We describe an approach for planning grasps of multifingered robot hands based on a small vibration model. Using features of the grasp configuration, we analyze asymptotic stability, contact situations, and uniaxial fingertip force constraints for the combined planning of finger posture and finger position, and characterize the generalized mass, damping, and stiffness. Choosing the largest time constant of the vibration model as an optimization criterion for planning finger postures and positions, the original problem of dynamic grasp planning is formulated as a nonlinear program. Simulation examples for a three-fingered robot hand grasping a spherical object demonstrate the effectiveness of the approach.
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