A dynamic coupling index for underactuated manipulators

Abstract

In recent years, researchers have been dedicated to the study of underactuated manipulators which have more joints than control actuators. In previous works, one always assumes that there is enough dynamic coupling between the active and the passive joints of the manipulator, for it to be possible to control the position of the passive joints via the dynamic coupling. In this work, the authors aim to develop an index to measure the dynamic coupling, so as to address when control of the underactuated system is possible, and how the motion and robot configuration can be designed. We discuss extensively the nature of the dynamic coupling and of the proposed coupling index, and their applications in the analysis and design of underactuated systems, through a detailed mathematical analysis and several illustrative examples.