrated grasp and motion planning algorithm is presented where the task of finding a suitable grasping pose is combined with searching collision free grasping motions. Ciocarlie et al. [11] introduced the concept of eigengrasps which allows for grasp planning in a low-dimensional subspace of the actual hand configuration space. Goldfeder et al. [12] used the eigengrasp planner to build a grasp database containing several hands, a multitude of objects and the associated grasps. They used Zernike descriptors to exploit shape similarity between object models to synthesize grasps for objects by searching for geometrically similar objects in their database. They extended this approach to novel objects [13], where partial 3D data of an object are matched and aligned to known objects in the database to find suitable grasps. A number of simulator-based approaches to grasp planning rely on shape approximation of 3D object models. The basic idea underlying these approaches is that many objects can be decomposed into component parts that can be represented by simplified geometric shapes. Then rules are defined to gene- rate candidate grasps on these components which allows for pruning of the search space of possible hand configurations. This concept is also known as grasping by parts. The first method in this context was presented by Miller et al. [14] who used boxes, spheres, cylinders and cones to approximate the shape of the object. However, the user has to perform the decomposition of the object into these primitives manually. Goldfeder et al. [15] presented a method that automatically approximates an object’s geometry by a tree of superquadrics and generates candidate grasps on those. Huebner et al. [16] developed an algorithm that decomposes objects into a set of minimum volume bounding boxes. While these approaches significantly reduce the complexity of grasp planning, this comes at a price. Many grasps a human would intuitive- ly use might not be found due to poor object geometry approximation. Especially box decomposition yields only a The 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems October 18-22, 2010, Taipei, Taiwan 978-1-4244-6676-4/10/$25.00 ©2010 IEEE 1592