In this paper, a numerically efficient flexible control scheme for the absolute accuracy of industrial robots is presented and experimentally validated. A model-based controller that leverages all typically available parameters is combined with an online path iterative learning controller (ILC). The ILC law is employed to compensate for the unknown residual error dynamics caused by elastic and transmission effects. The proposed approach combines several benefits, including the possibility of a continuous execution of trials, a straightforward generalization of the learned data to different execution speeds, and learning from partial trials. The experimental validations on a 6-axis industrial robot with a laser tracker absolute measurement system show a 95% improvement in absolute accuracy after two trials. When the laser tracker is removed, the learned feedforward controller can sustain the accuracy achieved even without trial-by-trial learning.