The precise localization of mobile robots in unstructured environments is of utmost importance for many industrial and field applications, especially when the mobile robot is part of a more complex kinematic chain, such as a mobile manipulator. Being able to precisely localize 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). Problems arise when precise localization is needed in dynamic and unstructured environments where generally applicable methods won’t perform adequately or might be time-consuming to set up. In this work, we propose a cloud-edge computing architecture to deploy a recurrent neural network (RNN) based registration system, which uses a pair of consecutive LiDAR readings to estimate a fixed transformation. The capability of RNNs to process contiguous inputs will help neglect errors embedded in punctual laser scanner readings 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. To tackle the dynamic and unstructured environments, the model is firstly tuned on synthetic LiDAR data to embed rigid transformations into the deep learning model, for then rapidly fine-tuned on local scenarios. After model architecture and optimization of hyperparameters, the devised model is tested in different scenarios, comparing the precise positioning capability of the AMR(autonomous mobile robot) with that of 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.