Mode shape analysis, modal linearization, and control of an elastic two-link manipulator based on the normal modes

Accurate determination of mode shapes and resonant frequencies of high-speed slender robotic arms, known as flexible link manipulators, is fundamental for mechanical design, dynamic analysis, identification, and control of the manipulators. This paper presents a Finite Element (FE) modeling, modal analysis, linearization, and control of a Two-Link Flexible Manipulator (TLFM) based on the global vibration modes, which are essentially more precise than the component mode analysis used in most previous studies. The resonant frequencies and the global vibration modes are employed, then, for analyzing the influence of configuration and payload variations, as well as architecture variations using a prismatic joint in the upper arm. The Modal Assurance Criterion (MAC) is adopted as a tool for comparing the mode shapes. Finally, based on the system modes and MAC calculations, a new modal control scheme is proposed for a multi-stage rest-to-rest maneuver of the manipulator.