Automatic generation of grasp positions using the partial differentiation of the grasp stiffness matrix

It is important for robots to obtain appropriate grasp positions autonomously to make stable grasps. In this paper, we propose an algorithm for automatically generating an optimum planar grasp based on grasp stability. Every finger is replaced with a two-dimensional linear spring model. Grasp stability is evaluated by using the eigenvalues of the grasp stiffness matrix derived from the potential energy of the spring. To decrease the number of searching iterations, we derive the partial differentiation of the matrix by the contact point parameters. Based on the differentiation, we propose an algorithm for regulating the grasp positions in order to increase the grasp stability. Effectiveness of our method is demonstrated through numerical examples. In our method, the shape of an object, its normal direction and local curvature are required. We derive the parameters acquired from a camera image. Our method is applied to practical experiments and its validity is confirmed. Keywords—Multi-finger hand, Static grasp stability, Grasp stiffness matrix, Partial differentiation, Optimum grasp