On the role of high-gain feedback in P-type learning control of robot arms

An alternative proof of the convergence of known P-type learning control schemes for unconstrained and constrained robot arms is presented. The analysis carried out is based on a singular perturbation approach and points out the role played by high gain velocity and force feedbacks and by actuator/output co-location. The singular perturbation analysis developed clearly displays that the P-type learning algorithm is geometrically convergent, and that, thanks to the high gain feedback, this convergence does not depend on the knowledge of the robot parameters. Robustness with respect to some classes of disturbances is also addressed. The stability of the high gain closed loop system in case of robots in contact with the environment is shown to rely on a sufficiently good knowledge of the constraining surface