In recent years, the demand for customized, on-demand production has grown in the manufacturing sector. Additive Manufacturing (AM) has emerged as a promising technology to enhance customization capabilities, enabling greater flexibility, reduced lead times, and more efficient material usage. However, traditional AM systems remain constrained by static setups and human worker dependencies, resulting in long lead times and limited scalability. Mobile robots can improve the flexibility of production systems by transporting products to designated locations in a dynamic environment. By integrating AM systems with mobile robots, manufacturers can optimize travel time for preparatory tasks and distributed printing operations. Mobile AM robots have been deployed for on-site production of large-scale structures, but often neglect critical print quality metrics like surface roughness. Additionally, these systems do not have the precision necessary for producing small, intricate components. We propose a model predictive control framework for a mobile AM platform that ensures safe navigation on the plant floor while maintaining high print quality in a dynamic environment. Three case studies are used to test the feasibility and reliability of the proposed systems.