Tip Trajectory Tracking for Multilink Flexible Manipulators Using Stable Inversion

The recently developed stable inversion theory for nonminimum phase nonlinear systems is applied to output tracking for multilink exible robot manipulators. The stable inversion theory and a numerical solution to stable inverses are brie y reviewed. Forward dynamics of a two-link exible manipulatorwith tip position as the output is then given using the assumed modes method. From that, an inverse model is derived and a two-point boundary value condition is set up. This condition guarantees that the inverse solution for a given desired tip trajectory will be stable regardless of the fact that a exible manipulator is a nonminimum-phase system. The stable inverse is incorporated into an output tracking controller that uses only joint-angle feedback. Excellent tracking is achieved with no transient or steady-state errors and no internal vibration buildup. I.