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The recently developed stable inversion theory for nonminimum phase nonlinear systems is applied to output tracking for multilink è exible robot manipulators. The stable inversion theory and a numerical solution to stable inverses are brieè y reviewed. Forward dynamics of a two-link è 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 è 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. internal-dynamicsinstabilityprobleminclassicalinversion.Asare- sult, remarkably accurate output tracking together with closed-loop stability will be achieved. The remainder of the paper is organized as follows. Section II brieè y reviews the stable inversion theory and a numerical solution to stable inverses.Section III describes the for- ward dynamics of a two-link è exible manipulator and derives its stable inverse dynamics. In Sec. IV, conditions for applying stable inversion are verié ed and the effectiveness of stable inversion to output tracking for nonminimum-phase systems is demonstrated by simulation. A conclusion is given in Sec. V.

Tip Trajectory Tracking for Multilink Flexible Manipulators Using Stable Inversion