The precise localization of mobile robots is of utmost importance for many industrial applications, especially when the mobile robot is part of a more complex kinematic chain, such as in a mobile manipulator. Furthermore, precise localization hugely affects the outcome of tasks that rely on an open-loop kinematic computation, such as work-station docking procedures. To achieve a repeatable and precise localization and positioning, mobile robots generally rely on onboard sensors, most commonly 2D laser scanners, whose readings are subjected to noise and numerous disturbing factors ( e.g., materials reluctance). In this work, we propose a recurrent neural network (RNN) based registration system, which uses a pair of consecutive LiDAR readings and estimates a fixed transformation. The capability of RNNs to process contiguous inputs will help neglect errors embedded in punctual laser scanner reading and output a more precise registration estimation. In such a way, the RNN can estimate a displacement error based on multiple consecutive readings and act as a sensor to be employed in a closed-loop control scheme. After a model architecture and optimization of hyperparameters, the devised model is tested in different scenarios, comparing the AMR precise positioning capability with a classical registration algorithm. The results suggest that an RNN model can greatly improve the registration precision of laser scanner signals and, consequently, the precise positioning efficiency of AMRs.