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The proposed algorithm, which we call Sequential Contact-based Adaptive Grasping, can be used to reactively modify a given grasp plan according to contacts arising between the hand and the object. This technique, based on a systematic constraint categorization and an iterative task inversion procedure, is shown to lead to synchronized motions of the fingers and the wrist, as it can be observed in humans, and to increase grasp success rate by substantially mitigating the relevant problems of object slippage during hand closure and of uncertainties caused by the environment and by the perception system. After describing the grasping problem in its quasi-static aspects, the algorithm is derived and discussed with some simple simulations. The proposed method is general as it can be applied to different kinds of robotic hands. It refines a priori defined grasp plans and significantly reduces their accuracy requirements by relying only on a forward kinematic model and elementary contact information. 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