In this paper, we present a grasp representation in task space exploiting position information of the fingertips. We propose a new way for grasp representation in the task space, which provides a suitable basis for grasp imitation learning. Inspired by neuroscientific findings, finger movement synergies in the task space together with fingertip positions are used to derive a parametric low-dimensional grasp representation. Taking into account correlating finger movements, we describe grasps using a system of virtual springs to connect the fingers, where different grasp types are defined by parameterizing the spring constants. Based on such continuous parameterization, all instantiation of grasp types and all hand preshapes during a grasping action (reach, preshape, enclose, open) can be represented. We present experimental results, in which the spring constants are merely estimated from fingertip motion tracking using a stereo camera setup of a humanoid robot. The results show that the generated grasps based on the proposed representation are similar to the observed grasps.
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