Robotic arms are essential tools in the space industry, enabling a wide range of tasks from handling payloads and conducting repairs to sample collection and construction. Their importance in the space industry continues to grow as technology advances and space activities expand. In this research endeavor, an in-depth exploration of the intricacies involved in the operation of a robotic arm within a dynamic, non-fixed reference frame is undertaken. The research commences with the development of a sophisticated mathematical model meticulously crafted to encompass the dynamic characteristics of the platform to which the robotic arm is intricately linked. This model serves as the bedrock for systematic analysis of the inputs that govern the robotic arm’s movements and actions. Through rigorous numerical analysis of this model, a comprehensive survey of various operational methods is undertaken, subjecting each to a meticulous examination of their distinct advantages and disadvantages. Moreover, the inquiry extends to an in-depth investigation into the reaction forces exerted upon the platform during the execution of each operational mode. As the investigation unfolds, data and analysis are drawn upon to identify the conditions under which a robotic arm, operating on a mobile base, can be consistently controlled with optimal precision and reliability. Ultimately, the findings underscore the importance of tailoring control modes to align with the specific application of the robotic arm. This adaptable approach offers the potential for significant benefits, enhancing the performance, efficiency, and overall utility of robotic arm systems across a wide spectrum of industrial applications.