Optimization of grasp positions using the partial differentiation of the grasp stiffness matrix

In this paper, we propose an algorithm for automatically generating an optimum planar grasp. 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 position 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.