# Algorithm for Determining the Position of a Ship Hull-Cleaning Robot
## 1 Introduction  
The accurate positioning and navigation of autonomous robots operating on ship hull surfaces is a critical challenge in maritime robotics. Regular cleaning of the ship hulls is essential to maintain vessel efficiency, reduce fuel consumption, and minimize environmental impact by preventing biofouling. Traditionally, hull cleaning operations require ships to be docked or dry-docked, resulting in downtime and increased operational costs. Autonomous hull cleaning robots offer a promising alternative, enabling efficient and continuous maintenance without the need to remove vessels from the water. However, the effectiveness of these robots is highly dependent on their ability to precisely determine their position and orientation on the hull surface, especially in challenging underwater environments. However, although positioning is widely recognized as an important factor for hull cleaning robots, most prior work focuses primarily on the design and construction of robots tailored to specific cleaning tasks or hull environments, rather than on the development of positioning algorithms. Many studies present robots with unique mechanical architectures or cleaning mechanisms, such as morphologically intelligent underactuated robots for non-magnetic hulls [1], hybridasting reconfigurable robots [2], or systems equipped with hydraulic manipulator arms for cleaning niche areas [3]. In these works, the positioning subsystem is often closely coupled to the specific hardware and operational context of the robot. When positioning is addressed, it is frequently realized through specialized sensor suites or infrastructure-dependent methods. Some robots rely on vision-based simultaneous localization and mapping (SLAM) algorithms using cameras [4], or on the fusion of laser scanners and 3D CAD models [3], which require visual data and prior models of the hull. Others employ optical dead-reckoning systems based on mouse sensors [5; 6], or magnetic landmark recognition systems that depend on the internal structure of the hull. Advanced approaches integrate Doppler velocity logs, imaging sonars, and monocular cameras within SLAM frameworks [7], or utilize networks of ultrasonic beacons for 3D location [2]. Although these methods can achieve high accuracy, they often require additional infrastructure (e.g., beacons, reference landmarks), complex sensor fusion, or are limited to specific operational scenarios. This paper focuses specifically on the development and evaluation of a general-purpose positioning algorithm for ship hull cleaning robots, independent of the robot's mechanical design or the need for external infrastructure. Our approach combines classical kinematic computations with advanced sensor data processing techniques. By integrating odometry and inertial measurement unit (IMU) data, enhanced with state-of-the-art methods such as Kalman filtering, our work aims to improve the accuracy and reliability of the robot's navigation along the side of the ship. Our system detects and corrects the effects of wheel slippage, a common source of error in odometry-based positioning, by correlating encoder readings with observed orientation changes from IMU sensors. Unlike prior works that require additional sensors (e.g., Lidar, sonar, beacons) or hull modifications (e.g., magnetic landmarks), our method is designed to operate with a minimal sensor set--wheel encoders and an IMU. To evaluate our approach, we developed an experimental framework tested on publicly available datasets and simulated data modeling real-world scenarios, including artificial slip events.The real-world scenarios were prepared in collaboration with SR Robotics (https://sr Robotics.pl/), a company specializing in the design and construction of remotely operated and autonomous underwater and surface robots that support operations in marine and inland water environments. The contributions of this paper are as follows.