Grasp stiffness matrix-fundamental properties in analysis of grasping and manipulation

In this paper, we present fundamental properties of stiffness matrix as applied to analysis of grasping and dextrous manipulation. The investigation unveils insights of stiffness matrix which are important in grasping and manipulation for robotic hands and fingers in R³ space. A general grasp stiffness matrix can be broken into two parts-symmetric and antisymmetric. The symmetric part is derived from a conservative quadratic potential function in the Hermitian form; while the antisymmetric part is a function of nonconservative curl vector field of the grasp. The conservative part stores and interchanges energy with the environment with which the fingers make contact. The nonconservative part dissipates or increases energy. The theory suggests that it is possible to introduce a nonsymmetric stiffness matrix in robotic control so as to have energy dissipation (damping) effects. This is useful when passive damping effects are desirable in grasping. Application of the theory to the analysis of stiffness matrix in 3D is presented for analysis of grasping and manipulation