## 1 Introduction  
The autonomous recharging process is an important part of a mobile robot's autonomous operations, enabling it to work continuously without any human intervention. Docking [1] can be understood as the navigation and localization of a robot toward a desired location. Docking requires an accurate estimation of the robot's pose, often from a position close to the docking station, through path planning [2]. Mobile robots are used across various fields [3, 4, 5, 6, 7, 8], including surveillance, planetary exploration, dangerous environments, factory automation, search and rescue operations, and indoor manufacturing environments. The role of mobile robots has become increasingly important for present and future applications. Thus, independent autonomous recharging has become a fundamental requirement through which to ensure the autonomous operation of mobile robots in various conditions. For a mobile robot to initiate the docking and recharging process, it first needs to identify the charging station and then align itself with the charger autonomously by following a series of rotational and translational steps. The location of the charging station (e.g., indoor or outdoor) plays an important role in the selection of sensors for a docking procedure. Outdoor environments are more complex, unpredictable, and dynamic due to the presence of moving objects and obstacles. Moreover, the performance of non-visual sensors, such as Lidar sensors, which are used for docking, can depreciate in outdoor weather conditions, such as snow, dust, and fog [9]. Based on the sensor implemented, the autonomous docking techniques described in the literature are divided into the three following categories: (i) infrared (IR) sensor-based methods [10], (ii) computer vision [11], and (iii) laser-based approaches [12]. To receive IR signals properly, the IR receiver needs to be implemented in a specific location on the mobile platform, which limits the mechanical design of mobile robots [10]. Computer vision and laser-based techniques, such as object detection [13] and Lidar-based approaches, are the most commonly used methods through which to solve odometry-related problems. However, both techniques have their respective limitations and benefits. Although Lidar methods [14] can extract different features from the environment, without being affected by changes in lighting conditions, and can obtain more accurate range measurements than cameras, Lidar data are sparsely distributed and have limited visibility. Furthermore, this technique's operation is based on collecting large amounts of data, which requires more computational power than a camera. In contrast, a camera provides rich and thick data that do not have limited visibility. However, a standard camera without a 360-degree view has a limited visibility angle, resulting in a blind spot [11]. To overcome the challenges of conventional methods, the combination of different sensors has been investigated for years, and recent research has proven that the fusion approach yields better performance than a single-sensor method [14]; the limitations of IR-based, laser-based, and vision-based methods for autonomous docking and recharging are overcome by combining multiple sensors. The authors of [15] attempted to integrate a camera and IR sensor with laser range finders in order to improve the reliability of the autonomous docking process. In [16], a vision-based autonomous docking and recharging approach was applied to a security robot. An artificial landmark was installed on top of a charging station, at the same height as the camera, to assist the robot in detecting and locating the charging station area. The rotational and translational errors were counteracted using a virtual spring model motion control approach. The model presented in [16] assumed that the robot and the charger could be connected with a virtual spring, and the compliant forces in the direction of the translation deformation and bending determined the motion control.