EXPONENTIAL CONVERGENCE OF A LEARNING CONTROLLER FOR ROBOT MANIPULATORS

This note presents the proof for the exponential convergence of a class of learning and repetitive control algorithms for robot manipulators. The learning process involves the identification of the robot inverse dynamics function by having the robot execute a set of tasks repeatedly. Using the concepts of functional persistence of excitation (PE) and functional uniform complete observability (UCO), it is shown that, when a training task is selected for the robot which is persistently exciting, the learning controllers are globally exponentially stable. Repetitive controllers are always exponentially stable.