Stability analysis of the force distribution algorithm for flexible-link cooperating manipulators

Inverse dynamic solutions for flexible-link manipulators are generally know n to be unstable E. Bayo, A finite-element approach to control of the end-p oint motron of a single-link flexible robot, Journal of Robotic Systems 4 ( 1987) 63-75 [1]. This is due to the non-minimum phase property of the forwa rd dynamic system resulting from the non-collocation of the input joint act uator torques and the output tip rates R. H. Connon, E. Schmitz, Initral ex periments on the end-pont control of a flexible one-link robot, The Interna tional Journal of Robotics Research 3(3) (1984) 63-75 [2]. In dealing with the same problem for cooperating manipulators, however, we observed that a certain degree of collocation of the input torques and the output rates can be achieved by actively choosing the tip wrench. Therefore, force distribu tion schemes can be designed to obtain stable inverse dynamic torques. In o ur previous research, we showed that different force distribution schemes g ive different dynamic behaviors of the system. In this paper, we establish a theoretical basis which provides an explanation for the performance of th e force distribution schemes. This is done by considering the stability of the internal dynamics of the system. (C) 1998 Elsevier Science Ltd. All rig hts reserved.