Vibration Controllability of 3D Flexible Manipulators

Abstract

Structural vibrations of flexible robots are not always fully controllable in all the workspace. In some cases, there exist configurations where the actuators cannot affect some of the vibration modes, and thus cannot control their vibrations. This problem has been neglected in the case of the one-link and two-link planar manipulators; however, it must be dealt with in depth when trying to control a 3D flexible robot. This paper discusses the vibration controllability of flexible manipulators. Vibration uncontrollable configurations are estimated both by the minimum singular values of the controllability matrix and the closed-loop behavior. A 2-link 3-joint prototype flexible manipulator is used for a case study, and the uncontrollable configurations of the manipulator are found.