An adaptive approach to Iterative Learning Control (ILC) based on Kalman filters and optimization of a quadratic criterion is presented. The idea is to estimate one of the design parameters in the Kalman filter and hence create an adaptive gain in the ILC updating formula. The proposed ILC design is compared with two other ILC schemes and they are all implemented on an industrial robot. The results show that the proposed adaptive ILC scheme is fast, and also robust since the gain is reduced as the error is decreased.