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This paper presents an approach to synthesizing the control required by a dextrous multifingered robot hand to reach and safely grasp an arbitrary target object. The synthesis is based on analysis of the grasping task as performed by human beings. We divide the task into (1) a target approach phase (including target identification, hand structure and grasp mode selection, selection of approach trajectory, hand preshaping and orientation) and (2) a grasp execution phase (including shape and force adaptation). Each aspect of the required control is discussed. Particular attention is paid to the role of geometric modeling in target identification, to preshaping during the approach trajectory and to the requirements for autonomy in completion of the grasping task. The underlying philosophy is that of reflex control; each aspect of the grasping task is initiated and terminated using sensory data and rules of behavior derived from human expertise in such tasks. The contents and organization of the knowledge base which codifies this expertise are discussed. The fundamental assumptions upon which this control philosophy is based are identified throughout the paper. Preliminary results of a graphical simulation of hand preshaping are given.