Mathematical Methods for Environment Representation in Collaborative Robotics: Comparative Analysis and Application Recommendations

Abstract

The work examines the main mathematical methods used to describe the environment of collaborative mobile robots in digital twin and intelligent navigation systems. The analysis focuses on grid-based, geometric, graph-based, probabilistic, and dynamic models, including Occupancy Grid Map, Configuration Space SE(2) and SE(3), graph-based models, potential field models, probabilistic representations, point cloud models, and dynamic obstacle models. Their mathematical foundations, computational complexity, accuracy, scalability, and suitability for real-time applications are compared. The advantages and limitations of each approach are evaluated, and practical recommendations for their use in intelligent robotic systems are provided. The results are intended for researchers and engineers developing autonomous collaborative robotic systems operating in structured and dynamic environments.