Online Computation of the Stiffness Matrix in Robotic Structures Using Finite Element Analysis

Finite Element Analysis (FEA) is known to be a highly reliable tool for structural analysis, but this is usually conducted offline. Online use of FEA is usually out of the question because it is highly demanding in terms of computing time. We show in this report how the Cartesian stiffness matrix of robotic structures of a certain class can be computed online with FEA support. The procedure is based on an extension of the concept of generalized spring that is capable of handling anisotropic linearly elastic structures. In this way, FEA is conducted offline, to compute the Cartesian stiffness matrix of a structural part of a complex shape. This matrix is then used to update the posture-dependent Cartesian stiffness matrix of the overall structure. As an illustrative example, the procedure is applied to a Schönflies motion generator that features two parallelogram linkages fabricated of carbon fiber. In order to illustrate the online feasibility of the computation involved, the root-mean square value of the eigenvalues of a dimensionless factor of the stiffness matrix is plotted along a standard trajectory adopted by the industry.