Exponentially Stable Tracking Control for Multijoint Flexible-Link Manipulators

In this paper we describe a new tracking control law for multijoint flexible-link manipulators. The scheme is a synthesis of the inverse dynamics solution for flexible manipulators developed by Bayo at UCSB and tracking control theory for rigid-link manipulators put forth by Bayard, Wen and others. We show that passive joint controllers, together with the feedforward of nominal joint torques corresponding to a desired end-effector trajectory, results in exponentially stable tracking control. Stability is proved (local to the desired trajectory) for a large class of passive controllers which include proportional and derivative controllers, and lead compensators. The proof is based on a simple Lyapunov analysis and the Positive-Real lemma.