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The need, in robot manipulation, for higher levels of dexterity and versatility than those provided by grippers and by special-purpose end-effectors has prompted much research effort during the last decade on the design and control of multifingered hands. Most work on multifingered robot hands has dealt with low-level, numeric control, commonly based on screw theory and tools drawn from line geometry, differential geometry, kinematics, and dynamics. Current numeric, contact-based schemes, however, are limited to tip prehension (intentional grasping by the fingertips). The intriguing ease with which humans perform grasping and manipulation activities has concurrently triggered new investigations to provide robots with humanlike, prehensile capability for complex tasks in unstructured environments. These investigations have resulted in numerous AI-oriented, task-directed, distributed, symbolic schemes that have been conducted essentially independently. Efforts to link symbolic and numeric schemes have been undertaken, but the results have been rather modest. This paper deals with an intelligent, integrated symbolic-numeric scheme for dextrous manipulation, using a topological approach. In this paper, we introduce a reasoning scheme called topological reasoning that is used in conjunction with a grasp-based, topological model for uniform representations of multifingered robot hands at different levels of detail (e.g., whole hand, finger, joint), and discuss its application to dextrous manipulation (grasp selection and regrasping). We show that using topological reasoning, both hand posture and hand functionality can be derived from symbolic, high-level task requirements and object attributes, and can be transformed into numeric, low-level, joint space variables. Furthermore, the reasoning scheme is applicable not only to tip prehension, but also to palm prehension and any combination of the two.
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