# Mobile Robots: Trajectory Analysis, Positioning and Control
## 2 The Present Issue  
This Special Issue received a total of 17 submissions, each of which was meticulously assessed by at least one Guest Editor to ensure alignment with the core themes of mobile robotics. Submissions that matched the scope were subjected to a comprehensive review process, which included evaluation by at least two external reviewers, while those outside the thematic focus were declined. Following this rigorous peer review process, 10 articles and 1 review were ultimately selected for publication. A detailed summary of the key findings and contributions of each article is provided in the following. The authors of Contribution 1 introduce an orthogonal wheel odometer system designed for the precise positioning of mobile robots on floating surfaces such as ship decks. This innovative system utilizes four orthogonal wheels equipped with encoders to achieve centimeter-level accuracy in determining position and orientation in a relative coordinate system, overcoming the limitations of traditional gyroscope-based methods. Their experimental results demonstrate the system's effectiveness in mitigating errors caused by the irregular movements of floating surfaces. Their system consistently delivered accurate results across various motion scenarios, including linear, curved, and rotational movements. Notably, in tests conducted on a simulated floating platform, the maximum recorded error was 2.43 cm, with a root mean square error (RMSE) of 1.51 cm. These findings underscore the system's potential for applications in challenging environments where conventional positioning systems struggle. The authors of Contribution 2 propose a systematic method for evaluating and correcting odometry errors in a human-sized, three-wheel omnidirectional mobile robot. Using a novel flower-shaped calibration trajectory consisting of 36 individual paths, the study iteratively adjusts the robot's kinematic parameters to minimize discrepancies between odometry data and ground truth trajectories obtained via a 2D LIDAR sensor. The experimental results demonstrate significant improvements in the robot's positional accuracy, with an average reduction of 82.14% in the error of final position and orientation after calibration. This approach highlights the effectiveness of using both straight and curved trajectories for comprehensive calibration, offering a robust solution for improving odometry in omnidirectional robots designed for diverse indoor applications. The authors of Contribution 3 present a virtual reality (VR)-based interface designed to enhance the teleoperation of mobile robots in unknown environments. The interface aims to provide an intuitive and immersive user experience, enabling seamless interaction between the operator and the robot. Unlike traditional approaches, this system focuses on simplifying the control process by including essential virtual elements, such as a real-time 3D map of the environment, the robot's position, and any detected obstacles, rather than prioritizing hyper-realistic visuals. The VR interface leverages a potential field-based navigation method to assist the user in guiding the robot while automatically avoiding obstacles. Using a Turtlebot3 Burger robot (which is manufactured by the ROBOTIS company, located in Seoul, Korea) equipped with a LiDAR sensor, the system demonstrated its ability to ensure collision-free navigation in both simulated and real-world scenarios. The researchers also incorporated a gamepadfor interaction, prioritizing user ergonomics and long-term usability over conventional VR controllers. User studies involving participants of various ages and backgrounds highlighted the system's usability and effectiveness. Feedback showed high levels of immersion and user satisfaction, with participants finding the interface easy to learn and operate. The authors conclude that the VR-based interface successfully combines the adaptability of human guidance with the precision of automated navigation, making it suitable for tasks such as search and rescue or industrial inspection.