Leveraging the communication-based cooperation of multiple robotic systems has the potential to significantly further the state of the art of what is achievable with robotic automation. Therefore, reconfigurable robotic networks have come to the attention of research and industry. However, despite the potential to increase flexibility, robustness, and performance, robotic networks are not yet in widespread application, with many research challenges remaining. Hence, to better understand and subsequently overcome these challenges, distributed robotics is still in a state where it can benefit significantly from research that tackles well-defined benchmark problems. Consequently, this thesis faces the challenges of distributed robotics at the example of a cooperative transportation task. In the task, omnidirectional mobile robots cooperate to maneuver polygonal objects purely by pushing forces and in a completely self-reliant manner. The task is found to be a formidable benchmark problem since it raises all major challenges of the field. The dissertation discusses all aspects of the task in an encompassing manner, not only including the design of the employed control and organization methods, but also the software architecture and even the custom robotic hardware employed. Results from simulations and real-world hardware experiments show that the proposed scheme is of unprecedented versatility, putting into practice all major promises of distributed robotics, including plug-and-play control for online reconfigurations of the robotic network.