Linear Repetitive Learning Controls for Robotic Manipulators by Padé Approximants

The aim of this brief is to present the use of [m, m]-Padé approximants in the implementation of repetitive learning controls for the asymptotic joint position tracking of robotic manipulators with uncertain dynamics and periodic position reference signals (with known period). The resulting linear learning controls, which are derived through a detailed stability proof (involving the use of a suitable Lyapunov-like function), are described by transfer functions exhibiting all their poles with a negative real part while allowing of experimental improvements in the output tracking errors as the approximation order m increases. Analyses from both theoretical and experimental points of view are included. Such control laws are good candidates to be implemented in industrial robot control units for repetitive tasks in place of classical proportional-integralderivative (PID) controls.