# Mobile Robots: Trajectory Analysis, Positioning and Control
###### Abstract  
The rapid evolution of mobile robotics over the last decade has reshaped the landscape of technology and its applications in society [1, 2, 3]. From autonomous vehicles revolutionizing urban mobility to drones transforming delivery systems and robots performing tasks in extreme or hazardous environments, mobile robotics have transcended experimental boundaries to become a tangible part of our daily lives [4, 5, 6, 7]. These advancements are driven by an interplay of disciplines, including artificial intelligence (AI), robotics, computer vision, and control theory, which continue to push the limits of what mobile robots can achieve in terms of autonomy, efficiency, and adaptability [8, 9, 10].  
One of the most significant challenges in mobile robotics lies in trajectory analysis, positioning, and control. Accurate trajectory planning and execution are critical for robots to navigate dynamic environments, avoid obstacles, and operate effectively alongside humans. Simultaneous Localization and Mapping (SLAM) technologies [11, 12], coupled with robust navigation algorithms [13, 14], have advanced significantly, enabling robots to construct detailed maps of their surroundings while localizing themselves in real time. These developments are essential for the deployment of mobile robots in unstructured and unpredictable environments, such as urban settings or disaster-stricken areas [15].  
Control systems also play a pivotal role in ensuring the reliability and stability of mobile robots. Advances in control theory have enabled the creation of sophisticated models that adapt to uncertainties and dynamic conditions. Techniques such as model predictive control (MPC), adaptive control, and reinforcement learning-based controllers are empowering robots with the capability to make intelligent decisions in complex scenarios [9, 16, 17, 18, 20, 21]. These innovations ensure precision in tasks ranging from trajectory tracking to collaborative operations with other robots or humans.  
Another layer of complexity arises from the increasing presence of mobile robots in human-centric environments. This integration introduces the challenge of human-robot interaction (HRI), which requires robots to not only perform tasks autonomously but also communicate, cooperate, and adapt to human behavior [22, 23, 24, 25]. Designing intuitive and safe HRI systems is a critical research area, especially as robots become more involved in healthcare, logistics, and personal assistance. Tools such as natural language processing, gesture recognition, and emotion detection are being integrated into robotic systems to make interactions more seamless and user-friendly [26, 27, 28].  
Emerging technologies such as augmented reality (AR) and virtual reality (VR) are opening up new frontiers in the field of mobile robotics [29, 30, 31]. These tools provide enhanced visualization and interaction capabilities, enabling humans to better understand and control robotic systems. AR and VR also offer new possibilities for training robots, simulating complex environments, and improving remote operations, particularly in scenarios where direct human presence is challenging or impossible.  
The integration of these advancements in mobile robotics highlights the interdisciplinary nature of this field. It requires collaboration between AI researchers, control engineers, computer scientists, and human-machine interaction specialists to address the multifaceted challenges and opportunities it presents [10]. This Special Issue brings together cutting-edge research and methodologies from these domains, providing a comprehensive overview of current trends and fostering innovation in this vibrant area.