Analysis and control for manipulators with both joint and link flexibility

An analysis of manipulators with both joint and link flexibility is presented. Due to the different order of joint and link stiffness, the full-order nonlinear system can be decomposed into different time-scale subsystems, namely, a slow subsystem, a mid-speed subsystem, and a fast subsystem. It is shown that when the link stiffness is much greater than joint stiffness or when the two kinds of stiffness are comparable, the vibrations due to joint or link flexibility can be suppressed regardless of what control effort is made. A composite control law is proposed in the case where the joint stiffness is much greater than the link stiffness to eliminate the structural vibrations while the tracking objective is achieved