Manipulation of a flexible object by dual manipulators

Proposes a control algorithm of dual manipulators handling a flexible sheet metal. How to bend a sheet metal and how to manipulate the deformed sheet are discussed in this paper. First the authors derive the relation between the static deformation of the sheet metal and the bending moments exerted on the sheet using Lagrange's equation based on a finite element model of the sheet. The authors then design a control algorithm by which the motion of the manipulated sheet is controlled using the resultant force applied to the sheet and the deformation of the sheet is controlled using the internal force applied to the sheet. Since the rigidity of the deformed sheet is not uniform, that is, the stiffness of the deformed sheet may depend on the direction along which the external force is applied, the authors cannot use the compliance of the flexible sheet for tasks having interactions between the sheet and its environment. The proposed control algorithm is designed so that the apparent impedance of the manipulated sheet metal is specified. The experimental results using industrial robots illustrate the validity of the proposed control system.