Command shaping for nonlinear tracking control of a two-link flexible manipulator

This paper considers the problem of minimum time tracking a periodic trajectory with the end point of a two-arm robot made of flexible beams connected by revolute joints. Beam flexibility is modeled by a series of rigid rods connected by rotational springs, and an order-n dynamical formulation is used for efficiency in computing the overall dynamical model. A simple linear control law as well as a nonlinear control law employing feedback linearization are designed ignoring beam flexibility. Control-excited vibration of the flexible beams produces an error in end point tracking. Input shaping is used to reduce this control-structure interaction. Simulation results are used to study the effectiveness and robustness of this approach.