The CX-space: a unified paradigm for grasping using multifingered hands

Grasp planning is formulated as a unified problem, fusing the previously decoupled subproblems of locating and matching contacts on the hand and on the payload. To achieve this, the problem is formulated in the CX-space which is denoted as the Cartesian product of the hand´s configuration space (Cspace), and a space of relative poses between the hand and the payload (X-space). This approach alleviates some difficulties which are unresolved when a search is performed in the hand´s C-space alone. A number of kinematic aspects of grasping are addressed by associating them with sets in the CX-space. Solving for a desired grasp then requires identifying a CX-space configuration which lies in the intersection of these sets. Rather than recommending a search technique, this paper presents the framework for this novel formulation. As a demonstration, portions of the CX-space associated with a simulated Utah-MIT hand and a spherical payload are examined