In robotics, much emphasis is placed on mathematical modeling, as the creation, control, and optimization of robots for a wide field of work must be achieved precisely and adaptively. The aim of this paper is to present a systematic and structured approach to the literature review of mathematical models in robotics, critically considering mathematical frameworks that influence and shape robotics in light of current and prevailing trends. The paper underlines the complexities of maintaining accurate dynamic representations in robotic systems, revealing the challenges that arise from numerical simplifications. The study outlines the development of efficient remote-control systems that consider dynamic relationships among the components comprising the robot. The findings of the recent simulation prove that the developed mathematical model effectively supports designing an adaptive control system with artificial intelligence features, especially for autonomous mobile robotics with manipulators that are inherently complex and networked systems. If models are to accelerate robotics progress toward increasingly intelligent, adaptive, and efficient systems, they must learn to overcome some of the computational challenges while leveraging disciplinary synergies.