Exact and stable tip trajectory tracking for multi-link flexible manipulator

In this paper, the recently developed stable inversion theory for nonlinear nonminimum phase systems is applied to output tracking for multi-link flexible robot manipulators. First, a mathematical model is developed for a two-link flexible manipulator using assumed mode technique with tip position as output. Then an inverse model is derived and a two-point boundary value problem is set up to guarantee that the inverse obtained is a stable one regardless of the fact that a flexible manipulator is a nonminimum phase system. The eigenvalues of the Jacobian matrix of the inverse system are calculated to verify the hyperbolicity of the fixed point. Following a recent general result, an iterative procedure is presented to numerically construct the stable inverse for a given desired tip trajectory. This inverse is used as a feedforward together with joint angle feedback to control the tip position. Excellent output tracking is achieved with no transient or steady state errors and no internal vibration buildup