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This work proposes a solution to the grasp synthesis problem, which consist of finding the best hand configuration to grasp a given object for a specific manipulation task while satisfying all the necessary constraints. This problem had been divided into sequential sub-problems, including contact region determination, hand inverse kinematics and force distribution, with the particular constraints of each step tackled independently. This may lead to unnecessary effort, such as when one of the problems has no solution given the output of the previous step as input. To overcome this issue, we present a kinestatic formulation of the grasp synthesis problem that introduces compliance both at the joints and the contacts. This provides a proper framework to synthesize a feasible and prehensile grasp by considering simultaneously the necessary grasping constraints, including contact reachability, object restraint, and force controllability. As a consequence, a solution of the proposed model results in a set of hand configurations that allows to execute the grasp using only a position controller. The approach is illustrated with experiments on a simple planar hand using two fingers and an anthropomorphic robotic hand using three fingers.

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