Leveraging explicit communication and cooperation of multiple robots brings about multiple advantages in the solution of tasks with autonomous robotic agents. For this reason, to the end of transporting polygonal objects with a group of mobile robots, the aim of this article is to develop a fully distributed decision-making and control scheme that lets the robots cooperate as equals, without any kind of central control instance. Apart from coordinating the motions of the robots in a distributed manner, challenges include the self-reliant determination of configurations of the robots around the object, as well as the interrobot negotiation on which robot takes which role or position in the transportation process. Based on some assumptions on the properties of the robots and the considered types of objects, all major aspects of the control scheme are explained in detail, with the most crucial parts making use of optimization-based schemes. This enables unprecedented flexibility by letting the robots automatically adapt to a wide range of scenarios, with different numbers of robots cooperating, and accommodating intricate object shapes. A simulation-based analysis reveals some of the key properties of the proposed scheme, whereas hardware-in-the-loop experiments show the practical applicability with inexpensive hardware. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article was motivated by the potential to further the state of the art of what is possible to achieve with autonomous robots when, instead of using one single robot, a group of robots cooperates self-reliantly to solve a task. The scenario studied in this article is a transportation task in which the robots shall cooperatively push an object to transport it along the desired path. The scheme proposed in this article deals with all major aspects of solving this transportation task, with simulations and hardware-in-the-loop experiments showing the practical applicability of the scheme. While the experiments have been conducted in a laboratory environment, one may readily imagine a more productive application, e.g., in logistics, when employing suitably designed hardware. On another note, maybe more importantly, the general architecture devised to solve the present task may serve as an inspiration or blueprint for the development of decision-making and control schemes that deal with alternative cooperative robotic tasks, especially with regard to the usage of optimization-based schemes on multiple levels allowing a flexible, yet still intuitive problem formulation.