Vibration controllability of underactuated robots with flexible links

The controllability analysis of underactuated robots with flexible links is the important preparatory step to efficiently control the system. In this paper, based on the dynamic model using the assumed mode method, controllability of a planar 3DOF underactuated manipulator with one passive joint and the 3-rd flexible link is analyzed in two stages. Firstly, neglecting the elastic deformations of the link, the state controllability results of the corresponding rigid system at various actuator placements is directly introduced from the preceding study; secondly, the structural vibration controllability of underactuated flexible one is investigated according to the state controllability result. It is shown that the vibration controllability of an underactuated flexible manipulator is both joint-configuration-dependent and actuator-placement-dependent. If an underactuated rigid robot is not state controllable, then the vibration controllability of the corresponding flexible one is uncertain and meaningless. By comparing the simulation of the modal accessibility index of two vibration controllable systems at different actuator placements, a conclusion can be drawn that the system with the second passive joint is easier than the one with the third passive joint to control the vibration of flexible link. Finally, the proposed method is extended to n-DOF underactuated flexible robots with one passive joint.