On the singular perturbation approach to trajectory control of a multilink manipulator with flexible links and joints

The singular perturbation approach has been shown to be successful in controlling both flexible link manipulators and flexible joint manipulators. In this paper, the technique is extended to control both link and joint flexibility of a multilink manipulator simultaneously while a desired trajectory is being tracked. A comprehensive, closed-form, Euler-Lagrange, assumed-mode model of a multilink manipulator has been formulated in which the effects of the link and joint flexibility are incorporated. This is then converted into a two-time-scale, state-space, singular perturbation model where the slow subsystem involves the link angles and the fast subsystem consists of the joint deflection and the link deflection variables. A composite controller is designed based on the two-time-scale model of the flexible link and joint manipulator. Numerical simulation results confirm that the proposed controller satisfactorily suppresses the tip deflection and joint flexibility of the manipulator while very good trajectory tracking is achieved.