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Static Stability Analysis of Spatial Grasps Including Contact Surface Geometry

In this study, we analyze the three-dimensional (3-D) static grasp stability of a single object. Our model takes into account the contact surface geometry (metric tensor, curvature and torsion) and the contact condition (rolling contact and sliding contact). In the case of rolling and sliding contacts, each finger rolls and slides on the object surface, respectively. Each finger is replaced with a 3-D orthogonal virtual spring model and grasp stability is evaluated from the potential energy stored in the grasp. A grasp stiffness matrix including the effects of contact surface geometry and contact condition is derived. The stability is evaluated from the eigenvalues of the matrix. Configuration displacement of the object in terms of position and orientation is decomposed into stable and unstable directions using the corresponding eigenvectors. The effectiveness of our proposed method is demonstrated by several examples.