INTERNATIONAL JOURNAL OF COMPUTATIONAL COGNITION (HTTP://WWW.IJCC.US), VOL. 6, NO. 3, SEPTEMBER 2008 1 QualGrasp-Grasp Synthesis through Qualitative Reasoning Shyamanta M. Hazarika Abstract— This paper extends results from qualitative kinemat- ics to formulate a grasp synthesis procedure. Being concerned with constructing grasps within a qualitative framework the analysis is intrinsically geometric. The paper is focused on the problem of synthesis of form closure grasp i.e., given the object geometry place contacts so as to prevent object motions. A procedure ‘QualGrasp’ is developed to compute location configuration of point constraints for complete immobilization of an object in 2D. The grasps so obtained are shown to satisfy the efficiency criteria given by Quantitative Steinitz’s Theorem. Copyright c  2008 Yang’s Scientific Research Institute, LLC. All rights reserved. Index Terms— Cognitive robotics, grasping, closure grasp, qualitative reasoning, qualitative kinematics. I. I NTRODUCTION T HE AVENUE of coordinated manipulation by multi- fingered mechanical hands has gained importance in the area of automated grasping. Versatility of multi-fingered hands for dexterous and fine manipulation accrues from the fact that they can be used for different objects, objects with large tolerances and objects undergoing change of shape. The use of robotic hands obviates the need for custom end effectors. Literature on multi-fingered hands has dealt with kinematic design of hands, automatic generation of stable grasping configuration and the use of task requirement as a criterion for selecting grasps. See (Bicchi and Kumar, 2000) for a detailed review. There have been two principal approaches to grasping. The first relies on accurate geometric model of the world (Hanafusa & Asada, 1982). In the second approach, grasping is accomplished with very little information about the shape of the object relying upon primitive behaviours that accomplish somewhat intelligent actions (Chammas, 1990; Bowers & Lumia, 2003). Grasping an object consists of finding a set of fingers whose contact with the object prevents its motion. Grasps are analyzed based on closure properties. Ohwovoriole (1980) and Salisbury (1982) introduced closure properties in robotic literature. Form closure originally investigated by Reuleaux (1876) is related to the ability of constraining devices to prevent motion of grasped object, relying only on unilateral frictionless contact constraints. An object is said to be in form closure if a set of contacts along its boundary constraints all Manuscript received February 01, 2008; revised July 08, 2008. Shyamanta M. Hazarika, Dept. of Computer Science and Engineering, Tezpur University, Tezpur, India. Email: smh@tezu.ernet.in Publisher Item Identifier S 1542-5908(08)10302-5/$20.00 Copyright c 2008 Yang’s Scientific Research Institute, LLC. All rights reserved. The online version posted on September 22, 2008 at http://www.YangSky.com/ijcc/ijcc63.htm finite and infinitesimal motions of the body (Reuleaux, 1876; Ding et. al., 2001). Force closure is related with the capability of the fingers being considered to apply forces through contact (Cheong & Herman, 2003). An object is said to be in force closure if any force and couple applied to the object externally can be cancelled by some set of positive forces at the fingers. Positive forces are those force vectors whose inner product with the inward normal to the contacting surface at the point of contact is positive. Work has been done on form and force closure properties of grasps (Bicchi, 1994; Pollard, 2004). Synthesis of force closure grasps has been considered by Nguyen (1988), Ponce & Faverjon (1995), Ponce et al. (1993; 1997) and more recently by Van der Stappen (2000) and Li et al. (2002). Computational time remains a major problem in developing grasping algorithms. For example, the grasping algorithm de- veloped by Balkcom & Trinkle (2002) based on wrench cones suffers from exponential complexity on number of contacts. In contrast, for human beings the act of grasping an object (with an objective) is a trivial task accomplished without much difficulty. This is partly because our everyday interaction with the physical world is driven through qualitative abstractions rather than complete quantitative knowledge a priori (Cohn & Hazarika, 2001). There in lies the motivation for a qualitative approach to grasp synthesis within the realms of qualitative reasoning. The work in this paper is concerned with develop- ing a qualitative framework for automatic generation of grasps. Even though much progress has been made in the area of qualitative reasoning, the emphasis on vision, sensing and control in most of traditional robotics still remains a complete quantitative model a priori. In contrast, cognitive robotics is an attempt at endowing robots with high level cognitive functions that allow them to exhibit behaviours more akin to human cognition (cf. Lui & Coghill, 2005). Within cognitive robotics qualitative representation and reasoning is being used. Qualitative reasoning is an approach for dealing with common- sense knowledge without recourse to complete quantitative knowledge. Representation of knowledge is through a limited repository of qualitative abstractions. Such an approach iden- tifies the core knowledge that underlines physical intuition. Moreover, a qualitative approach arrives at a solution through a simpler process than classical kinematic analysis. However, it retains important distinctions of kinematic behaviour of objects without invoking the myriad equations including differential equations (Forbus, 1989). Being concerned with constructing grasps within a qual- itative framework the analysis is intrinsically geometric, in so far that the kinematics of the grasping mechanism or