General-Purpose Expression of Structural Connectivity in the Parallel Solution Scheme and Its Application

Abstract

In this paper, an algorithm for the general-purpose expression of structural connectivity is developed and implemented into the parallel solution scheme, which was previously proposed and successively applied to the feed-forward control of link mechanisms under various boundary conditions. The parallel solution scheme calculates the inverse dynamics of link systems by using a matrix-form equation separated into individual terms of di ff erent parameters. Therefore, the connectivity of link members can be expressed explicitly by one of the matrices, the member length matrix. Generated forces for the control can also be considered, without using any Jacobian matrices, simply by adding the values into one of the components in the equation, the vector related to nodal forces. We describe the forming process of the member length matrix and verify the validity of the calculated torque values, by presenting simple numerical results and experimental results for a structure-varying link system. We also perform a force control experiment on a quick motion, two-arm link system holding an object, where both generated forces and dynamical e ff ects should be considered. Numerical and experimental results show the validity and the extensive ability of the scheme.