Tip Trajectory Tracking for Multilink Flexible Manipulators Using Stable Inversion

Abstract

The recently developed stable inversion theory for nonminimum phase nonlinear systems is applied to output tracking for multilink e exible robot manipulators. The stable inversion theory and a numerical solution to stable inverses are briee y reviewed. Forward dynamics of a two-link e exible manipulator with 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 e 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.