This doctoral thesis navigates the complex landscape of motion coordination and formation control within teams of rotary-wing Micro Aerial Vehicles (MAVs). Prompted by the intricate demands of real-world applications such as search and rescue or surveillance, the research aims to improve the performance, safety, and autonomy of such multi-robot systems by leveraging onboard resources exclusively. It explores the distributed real-time optimization of multi-objective performance under a range of constraints while emphasizing the role of relative sensing. A Distributed Nonlinear Model Predictive Control (D-NMPC) framework is employed as the principal methodology for systematically handling these objectives and constraints within a uniform architecture. To address the challenges of stability guarantees and environmental uncertainties, a robust distributed approach incorporating tube-based MPC is also investigated. The design and implementation of vision-based and IR-based relative localization systems are performed to improve the autonomy of the multi-robot system. A multi-level design and iteration framework is adopted, spanning low- and high-fidelity simulations and real-world experiments. This framework serves as a systematic approach for bridging the theoretical and practical aspects of this research. The thesis also incorporates a rigorous validation process through a series of iterative experiments conducted both in simulated and physical environments with a fleet of custom-built quadrotors. These experiments aim to quantify the effectiveness of the proposed methodologies in terms of accuracy, constraint satisfaction, robustness, resource utilization, and scalability. This thesis also provides a comparative study involving various large-scale model predictive control architectures as well as a conventional algebraic graph theory-based formation control method. The goal of this comparison is to provide a nuanced perspective on the potential advantages and limitations of the MPC-based approaches. The work concludes by summarizing key findings, suggesting avenues for future research and potential applications of multi-robot aerial systems executing formation tasks in a predictive framework.